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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?
106 lines
4.2 KiB
Markdown
106 lines
4.2 KiB
Markdown
# Current Research Targets
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**Last updated:** 2026-07-03
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**Changes daily.** Old versions in git history.
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## Active Targets
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### 1. Invariant Computation Geometry [OPEN]
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**Goal:** Determine which NP properties have polynomial-size spectral
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invariant embeddings (the octagon question at O(n) dimension).
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**Status:** One measured success (Sidon 4/4), one known failure
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(cospectral graphs on Hamiltonicity), one proven existence at O(n²)
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(Etesami-Haemers 2019). The O(n) question is open.
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**Links:**
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- [Octagon Principle](../research/OCTAGON_PRINCIPLE.md)
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- [Invariant Computation Geometry](../research/INVARIANT_COMPUTATION_GEOMETRY.md)
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### 2. Reaction Prime Decomposition [SPECULATIVE]
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**Goal:** Define irreducible DNA computational operations (reaction
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primes) and determine if every computation factors uniquely.
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**Status:** Framework proposed (reaction algebra, information primes,
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category theory). No measurements yet. Connects to the conservation
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law (prime total ≥ K(data)) and the pipeline (each stage = one
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prime decomposition step).
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**Links:**
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- [Reaction Primes](../research/REACTION_PRIMES.md)
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- [O(1) Transforms](../research/O1_TRANSFORMS.md)
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### 3. Merged O(1) Transform [SPECULATIVE]
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**Goal:** Determine if DNA hybridization can simultaneously search,
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reconstruct (CRT), and verify (energy) in one physical step.
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**Status:** Framework documented. The wall is O(n) readout (conservation
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law). The decision-problem shortcut (1-bit answer = O(1) readout) is
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the most promising path. Needs: design CRT-coprime hachimoji pairing
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rules, simulate energy landscape, measure gap vs n.
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**Links:**
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- [Merged O(1) Transform](../research/MERGED_O1_TRANSFORM.md)
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- [Conservation Law](../weird_machine_conservation_law.md)
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### 4. Formal Verification Cleanup [MEASURED]
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**Goal:** Close all remaining sorries and remove all native_decide
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from the active build.
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**Status:** 10 active sorries (all tagged CITED/CONJECTURE, all
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genuinely blocked on Mathlib API). 21 axioms (all justified).
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Anti-smuggle scanner passes. 84 modules registered in lakefile.
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**Links:**
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- [AGENTS.md](../../AGENTS.md) — current status table
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### 5. Encoder Fidelity [MEASURED]
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**Goal:** Maintain 20/20 injective DNA encoding with exact arithmetic
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(no floats) across all input types.
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**Status:** 20/20 injective (p-adic + neg-pi). BioSight embed.py
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updated to v3 (exact arithmetic). Universal pipeline 14/14 PASS.
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Round-trip lossless on all text types including LaTeX/CJK/emoji.
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**Links:**
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- [Compression Findings](../research/COMPRESSION_HONEST_FINDINGS.md)
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## Dead Targets (measured, not pursuing)
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### ~~Compression via spectral methods~~ [DEAD]
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**Result:** Conservation law forbids it. 8 branches measured, all
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fail. Polynomial = receipt, not compressor. xz beats everything.
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### ~~16D braid / golden spiral GW compression~~ [DEAD]
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**Result:** 583x was zero-noise artifact. 1.5x at 30dB (ties LPC).
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16D adds nothing over 50-year-old LPC.
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### ~~Braille/T9 text compression~~ [DEAD]
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**Result:** 4.167 b/B, worse than order-2 PPM (3.088), far behind
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xz (1.989). 64-cell alphabet too small for 256 bytes.
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## Candidate Targets (not yet committed)
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### 6. cmix Weight Matrix SVD [OPEN]
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**Goal:** Extract the 23×461 weight matrix from cmix, compute SVD,
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determine if the top-k singular values capture most compression
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quality. If yes, search the low-rank subspace for better configs.
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### 7. 3-SAT Spectral Embedding [OPEN]
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**Goal:** Build a clause-incidence matrix for 3-SAT, compute its
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spectrum, check if satisfiability is spectrally detectable. This
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is the P vs NP experimental program's first NP-complete test case.
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### 8. Quandela SLOS Shortcut [OPEN]
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**Goal:** For linear optical circuits, replace full SLOS (O(n × M_n))
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with eigenvalue product computation (O(n^m)). Only works for linear
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systems. Needs: verify eigenvalue products match SLOS output on
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the Sidon crossing matrix.
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## ~~Prime-Sidon spectral detection~~ [DEAD — 2026-07-03]
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**Result:** Honest negative. 35 test cases, 0/35 significant after
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Bonferroni. The prime distribution does NOT have a Sidon-detectable
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spectral signature through SLOS. Adversarial review caught a tautology
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in the original methodology, null was properly added, negative is
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bounded. ENE session: prime-sidon-negative-001 (promoted).
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