e4cb242619
New folder: docs/living/ — for goals that change daily, not stable findings (those stay in docs/research/). Documents: - README.md: rules for living docs (overwrite freely, one sentence per target, link to findings, honesty tag) - TARGETS.md: 5 active targets (invariant geometry, reaction primes, merged O(1), formal cleanup, encoder fidelity) + 3 dead + 3 candidate - PROJECT_MAP.md: what SilverSight IS right now (not what it was) - MILESTONES.md: 5 near-term milestones with success criteria (3-SAT spectral test, cmix SVD, SLOS eigenvalue products, CRT hachimoji pairing, reaction prime proof) - OPEN_QUESTIONS.md: 8 unanswered questions - DIRECTION_LOG.md: 5 direction changes from this session, with the reason for each Living docs rules: - No measurement required (goals, not findings) - Overwrite freely (git history preserves old versions) - One sentence per target - Link to docs/research/ for backing evidence - Honesty tag: MEASURED / OPEN / SPECULATIVE
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Milestones — Near-Term with Success Criteria
Last updated: 2026-07-03
M1: 3-SAT Spectral Test [NEXT]
Goal: Build clause-incidence matrix for a small 3-SAT instance, compute eigenvalue spectrum, check if satisfiability is spectrally distinguishable.
Success criteria:
- Build matrix for ≥3 different 3-SAT instances (satisfiable + unsatisfiable)
- Compute eigenvalue spectra
- Report: can the spectra distinguish SAT from UNSAT?
If YES: First NP-complete data point for the octagon. P=NP route strengthened. Write up as measurement.
If NO: Natural P≠NP witness on the canonical NP-complete problem. The octagon has a limit. Write up as measurement.
Estimated effort: 2-4 hours (Python script, small instances)
M2: cmix Weight Matrix SVD [NEXT]
Goal: Extract cmix's 23×461 layer-0 weight matrix, compute SVD, check if top-5 singular values capture 95% of compression quality.
Success criteria:
- Modify cmix to dump weight matrix after training on enwik8
- Compute SVD (23 singular values)
- Rank-k approximation: does k=5 preserve ≥95% of compression ratio?
If YES: Search space reduces from 23×461 to 5D. The octagon works for cmix (linear system, rich invariants).
If NO: cmix's weight structure is genuinely full-rank. No spectral shortcut for context mixing.
Estimated effort: 4-8 hours (C++ modification + SVD computation)
M3: Quandela SLOS Eigenvalue Product Verification [NEXT]
Goal: Verify that eigenvalue products of the Sidon crossing matrix match the full SLOS output distribution.
Success criteria:
- Compute eigenvalue products for the 4-block Sidon matrix
- Compare against SLOS K=2 output
- Report: do they match?
If YES: SLOS shortcut confirmed for linear optical. Replace SLOS with eigenvalue products (400x speedup on block-diagonal circuits).
If NO: The K=1 spectrum doesn't determine K=2 output (despite linearity). Need to find what's missing.
Estimated effort: 2-4 hours (Python + Perceval)
M4: CRT-Coprime Hachimoji Pairing Rules [FUTURE]
Goal: Design 8 hachimoji bases with 4 coprime pairing rules. Verify CRT reconstruction works.
Success criteria:
- 4 pairing rules with gcd(L_i, L_j) = 1 for all i≠j
- Each base has a unique partner under each rule
- CRT lift reconstructs the base index from 4 residues
If YES: The DNA-CRT bridge is designed. Next: simulate hybridization energy landscape.
Estimated effort: 4-8 hours (design + verification)
M5: Reaction Prime Existence Proof [FUTURE]
Goal: Prove (or disprove) that every DNA computation factors into reaction-primes.
Success criteria:
- Define the reaction algebra formally (generators, relations)
- Prove existence of factorization (or find a counterexample)
- If existence: prove uniqueness (or find non-unique factorization)
If EXISTS + UNIQUE: Reaction-prime framework is sound. The conservation law = FTA for computation.
If NON-EXISTENT or NON-UNIQUE: The framework needs refinement. The prime decomposition isn't universal.
Estimated effort: 8-16 hours (Lean formalization)