Legacy Genetic Sequence Analysis

What the BigCalc2 “gene” machinery was trying to do: treat constants as circular tapes, ask whether one tape can spell another with very simple bit transforms, then ask whether the XOR-running Z0 tape emits useful words from the larger constants catalog.

Core Interpretation

The old code was not merely searching for cute substrings. It was building a compression grammar over binary constants. Each published constant becomes a circular bit tape. Other constants become named tokens. The decomposer asks: how many literal bits remain if this source tape is spelled with known tokens under only simple transforms?

constant bits -> circular tape
catalog constants -> token words
allowed transforms -> forward, reverse, inverse, inverse-reverse, rotation
score -> literal bits left + token penalty

In this language, “genetic sequence” means a recipe for expressing one constant as a small sequence of named bit-words from other constants.

Algorithm Layers

Direct Tape Compression

The first mode asks whether one constant can be expressed by other constant tokens on a circular tape. The output field GeneString is the proposed recipe.

Source: characteristic impedance of vacuum
BitsLen: 39
BestOrientation: Reverse
LiteralsCost_Bits: 0
TokensUsed: 4
GeneString:
  {Q_DOWN|F|rot=0}
  {AME20 35Mg(p,n)35Al Q_cKeV|R|rot=3}
  {Q_DOWN|F|rot=0}
  {Q_38MeV|R|rot=4}

This says Z0 itself was found as a zero-literal recipe in named words under simple transforms. That is interesting, but by itself it is not the strongest evidence because a rich catalog can overfit.

Z0 As Substrate

The Z0-facet mode is more radical. It lets raw contiguous substrings of the Z0 ring become available as tokens. Then it asks whether other constants can be spelled from pieces of Z0.

Example from the legacy output:

weak mixing angle -> {Characteristic impedance of vacuum|F|rot=25}
                     {Characteristic impedance of vacuum|F|rot=1}

Q_UP              -> {Characteristic impedance of vacuum|F|rot=7}
Q_DOWN            -> {Characteristic impedance of vacuum|F|rot=2}
Q_STRANGE         -> {Characteristic impedance of vacuum|F|rot=16}
Q_CHARM           -> {Characteristic impedance of vacuum|I|rot=19}

Ablation Result

The ablation output is the most honest legacy warning. For the AME proton-neutron threshold cohort:

Z0 As Running Program

The run-tape mode is closest to the “simplest possible Turing tape” idea. Start with the Z0 seed. Each step replaces the state with its XOR against a one-bit rotation. Tap one emitted bit per step. The result is a generated tape.

S_next = S XOR RotL1(S)
emit   = S_next[0]

This is a very small machine: one state string, one rotation, one XOR, one tap. The research question becomes:

Does this running Z0 tape emit substrings that reconstruct other physical constants better than chance?

In the filtered legacy run output (min token length > 20):

This is the cleaner direction: not merely “Z0 contains substrings,” but “Z0, when run as a minimal machine, emits tape fragments that anchor other constants.”

What Should Be Ported First

Porting Discipline

The old C# was an exploratory bench. The Python version should separate four questions that were blurred together: