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docs(sorry-protocol): add 3-agent verification rule + first verified formula d_F=0.440258
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@ -8,6 +8,11 @@ author rather than verify the arithmetic.
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**The rule:** Encounter a sorry → STOP → Assess → Decide → Only then proceed.
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**The 3-agent rule:** Every formula must be verified by 3 independent agents.
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All 3 must agree on every intermediate term and the final result to 6 decimal
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places. If any agent disagrees, the formula is a SORRY. STOP. Investigate. All
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3 must agree before the formula is accepted.
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---
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## THE STOP PROTOCOL
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@ -262,6 +267,66 @@ The wall:
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---
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## THE 3-AGENT VERIFICATION PROCESS
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```
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FORMULA CLAIMED
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│
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▼
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┌─────────────────────┐
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│ Agent Alpha computes │ Independent. Shows all steps.
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│ from scratch │ Reports to 6 decimal places.
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└──────────┬──────────┘
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│
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┌────┴────┐
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▼ ▼
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┌─────────┐ ┌─────────┐
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│ Agent │ │ Agent │ Independent. No sharing.
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│ Beta │ │ Gamma │ Same formula, same inputs.
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│ computes│ │ computes│ All steps shown.
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│ scratch │ │ scratch │
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└────┬────┘ └────┬────┘
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│ │
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└─────┬──────┘
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▼
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┌─────────────────────┐
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│ Orchestrator compares│
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│ all 3 results │
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└──────────┬──────────┘
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│
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┌─────┴─────┐
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▼ ▼
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┌─────────┐ ┌─────────┐
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│ ALL 3 │ │ ANY 2 │
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│ AGREE │ │ DISAGREE│
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│ │ │ │
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│ ✓ Log │ │ ✗ STOP │
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│ ✓ Accept│ │ ✗ Find │
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│ ✓ Proceed│ │ error │
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│ │ │ ✗ Recomp│
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└─────────┘ └─────────┘
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```
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**Agreement means:** Every intermediate term matches to 6 decimal places.
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The final result matches to 6 decimal places. No rounding differences. No
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off-by-one in indices. Exact match.
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**Disagreement means:** Any intermediate term or final result differs by
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more than 10^{-6}. STOP. All 3 agents recompute. If disagreement persists,
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the formula is a SORRY. Apply the STOP protocol.
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---
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## VERIFICATION LOG (formulas verified)
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| # | Formula | Inputs | Consensus Value | Date | Status |
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|---|---------|--------|-----------------|------|--------|
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| 001 | d_F(p,q) = 2·arccos(Σ√(pᵢqᵢ)) | p=(0.3,0.1,0.15,0.05,0.2,0.08,0.07,0.05), q=(0.2,0.2,0.1,0.1,0.15,0.1,0.1,0.05) | 0.440258 | 2026-06-23 | ✅ VERIFIED |
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See `VERIFICATION_LOG.md` for full details.
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---
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## NEXT ACTIONS
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1. **Resolve S1-S3 (Chentsov):** WEAKEN theorem to invariance only. Write the
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