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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
54 lines
2.4 KiB
Markdown
54 lines
2.4 KiB
Markdown
# Open Questions
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**Last updated:** 2026-07-03
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## Q1: Does 3-SAT have a spectral signature?
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The first NP-complete test case for the octagon. If YES → P=NP route
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via spectral methods. If NO → natural P≠NP witness.
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[Link: OCTAGON_PRINCIPLE.md §P vs NP]
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## Q2: Can eigenvalue products replace SLOS for linear optical circuits?
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SLOS is linear → U^(⊗m) determined by U's spectrum → eigenvalue products
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should determine the output. Measured K=1 failed, but FULL spectrum
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(all products) is untested.
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[Link: MERGED_O1_TRANSFORM.md §SLOS linearity]
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## Q3: Is the cmix weight matrix low-rank?
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If the 23 singular values are dominated by top-5, the compression
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shape lives in 5D. The search for better compressors becomes 5D,
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not 23×461.
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[Link: cmix_epigenetic_analysis.md]
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## Q4: Does every DNA computation factor into reaction-primes?
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The algebraic version of "is there a fundamental theorem of
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arithmetic for computation?" If yes → conservation law = FTA.
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If no → the framework needs a different algebraic structure.
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[Link: REACTION_PRIMES.md]
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## Q5: Can the three O(1) transforms merge into one physical step?
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Adleman (search) + CRT lift (reconstruct) + CRT gradient (verify)
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as one DNA hybridization. The wall is O(n) readout. The decision-problem
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shortcut (1-bit answer) is the most promising escape.
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[Link: MERGED_O1_TRANSFORM.md]
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## Q6: What is the Φ-metric?
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The "geometry of observability" — what defines what counts as "same
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object" before physics processes it. Is it a kernel? A distance?
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An operator-valued metric? This is the formalization gap between the
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vision and a computable system.
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[Link: INVARIANT_COMPUTATION_GEOMETRY.md]
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## Q7: At what n does the DNA hybridization energy gap fail?
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The SNR cliff question. For the merged O(1) transform: the energy
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gap between correct and near-correct hybridization is constant
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(~1 mismatch), but the number of near-correct candidates grows with n.
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When does the gap become too small for thermodynamic selection?
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Same cliff as superposition (k=16: lossless, k=48: lost).
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[Link: MERGED_O1_TRANSFORM.md §The Energy Gap Problem]
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## Q8: Does the Sidon spectral signature generalize to other NP properties?
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Sidon = pairwise-sum matrix → eigenvalue degeneracy. Does the
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unit-distance property have a spectral signature in the distance
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matrix? Does graph coloring (beyond Hoffman bound)? Does clique
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number (beyond Lovász theta)?
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[Link: OCTAGON_PRINCIPLE.md §Fast-Forward]
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