From a239fb42b422d87b18dfb4478fa74c410775990f Mon Sep 17 00:00:00 2001 From: allaun Date: Sat, 4 Jul 2026 02:40:10 -0500 Subject: [PATCH] docs: add comprehensive next steps plan - Verification summary of all previous session work - Prioritized action items (immediate, short-term, medium-term, long-term) - Dependencies and success criteria - Starting with immediate items: SLOS disclaimer, review count clarification, container status --- docs/research/NEXT_STEPS_PLAN.md | 176 +++++++++++++++++++++++++++++++ 1 file changed, 176 insertions(+) create mode 100644 docs/research/NEXT_STEPS_PLAN.md diff --git a/docs/research/NEXT_STEPS_PLAN.md b/docs/research/NEXT_STEPS_PLAN.md new file mode 100644 index 00000000..8350334b --- /dev/null +++ b/docs/research/NEXT_STEPS_PLAN.md @@ -0,0 +1,176 @@ +# Next Steps Plan + +**Date:** 2026-07-04 +**Status:** VERIFICATION COMPLETE — Planning next phase + +--- + +## Verification Summary + +### ✅ Confirmed from Previous Session + +1. **CRTSidon.lean** — 0 sorries, both theorems proven + - `sidon_preserved`: Componentwise CRT Sidon preservation + - `sidon_preserved_mod`: Modular CRT Sidon preservation + - Supporting lemmas: `mod_eq_dvd`, `dvd_mod_eq`, `mod_eq_of_coprime` + +2. **de Grey Graph** — 1581-vertex construction verified + - `hn_hoffman_bound.py`: Computes χ ≥ 3 via spectral method + - Eigenvalue computation confirmed + +3. **Sidon-Sofa Coloring** — v2 and v3 scripts present + - v2: Coarse q-sweep (5 values), n ∈ {8, 13, 21} + - v3: Fine q-sweep (100 values), n ∈ {8, 13, 21, 34} + +4. **StrandCapacityBound Triviality** — Flagged in AGENTS.md + - Known limitation documented + +5. **CITATION.cff** — Prior art references added + - Elsasser (1946) toroidal/poloidal decomposition + - Wikipedia toroidal/poloidal coordinates + +6. **Quandela API Key** — Encrypted and stored + - `secrets/quandela_api_key.enc.yaml` (sops/age encrypted) + - `.sops.yaml` configuration present + +7. **Golden Centering Constant** — Fixed to 40504 + - `formal/SilverSight/GoldenSpiral.lean`: phiInvQ16 = 40504 + - `formal/CoreFormalism/BraidEigensolid.lean`: Consistent value + +8. **Adversarial Review** — 18 findings documented + - 4 Critical, 5 High, 6 Medium, 3 Low + - Commit `54fd2283`: Repaired sofa coloring scripts + Hoffman bound + - `SIDON_SOFA_COLORING_REVIEW.md`: Full review receipt + +9. **Photonic Sidon Search** — All 18 tests passing + - `photonic_sidon_search.py`: Exact integer verification + - Encoders imported: `encoder_q16.py`, `padic_encoder.py` + - Test evidence: `.openresearch/artifacts/photonic_sidon_evidence.jsonl` + +### ⚠️ Uncertain / Not Found + +1. **SLOS Classical-Sim Disclaimer** — Not explicitly found + - File header mentions "exact integer verification" + - No explicit disclaimer about classical simulation limitations + - **Action needed:** Add disclaimer to script header + +2. **Container (silver-autoproof:latest)** — Not found in this branch + - No Dockerfile or docker-compose for silver-autoproof + - Only package Dockerfiles in `.lake/packages/` + - **Action needed:** Document status or create container + +3. **Adversarial Review Count Discrepancy** + - Session summary mentions "14 issues" + - Review document shows 18 findings (4+5+6+3) + - **Action needed:** Clarify count (may be different categorization) + +4. **TOROIDAL_POLOIDAL_REFINEMENT.md** — Planning document only + - 6 refinement actions (R1-R6) all marked TODO or BLOCKED + - No implementation yet + - **Action needed:** Prioritize and implement + +--- + +## Next Steps (Prioritized) + +### Immediate (Low Effort, High Impact) + +1. **Add SLOS Disclaimer** (15 min) + - Add to `photonic_sidon_search.py` header + - Clarify classical vs quantum simulation + - Document empirical nature of Omega-Sidon correlation + +2. **Clarify Adversarial Review Count** (10 min) + - Check if "14 issues" refers to unique issues vs total findings + - Update session summary or review document for consistency + +3. **Document Container Status** (20 min) + - If silver-autoproof exists in another branch/repo, document location + - If not, create Dockerfile based on current autoproof infrastructure + - Update README with container usage instructions + +### Short-term (Medium Effort, Research Value) + +4. **Run Sidon-Sofa Coloring v3** (2-4 hours) + - Generate artifacts for fine q-sweep + n=34 + - Analyze q=1 phase boundary behavior + - Compare with v2 results + +5. **Verify Photonic Search Reproducibility** (30 min) + - Confirm all 18 tests still pass + - Check test evidence matches committed version + +6. **Address TOROIDAL_POLOIDAL_REFINEMENT.md TODOs** (4-8 hours) + - **R1 (High):** Redefine modulus selection as q-profile design + - **R2 (High):** Add cross-pair q-ratio coprimality check + - **R4 (Medium):** Document 1.9× optimum as A2 sweet spot + - **R5 (High):** Formalize discrete Elsasser decomposition + +### Medium-term (High Effort, Strategic Value) + +7. **Formalize Discrete Elsasser Decomposition** (1-2 days) + - Extend CRTSidon.lean with toroidal/poloidal coordinate system + - Prove equivalence between CRT embedding and Elsasser decomposition + - Connect to plasma physics literature (Elsasser 1946) + +8. **Implement q-Profile Design** (2-3 days) + - Refactor modulus selection to use q-profile (q = L₂/L₁) + - Systematic sweep: q ∈ {0.5, 0.75, 1.0, 1.33, 2.0} + - Analyze Sidon preservation as function of q + - Identify optimal q-regime (conjectured: q < 1, poloidal-dominated) + +9. **Create silver-autoproof Container** (1 day) + - Dockerfile based on `scripts/mcp_autoproof.py` + - Include Lean 4 toolchain + Mathlib + - Expose MCP server endpoint for remote proof filling + - Update CI/CD to use container for automated proof checking + +### Long-term (Research Directions) + +10. **Extend to Larger Sidon Sets** (ongoing) + - Current: n ≤ 34 (v3 script) + - Target: n = 50, 100, 200 + - Requires GPU acceleration or distributed computation + +11. **Quantum Photonic Simulation** (exploratory) + - Replace classical SLOS with quantum circuit simulation + - Test if quantum Omega shows stronger Sidon correlation + - Requires Quandela API access (key already encrypted) + +12. **Connect to Hadwiger-Nelson Problem** (theoretical) + - Use Sidon-Sofa coloring results to bound χ(ℝ²) + - Current lower bound: χ ≥ 5 (de Grey 2018) + - Can Sidon structure improve this? + +--- + +## Immediate Action Items + +- [ ] Add SLOS disclaimer to `photonic_sidon_search.py` +- [ ] Clarify adversarial review count (14 vs 18) +- [ ] Document silver-autoproof container status +- [ ] Run `sidon_sofa_coloring_v3.py` and analyze results +- [ ] Verify `photonic_sidon_search.py` reproducibility +- [ ] Prioritize TOROIDAL_POLOIDAL_REFINEMENT.md TODOs + +--- + +## Dependencies + +- **Perceval tokens:** Required for R3 (SLOS K=4, K=5 tests) +- **GPU access:** Required for large-scale Sidon-Sofa coloring (n > 34) +- **Quandela API:** Required for quantum photonic simulation (optional) + +--- + +## Success Criteria + +- All immediate action items completed +- Sidon-Sofa Coloring v3 artifacts generated and analyzed +- Photonic Sidon Search reproducibility confirmed +- At least 2 refinement TODOs implemented (R1, R2, or R5) +- Container status documented or container created + +--- + +**Next Session Start:** Begin with immediate action items, then proceed to short-term tasks based on results.