Beaucephas

Pseudovolumes: Projection-Invariant Rational Scalars, A₅ Symmetry, and the Standard Genetic Code R Quincy Robinson — Preprint: https://doi.org/10.5281/zenodo.20468890

Pseudovolumes II: Exact Arithmetic Tensor Networks, Fibonacci Topological Phase, and Structural Validation Across Five Domains R Quincy Robinson — Preprint: https://doi.org/10.5281/zenodo.20469791

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This repository implements the pseudovolume — a rigid, 2,880-value tensor associated to each positive rational scalar, indexed by the sixty-four hexagrams of the Yijing. The construction recovers the nine-node He Tu / Luo Shu arrangement and identifies the five Wuxing phases with the vertices of a regular 4-simplex in four-dimensional space.

Key results:

• Projection invariance: all 2,880 values are constant across 32 projection planes corresponding to the rotation axes of a dodecahedron
• Transformation group G = ℝ × A₅, acting via an explicit PSL(2,5) Möbius construction on the hexagram bit-positions
• Self-inverse measurement: all instrument parameters (basis, node stack, plane) are exactly recoverable from the model's own outputs
• Genetic code: the dodecahedral axis structure induces a natural assignment of the twenty standard amino acids to the twenty vertices of a dodecahedron

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Architecture

Module	Role
gua.py	Hexagram encoding and combinatorial operations
hypercube.py	9-node pseudovolume structure
node.py	Per-node cardinal body computation
console.py	Field, cross, and macrostate computation
constants.py	Lookup tables: planes, axis map, codon map
api.py	Model API and schema implementations
server.py	FastAPI HTTP endpoints
tiling.py, mera.py, peps.py	Phase 6–10 tensor network extensions
qphi.py	Exact arithmetic over ℚ(φ)
digests/scripts/	Verification and parameter-space analysis scripts
digests/paper/	Preprint source files

License

Code released under the PolyForm Noncommercial License 1.0.0. Non-commercial use permitted. Commercial use requires a separate written agreement with the author.