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.
