xiangfu0 commented on code in PR #19795:
URL: https://github.com/apache/pinot/pull/19795#discussion_r4253127790


##########
pinot-segment-local/src/main/java/org/apache/pinot/segment/local/customobject/tdigest/TDigestAccumulator.java:
##########
@@ -104,64 +110,204 @@ public TDigestAccumulator(int compression) {
     this((double) compression, true, true);
   }
 
+  public TDigestAccumulator(double compression) {
+    this(compression, true, true);
+  }
+
   private TDigestAccumulator(double compression, boolean allocateRawBuffer, 
boolean allocateMergeBuffers) {
-    if (!(compression > 0.0) || !Double.isFinite(compression)) {
-      throw new IllegalArgumentException("TDigest compression must be 
positive: " + compression);
-    }
-    super.setScaleFunction(ScaleFunction.K_1);
-    _compression = Math.max(MIN_COMPRESSION, compression);
+    this(compression, allocateRawBuffer, allocateMergeBuffers, false);
+  }
+
+  private TDigestAccumulator(double compression, boolean allocateRawBuffer, 
boolean allocateMergeBuffers,
+      boolean useTwoLevelRawCompression) {
+    _compression = TDigestCodec.normalizeCompression(compression);
+    _useTwoLevelRawCompression = useTwoLevelRawCompression;
     _workingCompression = TWO_LEVEL_COMPRESSION_MULTIPLIER * _compression;
     _publicMaxWeightScale = calculateK1MaxWeightScale(_compression);
     _workingMaxWeightScale = calculateK1MaxWeightScale(_workingCompression);
     long roundedCompression = (long) Math.ceil(_compression);
-    _centroidCapacity = getCentroidCapacity(_compression);
-    _pendingCentroidCapacity = getPendingCentroidCapacity(_centroidCapacity);
+    _centroidCapacity = TDigestCodec.getDefaultCentroidCapacity(_compression);
+    _pendingCentroidCapacity = getPendingCentroidCapacity(_centroidCapacity, 
useTwoLevelRawCompression);
     if (allocateRawBuffer) {
-      _rawValues = new double[getRawBufferSize(roundedCompression)];
+      _rawValues = new double[getInitialRawBufferSize(roundedCompression)];
     }
     if (allocateMergeBuffers) {
-      _centroidMeans = new double[_centroidCapacity];
-      _centroidWeights = new double[_centroidCapacity];
-      _outputMeans = new double[_centroidCapacity];
-      _outputWeights = new double[_centroidCapacity];
+      int initialCapacity = Math.min(_centroidCapacity, MIN_RAW_BUFFER_SIZE);
+      _centroidMeans = new double[initialCapacity];
+      _centroidWeights = new double[initialCapacity];
+      _outputMeans = new double[initialCapacity];
+      _outputWeights = new double[initialCapacity];
     }
   }
 
-  public static TDigestAccumulator forSerializedTDigest(byte[] bytes) {
-    return new TDigestAccumulator(readCompression(bytes), false, false);
+  /// Creates a lazy digest with the legacy two-level compression used by 
Star-tree and general digest aggregation.
+  public static TDigestAccumulator forLegacyAggregation(double compression) {
+    return new TDigestAccumulator(compression, false, false, true);
   }
 
-  public static TDigestAccumulator forSerializedTDigest(SerializedTDigestInput 
input) {
-    return new TDigestAccumulator(input._compression, false, false);
+  /// Reads and retains one legacy digest, preserving the general aggregation 
compression policy.
+  public static TDigestAccumulator fromBytes(byte[] bytes) {
+    return fromBytes(ByteBuffer.wrap(bytes));
   }
 
-  public static TDigestAccumulator forSerializedTDigestWithMergeBuffers(byte[] 
bytes) {
-    return new TDigestAccumulator(readCompression(bytes), false, true);
+  /// Reads one payload and advances the buffer past it.
+  public static TDigestAccumulator fromBytes(ByteBuffer bytes) {
+    SerializedTDigestInput input = new SerializedTDigestInput();
+    input.reset(bytes);
+    return fromBytes(input);
   }
 
-  public static TDigestAccumulator forSerializedTDigest(ByteBuffer input) {
-    byte[] bytes = new byte[input.remaining()];
-    input.get(bytes);
-    TDigestAccumulator accumulator = forSerializedTDigest(bytes);
-    accumulator.addSerializedTDigest(bytes);
-    return accumulator;
+  /// Retains an already validated input without rescanning its centroid bytes.
+  public static TDigestAccumulator fromBytes(SerializedTDigestInput input) {
+    TDigestAccumulator digest = forLegacyAggregation(input.getCompression());
+    digest.addSerializedTDigest(input);
+    return digest;
   }
 
   public static TDigestAccumulator forReduction(double compression) {
     return new TDigestAccumulator(compression, false, false);
   }
 
+  /// Snapshots buffered inputs and centroid state without materializing or 
compressing the source. Mutable buffers
+  /// are copied; immutable retained bytes and metadata are shared. Merge and 
sort scratch buffers remain lazy.
+  /// Raw capacity is retained so future flush timing is unchanged.
+  TDigestAccumulator copy() {
+    return copy(_rawValues != null ? _rawValues.length : 0);
+  }
+
+  private TDigestAccumulator copy(int rawBufferSize) {
+    TDigestAccumulator copy =
+        new TDigestAccumulator(_compression, false, false, 
_useTwoLevelRawCompression);
+    copy._rawValues = rawBufferSize > 0 ? Arrays.copyOf(_rawValues, 
rawBufferSize) : null;
+    copy._centroidMeans = _numCentroids > 0 ? Arrays.copyOf(_centroidMeans, 
_numCentroids) : null;
+    copy._centroidWeights = _numCentroids > 0 ? 
Arrays.copyOf(_centroidWeights, _numCentroids) : null;
+    copy._incomingMeans = _numIncomingCentroids > 0 ? 
Arrays.copyOf(_incomingMeans, _numIncomingCentroids) : null;
+    copy._incomingWeights = _numIncomingCentroids > 0 ? 
Arrays.copyOf(_incomingWeights, _numIncomingCentroids) : null;
+    copy._pendingSerializedTDigest = _pendingSerializedTDigest;
+    copy._pendingSerializedMetadata = _pendingSerializedMetadata;
+    copy._originalFractionalBytes = _originalFractionalBytes;
+    copy._originalBoundaryBytes = _originalBoundaryBytes;
+    copy._historicalFractionalMinMean = _historicalFractionalMinMean;
+    copy._historicalFractionalMaxMean = _historicalFractionalMaxMean;
+    copy._freshFractionalMinMean = _freshFractionalMinMean;
+    copy._freshFractionalMaxMean = _freshFractionalMaxMean;
+    copy._legacyDegraded = _legacyDegraded;
+    copy._hasFractionalWeights = _hasFractionalWeights;
+    copy._deferBoundaryNormalization = _deferBoundaryNormalization;
+    copy._numRawValues = _numRawValues;
+    copy._numCentroids = _numCentroids;
+    copy._numIncomingCentroids = _numIncomingCentroids;
+    copy._mergeCount = _mergeCount;
+    copy._publiclyCompressed = _publiclyCompressed;
+    copy._incomingCentroidsSorted = _incomingCentroidsSorted;
+    copy._totalWeight = _totalWeight;
+    copy._incomingWeight = _incomingWeight;
+    copy._min = _min;
+    copy._max = _max;
+    return copy;
+  }
+
+  /// Copies primitive centroids without encoding and decoding them. Zero 
weights are ignored, and unordered
+  /// means are sorted when initializing a stored, already compressed 
distribution; caller arrays are not mutated.
+  /// Subsequent inputs use the normal buffered merge. Positive weights and 
consistent extrema are required.
+  public void addCentroids(double[] means, double[] weights, int count, double 
min, double max,
+      boolean alreadyCompressed) {
+    addCentroids(means, weights, count, min, max, alreadyCompressed, false);
+  }
+
+  /// Adds validated legacy centroids without marking their existing 
fractional mass as fresh input.
+  void addHistoricalCentroids(double[] means, double[] weights, int count, 
double min, double max,
+      boolean alreadyCompressed) {
+    addCentroids(means, weights, count, min, max, alreadyCompressed, true);
+  }
+
+  private void addCentroids(double[] means, double[] weights, int count, 
double min, double max,
+      boolean alreadyCompressed, boolean historical) {
+    requireMutable();
+    if (count < 0 || count > means.length || count > weights.length) {
+      throw new IllegalArgumentException("Invalid TDigest centroid count: " + 
count);
+    }
+    double totalWeight = 0.0;
+    int positiveCount = 0;
+    boolean sorted = true;
+    boolean fractionalWeights = false;
+    double previousMean = Double.NEGATIVE_INFINITY;
+    for (int i = 0; i < count; i++) {
+      double weight = weights[i];
+      if (weight == 0.0) {
+        continue;
+      }
+      double mean = means[i];
+      if (!(weight > 0.0) || !Double.isFinite(weight) || !(mean >= min && mean 
<= max)) {
+        throw new IllegalArgumentException("Invalid TDigest centroid");
+      }
+      totalWeight += weight;
+      sorted &= mean >= previousMean;
+      previousMean = mean;
+      fractionalWeights |= weight != Math.rint(weight);
+      positiveCount++;
+    }
+    checkTotalWeight(getTotalWeight() + totalWeight);
+    if (positiveCount == 0) {
+      return;
+    }
+    prepareForMutation();
+    _originalFractionalBytes = null;
+    _hasFractionalWeights |= fractionalWeights;
+    if (!historical && fractionalWeights) {
+      for (int i = 0; i < count; i++) {
+        recordFreshFractionalMean(means[i], weights[i]);
+      }
+    }
+    if (hasNoInputs() && alreadyCompressed) {
+      ensureCentroidCapacity(Math.addExact(positiveCount, 2));
+      for (int i = 0; i < count; i++) {
+        if (weights[i] > 0.0) {
+          _centroidMeans[_numCentroids] = means[i];
+          _centroidWeights[_numCentroids++] = weights[i];
+        }
+      }
+      if (!sorted) {
+        sortCentroids(_centroidMeans, _centroidWeights, _numCentroids);
+      }
+      _totalWeight = totalWeight;
+      _min = min;
+      _max = max;
+      if (!historical) {
+        normalizeBoundaryCentroids();
+      }
+      _publiclyCompressed = true;
+    } else {
+      if (sorted && positiveCount == count) {
+        bufferIncomingCentroids(means, weights, count, totalWeight, min, max);
+      } else {
+        // Caller-owned arrays are copied only when filtering or sorting is 
necessary.
+        double[] sortedMeans = new double[positiveCount];
+        double[] sortedWeights = new double[positiveCount];
+        int index = 0;
+        for (int i = 0; i < count; i++) {
+          if (weights[i] > 0.0) {
+            sortedMeans[index] = means[i];
+            sortedWeights[index++] = weights[i];
+          }
+        }
+        if (!sorted) {
+          sortCentroids(sortedMeans, sortedWeights, positiveCount);
+        }
+        bufferIncomingCentroids(sortedMeans, sortedWeights, positiveCount, 
totalWeight, min, max);
+      }
+    }
+  }
+
   public void add(double[] values, int from, int toExclusive) {

Review Comment:
   **[partial commit on invalid input]** `add(double[], from, toExclusive)` 
stages (and possibly flushes into centroids at a buffer boundary) earlier 
values of the batch before NaN validation of later values completes, so `{1.0, 
2.0, NaN}` throws with the digest already holding the pre-NaN prefix — unlike 
`add(double)`, which validates before any mutation. A caller that catches 
per-row exceptions and keeps/reuses the result holder (or retries the row) 
double-counts the prefix.
   
   Cheap fix: pre-scan the chunk for NaN before staging, making the array path 
all-or-nothing like the single-value path.



##########
pinot-segment-local/src/main/java/org/apache/pinot/segment/local/customobject/tdigest/TDigestAccumulator.java:
##########
@@ -81,17 +82,22 @@ public final class TDigestAccumulator extends TDigest {
   private double[] _incomingWeights;
   private double[] _sortedIncomingMeans;
   private double[] _sortedIncomingWeights;
-  private int[] _incomingOrder;
   private SerializedTDigestInput _serializedTDigestInput;
   private byte[] _pendingSerializedTDigest;
-  private double _pendingSerializedTotalWeight = Double.NaN;
-  private boolean _hasSerializedInput;
+  private byte[] _originalFractionalBytes;
+  private byte[] _originalBoundaryBytes;
+  private double _historicalFractionalMinMean = Double.NaN;
+  private double _historicalFractionalMaxMean = Double.NaN;
+  private double _freshFractionalMinMean = Double.NaN;
+  private double _freshFractionalMaxMean = Double.NaN;
+  private SerializedTDigestMetadata _pendingSerializedMetadata;
+  private boolean _legacyDegraded;

Review Comment:
   **[cleanup — state machine]** Degraded/retained legacy state is a four-way, 
priority-ordered flag machine (`_legacyDegraded`, `_pendingSerializedTDigest`, 
`_originalFractionalBytes`, `_originalBoundaryBytes`) threaded through this 
1700+-line class (~20 `_legacyDegraded` branch sites; `serialize()` resolves 
the modes by ordered null checks, including a repeated `_originalBoundaryBytes 
!= null` whose reachability depends on `materializePendingSerializedTDigest()` 
side effects). Every new method or merge path must remember all four checks in 
the right order; missing one silently feeds corrupt centroids into the K1 
kernel or drops retained bytes.
   
   Deeper fix: encode the states in types — an immutable `OpaqueLegacyTDigest` 
for corrupted payloads and one `RetainedPayload{bytes, metadata, reason}` 
abstraction — so `requireMutable()` becomes structural and the healthy kernel 
carries no corruption branches.



##########
pinot-segment-local/src/main/java/org/apache/pinot/segment/local/customobject/tdigest/TDigest.java:
##########
@@ -0,0 +1,113 @@
+/**
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *   http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing,
+ * software distributed under the License is distributed on an
+ * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.  See the License for the
+ * specific language governing permissions and limitations
+ * under the License.
+ */
+package org.apache.pinot.segment.local.customobject.tdigest;
+
+import java.util.Collection;
+import java.util.List;
+
+/// Mutable percentile digest base for Pinot aggregation and legacy t-digest 
byte encodings.
+/// Implementations require external synchronization. Historical corrupted 
payloads can be retained unchanged,
+/// but cannot be mutated or mixed with healthy state.
+public abstract class TDigest {
+  public abstract void add(double value);
+
+  public void add(double value, int weight) {
+    add(value, (double) weight);
+  }
+
+  /// Adds positive finite mass; rejects total-weight overflow. Fractional 
interior mass is supported, but
+  /// serialization rejects fresh endpoint mass below one or singleton mass 
between one and two: legacy readers
+  /// require unit endpoints. Thus `add(5, 0.5)` is accepted but cannot be 
serialized alone.
+  public abstract void add(double value, double weight);
+
+  /// Merges an exclusively owned source; implementations may compress that 
mutable source in place.
+  public abstract void add(TDigest other);
+
+  public void add(List<? extends TDigest> others) {
+    for (TDigest other : others) {
+      add(other);
+    }
+  }
+
+  public abstract void compress();
+
+  /// Returns the legacy long size view, saturating when the precise mass 
exceeds its range.
+  public long size() {
+    return (long) getTotalWeight();
+  }
+
+  /// Returns mass without narrowing fractional or large weights. Add/merge 
reject overflow of a valid total.
+  /// Invalid historical payloads may report their original negative or 
non-finite total, but cannot be merged.
+  public abstract double getTotalWeight();
+
+  /// Returns false when historical numerical corruption leaves the 
distribution unknown.
+  public boolean hasValidStatistics() {
+    return true;
+  }
+
+  /// An unknown distribution remains present even when its historical weights 
sum to zero.
+  public boolean isEmpty() {
+    return getTotalWeight() == 0.0 && hasValidStatistics();
+  }
+
+  public abstract double cdf(double value);
+
+  public abstract double quantile(double quantile);
+
+  /// Returns immutable centroid values with their precise double weights.
+  /// Reading this view may flush buffered inputs without applying the final 
public compression.
+  public abstract Collection<Centroid> centroids();
+
+  public abstract double compression();
+
+  /// Serializes one independently owned legacy-compatible payload. 
Implementations own their compression policy.
+  /// Unchanged historical encodings may be retained byte-exactly; fresh 
unrepresentable boundaries are rejected.
+  public abstract byte[] serialize();
+
+  /// Finalizes an independently owned result without changing a live 
aggregation that may receive more inputs.
+  protected abstract byte[] serializeSnapshot();
+
+  /// Bounds independently owned serialization without requiring a two-step 
size/write protocol.
+  /// Mutable implementations can override this to avoid flushing buffered 
inputs.
+  public int maxSerializedByteSize() {
+    return serialize().length;
+  }
+
+  public abstract int centroidCount();
+
+  public abstract double getMin();
+
+  public abstract double getMax();
+
+  /// Returns the inherited unsupported fractional endpoint mean, or NaN. 
Mergers propagate this provenance
+  /// from validated legacy bytes without granting permission to new 
fractional extrema.
+  double getHistoricalFractionalBoundaryMean(boolean lowerBoundary) {

Review Comment:
   **[cleanup — provenance by convention]** Fractional-boundary serialization 
provenance 
(`getHistoricalFractionalBoundaryMean`/`getFreshFractionalBoundaryMean`) is 
exposed as polymorphic hooks on the abstract base and propagated manually at 6+ 
merge sites (TDigestAccumulator, NonFiniteAwareTDigest, 
SerializedTDigestInput), plus a boolean threaded through TDigestCodec. The 
invariant "only means inherited from validated legacy bytes may keep sub-unit 
endpoint weights" is enforced purely by convention: one missed 
`inheritHistoricalFractionalBoundaries()` call silently re-grants or revokes 
legacy serialization permission (emitting bytes old readers assert on, or 
throwing on valid state).
   
   `SerializedTDigestMetadata` already carries 
`historicalFractionalMinMean`/`MaxMean` — carrying provenance with the retained 
payload and letting the codec consult it at write time would remove the 
base-class hooks and per-merge propagation.



##########
pinot-segment-local/src/main/java/org/apache/pinot/segment/local/customobject/tdigest/TDigestCodec.java:
##########
@@ -0,0 +1,859 @@
+/**
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *   http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing,
+ * software distributed under the License is distributed on an
+ * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.  See the License for the
+ * specific language governing permissions and limitations
+ * under the License.
+ */
+package org.apache.pinot.segment.local.customobject.tdigest;
+
+import java.lang.invoke.MethodHandles;
+import java.lang.invoke.VarHandle;
+import java.nio.BufferUnderflowException;
+import java.nio.ByteBuffer;
+import java.nio.ByteOrder;
+import java.util.Arrays;
+
+/// Reads and writes the legacy t-digest 3.2/3.3 formats, validating lengths 
before allocating centroid arrays.
+/// Fresh output respects both readers' capacities without narrowing doubles. 
Historical fractional endpoints and
+/// opaque corrupted payloads retain their original limitations; byte 
preservation does not ensure reverse upgrades.
+/// Endpoint repair, capacity fallback and point-mass interpolation can change 
quantiles on historical data.
+/// This utility has no shared mutable state; callers must exclusively own 
input buffers and parser state.
+public final class TDigestCodec {
+  public static final int VERBOSE_ENCODING = 1;
+  public static final int SMALL_ENCODING = 2;
+  private static final int LEGACY_CAPACITY_PADDING = 10;
+  public static final int VERBOSE_HEADER_SIZE = 32;
+  public static final int VERBOSE_CENTROID_SIZE = 16;
+  public static final int SMALL_HEADER_SIZE = 30;
+  public static final int SMALL_CENTROID_SIZE = 8;
+  public static final int DEFAULT_MERGE_BUFFER_MULTIPLIER = 5;
+
+  private TDigestCodec() {
+  }
+
+  /// Reads the compression from a validated header without decoding centroid 
arrays.
+  public static double readCompression(byte[] bytes) {
+    return readSerializedHeader(ByteBuffer.wrap(bytes)).compression();
+  }
+
+  /// Rejects non-finite compression while retaining the legacy clamping of 
finite settings below ten.
+  public static void validateCompression(double compression) {
+    if (!Double.isFinite(compression)) {
+      throw new IllegalArgumentException("Invalid TDigest compression: " + 
compression);
+    }
+  }
+
+  /// Applies the legacy minimum compression to query, ingestion and 
serialized-header settings.
+  public static double normalizeCompression(double compression) {
+    validateCompression(compression);
+    return Math.max(compression, 10.0);
+  }
+
+  /// Writes validated centroid arrays in the standard verbose encoding 
without sorting or recompression.
+  /// The caller retains the arrays; only the first `count` entries are 
written, with normalized compression.
+  public static byte[] serializeCentroids(double compression, double min, 
double max, double[] means,
+      double[] weights, int count) {
+    if (count < 0 || count > means.length || count > weights.length) {
+      throw new IllegalArgumentException("Invalid TDigest centroid count: " + 
count);
+    }
+    ByteBuffer encoded = ByteBuffer.allocate(Math.addExact(VERBOSE_HEADER_SIZE,
+        Math.multiplyExact(VERBOSE_CENTROID_SIZE, count)));
+    
encoded.putInt(VERBOSE_ENCODING).putDouble(min).putDouble(max).putDouble(normalizeCompression(compression));
+    encoded.putInt(count);
+    for (int i = 0; i < count; i++) {
+      encoded.putDouble(weights[i]).putDouble(means[i]);
+    }
+    return encoded.array();
+  }
+
+  /// Encodes validated, sorted native centroids and selects a 
legacy-compatible representation.
+  static byte[] serializeCompatibleCentroids(double compression, double min, 
double max, double[] means,
+      double[] weights, int count, boolean inheritedFractionalBoundaries) {
+    if (count < 0 || count > 0 && (count > means.length || count > 
weights.length || !(min <= max))) {
+      throw new IllegalArgumentException("Invalid TDigest centroid count or 
extrema");
+    }
+    ByteBuffer buffer = ByteBuffer.allocate(
+        Math.addExact(VERBOSE_HEADER_SIZE,
+            Math.multiplyExact(VERBOSE_CENTROID_SIZE, count)));
+    buffer.putInt(VERBOSE_ENCODING);
+    buffer.putDouble(min);
+    buffer.putDouble(max);
+    buffer.putDouble(compression);
+    buffer.putInt(count);
+    double encodedWeight = 0.0;
+    boolean hasNonFiniteMeans = false;
+    boolean fractionalWeights = false;
+    for (int i = 0; i < count; i++) {
+      if (!(weights[i] > 0.0) || !Double.isFinite(weights[i]) || !(means[i] >= 
min && means[i] <= max)) {
+        throw new IllegalArgumentException("Invalid TDigest centroid");
+      }
+      buffer.putDouble(weights[i]);
+      buffer.putDouble(means[i]);
+      encodedWeight += weights[i];
+      hasNonFiniteMeans |= !Double.isFinite(means[i]);
+      fractionalWeights |= weights[i] != Math.rint(weights[i]);
+    }
+    if (!Double.isFinite(encodedWeight)) {
+      throw new IllegalArgumentException("TDigest total weight exceeds the 
supported range");
+    }
+    boolean weightedBoundaries = count == 1 ? weights[0] >= 2.0
+        : count > 1 && (weights[0] > 1.0 || weights[count - 1] > 1.0);
+    // Collect exact wire metadata during the write rather than decoding and 
validating our fresh bytes again.
+    SerializedTDigestMetadata metadata = new 
SerializedTDigestMetadata(VERBOSE_ENCODING, min, max,
+        compression, count,
+        VERBOSE_HEADER_SIZE, VERBOSE_CENTROID_SIZE, buffer.capacity(), 
encodedWeight,
+        hasNonFiniteMeans, false, false, fractionalWeights, 
weightedBoundaries, false, compression, Double.NaN,
+        Double.NaN, Double.NaN);
+    return makeLegacyCompatible(buffer.array(), metadata, 
inheritedFractionalBoundaries);
+  }
+
+  /// Rejects fresh boundary masses that legacy readers cannot recompress 
without inventing mass.
+  /// Call after boundary normalization and removing zero-weight centroids; 
fractional interior mass is supported.
+  static void checkLegacyBoundaryWeights(int count, double firstWeight, double 
lastWeight) {
+    if (count > 0 && (firstWeight < 1.0 || lastWeight < 1.0
+        || count == 1 && firstWeight != 1.0 && firstWeight < 2.0)) {
+      throw new IllegalArgumentException("Cannot serialize fractional TDigest 
boundary mass for legacy readers");
+    }
+  }
+
+  /// Allows unsupported endpoints only at exact means inherited from 
validated legacy bytes. A tolerance could
+  /// grant the exception to fresh extrema. Fresh fractional input at or 
beyond an endpoint permanently excludes it,
+  /// even if its historical mass was merged away or the new weight equals the 
historical weight.
+  static boolean hasInheritedFractionalBoundaryEncoding(TDigest source, int 
count, double firstMean,
+      double firstWeight, double lastMean, double lastWeight) {
+    if (count <= 0 || !source.hasValidStatistics() || !(firstWeight > 0.0) || 
!(lastWeight > 0.0)
+        || !Double.isFinite(firstWeight) || !Double.isFinite(lastWeight)) {
+      return false;
+    }
+    boolean singleton = count == 1 && firstWeight != 1.0 && firstWeight < 2.0;
+    boolean firstUnsupported = firstWeight < 1.0 || singleton;
+    boolean lastUnsupported = lastWeight < 1.0 || singleton;
+    return (firstUnsupported || lastUnsupported)
+        && (!firstUnsupported || firstMean == 
source.getHistoricalFractionalBoundaryMean(true)
+            && !(source.getFreshFractionalBoundaryMean(true) <= firstMean))
+        && (!lastUnsupported || lastMean == 
source.getHistoricalFractionalBoundaryMean(false)
+            && !(source.getFreshFractionalBoundaryMean(false) >= lastMean));
+  }
+
+  private static void checkSerializedBoundaryWeights(byte[] bytes, 
SerializedTDigestMetadata metadata) {
+    int count = metadata.centroidCount();
+    if (count > 0) {
+      ByteBuffer encoded = ByteBuffer.wrap(bytes);
+      int firstOffset = metadata.centroidOffset();
+      int lastOffset = firstOffset + (count - 1) * metadata.centroidSize();
+      double firstWeight = metadata.encoding() == VERBOSE_ENCODING
+          ? encoded.getDouble(firstOffset) : encoded.getFloat(firstOffset);
+      double lastWeight = metadata.encoding() == VERBOSE_ENCODING
+          ? encoded.getDouble(lastOffset) : encoded.getFloat(lastOffset);
+      checkLegacyBoundaryWeights(count, firstWeight, lastWeight);
+    }
+  }
+
+  /// Converts a verbose `MergingDigest` payload to a representation readable 
by t-digest 3.2 and 3.3.
+  ///
+  /// The input must use the standard verbose `MergingDigest` encoding. The 
returned payload stays verbose when it
+  /// already fits both legacy default capacities, uses compact encoding only 
when every narrowed field is exact, and
+  /// otherwise reduces interior centroids without narrowing doubles. 
Compression below ten is normalized in the
+  /// output header because the 3.2 verbose reader sizes its arrays from the 
raw header before applying that minimum.
+  /// Opaque degraded state is retained without reducing its unknown 
distribution, including over-capacity payloads.
+  /// Fresh fractional endpoints that legacy unit-boundary repair cannot 
represent are rejected without reweighting.
+  public static byte[] makeLegacyCompatible(byte[] verboseBytes) {
+    return makeLegacyCompatible(verboseBytes, 
inspectSerialized(ByteBuffer.wrap(verboseBytes), false));
+  }
+
+  /// Uses metadata validated for these exact retained bytes, avoiding another 
centroid validation walk.
+  public static byte[] makeLegacyCompatible(byte[] verboseBytes, 
SerializedTDigestMetadata metadata) {
+    return makeLegacyCompatible(verboseBytes, metadata, false);
+  }
+
+  /// Retains exact verbose weights for inherited historical fractional 
endpoints that cannot become unit endpoints.
+  /// All other compatibility checks apply. These payloads keep their 
historical assertion-enabled 3.3 read/merge
+  /// limitation; callers must establish inherited endpoint provenance before 
enabling this exception.
+  static byte[] makeLegacyCompatible(byte[] verboseBytes, 
SerializedTDigestMetadata metadata,
+      boolean inheritedFractionalBoundaries) {
+    if (metadata.encoding() != VERBOSE_ENCODING) {
+      throw new IllegalArgumentException("Expected verbose TDigest encoding");
+    }
+    if (metadata.needsLegacyFallback()) {
+      return verboseBytes;
+    }
+    if (!Double.isNaN(metadata.recoveredInfinityMean())) {
+      double[] means = new double[metadata.centroidCount()];
+      double[] weights = new double[means.length];
+      decodeSerializedCentroids(ByteBuffer.wrap(verboseBytes), metadata, 
means, weights);
+      if (!inheritedFractionalBoundaries) {
+        return serializeRecoveredCentroids(metadata, means, weights);
+      }
+      verboseBytes = serializeCentroids(metadata.compression(), 
metadata.min(), metadata.max(), means, weights,
+          means.length);
+      metadata = inspectSerialized(ByteBuffer.wrap(verboseBytes), false);
+    }
+    if (metadata.hasZeroWeightCentroids()) {
+      verboseBytes = removeZeroWeightCentroids(verboseBytes, metadata);
+      metadata = inspectSerialized(ByteBuffer.wrap(verboseBytes), false);
+    }
+    if (!inheritedFractionalBoundaries) {
+      checkSerializedBoundaryWeights(verboseBytes, metadata);
+    }
+    double compression = metadata.compression();
+    if (metadata.encodedCompression() != compression) {
+      verboseBytes = verboseBytes.clone();
+      ByteBuffer.wrap(verboseBytes).putDouble(20, compression);
+    }
+    int centroidCount = metadata.centroidCount();
+    int legacyCapacity =
+        Math.min(getLegacyDefaultCentroidCapacity(compression), 
getDefaultCentroidCapacity(compression));
+    if (centroidCount <= legacyCapacity) {
+      return verboseBytes;
+    }
+    int mainCapacity = getDefaultCentroidCapacity(compression);
+    long bufferCapacity = DEFAULT_MERGE_BUFFER_MULTIPLIER * (long) 
mainCapacity;
+    if (centroidCount > mainCapacity || inheritedFractionalBoundaries || 
(double) (float) compression != compression
+        || centroidCount > Short.MAX_VALUE
+        || mainCapacity > Short.MAX_VALUE || bufferCapacity > Short.MAX_VALUE) 
{
+      return reduceVerboseCentroids(verboseBytes, legacyCapacity);
+    }
+    ByteBuffer verbose = ByteBuffer.wrap(verboseBytes);
+    ByteBuffer centroids = verbose.duplicate();
+    centroids.position(metadata.centroidOffset());
+    for (int i = 0; i < centroidCount; i++) {
+      double weight = centroids.getDouble();
+      double mean = centroids.getDouble();
+      if ((double) (float) weight != weight || (double) (float) mean != mean) {
+        return reduceVerboseCentroids(verboseBytes, legacyCapacity);
+      }
+    }
+
+    ByteBuffer small = ByteBuffer.allocate(SMALL_HEADER_SIZE + 
SMALL_CENTROID_SIZE * centroidCount);
+    verbose.rewind();
+    verbose.getInt();
+    small.putInt(SMALL_ENCODING);
+    small.putDouble(verbose.getDouble());
+    small.putDouble(verbose.getDouble());
+    verbose.getDouble();
+    verbose.getInt();
+    small.putFloat((float) compression);
+    small.putShort((short) mainCapacity);
+    small.putShort((short) bufferCapacity);
+    small.putShort((short) centroidCount);
+    for (int i = 0; i < centroidCount; i++) {
+      small.putFloat((float) verbose.getDouble());
+      small.putFloat((float) verbose.getDouble());
+    }
+    return small.array();
+  }
+
+  private static byte[] serializeRecoveredCentroids(SerializedTDigestMetadata 
metadata, double[] means,
+      double[] weights) {
+    TDigestAccumulator digest = 
TDigestAccumulator.forLegacyAggregation(metadata.compression());
+    digest.addHistoricalCentroids(means, weights, means.length, 
metadata.min(), metadata.max(), true);
+    
digest.inheritHistoricalFractionalBoundaries(metadata.historicalFractionalMinMean(),
+        metadata.historicalFractionalMaxMean());
+    return digest.serialize();
+  }
+
+  private static byte[] removeZeroWeightCentroids(byte[] verboseBytes, 
SerializedTDigestMetadata metadata) {
+    ByteBuffer source = ByteBuffer.wrap(verboseBytes);
+    source.position(metadata.centroidOffset());
+    ByteBuffer filtered = ByteBuffer.allocate(metadata.encodedLength());
+    filtered.put(verboseBytes, 0, VERBOSE_HEADER_SIZE);
+    int count = 0;
+    for (int i = 0; i < metadata.centroidCount(); i++) {
+      double weight = source.getDouble();
+      double mean = source.getDouble();
+      if (weight != 0.0) {
+        filtered.putDouble(weight).putDouble(mean);
+        count++;
+      }
+    }
+    filtered.putInt(28, count);
+    return Arrays.copyOf(filtered.array(), filtered.position());
+  }
+
+  /// Validates serialized lengths and centroid values without allocating 
centroid arrays.
+  public static double validateSerialized(byte[] bytes) {
+    return validateSerialized(ByteBuffer.wrap(bytes));
+  }
+
+  /// Validates one legacy digest without changing `input` and returns its 
total centroid weight.
+  ///
+  /// Trailing bytes remain available to the caller for intermediate values 
containing several objects.
+  public static double validateSerialized(ByteBuffer input) {
+    return validateSerialized(input, true);
+  }
+
+  private static double validateSerialized(ByteBuffer input, boolean 
checkCapacity) {
+    return inspectSerialized(input, checkCapacity).totalWeight();
+  }
+
+  /// Header and numerical metadata for one legacy byte payload. The centroid 
bytes remain owned by the caller.
+  /// Header-only inspection leaves total weight as NaN until centroid 
inspection validates the numerical fields.
+  ///
+  /// Legacy writers can emit poisoned numerical state after overflow or 
broken fractional boundary repair.
+  /// Such state is retained with degraded quantiles, rather than being passed 
to the sorted K1 kernel.
+  public record SerializedTDigestMetadata(int encoding, double min, double 
max, double compression,
+      int centroidCount, int centroidOffset, int centroidSize,
+      int encodedLength, double totalWeight, boolean hasNonFiniteMeans, 
boolean needsLegacyFallback,
+      boolean unorderedMeans, boolean fractionalWeights, boolean 
weightedBoundaries, boolean hasZeroWeightCentroids,
+      double encodedCompression, double recoveredInfinityMean, double 
historicalFractionalMinMean,
+      double historicalFractionalMaxMean) {
+    /// Whether the encoded centroid view can be used unchanged by healthy 
pending-state readers and writers.
+    public boolean isCanonicalPayload() {
+      return !needsLegacyFallback && !weightedBoundaries && !unorderedMeans && 
!hasZeroWeightCentroids
+          && Double.isNaN(recoveredInfinityMean);
+    }
+  }
+
+  /// Invocation-local parser state. Primitive byte-array reads avoid per-row 
buffer and metadata allocations.
+  /// Public metadata and retained pending payloads receive immutable 
snapshots instead of sharing this state.
+  static final class SerializedTDigestState {
+    private static final VarHandle SHORT_VIEW =
+        MethodHandles.byteArrayViewVarHandle(short[].class, 
ByteOrder.BIG_ENDIAN);
+    private static final VarHandle INT_VIEW = 
MethodHandles.byteArrayViewVarHandle(int[].class, ByteOrder.BIG_ENDIAN);
+    private static final VarHandle LONG_VIEW = 
MethodHandles.byteArrayViewVarHandle(long[].class, ByteOrder.BIG_ENDIAN);
+
+    int _encoding;
+    double _min;
+    double _max;
+    double _compression;
+    int _centroidCount;
+    int _centroidOffset;
+    int _centroidSize;
+    int _encodedLength;
+    double _totalWeight;
+    boolean _hasNonFiniteMeans;
+    boolean _needsLegacyFallback;
+    boolean _unorderedMeans;
+    boolean _fractionalWeights;
+    boolean _weightedBoundaries;
+    boolean _hasZeroWeightCentroids;
+    double _encodedCompression;
+    double _recoveredInfinityMean;
+    double _historicalFractionalMinMean;
+    double _historicalFractionalMaxMean;
+    private byte[] _bytes;
+    private ByteBuffer _buffer;
+    private int _position;
+    private int _limit;
+
+    void reset(byte[] bytes) {
+      _bytes = bytes;
+      _buffer = null;
+      _position = 0;
+      _limit = bytes.length;
+    }
+
+    void reset(ByteBuffer input) {
+      _bytes = null;
+      _buffer = input.slice().order(ByteOrder.BIG_ENDIAN);
+      _position = 0;
+      _limit = _buffer.limit();
+    }
+
+    void copyFrom(SerializedTDigestMetadata metadata) {

Review Comment:
   **[cleanup — 19-field mirror]** `SerializedTDigestState` hand-mirrors every 
component of the `SerializedTDigestMetadata` record, so each attribute lives in 
5 coordinated places: record component, state field, `copyFrom()` line, 
`snapshot()` line, and the bulk assignment blocks in 
`readSerializedHeader`/`inspectSerialized`. The newest additions 
(`recoveredInfinityMean`, `historicalFractional*Mean`) show the cost; a missed 
line silently desynchronizes metadata.
   
   Simpler: have the parser build the immutable record once per inspected input 
and let the state hold that record reference plus the byte cursor (one small 
allocation per input reset), deleting `copyFrom`/`snapshot`.



##########
pinot-segment-local/src/main/java/org/apache/pinot/segment/local/customobject/tdigest/TDigestCodec.java:
##########
@@ -0,0 +1,859 @@
+/**
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *   http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing,
+ * software distributed under the License is distributed on an
+ * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.  See the License for the
+ * specific language governing permissions and limitations
+ * under the License.
+ */
+package org.apache.pinot.segment.local.customobject.tdigest;
+
+import java.lang.invoke.MethodHandles;
+import java.lang.invoke.VarHandle;
+import java.nio.BufferUnderflowException;
+import java.nio.ByteBuffer;
+import java.nio.ByteOrder;
+import java.util.Arrays;
+
+/// Reads and writes the legacy t-digest 3.2/3.3 formats, validating lengths 
before allocating centroid arrays.
+/// Fresh output respects both readers' capacities without narrowing doubles. 
Historical fractional endpoints and
+/// opaque corrupted payloads retain their original limitations; byte 
preservation does not ensure reverse upgrades.
+/// Endpoint repair, capacity fallback and point-mass interpolation can change 
quantiles on historical data.
+/// This utility has no shared mutable state; callers must exclusively own 
input buffers and parser state.
+public final class TDigestCodec {
+  public static final int VERBOSE_ENCODING = 1;
+  public static final int SMALL_ENCODING = 2;
+  private static final int LEGACY_CAPACITY_PADDING = 10;
+  public static final int VERBOSE_HEADER_SIZE = 32;
+  public static final int VERBOSE_CENTROID_SIZE = 16;
+  public static final int SMALL_HEADER_SIZE = 30;
+  public static final int SMALL_CENTROID_SIZE = 8;
+  public static final int DEFAULT_MERGE_BUFFER_MULTIPLIER = 5;
+
+  private TDigestCodec() {
+  }
+
+  /// Reads the compression from a validated header without decoding centroid 
arrays.
+  public static double readCompression(byte[] bytes) {
+    return readSerializedHeader(ByteBuffer.wrap(bytes)).compression();
+  }
+
+  /// Rejects non-finite compression while retaining the legacy clamping of 
finite settings below ten.
+  public static void validateCompression(double compression) {
+    if (!Double.isFinite(compression)) {
+      throw new IllegalArgumentException("Invalid TDigest compression: " + 
compression);
+    }
+  }
+
+  /// Applies the legacy minimum compression to query, ingestion and 
serialized-header settings.
+  public static double normalizeCompression(double compression) {
+    validateCompression(compression);
+    return Math.max(compression, 10.0);
+  }
+
+  /// Writes validated centroid arrays in the standard verbose encoding 
without sorting or recompression.
+  /// The caller retains the arrays; only the first `count` entries are 
written, with normalized compression.
+  public static byte[] serializeCentroids(double compression, double min, 
double max, double[] means,
+      double[] weights, int count) {
+    if (count < 0 || count > means.length || count > weights.length) {
+      throw new IllegalArgumentException("Invalid TDigest centroid count: " + 
count);
+    }
+    ByteBuffer encoded = ByteBuffer.allocate(Math.addExact(VERBOSE_HEADER_SIZE,
+        Math.multiplyExact(VERBOSE_CENTROID_SIZE, count)));
+    
encoded.putInt(VERBOSE_ENCODING).putDouble(min).putDouble(max).putDouble(normalizeCompression(compression));
+    encoded.putInt(count);
+    for (int i = 0; i < count; i++) {
+      encoded.putDouble(weights[i]).putDouble(means[i]);
+    }
+    return encoded.array();
+  }
+
+  /// Encodes validated, sorted native centroids and selects a 
legacy-compatible representation.
+  static byte[] serializeCompatibleCentroids(double compression, double min, 
double max, double[] means,
+      double[] weights, int count, boolean inheritedFractionalBoundaries) {
+    if (count < 0 || count > 0 && (count > means.length || count > 
weights.length || !(min <= max))) {
+      throw new IllegalArgumentException("Invalid TDigest centroid count or 
extrema");
+    }
+    ByteBuffer buffer = ByteBuffer.allocate(
+        Math.addExact(VERBOSE_HEADER_SIZE,
+            Math.multiplyExact(VERBOSE_CENTROID_SIZE, count)));
+    buffer.putInt(VERBOSE_ENCODING);
+    buffer.putDouble(min);
+    buffer.putDouble(max);
+    buffer.putDouble(compression);
+    buffer.putInt(count);
+    double encodedWeight = 0.0;
+    boolean hasNonFiniteMeans = false;
+    boolean fractionalWeights = false;
+    for (int i = 0; i < count; i++) {
+      if (!(weights[i] > 0.0) || !Double.isFinite(weights[i]) || !(means[i] >= 
min && means[i] <= max)) {
+        throw new IllegalArgumentException("Invalid TDigest centroid");
+      }
+      buffer.putDouble(weights[i]);
+      buffer.putDouble(means[i]);
+      encodedWeight += weights[i];
+      hasNonFiniteMeans |= !Double.isFinite(means[i]);
+      fractionalWeights |= weights[i] != Math.rint(weights[i]);
+    }
+    if (!Double.isFinite(encodedWeight)) {
+      throw new IllegalArgumentException("TDigest total weight exceeds the 
supported range");
+    }
+    boolean weightedBoundaries = count == 1 ? weights[0] >= 2.0
+        : count > 1 && (weights[0] > 1.0 || weights[count - 1] > 1.0);
+    // Collect exact wire metadata during the write rather than decoding and 
validating our fresh bytes again.
+    SerializedTDigestMetadata metadata = new 
SerializedTDigestMetadata(VERBOSE_ENCODING, min, max,
+        compression, count,
+        VERBOSE_HEADER_SIZE, VERBOSE_CENTROID_SIZE, buffer.capacity(), 
encodedWeight,
+        hasNonFiniteMeans, false, false, fractionalWeights, 
weightedBoundaries, false, compression, Double.NaN,
+        Double.NaN, Double.NaN);
+    return makeLegacyCompatible(buffer.array(), metadata, 
inheritedFractionalBoundaries);
+  }
+
+  /// Rejects fresh boundary masses that legacy readers cannot recompress 
without inventing mass.
+  /// Call after boundary normalization and removing zero-weight centroids; 
fractional interior mass is supported.
+  static void checkLegacyBoundaryWeights(int count, double firstWeight, double 
lastWeight) {
+    if (count > 0 && (firstWeight < 1.0 || lastWeight < 1.0
+        || count == 1 && firstWeight != 1.0 && firstWeight < 2.0)) {
+      throw new IllegalArgumentException("Cannot serialize fractional TDigest 
boundary mass for legacy readers");
+    }
+  }
+
+  /// Allows unsupported endpoints only at exact means inherited from 
validated legacy bytes. A tolerance could
+  /// grant the exception to fresh extrema. Fresh fractional input at or 
beyond an endpoint permanently excludes it,
+  /// even if its historical mass was merged away or the new weight equals the 
historical weight.
+  static boolean hasInheritedFractionalBoundaryEncoding(TDigest source, int 
count, double firstMean,
+      double firstWeight, double lastMean, double lastWeight) {
+    if (count <= 0 || !source.hasValidStatistics() || !(firstWeight > 0.0) || 
!(lastWeight > 0.0)
+        || !Double.isFinite(firstWeight) || !Double.isFinite(lastWeight)) {
+      return false;
+    }
+    boolean singleton = count == 1 && firstWeight != 1.0 && firstWeight < 2.0;
+    boolean firstUnsupported = firstWeight < 1.0 || singleton;
+    boolean lastUnsupported = lastWeight < 1.0 || singleton;
+    return (firstUnsupported || lastUnsupported)
+        && (!firstUnsupported || firstMean == 
source.getHistoricalFractionalBoundaryMean(true)
+            && !(source.getFreshFractionalBoundaryMean(true) <= firstMean))
+        && (!lastUnsupported || lastMean == 
source.getHistoricalFractionalBoundaryMean(false)
+            && !(source.getFreshFractionalBoundaryMean(false) >= lastMean));
+  }
+
+  private static void checkSerializedBoundaryWeights(byte[] bytes, 
SerializedTDigestMetadata metadata) {
+    int count = metadata.centroidCount();
+    if (count > 0) {
+      ByteBuffer encoded = ByteBuffer.wrap(bytes);
+      int firstOffset = metadata.centroidOffset();
+      int lastOffset = firstOffset + (count - 1) * metadata.centroidSize();
+      double firstWeight = metadata.encoding() == VERBOSE_ENCODING
+          ? encoded.getDouble(firstOffset) : encoded.getFloat(firstOffset);
+      double lastWeight = metadata.encoding() == VERBOSE_ENCODING
+          ? encoded.getDouble(lastOffset) : encoded.getFloat(lastOffset);
+      checkLegacyBoundaryWeights(count, firstWeight, lastWeight);
+    }
+  }
+
+  /// Converts a verbose `MergingDigest` payload to a representation readable 
by t-digest 3.2 and 3.3.
+  ///
+  /// The input must use the standard verbose `MergingDigest` encoding. The 
returned payload stays verbose when it
+  /// already fits both legacy default capacities, uses compact encoding only 
when every narrowed field is exact, and
+  /// otherwise reduces interior centroids without narrowing doubles. 
Compression below ten is normalized in the
+  /// output header because the 3.2 verbose reader sizes its arrays from the 
raw header before applying that minimum.
+  /// Opaque degraded state is retained without reducing its unknown 
distribution, including over-capacity payloads.
+  /// Fresh fractional endpoints that legacy unit-boundary repair cannot 
represent are rejected without reweighting.
+  public static byte[] makeLegacyCompatible(byte[] verboseBytes) {
+    return makeLegacyCompatible(verboseBytes, 
inspectSerialized(ByteBuffer.wrap(verboseBytes), false));
+  }
+
+  /// Uses metadata validated for these exact retained bytes, avoiding another 
centroid validation walk.
+  public static byte[] makeLegacyCompatible(byte[] verboseBytes, 
SerializedTDigestMetadata metadata) {
+    return makeLegacyCompatible(verboseBytes, metadata, false);
+  }
+
+  /// Retains exact verbose weights for inherited historical fractional 
endpoints that cannot become unit endpoints.
+  /// All other compatibility checks apply. These payloads keep their 
historical assertion-enabled 3.3 read/merge
+  /// limitation; callers must establish inherited endpoint provenance before 
enabling this exception.
+  static byte[] makeLegacyCompatible(byte[] verboseBytes, 
SerializedTDigestMetadata metadata,
+      boolean inheritedFractionalBoundaries) {
+    if (metadata.encoding() != VERBOSE_ENCODING) {
+      throw new IllegalArgumentException("Expected verbose TDigest encoding");
+    }
+    if (metadata.needsLegacyFallback()) {
+      return verboseBytes;
+    }
+    if (!Double.isNaN(metadata.recoveredInfinityMean())) {
+      double[] means = new double[metadata.centroidCount()];
+      double[] weights = new double[means.length];
+      decodeSerializedCentroids(ByteBuffer.wrap(verboseBytes), metadata, 
means, weights);
+      if (!inheritedFractionalBoundaries) {
+        return serializeRecoveredCentroids(metadata, means, weights);
+      }
+      verboseBytes = serializeCentroids(metadata.compression(), 
metadata.min(), metadata.max(), means, weights,
+          means.length);
+      metadata = inspectSerialized(ByteBuffer.wrap(verboseBytes), false);
+    }
+    if (metadata.hasZeroWeightCentroids()) {
+      verboseBytes = removeZeroWeightCentroids(verboseBytes, metadata);
+      metadata = inspectSerialized(ByteBuffer.wrap(verboseBytes), false);
+    }
+    if (!inheritedFractionalBoundaries) {
+      checkSerializedBoundaryWeights(verboseBytes, metadata);
+    }
+    double compression = metadata.compression();
+    if (metadata.encodedCompression() != compression) {
+      verboseBytes = verboseBytes.clone();
+      ByteBuffer.wrap(verboseBytes).putDouble(20, compression);
+    }
+    int centroidCount = metadata.centroidCount();
+    int legacyCapacity =
+        Math.min(getLegacyDefaultCentroidCapacity(compression), 
getDefaultCentroidCapacity(compression));
+    if (centroidCount <= legacyCapacity) {
+      return verboseBytes;
+    }
+    int mainCapacity = getDefaultCentroidCapacity(compression);
+    long bufferCapacity = DEFAULT_MERGE_BUFFER_MULTIPLIER * (long) 
mainCapacity;
+    if (centroidCount > mainCapacity || inheritedFractionalBoundaries || 
(double) (float) compression != compression
+        || centroidCount > Short.MAX_VALUE
+        || mainCapacity > Short.MAX_VALUE || bufferCapacity > Short.MAX_VALUE) 
{
+      return reduceVerboseCentroids(verboseBytes, legacyCapacity);
+    }
+    ByteBuffer verbose = ByteBuffer.wrap(verboseBytes);
+    ByteBuffer centroids = verbose.duplicate();
+    centroids.position(metadata.centroidOffset());
+    for (int i = 0; i < centroidCount; i++) {
+      double weight = centroids.getDouble();
+      double mean = centroids.getDouble();
+      if ((double) (float) weight != weight || (double) (float) mean != mean) {
+        return reduceVerboseCentroids(verboseBytes, legacyCapacity);
+      }
+    }
+
+    ByteBuffer small = ByteBuffer.allocate(SMALL_HEADER_SIZE + 
SMALL_CENTROID_SIZE * centroidCount);
+    verbose.rewind();
+    verbose.getInt();
+    small.putInt(SMALL_ENCODING);
+    small.putDouble(verbose.getDouble());
+    small.putDouble(verbose.getDouble());
+    verbose.getDouble();
+    verbose.getInt();
+    small.putFloat((float) compression);
+    small.putShort((short) mainCapacity);
+    small.putShort((short) bufferCapacity);
+    small.putShort((short) centroidCount);
+    for (int i = 0; i < centroidCount; i++) {
+      small.putFloat((float) verbose.getDouble());
+      small.putFloat((float) verbose.getDouble());
+    }
+    return small.array();
+  }
+
+  private static byte[] serializeRecoveredCentroids(SerializedTDigestMetadata 
metadata, double[] means,
+      double[] weights) {
+    TDigestAccumulator digest = 
TDigestAccumulator.forLegacyAggregation(metadata.compression());
+    digest.addHistoricalCentroids(means, weights, means.length, 
metadata.min(), metadata.max(), true);
+    
digest.inheritHistoricalFractionalBoundaries(metadata.historicalFractionalMinMean(),
+        metadata.historicalFractionalMaxMean());
+    return digest.serialize();
+  }
+
+  private static byte[] removeZeroWeightCentroids(byte[] verboseBytes, 
SerializedTDigestMetadata metadata) {
+    ByteBuffer source = ByteBuffer.wrap(verboseBytes);
+    source.position(metadata.centroidOffset());
+    ByteBuffer filtered = ByteBuffer.allocate(metadata.encodedLength());
+    filtered.put(verboseBytes, 0, VERBOSE_HEADER_SIZE);
+    int count = 0;
+    for (int i = 0; i < metadata.centroidCount(); i++) {
+      double weight = source.getDouble();
+      double mean = source.getDouble();
+      if (weight != 0.0) {
+        filtered.putDouble(weight).putDouble(mean);
+        count++;
+      }
+    }
+    filtered.putInt(28, count);
+    return Arrays.copyOf(filtered.array(), filtered.position());
+  }
+
+  /// Validates serialized lengths and centroid values without allocating 
centroid arrays.
+  public static double validateSerialized(byte[] bytes) {
+    return validateSerialized(ByteBuffer.wrap(bytes));
+  }
+
+  /// Validates one legacy digest without changing `input` and returns its 
total centroid weight.
+  ///
+  /// Trailing bytes remain available to the caller for intermediate values 
containing several objects.
+  public static double validateSerialized(ByteBuffer input) {
+    return validateSerialized(input, true);
+  }
+
+  private static double validateSerialized(ByteBuffer input, boolean 
checkCapacity) {
+    return inspectSerialized(input, checkCapacity).totalWeight();
+  }
+
+  /// Header and numerical metadata for one legacy byte payload. The centroid 
bytes remain owned by the caller.
+  /// Header-only inspection leaves total weight as NaN until centroid 
inspection validates the numerical fields.
+  ///
+  /// Legacy writers can emit poisoned numerical state after overflow or 
broken fractional boundary repair.
+  /// Such state is retained with degraded quantiles, rather than being passed 
to the sorted K1 kernel.
+  public record SerializedTDigestMetadata(int encoding, double min, double 
max, double compression,
+      int centroidCount, int centroidOffset, int centroidSize,
+      int encodedLength, double totalWeight, boolean hasNonFiniteMeans, 
boolean needsLegacyFallback,
+      boolean unorderedMeans, boolean fractionalWeights, boolean 
weightedBoundaries, boolean hasZeroWeightCentroids,
+      double encodedCompression, double recoveredInfinityMean, double 
historicalFractionalMinMean,
+      double historicalFractionalMaxMean) {
+    /// Whether the encoded centroid view can be used unchanged by healthy 
pending-state readers and writers.
+    public boolean isCanonicalPayload() {
+      return !needsLegacyFallback && !weightedBoundaries && !unorderedMeans && 
!hasZeroWeightCentroids
+          && Double.isNaN(recoveredInfinityMean);
+    }
+  }
+
+  /// Invocation-local parser state. Primitive byte-array reads avoid per-row 
buffer and metadata allocations.
+  /// Public metadata and retained pending payloads receive immutable 
snapshots instead of sharing this state.
+  static final class SerializedTDigestState {
+    private static final VarHandle SHORT_VIEW =
+        MethodHandles.byteArrayViewVarHandle(short[].class, 
ByteOrder.BIG_ENDIAN);
+    private static final VarHandle INT_VIEW = 
MethodHandles.byteArrayViewVarHandle(int[].class, ByteOrder.BIG_ENDIAN);
+    private static final VarHandle LONG_VIEW = 
MethodHandles.byteArrayViewVarHandle(long[].class, ByteOrder.BIG_ENDIAN);
+
+    int _encoding;
+    double _min;
+    double _max;
+    double _compression;
+    int _centroidCount;
+    int _centroidOffset;
+    int _centroidSize;
+    int _encodedLength;
+    double _totalWeight;
+    boolean _hasNonFiniteMeans;
+    boolean _needsLegacyFallback;
+    boolean _unorderedMeans;
+    boolean _fractionalWeights;
+    boolean _weightedBoundaries;
+    boolean _hasZeroWeightCentroids;
+    double _encodedCompression;
+    double _recoveredInfinityMean;
+    double _historicalFractionalMinMean;
+    double _historicalFractionalMaxMean;
+    private byte[] _bytes;
+    private ByteBuffer _buffer;
+    private int _position;
+    private int _limit;
+
+    void reset(byte[] bytes) {
+      _bytes = bytes;
+      _buffer = null;
+      _position = 0;
+      _limit = bytes.length;
+    }
+
+    void reset(ByteBuffer input) {
+      _bytes = null;
+      _buffer = input.slice().order(ByteOrder.BIG_ENDIAN);
+      _position = 0;
+      _limit = _buffer.limit();
+    }
+
+    void copyFrom(SerializedTDigestMetadata metadata) {
+      _encoding = metadata.encoding();
+      _min = metadata.min();
+      _max = metadata.max();
+      _compression = metadata.compression();
+      _centroidCount = metadata.centroidCount();
+      _centroidOffset = metadata.centroidOffset();
+      _centroidSize = metadata.centroidSize();
+      _encodedLength = metadata.encodedLength();
+      _totalWeight = metadata.totalWeight();
+      _hasNonFiniteMeans = metadata.hasNonFiniteMeans();
+      _needsLegacyFallback = metadata.needsLegacyFallback();
+      _unorderedMeans = metadata.unorderedMeans();
+      _fractionalWeights = metadata.fractionalWeights();
+      _weightedBoundaries = metadata.weightedBoundaries();
+      _hasZeroWeightCentroids = metadata.hasZeroWeightCentroids();
+      _encodedCompression = metadata.encodedCompression();
+      _recoveredInfinityMean = metadata.recoveredInfinityMean();
+      _historicalFractionalMinMean = metadata.historicalFractionalMinMean();
+      _historicalFractionalMaxMean = metadata.historicalFractionalMaxMean();
+    }
+
+    SerializedTDigestMetadata snapshot() {
+      return new SerializedTDigestMetadata(_encoding, _min, _max, 
_compression, _centroidCount, _centroidOffset,
+          _centroidSize, _encodedLength, _totalWeight, _hasNonFiniteMeans, 
_needsLegacyFallback, _unorderedMeans,
+          _fractionalWeights, _weightedBoundaries, _hasZeroWeightCentroids, 
_encodedCompression, _recoveredInfinityMean,
+          _historicalFractionalMinMean, _historicalFractionalMaxMean);
+    }
+
+    double weight(int index) {
+      _position = _centroidOffset + index * _centroidSize;
+      return _centroidSize == VERBOSE_CENTROID_SIZE ? readDouble() : 
readFloat();
+    }
+
+    double mean(int index) {
+      _position = _centroidOffset + index * _centroidSize + _centroidSize / 2;
+      double mean = _centroidSize == VERBOSE_CENTROID_SIZE ? readDouble() : 
readFloat();
+      return Double.isNaN(mean) ? _recoveredInfinityMean : Math.max(_min, 
Math.min(mean, _max));
+    }
+
+    private int readPosition(int length) {
+      if (length > _limit - _position) {
+        throw new BufferUnderflowException();
+      }
+      int position = _position;
+      _position += length;
+      return position;
+    }
+
+    private int readInt() {
+      int position = readPosition(Integer.BYTES);
+      return _bytes != null ? (int) INT_VIEW.get(_bytes, position) : 
_buffer.getInt(position);
+    }
+
+    private short readShort() {
+      int position = readPosition(Short.BYTES);
+      return _bytes != null ? (short) SHORT_VIEW.get(_bytes, position) : 
_buffer.getShort(position);
+    }
+
+    private double readDouble() {
+      int position = readPosition(Double.BYTES);
+      return _bytes != null
+          ? Double.longBitsToDouble((long) LONG_VIEW.get(_bytes, position))
+          : _buffer.getDouble(position);
+    }
+
+    private float readFloat() {
+      int position = readPosition(Float.BYTES);
+      return _bytes != null ? Float.intBitsToFloat((int) INT_VIEW.get(_bytes, 
position)) : _buffer.getFloat(position);
+    }
+  }
+
+  /// Reads a finalized payload's quantile without cloning bytes or 
constructing a mutable digest.
+  static double quantile(byte[] bytes, double quantile) {
+    if (Double.isNaN(quantile) || quantile < 0.0 || quantile > 1.0) {
+      throw new IllegalArgumentException("q should be in [0,1], got " + 
quantile);
+    }
+    SerializedTDigestState state = new SerializedTDigestState();
+    state.reset(bytes);
+    readSerializedHeader(state, true);
+    if (Double.isNaN(state._totalWeight)) {
+      inspectSerialized(state, null, null);
+    }
+    if (state._needsLegacyFallback || state._totalWeight == 0.0) {
+      return Double.NaN;
+    }
+    if (state._unorderedMeans || state._hasZeroWeightCentroids) {
+      // Rare retained historical payloads need the reader's filtering and 
stable sort, but no recompression.
+      SerializedTDigestInput input = new SerializedTDigestInput();
+      input.reset(bytes, state.snapshot());
+      input.decode();
+      return TDigestAccumulator.quantile(quantile, input._numCentroids, 
state._totalWeight, state._min, state._max,
+          input._means, input._weights, null);
+    }
+    return TDigestAccumulator.quantile(quantile, state._centroidCount, 
state._totalWeight, state._min, state._max,
+        null, null, state);
+  }
+
+  /// Inspects one payload without mutating `input`, scanning the centroid 
values once.
+  public static SerializedTDigestMetadata inspectSerialized(ByteBuffer input) {
+    return inspectSerialized(input, true);
+  }
+
+  /// Inspects a payload, optionally enforcing the legacy decoder's declared 
centroid capacity.
+  public static SerializedTDigestMetadata inspectSerialized(ByteBuffer input, 
boolean checkCapacity) {
+    SerializedTDigestState state = new SerializedTDigestState();
+    state.reset(input);
+    readSerializedHeader(state, checkCapacity);
+    if (Double.isNaN(state._totalWeight)) {
+      inspectSerialized(state, null, null);
+    }
+    return state.snapshot();
+  }
+
+  /// Reads the fixed-size header without allocating centroid arrays; 
oversized historical state is also inspected.
+  public static SerializedTDigestMetadata readSerializedHeader(ByteBuffer 
input) {
+    return readSerializedHeader(input, true);
+  }
+
+  /// Reads a fixed-size header, optionally enforcing the declared centroid 
capacity.
+  ///
+  /// NaN or inverted nonempty extrema mark legacy degraded state. Oversized 
payloads require numerical inspection:
+  /// historical degraded state remains readable even if an old decoder's 
arrays could not hold its centroids.
+  public static SerializedTDigestMetadata readSerializedHeader(ByteBuffer 
input, boolean checkCapacity) {
+    SerializedTDigestState state = new SerializedTDigestState();
+    state.reset(input);
+    readSerializedHeader(state, checkCapacity);
+    return state.snapshot();
+  }
+
+  static void readSerializedHeader(SerializedTDigestState state, boolean 
checkCapacity) {
+    int encoding = state.readInt();
+    if (encoding != VERBOSE_ENCODING && encoding != SMALL_ENCODING) {
+      throw new IllegalStateException("Invalid format for serialized 
histogram");
+    }
+    double min = state.readDouble();
+    double max = state.readDouble();
+    double compression;
+    double encodedCompression;
+    int mainCapacity;
+    int bufferCapacity = 0;
+    int centroidCount;
+    int centroidSize;
+    if (encoding == VERBOSE_ENCODING) {
+      encodedCompression = state.readDouble();
+      compression = normalizeCompression(encodedCompression);
+      mainCapacity = Math.max(getDefaultCentroidCapacity(compression), 
getLegacyDefaultCentroidCapacity(compression));
+      centroidCount = state.readInt();
+      centroidSize = VERBOSE_CENTROID_SIZE;
+    } else {
+      encodedCompression = state.readFloat();
+      compression = normalizeCompression(encodedCompression);
+      mainCapacity = state.readShort();
+      bufferCapacity = state.readShort();
+      checkSmallArrayCapacity(mainCapacity);
+      checkSmallArrayCapacity(bufferCapacity);
+      if (mainCapacity == -1) {
+        mainCapacity = getDefaultCentroidCapacity(compression);
+      }
+      centroidCount = state.readShort();
+      centroidSize = SMALL_CENTROID_SIZE;
+    }
+    if (centroidCount < 0) {
+      throw new IllegalArgumentException("Invalid negative TDigest centroid 
count: " + centroidCount);
+    }
+    if (centroidCount > (state._limit - state._position) / centroidSize) {
+      throw new BufferUnderflowException();
+    }
+    int centroidOffset = state._position;
+    int encodedLength = centroidOffset + centroidCount * centroidSize;
+    state._encoding = encoding;
+    state._min = min;
+    state._max = max;
+    state._compression = compression;
+    state._centroidCount = centroidCount;
+    state._centroidOffset = centroidOffset;
+    state._centroidSize = centroidSize;
+    state._encodedLength = encodedLength;
+    state._totalWeight = Double.NaN;
+    state._hasNonFiniteMeans = false;
+    state._needsLegacyFallback = Double.isNaN(min) || Double.isNaN(max) || 
centroidCount > 0 && min > max;
+    state._unorderedMeans = false;
+    state._fractionalWeights = false;
+    state._weightedBoundaries = false;
+    state._hasZeroWeightCentroids = false;
+    state._encodedCompression = encodedCompression;
+    state._recoveredInfinityMean = Double.NaN;
+    state._historicalFractionalMinMean = Double.NaN;
+    state._historicalFractionalMaxMean = Double.NaN;
+    if (checkCapacity && centroidCount > mainCapacity) {
+      inspectSerialized(state, null, null);
+      if (!state._needsLegacyFallback) {
+        throw new IllegalArgumentException("TDigest centroid count exceeds 
capacity: " + centroidCount);
+      }
+    }
+  }
+
+  static void inspectSerialized(SerializedTDigestState state, double[] means, 
double[] weights) {

Review Comment:
   **[efficiency — hot decode path]** Every serialized-digest row decoded for 
an immediate merge runs this full provenance inspection (~15–20 ops/centroid: 
`Math.rint`, `Double.compare` endpoint tracking, the infinity-tail state 
machine, ULP rounding-tolerance bounds checks, fractional-boundary mean 
tracking), versus the base's lean fill+sum loop (~4 ops/centroid). Most of the 
computed flags are only consumed when a payload is retained pending or 
classified for legacy fallback — not on the merge-now path of a large 
pre-aggregated BYTES scan.
   
   Cheaper: lean decode (fill arrays, sum weight, track ordering/finite-ness) 
for rows merged immediately, running the full provenance scan only on anomaly 
or when retaining a pending payload.



##########
pinot-segment-local/src/test/java/org/apache/pinot/segment/local/customobject/tdigest/TDigestAccumulatorTest.java:
##########
@@ -0,0 +1,1130 @@
+/**
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *   http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing,
+ * software distributed under the License is distributed on an
+ * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.  See the License for the
+ * specific language governing permissions and limitations
+ * under the License.
+ */
+package org.apache.pinot.segment.local.customobject.tdigest;
+
+import java.lang.reflect.Field;
+import java.nio.ByteBuffer;
+import java.util.Arrays;
+import java.util.List;
+import java.util.Random;
+import java.util.SplittableRandom;
+import org.apache.pinot.segment.local.customobject.tdigest.TDigest.Centroid;
+import org.apache.pinot.spi.utils.BytesUtils;
+import org.testng.annotations.Test;
+
+import static org.mockito.Mockito.mock;
+import static org.mockito.Mockito.when;
+import static org.testng.Assert.assertEquals;
+import static org.testng.Assert.assertFalse;
+import static org.testng.Assert.assertTrue;
+import static org.testng.Assert.expectThrows;
+
+/// Regression tests for opaque legacy payloads, fractional statistics, and 
primitive centroid merging.
+public class TDigestAccumulatorTest {
+  @Test
+  public void testHistoricalCorruptionRemainsOpaqueAndRejectsMutation() {
+    for (byte[] poison : new byte[][]{verbose(new double[]{1, 2, 3}, new 
double[]{1, -0.5, 1}),
+        verbose(new double[]{1, 2}, new double[]{1, -200}),
+        verbose(new double[]{Double.NaN}, new double[]{1}),
+        verbose(new double[]{1, 3}, new double[]{3, -3})}) {
+      TDigestAccumulator digest = fromBytes(poison);
+      List<Centroid> original = List.copyOf(digest.centroids());
+      assertFalse(digest.hasValidStatistics());
+      assertFalse(digest.isEmpty(), "Unknown state cannot be discarded as 
empty");
+      assertTrue(Double.isNaN(digest.quantile(0.5)));
+      assertTrue(Double.isNaN(digest.cdf(1.5)));
+      digest.compress();
+      assertEquals(digest.serialize(), poison);
+      assertEquals(digest.centroidCount(), original.size());
+      double originalWeight = digest.getTotalWeight();
+      expectThrows(IllegalArgumentException.class, () -> digest.add(2));
+      expectThrows(IllegalArgumentException.class, () -> digest.add(2, 0.5));
+      expectThrows(IllegalArgumentException.class, () -> digest.add(new 
double[]{2}, 0, 1));
+      expectThrows(IllegalArgumentException.class, () -> 
digest.addSerializedTDigest(poison));
+      assertEquals(digest.getTotalWeight(), originalWeight);
+      assertEquals(List.copyOf(digest.centroids()), original);
+      assertEquals(digest.serialize(), poison);
+
+      TDigestAccumulator copy = TDigestAccumulator.forReduction(100);
+      copy.add(digest);
+      assertEquals(copy.serialize(), poison);
+      TDigestAccumulator healthy = TDigestAccumulator.forReduction(100);
+      healthy.add(10, 100);
+      expectThrows(IllegalArgumentException.class, () -> healthy.add(digest));
+      assertEquals(healthy.getTotalWeight(), 100.0, "Historical negative 
weights must not subtract valid mass");
+      assertEquals(healthy.quantile(0.5), 10.0);
+      expectThrows(IllegalArgumentException.class, () -> digest.add(healthy));
+      assertEquals(digest.serialize(), poison);
+    }
+  }
+
+  @Test
+  public void testSubUnitFractionalQuantileCdfAndHistoricalSerialization() {
+    TDigestAccumulator digest = TDigestAccumulator.forReduction(100);
+    digest.add(1, 0.3);
+    digest.add(2, 0.3);
+    assertEquals(digest.getTotalWeight(), 0.6);
+    assertEquals(digest.quantile(0), 1.0);
+    assertEquals(digest.quantile(0.5), 1.5, Math.ulp(1.5));
+    assertEquals(digest.quantile(0.99), 2.0);
+    assertEquals(digest.quantile(1), 2.0);
+    assertEquals(digest.cdf(1), 0.25);
+    assertEquals(digest.cdf(1.5), 0.5);
+    assertEquals(digest.cdf(2), 0.75);
+    expectThrows(IllegalArgumentException.class, digest::serialize);
+
+    TDigest wideBounds = 
TDigestAccumulator.fromBytes(TDigestCodec.serializeCentroids(100, 0, 3,
+        new double[]{1, 2}, new double[]{0.3, 0.3}, 2));
+    assertEquals(wideBounds.quantile(0.25), 1.0);
+    assertEquals(wideBounds.quantile(0.75), 2.0);
+    assertEquals(wideBounds.cdf(2.0), 0.75);
+
+
+    for (byte[] historical : new byte[][]{verbose(new double[]{1, 2}, new 
double[]{0.3, 0.3}),
+        verbose(new double[]{42}, new double[]{1.5}),
+        TDigestCodec.serializeCentroids(100, 0, 3, new double[]{1, 0, 2, 3}, 
new double[]{1, 0.3, 1, 1}, 4)}) {
+      TDigestAccumulator stored = fromBytes(historical);
+      assertEquals(stored.serialize(), historical);
+      stored.quantile(0.5);
+      stored.centroids();
+      assertEquals(stored.serialize(), historical, "Read-only materialization 
preserves unsupported original bytes");
+      for (double compression : new double[]{stored.compression(), 500}) {
+        TDigestAccumulator copy = TDigestAccumulator.forReduction(compression);
+        copy.add(stored);
+        assertEquals(copy.serialize(), historical, "Copying a queried source 
retains its original encoding");
+        copy.quantile(0.5);
+        copy.compress();
+        assertEquals(copy.serialize(), historical,
+            "Configured compression cannot rewrite an unchanged fractional 
input");
+        TDigestAccumulator adopted = 
TDigestAccumulator.forReduction(compression);
+        adopted.addSerializedTDigest(historical);
+        assertEquals(adopted.serialize(), historical);
+        adopted.quantile(0.5);
+        assertEquals(adopted.serialize(), historical);
+      }
+      expectThrows(IllegalArgumentException.class, () -> 
stored.add(Double.NaN));
+      expectThrows(IllegalArgumentException.class,
+          () -> stored.add(fromBytes(verbose(new double[]{Double.NaN}, new 
double[]{1}))));
+      assertEquals(stored.serialize(), historical, "Failed mutation preserves 
retained original bytes");
+      byte[] isolated = stored.serialize();
+      isolated[0] = 0;
+      assertEquals(stored.serialize(), historical);
+    }
+    TDigestAccumulator singleton = TDigestAccumulator.forReduction(100);
+    singleton.add(42, 1.5);
+    assertEquals(singleton.quantile(1), 42.0);
+    expectThrows(IllegalArgumentException.class, singleton::serialize);
+    singleton = fromBytes(verbose(new double[]{42}, new double[]{1.5}));
+    singleton.add(1);
+    assertFalse(singleton.hasOriginalFractionalPayload());
+    
assertEquals(TDigestAccumulator.fromBytes(singleton.serialize()).getTotalWeight(),
 2.5);
+  }
+
+  @Test
+  public void testQuantileRoundingAtLastCentroidRemainsMonotonic() {
+    byte[] historical = verbose(new double[]{1, 5}, new double[]{0.7, 0.9});
+    ByteBuffer.wrap(historical).putDouble(Integer.BYTES, 
0).putDouble(Integer.BYTES + Double.BYTES, 10);
+    TDigestAccumulator digest = fromBytes(historical);
+    // The loop accumulates the last center as 1.15; totalWeight - lastWeight 
/ 2 is 1.1500000000000001.
+    double quantile = Math.nextDown(0.71875);
+    double below = digest.quantile(Math.nextDown(quantile));
+    double at = digest.quantile(quantile);
+    double above = digest.quantile(Math.nextUp(quantile));
+    assertEquals(at, 5.0, Math.ulp(5.0));
+    assertTrue(below <= at && at <= above);
+    assertEquals(digest.getTotalWeight(), 1.6);
+    assertEquals(digest.quantile(0), 0.0);
+    assertEquals(digest.quantile(1), 10.0);
+    assertEquals(digest.serialize(), historical);
+  }
+
+  @Test
+  public void 
testMixedHistoricalFractionalBoundariesPreserveMassAndFiniteStatistics() {
+    byte[] historical = verbose(new double[]{0, 5, 10}, new double[]{0.5, 4, 
1});
+    for (boolean historyFirst : new boolean[]{false, true}) {
+      for (boolean direct : new boolean[]{false, true}) {
+        TDigestAccumulator digest = TDigestAccumulator.forReduction(200);
+        if (!historyFirst) {
+          digest.add(7);
+        }
+        if (direct) {
+          var input = new SerializedTDigestInput();
+          input.reset(historical);
+          digest.addSerializedTDigestDirect(input);
+        } else {
+          digest.addSerializedTDigest(historical);
+        }
+        if (historyFirst) {
+          digest.add(7);
+        }
+        assertEquals(digest.getTotalWeight(), 6.5);
+        double median = digest.quantile(0.5);
+        assertTrue(Double.isFinite(median));
+        assertTrue(Double.isFinite(digest.cdf(5)));
+        byte[] bytes = digest.serialize();
+        assertEquals(ByteBuffer.wrap(bytes).getInt(0), 
TDigestCodec.VERBOSE_ENCODING);
+        assertEquals(ByteBuffer.wrap(bytes).getDouble(32), 0.5);
+        TDigestAccumulator restored = fromBytes(bytes);
+        assertEquals(restored.getTotalWeight(), 6.5);
+        assertEquals(restored.quantile(0.5), median);
+        assertEquals(restored.getMin(), 0.0);
+        assertEquals(restored.getMax(), 10.0);
+
+        TDigestAccumulator copy = TDigestAccumulator.forReduction(500);
+        copy.add(digest);
+        assertEquals(fromBytes(copy.serialize()).getTotalWeight(), 6.5);
+        // Historical provenance may not authorize a newly added unsupported 
global endpoint.
+        copy.add(-1, 0.1);
+        expectThrows(IllegalArgumentException.class, copy::serialize);
+      }
+    }
+    for (boolean historyFirst : new boolean[]{false, true}) {
+      TDigestAccumulator fractional = TDigestAccumulator.forReduction(100);
+      if (!historyFirst) {
+        fractional.add(10);
+      }
+      fractional.add(fromBytes(verbose(new double[]{0}, new double[]{0.5})));
+      if (historyFirst) {
+        fractional.add(10);
+      }
+      assertEquals(fractional.getTotalWeight(), 1.5);
+      assertTrue(Double.isFinite(fractional.quantile(0.5)));
+      assertEquals(fromBytes(fractional.serialize()).getTotalWeight(), 1.5);
+      for (boolean newExtrema : new boolean[]{false, true}) {
+        TDigestAccumulator representable = fromBytes(historical);
+        representable.add(newExtrema ? -1 : 0);
+        ByteBuffer bytes = ByteBuffer.wrap(representable.serialize());
+        assertEquals(bytes.getDouble(32), 1.0, "Representable historical 
boundaries use the normal unit repair");
+        assertEquals(fromBytes(bytes.array()).getTotalWeight(), 6.5);
+      }
+    }
+    TDigestAccumulator fresh = TDigestAccumulator.forReduction(100);
+    fresh.add(0, 0.5);
+    fresh.add(10);
+    expectThrows(IllegalArgumentException.class, fresh::serialize);
+  }
+
+  @Test
+  public void testQueryCompressionRetainsLegacyClamping() {
+    assertEquals(new TDigestAccumulator(0).compression(), 10.0);
+    assertEquals(new TDigestAccumulator(-5).compression(), 10.0);
+    assertEquals(TDigestAccumulator.forReduction(0).compression(), 10.0);
+    byte[] historical = verbose(new double[]{1}, new double[]{1});
+    ByteBuffer.wrap(historical).putDouble(20, -5);
+    assertEquals(fromBytes(historical).compression(), 10.0);
+  }
+
+  @Test
+  public void testBulkCentroidsSortWithoutChangingCallerArrays() {
+    double[] means = {20, Double.NaN, 10, 30};
+    double[] weights = {2, 0, 1, 1};
+    TDigestAccumulator digest = TDigestAccumulator.forLegacyAggregation(100);
+    digest.addCentroids(means, weights, means.length, 10, 30, true);
+    assertEquals(means, new double[]{20, Double.NaN, 10, 30});
+    assertEquals(weights, new double[]{2, 0, 1, 1});
+    assertEquals(digest.getTotalWeight(), 4.0);
+    assertEquals(digest.quantile(0), 10.0);
+    assertEquals(digest.quantile(1), 30.0);
+    assertEquals(digest.centroids(), fromBytes(verbose(new double[]{10, 20, 
30}, new double[]{1, 2, 1})).centroids());
+    double[] copiedMeans = {-1, -1, -1, -1, -1};
+    double[] copiedWeights = {-1, -1, -1, -1, -1};
+    digest.copyCentroids(copiedMeans, copiedWeights, 1);
+    assertEquals(copiedMeans, new double[]{-1, 10, 20, 30, -1});
+    assertEquals(copiedWeights, new double[]{-1, 1, 2, 1, -1});
+    copiedMeans[2] = -2;
+    assertEquals(digest.quantile(0.5), 20.0);
+    digest.addCentroids(new double[]{5, 25}, new double[]{1, 1}, 2, 5, 25, 
false);
+    assertEquals(digest.getTotalWeight(), 6.0);
+    assertEquals(digest.quantile(0), 5.0);
+    assertEquals(digest.quantile(1), 30.0);
+    TDigestAccumulator pending = TDigestAccumulator.forReduction(100);
+    pending.addSerializedTDigest(TDigestCodec.serializeCentroids(100, 1, 9,
+        new double[]{5, 1, 9}, new double[]{1, 4, 1}, 3));
+    ByteBuffer ordered = ByteBuffer.wrap(pending.serialize());
+    ordered.position(28);
+    int count = ordered.getInt();
+    double previous = Double.NEGATIVE_INFINITY;
+    for (int i = 0; i < count; i++) {
+      double weight = ordered.getDouble();
+      double mean = ordered.getDouble();
+      assertTrue(mean >= previous);
+      if (i == 0 || i == count - 1) {
+        assertEquals(weight, 1.0);
+      }
+      previous = mean;
+    }
+    assertEquals(pending.getTotalWeight(), 6.0);
+    for (double[][] fixture : new double[][][]{
+        {{1, 5, 9}, {3, 1, 3}}, {{1, 5, 9}, {0, 1, 0}}, {{1, 5, 9}, {3, 0, 3}},
+        {{5, 1, 9}, {1, 3, 1}}, {{5, 1, 9, 6}, {1, 3, 3, 1}}
+    }) {
+      byte[] payload = TDigestCodec.serializeCentroids(100, 1, 9, fixture[0], 
fixture[1], fixture[0].length);
+      TDigestAccumulator normalized = fromBytes(payload);
+      int normalizedCount = normalized.centroidCount();
+      double[] normalizedMeans = new double[normalizedCount];
+      double[] normalizedWeights = new double[normalizedCount];
+      normalized.copyCentroids(normalizedMeans, normalizedWeights, 0);
+      assertEquals(normalized.centroids().size(), normalizedCount);
+      double totalWeight = 0.0;
+      for (double weight : normalizedWeights) {
+        assertTrue(weight > 0.0);
+        totalWeight += weight;
+      }
+      assertEquals(totalWeight, normalized.getTotalWeight());
+    }
+  }
+
+  @Test
+  public void testSerializationOwnsBytesAcrossMutationAndHistoricalRetention() 
{
+    TDigestAccumulator digest = TDigestAccumulator.forReduction(100);
+    digest.add(10);
+    byte[] first = digest.serialize();
+    byte[] snapshot = first.clone();
+    digest.add(20);
+    assertEquals(first, snapshot, "Subsequent mutations must not change 
returned bytes");
+    assertEquals(fromBytes(digest.serialize()).getTotalWeight(), 2.0);
+    first[0] = 0;
+    assertEquals(fromBytes(digest.serialize()).getTotalWeight(), 2.0);
+
+    byte[] historical = verbose(new double[]{1, 2}, new double[]{0.5, 1});
+    TDigestAccumulator retained = TDigestAccumulator.fromBytes(historical);
+    byte[] owned = retained.serialize();
+    historical[0] = 0;
+    owned[0] = 0;
+    assertEquals(retained.serialize(), verbose(new double[]{1, 2}, new 
double[]{0.5, 1}));
+    byte[] trailing = ByteBuffer.allocate(snapshot.length + 
Integer.BYTES).put(snapshot).putInt(1234).array();
+    TDigestAccumulator bounded = TDigestAccumulator.fromBytes(trailing);
+    assertEquals(bounded.serialize(), snapshot, "The reading factory retains 
only one complete payload");
+    assertEquals(bounded.maxSerializedByteSize(), snapshot.length);
+  }
+
+  @Test
+  public void testMixedCompressionOversizedSourcesSerializeBeforeAnyQuery() {
+    int count = 5000;
+    double[] means = new double[count];
+    double[] weights = new double[count];
+    for (int i = 0; i < count; i++) {
+      means[i] = i + 1;
+      weights[i] = i == 0 || i == count - 1 ? 1 : 2;
+    }
+    byte[] bytes = TDigestCodec.serializeCentroids(10000, 1, count, means, 
weights, count);
+    for (boolean legacy : new boolean[]{false, true}) {
+      for (boolean existing : new boolean[]{false, true}) {
+        for (int route = 0; route < 5; route++) {
+          TDigestAccumulator source = TDigestAccumulator.fromBytes(bytes);
+          source.add(2500);
+          TDigestAccumulator target = legacy ? 
TDigestAccumulator.forLegacyAggregation(100)
+              : TDigestAccumulator.forReduction(100);
+          if (existing) {
+            target.add(2500);
+          }
+          switch (route) {
+            case 0 -> target.add(source);
+            case 1 -> {
+              source.compress();
+              int sourceCount = source.centroidCount();
+              double[] sourceMeans = new double[sourceCount];
+              double[] sourceWeights = new double[sourceCount];
+              source.copyCentroids(sourceMeans, sourceWeights, 0);
+              double[] originalMeans = sourceMeans.clone();
+              double[] originalWeights = sourceWeights.clone();
+              target.addCentroids(sourceMeans, sourceWeights, sourceCount, 1, 
count, false);
+              assertEquals(sourceMeans, originalMeans);
+              assertEquals(sourceWeights, originalWeights);
+            }
+            case 2 -> {
+              TDigest generic = mock(TDigest.class);
+              when(generic.hasValidStatistics()).thenReturn(true);
+              when(generic.getTotalWeight()).thenReturn(9999.0);
+              when(generic.getMin()).thenReturn(1.0);
+              when(generic.getMax()).thenReturn((double) count);
+              when(generic.centroids()).thenReturn(source.centroids());
+              target.add(generic);
+            }
+            case 3 -> target.addSerializedTDigest(source.serialize());
+            case 4 -> {
+              SerializedTDigestInput input = new SerializedTDigestInput();
+              input.reset(source.serialize());
+              target.addSerializedTDigestDirect(input);
+            }
+            default -> throw new AssertionError();
+          }
+          // No query or centroid read of the target may repair it before the 
actual wire boundary.
+          TDigest restored = TDigestAccumulator.fromBytes(target.serialize());
+          assertTrue(restored.hasValidStatistics(), "route=" + route + ", 
legacy=" + legacy);
+          assertEquals(restored.getTotalWeight(), existing ? 10000.0 : 9999.0);
+          assertEquals(restored.getMin(), 1.0);
+          assertEquals(restored.getMax(), (double) count);
+          assertTrue(Double.isFinite(restored.quantile(0.198)));
+          assertEquals(restored.quantile(0.198), 990.901, 30.0);
+        }
+      }
+    }
+  }
+
+  @Test
+  public void testBufferBoundaryDoesNotSplitAnInteriorCentroidIntoPointMass() {
+    int count = 5 * TDigestCodec.getDefaultCentroidCapacity(100) - 3;
+    double[] values = new double[count];
+    Arrays.fill(values, -100);
+    for (boolean serialized : new boolean[]{false, true}) {
+      TDigestAccumulator digest = TDigestAccumulator.forLegacyAggregation(100);
+      digest.add(values, 0, values.length);
+      byte[] bytes = verbose(new double[]{0, 100, 200}, new double[]{1, 1000, 
1});
+      if (serialized) {
+        digest.addSerializedTDigest(bytes);
+      } else {
+        digest.add(fromBytes(bytes));
+      }
+      // The old chunked path ended its first batch at the weighted interior 
mean, then repaired it into
+      // adjacent (100, 999) and (100, 1) centroids that incorrectly pinned 
this quantile to 100.
+      TDigest restored = fromBytes(digest.serialize());
+      double quantile = restored.quantile(0.75);
+      assertTrue(quantile > 0 && quantile < 100);
+      List<Centroid> centroids = List.copyOf(restored.centroids());
+      assertEquals(centroids.stream().filter(centroid -> centroid.mean() == 
100).count(), 1L);
+      assertEquals(centroids.stream().mapToDouble(Centroid::weight).sum(), 
count + 1002.0);
+      assertEquals(centroids.stream().mapToDouble(centroid -> centroid.mean() 
* centroid.weight()).sum(),
+          -100.0 * count + 100_200.0, 1e-8);
+      assertEquals(restored.getMin(), -100.0);
+      assertEquals(restored.getMax(), 200.0);
+    }
+  }
+
+  @Test
+  public void testOrdinaryMixedCompressionSourcesStraddleOnePendingBatch() {
+    byte[][] inputs = new byte[2][];
+    for (int source = 0; source < inputs.length; source++) {
+      int count = source == 0 ? 600 : 500;
+      int offset = source == 0 ? 0 : 1000;
+      double[] means = new double[count];
+      double[] weights = new double[count];
+      for (int i = 0; i < count; i++) {
+        means[i] = offset + i;
+        weights[i] = i == 0 || i == count - 1 ? 1 : 2;
+      }
+      inputs[source] = TDigestCodec.serializeCentroids(10000, offset, offset + 
count - 1, means, weights, count);
+    }
+    for (boolean reversed : new boolean[]{false, true}) {
+      for (boolean serialized : new boolean[]{false, true}) {
+        TDigestAccumulator target = TDigestAccumulator.forReduction(100);
+        target.add(0.0);
+        for (int i = 0; i < inputs.length; i++) {
+          byte[] input = inputs[reversed ? inputs.length - i - 1 : i];
+          if (serialized) {
+            target.addSerializedTDigest(input);
+          } else {
+            target.add(TDigestAccumulator.fromBytes(input));
+          }
+        }
+        TDigest restored = TDigestAccumulator.fromBytes(target.serialize());
+        assertTrue(restored.hasValidStatistics());
+        assertEquals(restored.getTotalWeight(), 2197.0);
+        assertEquals(restored.getMin(), 0.0);
+        assertEquals(restored.getMax(), 1499.0);
+        double moment = restored.centroids().stream().mapToDouble(c -> 
c.mean() * c.weight()).sum();
+        assertEquals(moment, 1_605_802.0, 1e-8, "reversed=" + reversed + ", 
serialized=" + serialized);
+      }
+    }
+  }
+
+  @Test
+  public void testReadThenAddWeightedExtremaPreservesFirstMoment() {
+    for (double extreme : new double[]{-100, 100}) {
+      for (int read = 0; read < 3; read++) {
+        for (int route = 0; route < 6; route++) {
+          TDigestAccumulator target = TDigestAccumulator.forReduction(100);
+          target.add(10, 2);
+          switch (read) {
+            case 0 -> target.quantile(0.5);
+            case 1 -> target.centroids();
+            case 2 -> target.compress();
+            default -> throw new AssertionError();
+          }
+          TDigestAccumulator source = TDigestAccumulator.forReduction(100);
+          source.add(extreme, 2);
+          switch (route) {
+            case 0 -> target.add(extreme, 2);
+            case 1 -> target.addCentroids(new double[]{extreme}, new 
double[]{2}, 1, extreme, extreme, false);
+            case 2 -> target.add(source);
+            case 3 -> {
+              TDigest generic = mock(TDigest.class);
+              when(generic.hasValidStatistics()).thenReturn(true);
+              when(generic.getTotalWeight()).thenReturn(2.0);
+              when(generic.getMin()).thenReturn(extreme);
+              when(generic.getMax()).thenReturn(extreme);
+              when(generic.centroids()).thenReturn(List.of(new 
Centroid(extreme, 2)));
+              target.add(generic);
+            }
+            case 4 -> target.addSerializedTDigest(source.serialize());
+            case 5 -> {
+              SerializedTDigestInput input = new SerializedTDigestInput();
+              input.reset(source.serialize());
+              target.addSerializedTDigestDirect(input);
+            }
+            default -> throw new AssertionError();
+          }
+          TDigest restored = TDigestAccumulator.fromBytes(target.serialize());
+          assertTrue(restored.hasValidStatistics());
+          assertEquals(restored.getTotalWeight(), 4.0);
+          assertEquals(restored.getMin(), Math.min(10, extreme));
+          assertEquals(restored.getMax(), Math.max(10, extreme));
+          double moment = restored.centroids().stream().mapToDouble(c -> 
c.mean() * c.weight()).sum();
+          assertEquals(moment, 20 + 2 * extreme, "read=" + read + ", route=" + 
route);
+        }
+      }
+    }
+  }
+
+  @Test
+  public void testLegacyBoundaryResidualAllowsLocalRoundoff() {
+    double first = 0x1.117f03c25ccf8p+8;
+    double second = 0x1.174ec5c369cebp+8;
+    double mean = first + (second - first) / 2.0;
+    assertEquals(mean + (mean - first), Math.nextUp(second));
+    for (boolean reflected : new boolean[]{false, true}) {
+      double min = reflected ? -second : first;
+      double max = reflected ? -first : second;
+      double[] means = reflected ? new double[]{-second, -mean} : new 
double[]{mean, second};
+      double[] weights = reflected ? new double[]{1, 2} : new double[]{2, 1};
+      byte[] bytes = TDigestCodec.serializeCentroids(100, min, max, means, 
weights, 2);
+      for (boolean direct : new boolean[]{false, true}) {
+        TDigestAccumulator digest = TDigestAccumulator.forReduction(100);
+        double addedValue = reflected ? -mean : mean;
+        digest.add(addedValue);
+        if (direct) {
+          SerializedTDigestInput input = new SerializedTDigestInput();
+          input.reset(bytes);
+          digest.addSerializedTDigestDirect(input);
+        } else {
+          digest.add(fromBytes(bytes));
+        }
+        TDigest restored = fromBytes(digest.serialize());
+        assertEquals(restored.getTotalWeight(), 4.0);
+        assertEquals(restored.getMin(), min);
+        assertEquals(restored.getMax(), max);
+        double expectedMoment = (reflected ? -1 : 1) * (3 * mean + second);
+        assertEquals(restored.centroids().stream().mapToDouble(c -> c.mean() * 
c.weight()).sum(), expectedMoment,
+            4 * Math.ulp(expectedMoment));
+      }
+      // A materially inconsistent first moment must still reject mutation and 
retain the original payload.
+      means[reflected ? 1 : 0] += (reflected ? -8 : 8) * Math.ulp(mean);
+      byte[] inconsistent = TDigestCodec.serializeCentroids(100, min, max, 
means, weights, 2);
+      TDigestAccumulator rejected = fromBytes(inconsistent);
+      expectThrows(IllegalArgumentException.class, () -> rejected.add(min));
+      assertEquals(rejected.serialize(), inconsistent);
+      assertEquals(rejected.getTotalWeight(), 3.0);
+    }
+    expectThrows(IllegalArgumentException.class,
+        () -> TDigestAccumulator.checkedResidualWeight(0x1.0p54, 1.0));
+  }
+
+  @Test
+  public void testTwoPointBoundaryRepairAllowsLegacyMidpointRoundoff() {
+    double min = -0x1.f1e4d9b005593p+9;
+    double max = 0x1.0647b37be50b4p+9;
+    double mean = min + (max - min) / 2.0;
+    double midpoint = min / 2.0 + max / 2.0;
+    assertEquals(mean - midpoint, 2 * Math.ulp(midpoint));
+    for (double storedMean : new double[]{mean, -mean}) {
+      double lower = storedMean == mean ? min : -max;
+      double upper = storedMean == mean ? max : -min;
+      byte[] bytes = TDigestCodec.serializeCentroids(100, lower, upper, new 
double[]{storedMean}, new double[]{2}, 1);
+      TDigestAccumulator digest = fromBytes(bytes);
+      digest.add(0);
+      TDigest restored = fromBytes(digest.serialize());
+      assertEquals(restored.getTotalWeight(), 3.0);
+      assertEquals(restored.getMin(), lower);
+      assertEquals(restored.getMax(), upper);
+      assertEquals(restored.centroids().stream().mapToDouble(c -> c.mean() * 
c.weight()).sum(), 2 * storedMean,
+          4 * Math.ulp(max));
+      byte[] inconsistent = TDigestCodec.serializeCentroids(100, lower, upper,
+          new double[]{storedMean + 4 * Math.ulp(max)}, new double[]{2}, 1);
+      TDigestAccumulator rejected = fromBytes(inconsistent);
+      expectThrows(IllegalArgumentException.class, () -> rejected.add(0));
+      assertEquals(rejected.serialize(), inconsistent);
+    }
+  }
+
+  @Test
+  public void testObjectMergeIgnoresZeroWeightAndItsUnusedMean() {
+    TDigest source = mock(TDigest.class);
+    when(source.hasValidStatistics()).thenReturn(true);
+    when(source.getTotalWeight()).thenReturn(2.0);
+    when(source.getMin()).thenReturn(10.0);
+    when(source.getMax()).thenReturn(20.0);
+    when(source.centroids()).thenReturn(List.of(new Centroid(Double.NaN, 0), 
new Centroid(-100, 0),
+        new Centroid(10, 1), new Centroid(20, 1)));
+    TDigestAccumulator digest = TDigestAccumulator.forReduction(100);
+    digest.add(source);
+    assertEquals(digest.quantile(0), 10.0);
+    assertEquals(digest.quantile(1), 20.0);
+    assertEquals(digest.getTotalWeight(), 2.0);
+    assertEquals(digest.centroidCount(), 2);
+
+    when(source.getTotalWeight()).thenReturn(0.0);
+    when(source.getMin()).thenReturn(-100.0);
+    when(source.getMax()).thenReturn(100.0);
+    when(source.centroids()).thenReturn(List.of(new Centroid(Double.NaN, 0)));
+    digest.add(source);
+    assertEquals(digest.quantile(0), 10.0);
+    assertEquals(digest.quantile(1), 20.0);
+  }
+
+  @Test
+  public void testZeroMassBytesHaveConsistentEmptyViewsAndDoNotChangeExtrema() 
{
+    byte[] empty = verbose(new double[]{-100, 100}, new double[]{0, 0});
+    TDigestAccumulator pending = fromBytes(empty);
+    for (int phase = 0; phase < 2; phase++) {
+      assertTrue(pending.isEmpty());
+      assertEquals(pending.getMin(), Double.POSITIVE_INFINITY);
+      assertEquals(pending.getMax(), Double.NEGATIVE_INFINITY);
+      assertEquals(pending.centroidCount(), 0);
+      pending.compress();
+    }
+    for (boolean direct : new boolean[]{false, true}) {
+      TDigestAccumulator digest = TDigestAccumulator.forReduction(100);
+      digest.add(10);
+      digest.add(20);
+      if (direct) {
+        SerializedTDigestInput input =
+            new SerializedTDigestInput();
+        input.reset(empty);
+        digest.addSerializedTDigestDirect(input);
+      } else {
+        digest.addSerializedTDigest(empty);
+      }
+      assertEquals(digest.getTotalWeight(), 2.0);
+      assertEquals(digest.quantile(0), 10.0);
+      assertEquals(digest.quantile(1), 20.0);
+    }
+    byte[] poison = verbose(new double[]{Double.NaN}, new double[]{1});
+    TDigest genericEmpty = mock(TDigest.class);
+    when(genericEmpty.hasValidStatistics()).thenReturn(true);
+    when(genericEmpty.getTotalWeight()).thenReturn(0.0);
+    for (TDigest emptyObject : new TDigest[]{fromBytes(empty), genericEmpty}) {
+      for (boolean emptyFirst : new boolean[]{false, true}) {
+        TDigestAccumulator objectMerge = TDigestAccumulator.forReduction(100);
+        for (TDigest input : emptyFirst ? new TDigest[]{emptyObject, 
fromBytes(poison)}
+            : new TDigest[]{fromBytes(poison), emptyObject}) {
+          objectMerge.add(input);
+        }
+        assertFalse(objectMerge.hasValidStatistics());
+        assertEquals(objectMerge.serialize(), poison);
+        TDigest cancelledCorruption = fromBytes(verbose(new double[]{0, 1}, 
new double[]{1, -1}));
+        expectThrows(IllegalArgumentException.class, () -> 
objectMerge.add(cancelledCorruption));
+      }
+    }
+    for (boolean emptyFirst : new boolean[]{false, true}) {
+      for (boolean direct : new boolean[]{false, true}) {
+        TDigestAccumulator digest = TDigestAccumulator.forReduction(100);
+        for (byte[] bytes : emptyFirst ? new byte[][]{empty, poison} : new 
byte[][]{poison, empty}) {
+          if (direct) {
+            SerializedTDigestInput input =
+                new SerializedTDigestInput();
+            input.reset(bytes);
+            digest.addSerializedTDigestDirect(input);
+          } else {
+            digest.addSerializedTDigest(bytes);
+          }
+        }
+        assertFalse(digest.hasValidStatistics());
+        assertTrue(Double.isNaN(digest.quantile(0.5)));
+        assertEquals(digest.serialize(), poison);
+        assertEquals(digest.getTotalWeight(), 1.0);
+        byte[] cancelledCorruption = verbose(new double[]{0, 1}, new 
double[]{1, -1});
+        expectThrows(IllegalArgumentException.class, () -> 
digest.addSerializedTDigest(cancelledCorruption));
+      }
+    }
+  }
+
+  @Test
+  public void testSerializationRetainsFieldsThatOverflowOrUnderflowFloat() {
+    for (double[] centroid : new double[][]{{1e39, 1}, {-1e39, 1}}) {
+      TDigestAccumulator digest = TDigestAccumulator.forReduction(100);
+      digest.add(centroid[0], centroid[1]);
+      ByteBuffer encoded = ByteBuffer.wrap(digest.serialize());
+      assertEquals(encoded.getInt(0), TDigestCodec.VERBOSE_ENCODING);
+      TDigest restored = TDigestAccumulator.fromBytes(encoded.array());
+      assertTrue(restored.hasValidStatistics());
+      assertEquals(restored.getTotalWeight(), centroid[1]);
+      assertEquals(restored.getMin(), centroid[0]);
+      assertEquals(restored.getMax(), centroid[0]);
+    }
+    for (double weight : new double[]{1e-46, 1e39}) {
+      TDigestAccumulator digest = TDigestAccumulator.forReduction(100);
+      digest.add(0);
+      digest.add(1, weight);
+      digest.add(2);
+      ByteBuffer encoded = ByteBuffer.wrap(digest.serialize());
+      assertEquals(encoded.getInt(0), TDigestCodec.VERBOSE_ENCODING);
+      TDigest restored = TDigestAccumulator.fromBytes(encoded.array());
+      assertEquals(List.copyOf(restored.centroids()).get(1).weight(), weight,
+          "An interior mass must not narrow to compact zero or infinity");
+    }
+  }
+
+  @Test
+  public void testHighCompressionRetainsBoundedInputBatches() throws Exception 
{
+    double[] values = new double[100_000];
+    for (int i = 0; i < values.length; i++) {
+      values[i] = i;
+    }
+    for (double compression : new double[]{8_000, 20_000}) {
+      for (boolean weighted : new boolean[]{false, true}) {
+        TDigestAccumulator digest = 
TDigestAccumulator.forReduction(compression);
+        if (weighted) {
+          for (double value : values) {
+            digest.add(value, 0.5);
+          }
+        } else {
+          digest.add(values, 0, values.length);
+        }
+        digest.compress();
+        assertTrue((int) field(digest, "_mergeCount") <= 1_000, "Large 
compression must keep batching inputs");
+        assertEquals(digest.getTotalWeight(), weighted ? values.length / 2.0 : 
values.length);
+        assertEquals(digest.quantile(0), values[0]);
+        assertEquals(digest.quantile(1), values[values.length - 1]);
+      }
+    }
+    for (double compression : new double[]{100, 10_000}) {
+      int capacity = 5 * TDigestCodec.getDefaultCentroidCapacity(compression);
+      TDigestAccumulator legacy = 
TDigestAccumulator.forLegacyAggregation(compression);
+      double[] raw = new double[capacity - 2];
+      for (int i = 0; i < raw.length; i++) {
+        raw[i] = i;
+      }
+      legacy.add(raw, 0, raw.length);
+      assertEquals((int) field(legacy, "_mergeCount"), 0, "Legacy raw batches 
retain the original 5x buffer policy");
+      assertEquals(((double[]) field(legacy, "_rawValues")).length, capacity);
+      legacy.add(raw.length);
+      assertEquals((int) field(legacy, "_mergeCount"), 0);
+      legacy.add(raw.length + 1);
+      assertEquals((int) field(legacy, "_mergeCount"), 1);
+      assertEquals(legacy.getTotalWeight(), (double) capacity);
+    }
+    TDigestAccumulator extreme = 
TDigestAccumulator.forLegacyAggregation(Double.MAX_VALUE);
+    extreme.add(new double[10_001], 0, 10_001);
+    assertEquals((int) field(extreme, "_mergeCount"), 0);
+    assertEquals(((double[]) field(extreme, "_rawValues")).length, 20_000);
+    assertEquals(extreme.getTotalWeight(), 10_001.0);
+  }
+
+  @Test
+  public void testOverflowDuringFlushRetainsIncomingPairs() throws Exception {
+    TDigestAccumulator digest = TDigestAccumulator.forReduction(100);
+    // Unit endpoints keep boundary repair exact; this test targets overflow 
while flushing pending pairs.
+    digest.addSerializedTDigest(verbose(new double[]{0, 10, 40}, new 
double[]{1, Double.MAX_VALUE, 1}));
+    digest.compress();
+    digest.add(30, 5e291);
+    digest.add(20, 5e291);
+    double[] means = ((double[]) field(digest, "_incomingMeans")).clone();
+    double[] weights = ((double[]) field(digest, "_incomingWeights")).clone();
+    expectThrows(IllegalArgumentException.class, digest::compress);
+    assertEquals((int) field(digest, "_numIncomingCentroids"), 2);
+    assertEquals((double) field(digest, "_incomingWeight"), 1e292);
+    assertEquals(((double[]) field(digest, "_incomingMeans"))[0], means[0]);
+    assertEquals(((double[]) field(digest, "_incomingMeans"))[1], means[1]);
+    assertEquals(((double[]) field(digest, "_incomingWeights"))[0], 
weights[0]);
+    assertEquals(((double[]) field(digest, "_incomingWeights"))[1], 
weights[1]);
+    assertEquals((double) field(digest, "_totalWeight"), Double.MAX_VALUE);
+  }
+
+  private static Object field(TDigestAccumulator digest, String name) throws 
Exception {
+    Field field = TDigestAccumulator.class.getDeclaredField(name);
+    field.setAccessible(true);
+    return field.get(digest);
+  }
+
+  @Test
+  public void testCompatibleByteBoundCapsBufferedStateAndRetainsPendingBytes() 
throws Exception {
+    TDigestAccumulator buffered = TDigestAccumulator.forLegacyAggregation(100);
+    for (int i = 0; i < 1000; i++) {
+      buffered.add(i, 1000);
+    }
+    int legacyBound = TDigestCodec.VERBOSE_HEADER_SIZE + 210 * 
TDigestCodec.VERBOSE_CENTROID_SIZE;
+    assertEquals(buffered.maxSerializedByteSize(), legacyBound);
+    assertTrue(buffered.serialize().length <= legacyBound);
+
+    for (double sourceCompression : new double[]{100, 1000}) {
+      double[] means = new double[sourceCompression == 100 ? 100 : 500];
+      double[] weights = new double[means.length];
+      for (int i = 0; i < means.length; i++) {
+        means[i] = i;
+        weights[i] = 1.0;
+      }
+      byte[] verbose = TDigestCodec.serializeCentroids(sourceCompression, 0, 
means.length - 1, means, weights,
+          means.length);
+      TDigestAccumulator smaller = TDigestAccumulator.forLegacyAggregation(10);
+      smaller.addSerializedTDigest(verbose);
+      int bound = smaller.maxSerializedByteSize();
+      assertTrue(bound >= verbose.length, "Retained verbose input can exceed 
configured output capacity");
+      assertEquals((int) field(smaller, "_mergeCount"), 0, "Sizing must not 
compress retained input");
+      assertEquals(smaller.serialize(), verbose);
+      assertTrue(smaller.serialize().length <= bound);
+    }
+
+    int count = 500;
+    ByteBuffer compact = ByteBuffer.allocate(TDigestCodec.SMALL_HEADER_SIZE + 
count * TDigestCodec.SMALL_CENTROID_SIZE);
+    compact.putInt(TDigestCodec.SMALL_ENCODING).putDouble(0).putDouble(count - 
1).putFloat(100);
+    compact.putShort((short) count).putShort((short) (5 * 
count)).putShort((short) count);
+    for (int i = 0; i < count; i++) {
+      compact.putFloat(1).putFloat(i);
+    }
+    TDigestAccumulator pending = fromBytes(compact.array());
+    assertEquals(pending.maxSerializedByteSize(), compact.capacity());
+    byte[] retained = pending.serialize();
+    assertEquals(retained, compact.array());
+    retained[0] = 0;
+    assertEquals(pending.serialize(), compact.array());
+    pending.quantile(0.5);
+    assertEquals(pending.maxSerializedByteSize(), legacyBound);
+    byte[] rewritten = pending.serialize();
+    assertTrue(rewritten.length <= legacyBound);
+    assertEquals(ByteBuffer.wrap(rewritten).getInt(), 
TDigestCodec.VERBOSE_ENCODING);
+    assertEquals(fromBytes(rewritten).getTotalWeight(), (double) count);
+    assertEquals(pending.getMin(), 0.0);
+    assertEquals(pending.getMax(), count - 1.0);
+    TDigestAccumulator copy = TDigestAccumulator.forReduction(100);
+    copy.add(pending);
+    assertEquals(copy.getTotalWeight(), (double) count);
+    assertTrue(Double.isFinite(copy.quantile(0.5)));
+    assertTrue(copy.serialize().length <= copy.maxSerializedByteSize());
+  }
+
+  @Test
+  public void testSerializedResultComparisonMatchesRenderedDigest() {
+    TDigestAccumulator digest = TDigestAccumulator.forReduction(10);
+    TDigestAccumulator control = TDigestAccumulator.forReduction(10);
+    SplittableRandom random = new SplittableRandom(0);
+    for (int i = 0; i < 10000; i++) {
+      double value = random.nextDouble();
+      digest.add(value);
+      control.add(value);
+    }
+    double workingMedian = digest.quantile(0.5);
+    control.quantile(0.5);
+    control.compress();
+    double publicMedian = control.quantile(0.5);
+    assertTrue(workingMedian != publicMedian, "Exercise a reducer changed by 
public compression");
+    TDigestAccumulator nearby = new TDigestAccumulator(10);
+    nearby.add((workingMedian + publicMedian) / 2.0);
+    SerializedTDigest result = new SerializedTDigest(digest, 50);
+    SerializedTDigest other = new SerializedTDigest(nearby, 50);
+    int comparison = result.compareTo(other);
+    String rendered = result.toString();
+    TDigest decoded = fromBytes(BytesUtils.toBytes(rendered));
+    assertEquals(comparison, Double.compare(decoded.quantile(0.5), 
nearby.quantile(0.5)));
+    assertEquals(result.compareTo(other), comparison);
+    assertEquals(result.toString(), rendered);
+    assertEquals(digest.quantile(0.5), workingMedian, "Extracting a trim key 
must not compress the survivor");
+    digest.add(2);
+    assertEquals(result.compareTo(other), comparison);
+    assertEquals(result.toString(), rendered);
+  }
+
+  @Test
+  public void 
testRepeatedRawResultExtractionDoesNotChangeContinuingAggregation() {
+    for (boolean wrapped : new boolean[]{false, true}) {
+      TDigest control = wrapped
+          ? NonFiniteAwareTDigest.forLegacyAggregation(100) : 
TDigestAccumulator.forReduction(100);
+      TDigest trimmed = wrapped
+          ? NonFiniteAwareTDigest.forLegacyAggregation(100) : 
TDigestAccumulator.forReduction(100);
+      if (wrapped) {
+        control.add(Double.NEGATIVE_INFINITY);
+        control.add(Double.POSITIVE_INFINITY);
+        trimmed.add(Double.NEGATIVE_INFINITY);
+        trimmed.add(Double.POSITIVE_INFINITY);
+      }
+      Random random = new Random(7);
+      for (int shard = 0; shard < 32; shard++) {
+        TDigestAccumulator partial = TDigestAccumulator.forReduction(100);
+        for (int i = 0; i < 2_000; i++) {
+          partial.add(StrictMath.pow(random.nextDouble(), 8));
+        }
+        byte[] bytes = partial.serialize();
+        control.add(fromBytes(bytes));
+        trimmed.add(fromBytes(bytes));
+        if (shard % 4 == 3 && shard < 31) {
+          SerializedTDigest result = new SerializedTDigest(trimmed, 75);
+          String rendered = result.toString();
+          TDigestAccumulator reference = TDigestAccumulator.forReduction(100);
+          
reference.add(fromBytes(BytesUtils.toBytes(rendered)).quantile(0.75));
+          assertEquals(result.compareTo(new SerializedTDigest(reference, 75)), 
0);
+          assertEquals(new SerializedTDigest(trimmed, 75).toString(), 
rendered);
+        }
+      }
+      assertEquals(trimmed.serialize(), control.serialize(), "Trimming must 
preserve the continuing merge trajectory");
+    }
+  }
+
+  @Test
+  public void testSerializedResultComparisonUsesLegacyCapacityRewrite() {
+    double[] means = new double[51];
+    double[] weights = new double[51];
+    SplittableRandom random = new SplittableRandom(0);
+    for (int i = 0; i < means.length; i++) {
+      means[i] = random.nextDouble();
+      weights[i] = 1;
+    }
+    Arrays.sort(means);
+    TDigest digest = TDigestAccumulator.fromBytes(
+        TDigestCodec.serializeCentroids(20, means[0], means[50], means, 
weights, means.length));
+    double originalQuantile = digest.quantile(0.53);
+    SerializedTDigest result = new SerializedTDigest(digest, 53);
+    TDigest rendered = fromBytes(BytesUtils.toBytes(result.toString()));
+    double emittedQuantile = rendered.quantile(0.53);
+    assertTrue(originalQuantile != emittedQuantile, "Exercise the legacy 
writer's centroid-capacity reduction");
+    TDigestAccumulator nearby = new TDigestAccumulator(20);
+    nearby.add((originalQuantile + emittedQuantile) / 2.0);
+    assertEquals(result.compareTo(new SerializedTDigest(nearby, 53)),
+        Double.compare(emittedQuantile, nearby.quantile(0.53)));
+  }
+
+  @Test
+  public void 
testSerializedResultRetainsHistoricalStatisticsAcrossCompressionSettings() {
+    byte[] boundary = verbose(new double[]{1, 5}, new double[]{2, 2});
+    ByteBuffer.wrap(boundary).putDouble(Integer.BYTES, 
0).putDouble(Integer.BYTES + Double.BYTES, 10);
+    double[] means = new double[100];
+    double[] weights = new double[100];
+    SplittableRandom random = new SplittableRandom(63);
+    for (int i = 0; i < means.length; i++) {
+      means[i] = random.nextDouble();
+      weights[i] = 1.0;
+    }
+    Arrays.sort(means);
+    weights[0] = 0.5;
+    for (byte[] bytes : new byte[][]{boundary, verbose(means, weights)}) {
+      double expected = fromBytes(bytes).quantile(0.5);
+      for (boolean wrapped : new boolean[]{false, true}) {
+        TDigestAccumulator nativeDigest = TDigestAccumulator.forReduction(10);
+        nativeDigest.addSerializedTDigest(bytes);
+        TDigest digest = nativeDigest;
+        if (wrapped) {
+          digest = NonFiniteAwareTDigest.forLegacyAggregation(10);
+          digest.add(nativeDigest);
+        }
+        SerializedTDigest result = new SerializedTDigest(digest, 50);
+        assertEquals(digest.quantile(0.5), expected);
+        assertEquals(BytesUtils.toBytes(result.toString()), bytes);
+        assertEquals(digest.quantile(0.5), expected);
+      }
+    }
+  }
+
+  @Test
+  public void testStoredCentroidSortPreservesPairsAndTotalOrdering() {
+    double[] means = {Double.NaN, 1, 0.0, -0.0, 1, Double.NEGATIVE_INFINITY, 
Double.NaN, 99};
+    double[] weights = {1, 2, 3, 4, 5, 6, 7, 8};
+    TDigestAccumulator.sortCentroids(means, weights, 7);
+    assertEquals(means, new double[]{Double.NEGATIVE_INFINITY, -0.0, 0.0, 1, 
1, Double.NaN, Double.NaN, 99});
+    assertEquals(weights, new double[]{6, 4, 3, 2, 5, 1, 7, 8});
+  }
+
+  @Test
+  public void 
testPublicCompressionAndSerializationUseTheSameRawCompressionPolicy() {
+    for (boolean legacyAggregation : new boolean[]{false, true}) {
+      for (int count : new int[]{500, 2000}) {
+        TDigestAccumulator direct = legacyAggregation
+            ? TDigestAccumulator.forLegacyAggregation(100) : 
TDigestAccumulator.forReduction(100);
+        TDigestAccumulator compressed = legacyAggregation
+            ? TDigestAccumulator.forLegacyAggregation(100) : 
TDigestAccumulator.forReduction(100);
+        SplittableRandom random = new SplittableRandom(42);
+        for (int i = 0; i < count; i++) {
+          double value = random.nextDouble(1000);
+          direct.add(value);
+          compressed.add(value);
+        }
+        compressed.compress();
+        assertEquals(compressed.serialize(), direct.serialize());
+        assertEquals(compressed.quantile(0.86), direct.quantile(0.86));
+        assertEquals(compressed.quantile(0.95), direct.quantile(0.95));
+      }
+    }
+  }
+
+  @Test
+  public void 
testSnapshotKeepsBufferedSourceUnchangedAndOwnsItsMutableArrays() throws 
Exception {
+    for (boolean legacyAggregation : new boolean[]{false, true}) {
+      TDigestAccumulator source = legacyAggregation
+          ? TDigestAccumulator.forLegacyAggregation(100) : 
TDigestAccumulator.forReduction(100);
+      TDigestAccumulator control = legacyAggregation
+          ? TDigestAccumulator.forLegacyAggregation(100) : 
TDigestAccumulator.forReduction(100);
+      TDigestAccumulator continuingCopy = null;
+      SplittableRandom random = new SplittableRandom(7);
+      for (int i = 0; i < 2000; i++) {
+        double value = random.nextDouble(1000);
+        source.add(value);
+        control.add(value);
+        if (continuingCopy != null) {
+          continuingCopy.add(value);
+        }
+        if (i == 999) {
+          source.add(10, 3.5);
+          control.add(10, 3.5);
+          int mergeCount = (int) field(source, "_mergeCount");
+          int rawCount = (int) field(source, "_numRawValues");
+          TDigestAccumulator copy = source.copy();
+          assertEquals((int) field(source, "_mergeCount"), mergeCount);
+          assertEquals((int) field(source, "_numRawValues"), rawCount);
+          assertEquals(copy.getTotalWeight(), source.getTotalWeight());
+          copy.add(-100, 10);
+          copy.serialize();
+          assertEquals(source.getTotalWeight(), control.getTotalWeight());
+          continuingCopy = source.copy();
+        }
+      }
+      assertEquals(source.serialize(), control.serialize());
+      assertEquals(continuingCopy.serialize(), control.serialize(), "Copies 
must preserve future flush timing");
+      assertEquals(source.quantile(0.86), control.quantile(0.86));
+    }
+  }
+
+  @Test
+  public void testPendingMergesReuseReaderWithoutReplacingTheIncomingInput() {
+    TDigestAccumulator digest = TDigestAccumulator.forReduction(100);
+    for (double value : new double[]{1, 5, 9}) {
+      digest.add(fromBytes(verbose(new double[]{value}, new double[]{1})));
+    }
+    assertEquals(digest.getTotalWeight(), 3.0);
+    assertEquals(digest.getMin(), 1.0);
+    assertEquals(digest.getMax(), 9.0);
+    assertEquals(digest.quantile(0.5), 5.0);
+  }
+
+  @Test
+  public void testNativeMergeConsumesItsSourceAtPublicCompression() {
+    TDigestAccumulator empty = TDigestAccumulator.forReduction(100);
+    empty.add(empty);
+    assertTrue(empty.isEmpty());
+    TDigestAccumulator fractional = TDigestAccumulator.forReduction(100);
+    fractional.add(42.0, 1.5);
+    fractional.add(fractional);
+    assertEquals(fractional.getTotalWeight(), 3.0);
+    assertEquals(fractional.quantile(0.5), 42.0);
+    
assertEquals(TDigestAccumulator.fromBytes(fractional.serialize()).getTotalWeight(),
 3.0);
+
+    TDigestAccumulator source = TDigestAccumulator.forLegacyAggregation(100);
+    TDigestAccumulator expected = TDigestAccumulator.forLegacyAggregation(100);
+    SplittableRandom random = new SplittableRandom(10);
+    for (int i = 0; i < 94; i++) {
+      double value = random.nextDouble() * 10_000;
+      source.add(value);
+      expected.add(value);
+    }
+    expected.compress();
+    TDigestAccumulator parent = TDigestAccumulator.forLegacyAggregation(100);
+    parent.add(source);
+    assertEquals(source.centroids(), expected.centroids());
+    assertEquals(source.quantile(0.86), expected.quantile(0.86));
+    assertEquals(parent.getTotalWeight(), source.getTotalWeight());
+  }
+
+  @Test
+  public void testDuplicatePlateauKeepsItsFullMassAndCdfAgreesAtItsEdges() {
+    TDigestAccumulator digest = fromBytes(verbose(new double[]{0, 10, 10, 20, 
30},
+        new double[]{1, 2, 6, 2, 1}));
+    for (double index : new double[]{1.25, 4, 8.75}) {
+      assertEquals(digest.quantile(index / 12.0), 10.0);
+    }
+    assertEquals(digest.cdf(10), 5.0 / 12.0);
+    assertEquals(digest.cdf(5), 1.0 / 12.0);
+    assertEquals(digest.cdf(15), 9.5 / 12.0);
+    assertEquals(digest.quantile(digest.cdf(15)), 15.0);
+
+    TDigestAccumulator continuous = fromBytes(verbose(new double[]{0, 10, 20, 
30},
+        new double[]{1, 8, 2, 1}));
+    assertTrue(continuous.quantile(4.0 / 12.0) < 10.0);
+    assertTrue(continuous.quantile(8.75 / 12.0) > 10.0);
+    assertEquals(continuous.quantile(continuous.cdf(15)), 15.0);
+
+    TDigestAccumulator fractional = fromBytes(verbose(new double[]{0, 10, 10, 
20},
+        new double[]{1, 0.25, 0.25, 1}));
+    assertEquals(fractional.quantile(1.1 / 2.5), 10.0);
+    assertEquals(fractional.quantile(1.4 / 2.5), 10.0);
+
+    TDigestAccumulator first = fromBytes(verbose(new double[]{0, 0, 10, 20},
+        new double[]{1, 2, 3, 1}));
+    assertEquals(first.quantile(2.75 / 7.0), 0.0);
+    assertEquals(first.quantile(first.cdf(0)), 0.0);
+    TDigestAccumulator last = fromBytes(verbose(new double[]{0, 10, 20, 20},
+        new double[]{1, 3, 2, 1}));
+    assertEquals(last.quantile(4.25 / 7.0), 20.0);
+    assertEquals(last.quantile(last.cdf(20)), 20.0);
+
+    TDigestAccumulator huge = fromBytes(verbose(new double[]{0, 10, 10, 20, 
30},
+        new double[]{1, 1e300, 1e300, 1e300, 1}));
+    assertEquals(huge.quantile(0.6), 10.0);
+    assertEquals(huge.quantile(0), 0.0);
+    assertEquals(huge.quantile(1), 30.0);
+  }
+
+  @Test
+  public void testDuplicateHeavyRawValuesPreservePlateauRanks() {
+    TDigestAccumulator digest = TDigestAccumulator.forReduction(100);
+    for (int i = 0; i < 10_000; i++) {
+      digest.add(i < 7000 ? 0.1 : i < 9000 ? 0.5 : 0.9);
+    }
+    digest.serialize();
+    assertEquals(digest.quantile(0.69), 0.1);
+    assertEquals(digest.quantile(0.89), 0.5);
+    assertEquals(digest.quantile(0.99), 0.9);
+    assertTrue(digest.quantile(0.70) < 0.25, "Plateau mass must not leak into 
interpolation across the gap");
+    assertTrue(digest.quantile(0.90) < 0.6, "The upper plateau's edge stays 
close to its repeated value");
+    assertEquals(digest.getTotalWeight(), 10_000.0);
+  }
+
+  @Test
+  public void testWeightedSortKeepsPairsAndEqualMeanOrderAcrossFlushes() {
+    TDigestAccumulator digest = TDigestAccumulator.forReduction(1_000_000);
+    for (int iteration = 0; iteration < 2; iteration++) {
+      double offset = 10 * iteration;
+      digest.add(offset + 3, 0.25);
+      digest.add(offset + 1, 0.5);
+      digest.add(offset + 3, 0.75);
+      digest.add(offset + 2, 0.125);
+      List<Centroid> centroids = List.copyOf(digest.centroids());
+      int start = 4 * iteration;
+      assertEquals(centroids.subList(start, start + 4), List.of(new 
Centroid(offset + 1, 0.5),
+          new Centroid(offset + 2, 0.125), new Centroid(offset + 3, 0.25), new 
Centroid(offset + 3, 0.75)));
+      assertEquals(centroids.stream().mapToDouble(Centroid::weight).sum(), 
digest.getTotalWeight());
+    }
+  }
+
+  private static TDigestAccumulator fromBytes(byte[] bytes) {
+    TDigestAccumulator digest =
+        TDigestAccumulator.forReduction(TDigestCodec.readCompression(bytes));
+    digest.addSerializedTDigest(bytes);
+    return digest;
+  }
+
+  private static byte[] verbose(double[] means, double[] weights) {

Review Comment:
   **[test reuse]** This is one of 5+ hand-rolled copies of the legacy 
wire-format builders across test files 
(`TDigestCodecTest.verboseBytes`/`legacyBytes`, 
`PercentileTDigestValueAggregatorTest.createVerboseEncoding`/`createSmallEncoding`
 with the 210/1050 capacity pair copied verbatim, 
`PercentileRawTDigestAggregationFunctionTest.createVerbose/SmallUnitCentroidDigest`,
 inline buffers in `PercentileTDigestAggregationFunctionTest`). pinot-core 
tests already consume `TDigestTestUtils` via the segment-local test-jar, so one 
shared builder there (keeping only `TDigestCodecTest.legacyBytes` independent, 
since it tests the codec itself) would serve all of them; today a header-layout 
change must be tracked by hand in each copy.



##########
pinot-segment-local/src/main/java/org/apache/pinot/segment/local/utils/CustomSerDeUtils.java:
##########
@@ -215,17 +216,17 @@ public HyperLogLogPlus deserialize(ByteBuffer byteBuffer) 
{
 
     @Override

Review Comment:
   **[dead + divergent policy]** `CustomSerDeUtils.TDIGEST_SER_DE` has no 
production callers anymore (`SerializedTDigest` now uses 
`TDigestCodec.quantile` directly), and its deserialize policy (`fromBytes` → 
legacy-aggregation two-level compression) diverges from 
`ObjectSerDeUtils.TDIGEST_SER_DE` (`forReduction`). A future caller picking 
this serde for query intermediates would get different compression/merge 
accuracy than the type-10 path with no signal. Suggest removing it, or 
documenting which path owns which policy.



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