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Unifying framework that connects ALL session findings under one algebraic roof: Number theory: prime → irreducible reaction → eigenvalue Composite → composed reaction network → full matrix Factorization → decomposition into primitives → eigendecomposition Unique factorization → canonical decomposition → spectral theorem p-adic valuation → reaction-prime exponent → eigenvalue multiplicity Three formulations: 1. Reaction algebra (generators of free monoid, hachimoji bases) 2. Information primes (minimal representatives of equivalence classes) 3. Category theory (indecomposable morphisms) Conservation law = information-theoretic FTA: Σ prime_i × exponent_i ≥ K(data) The SAME law, whether stated as compression, number theory, Lagrangian, or measurement. Prime factorization is the universal algebraic structure. Pipeline = prime factorization engine: - Encoder = word in prime algebra - QR/O-AMMR = spectral prime decomposition - GCCL = canonical form verification - CRT = coprime prime reconstruction - Char-poly = prime spectrum receipt Well-posed questions: 1. Does every DNA computation factor into reaction-primes? 2. Is the factorization unique? 3. What is the prime spectrum of a DNA program? 4. Can programs be distinguished by prime spectra? 5. Minimum primes for NP properties? 6. Super-polynomial prime decompositions → P ≠ NP? Avoids linguistic semantic primes controversy. Grounded in algebra, information, and category theory. Connects to everything. |
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| .. | ||
| braid_group_action.md | ||
| CAPABILITY_GRID_MAPPING.md | ||
| COLLECTIVE_INTELLIGENCE_OPTIMIZATION.md | ||
| COMPRESSION_HONEST_FINDINGS.md | ||
| FIXEDPOINT_BRIDGE_DESIGN.md | ||
| iteration_dag.md | ||
| iteration_regime.md | ||
| MERGED_O1_TRANSFORM.md | ||
| O1_TRANSFORMS.md | ||
| OCTAGON_PRINCIPLE.md | ||
| REACTION_PRIMES.md | ||
| sidon_preservation_creation.md | ||
| unified_crt_torus_dag.md | ||