5c5c6f94b6
Claude Code completed the prime-Sidon spectral detection test:
- 35 test cases
- 0/35 significant after Bonferroni correction
- Adversarial review caught a tautology in original methodology
- Null hypothesis properly added
- Negative finding is properly bounded
ENE database: session prime-sidon-negative-001 (promoted)
GitHub: commit a0d95049
This is a third measured data point for the octagon:
- Sidon sets: YES (4/4)
- Graph coloring: YES (Hoffman)
- Prime distribution: NO (0/35) ← NEW
- Graph isomorphism: NO (cospectral)
- Text: NO (3.088 b/B)
The octagon is NOT universal. It works for some problems and
fails for others. The research question: what determines which
problems have spectral signatures?
4.2 KiB
Current Research Targets
Last updated: 2026-07-03 Changes daily. Old versions in git history.
Active Targets
1. Invariant Computation Geometry [OPEN]
Goal: Determine which NP properties have polynomial-size spectral invariant embeddings (the octagon question at O(n) dimension).
Status: One measured success (Sidon 4/4), one known failure (cospectral graphs on Hamiltonicity), one proven existence at O(n²) (Etesami-Haemers 2019). The O(n) question is open.
Links:
2. Reaction Prime Decomposition [SPECULATIVE]
Goal: Define irreducible DNA computational operations (reaction primes) and determine if every computation factors uniquely.
Status: Framework proposed (reaction algebra, information primes, category theory). No measurements yet. Connects to the conservation law (prime total ≥ K(data)) and the pipeline (each stage = one prime decomposition step).
Links:
3. Merged O(1) Transform [SPECULATIVE]
Goal: Determine if DNA hybridization can simultaneously search, reconstruct (CRT), and verify (energy) in one physical step.
Status: Framework documented. The wall is O(n) readout (conservation law). The decision-problem shortcut (1-bit answer = O(1) readout) is the most promising path. Needs: design CRT-coprime hachimoji pairing rules, simulate energy landscape, measure gap vs n.
Links:
4. Formal Verification Cleanup [MEASURED]
Goal: Close all remaining sorries and remove all native_decide from the active build.
Status: 10 active sorries (all tagged CITED/CONJECTURE, all genuinely blocked on Mathlib API). 21 axioms (all justified). Anti-smuggle scanner passes. 84 modules registered in lakefile.
Links:
- AGENTS.md — current status table
5. Encoder Fidelity [MEASURED]
Goal: Maintain 20/20 injective DNA encoding with exact arithmetic (no floats) across all input types.
Status: 20/20 injective (p-adic + neg-pi). BioSight embed.py updated to v3 (exact arithmetic). Universal pipeline 14/14 PASS. Round-trip lossless on all text types including LaTeX/CJK/emoji.
Links:
Dead Targets (measured, not pursuing)
Compression via spectral methods [DEAD]
Result: Conservation law forbids it. 8 branches measured, all fail. Polynomial = receipt, not compressor. xz beats everything.
16D braid / golden spiral GW compression [DEAD]
Result: 583x was zero-noise artifact. 1.5x at 30dB (ties LPC). 16D adds nothing over 50-year-old LPC.
Braille/T9 text compression [DEAD]
Result: 4.167 b/B, worse than order-2 PPM (3.088), far behind xz (1.989). 64-cell alphabet too small for 256 bytes.
Candidate Targets (not yet committed)
6. cmix Weight Matrix SVD [OPEN]
Goal: Extract the 23×461 weight matrix from cmix, compute SVD, determine if the top-k singular values capture most compression quality. If yes, search the low-rank subspace for better configs.
7. 3-SAT Spectral Embedding [OPEN]
Goal: Build a clause-incidence matrix for 3-SAT, compute its spectrum, check if satisfiability is spectrally detectable. This is the P vs NP experimental program's first NP-complete test case.
8. Quandela SLOS Shortcut [OPEN]
Goal: For linear optical circuits, replace full SLOS (O(n × M_n)) with eigenvalue product computation (O(n^m)). Only works for linear systems. Needs: verify eigenvalue products match SLOS output on the Sidon crossing matrix.
Prime-Sidon spectral detection [DEAD — 2026-07-03]
Result: Honest negative. 35 test cases, 0/35 significant after Bonferroni. The prime distribution does NOT have a Sidon-detectable spectral signature through SLOS. Adversarial review caught a tautology in the original methodology, null was properly added, negative is bounded. ENE session: prime-sidon-negative-001 (promoted).