Below can be found at least 12 viable and distinct hypotheses for LENR gain.
Given that some of the listings represent slight variations or enabler
mechanisms there are more than a dozen entries (16). All are related in some
way to hydrogen which is constrained in a lattice, and many require QM
tunneling.

The range of these, and the generally strong evidence for each are almost
conclusive evidence for me that LENR cannot be reduced to a "single"
reaction, nor even two - one for deuterium and one for protium. QM tunneling
is complex.

But the most controversial suggestion of all is that none of these are
mutually exclusive, and several, or even most of them, could be at work
simultaneously in any given experiment, if that reactor has all the
necessary components. 

There is not even a good candidate for "most likely" unless the reaction
involves only a limited range of options, such as palladium and deuterium
which only produces helium-4 as ash.

I am now dropping the attribution - since earlier there were numerous
overlooked contributors, like Mitchell Swartz who were not credited but who
are still fighting the USPTO for basic priority.

1)      The original theory of P&F applicable to palladium and deuterium,
involving gammaless fusion to helium caused by coherent electron effects
(screening)

2)      Coulomb mediated reactions in general, including the deflation
fusion model. When any one channel is highly favored, such as tritium or
He-3, then there will be another separate distinguishable reaction at play,
and it often involves an alloy or dopant to the lattice or to an
electrolyte. Thus it is distinctly unique, and not a channel reaction.
                
3)      The "hydrino" (or fractional hydrogen) mechanism. Several variations
now exist. The species may be a predecessor step for LENR and may actually
provide no excess heat unless it does proceed to a nuclear reaction.
                
4)      The dense hydrogen cluster or dense deuterium model, differentiated
as inverted Rydberg hydrogen or a DDL (deep Dirac layer). The DDL can be
applicable to deuterium and it can result in something completely different
from 1 and 2, such as heat only with no ash.
                
5)      The P-e-P mechanism for Ni-H, which envisions protons fusing to
deuterium via screening at much higher probability than in the solar model

6)      The NASA filing (US 20110255645) suggests an alternative method for
producing "heavy electrons" as a fusion catalyst in what looks like a beta
decay mechanism. This is similar to 2, 5 and 8 
                
7)      The proposal of a high temperature BEC - Bose Einstein Condensate
and/or the tetrahedral TSC model which is similar.
                
8)      The beta decay/ ultracold neutron mechanism popularized by
Widom-Larsen which is similar to a Brillouin/ NASA explanation.
                
9)      Proton addition - to the metal lattice atoms, which was the original
Focardi/Rossi conception. Rossi later refined this to emphasize only the
heavier nickel isotopes, especially Ni-62 but gammaless. 
                
10)     Piantelli has a version of Ni-H with gammas and transmutation.
                
11)     SPP or surface plasmon polariton catalysis in general - which is a
theory involving plasmons, phonons and photons. This is more of an "enabler"
pathway for several types of reactions.
                
12)     Casimir dynamics, in general, including a dynamical effect, called
DCE. This is an "enabler" pathway, as are other geometry constraints. 
                
13)     Accelerated nuclear decay. Some experiments benefit from unstable
isotopes like potassium-40 which can undergo accelerated decay rates,
                
14)     RPF or reversible proton fusion, which is based on the strong force,
QCD and a transient state called the diproton, deriving energy from excess
proton mass with no gammas.
                
15)     The "nanomagnetism" formative theory involving magnons and cyclical
phase change around the Curie point of Ni. This may be nonnuclear (ZPE
related).
                
16)     Any combination or permutation of the above - since none of them is
mutually exclusive, and most actual experiments cannot be defined by a
single hypothesis, adding to the confusion.

There are more, especially variations and refinements. Pardon me if I have
overlooked your favorite, but this is a running effort and your favorite may
appear on the next list.


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