Please allow me to try this one more time since I think I see why it did not make it into the posted archive and I have a change to my additional comment.
In #10 I discuss the length of the descriptive string. A better way to state what is said there may be to indicate that I am only interested in the structure of the finite prefix of what might be an infinite string. The infinite tail if there is one is "invaded" for lack of a better term as the length of the prefix increases until the prefix is itself infinite. This is an improved presentation of my current TOE model. Its a bit more than one page. I believe I see some shadow of both Juergen's approach and Bruno's approach in it. The intermediate step has unfinished business and the lowest level is a bit like a duplicator, transporter. 1) The single postulate is "The total system contains no information." 2) Two distinct expressions of "no information" are recognized by the model: a) The "Nothing" which is devoid of any information whatsoever. b) The "Everything" which contains all information. These are not identical. Rather they are antipodal in that neither can contain the other because of a stability issue. 3) The stability issue is the unavoidable emergence of a question of the stability of the manifestation of either of these expressions of "no information" should either actually become manifest. This manifestation must either be stable or not with respect to the alternate expressions of "no information". Thus the alternate expression must be separately available for manifestation and the stability question must have a resolution. 4) If either expression of "No information" becomes manifest then the resolution of the stability question represents information and violates the postulate. 5) A way to make the total system comply with the postulate: a) Both the "Nothing" and the "Everything" are in a simultaneous partial manifestation. b) To avoid any information including any permanent selection in this system and thus comply with the postulate the partial manifestation of the "Everything" is realized by the actual but temporary manifestation of randomly selected pieces of the "Everything" herein called patterns each of which has a manifestation of random duration. 6) Evolving universes are successive isomorphisms to some portion of those patterns with overlapping manifestations. 7) Enduring evolving universes with fully deterministic rules of isomorphism succession find no home in this model because they would find no sustainable state to state trajectory within the random nature of the partial manifestation of the "Everything". The rules of an enduring universe must be partly true noise. 8) The cascade representation for state Sj(i + 1) of universe j while in state Sj(i) is: (1) P'j(i + 1) = {R'j(i)[Pj(i)]} determines the group of pairs: {R'jk(i + 1),Sjk(i + 1)}; k = 1 to sj(i). Where: Pj(i) is the shortest self delimiting program that computes Sj(i). R'j(i) is the current full set of rules that act on the current state [represented in its compressed condition]. sj(i) is the number of acceptable successor {rule set, state} pairs to Sj(i) due to the true noise content of R'j(i). Pj(i) contains Rj(i) which is a deterministic derivative of R'j(i - 1) used only to allow the compression of the data in Sj(i) and a self delimiter DeL(i). R'j(i) is the full and partially non deterministic true noise containing successor to R'j(i - 1). 9) The first of the {R'jk(i + 1), Sjk(i + 1)} pairs to be represented in a sub section of one of the manifest patterns becomes the next state and its rules [isomorphic link] of universe j as the pattern supporting the current link loses its own manifestation. Once this happens the precursor program P'(i + 1) is replaced with Pj(i + 1) and the applicable Sjk(i + 1) becomes Sj(i + 1). So we get: (2) Pj(i + 1) = {Rj(i + 1)[P(i)] + DeL(i + 1)} computes Sj(i + 1). So operating on this with R'j(i + 1) in a manner similar to (1) gives the next iteration to the cascade: (3) P'j(i + 2) = {R'j(i + 1)[Pj(i + 1)} determines the group of pairs {R'jk(i + 2),Sjk(i + 2)}; k = 1 to sj(i + 1). and so on. 10) The model's focus on the use of a discrete point space for a universe is due to: a) Notice that each successive Pj() is longer than its predecessor if Rj() does not decrease in length and ultimately any such shortening of Rj() will be swamped out. Over the long haul then Pj() increases in length. b) As the length of Pj() increases the length of the string it computes and which represents Sj() must increase in length [perhaps not always synchronized with length changes in Pj()] if it is to maintain a degree of internal correlation - an aspect which is considered necessary to support SAS - but nevertheless contain more complexity. c) Finite strings can easily increase in length by adding short strings. Thus the string is considered finite and must describe the location of points within any space on a grid with finite pitch. The possibility of infinitely long highly correlated tails on the strings that are skipped by the rules of succession is considered an unnecessary entity. 11) Exploring the dynamics of (1), (2), and (3) is most interesting and will be covered in later posts. 12) The most interesting space so far explored is face centered cubic. Hal