mirror of
https://github.com/allaunthefox/SilverSight.git
synced 2026-07-31 01:25:21 +00:00
docs(verification): P1-P4 verified by 3 agents — all consensus values logged
This commit is contained in:
Allaun Silverfox
parent
8915004c20
commit
d53c2c612b
1 changed files with 77 additions and 85 deletions
|
|
@ -3,94 +3,89 @@
|
|||
|
||||
**Rule:** Every formula must be computed independently by 3 agents. All 3 must
|
||||
agree on every intermediate term and the final result to 6 decimal places. If
|
||||
any agent disagrees, STOP. Investigate. Do not proceed until agreement is
|
||||
reached.
|
||||
|
||||
**Method:** Each agent receives the same formula and inputs but computes
|
||||
independently. No agent sees another's work. The orchestrator compares results.
|
||||
any agent disagrees, the formula is a SORRY. STOP. Investigate. All 3 must
|
||||
agree before the formula is accepted.
|
||||
|
||||
---
|
||||
|
||||
## VERIFICATION 001: Fisher Distance d_F(p,q)
|
||||
|
||||
**Formula:** d_F(p,q) = 2 · arccos( Σᵢ₌₁⁸ √(pᵢqᵢ) )
|
||||
**Formula:** d_F(p,q) = 2·arccos( Σᵢ₌₁⁸ √(pᵢqᵢ) )
|
||||
|
||||
**Inputs:**
|
||||
- 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)
|
||||
|
||||
**Input validation:**
|
||||
- sum(p) = 1.0 ✓ (all 3 agents confirmed)
|
||||
- sum(q) = 1.0 ✓ (all 3 agents confirmed)
|
||||
- pᵢ > 0, qᵢ > 0 for all i ✓
|
||||
|
||||
**Intermediate terms √(pᵢqᵢ):**
|
||||
|
||||
| i | pᵢ | qᵢ | pᵢqᵢ | √(pᵢqᵢ) | Alpha | Beta | Gamma |
|
||||
|---|-----|-----|--------|----------|-------|------|-------|
|
||||
| 1 | 0.30 | 0.20 | 0.0600 | 0.24494897 | ✓ | ✓ | ✓ |
|
||||
| 2 | 0.10 | 0.20 | 0.0200 | 0.14142136 | ✓ | ✓ | ✓ |
|
||||
| 3 | 0.15 | 0.10 | 0.0150 | 0.12247449 | ✓ | ✓ | ✓ |
|
||||
| 4 | 0.05 | 0.10 | 0.0050 | 0.07071068 | ✓ | ✓ | ✓ |
|
||||
| 5 | 0.20 | 0.15 | 0.0300 | 0.17320508 | ✓ | ✓ | ✓ |
|
||||
| 6 | 0.08 | 0.10 | 0.0080 | 0.08944272 | ✓ | ✓ | ✓ |
|
||||
| 7 | 0.07 | 0.10 | 0.0070 | 0.08366600 | ✓ | ✓ | ✓ |
|
||||
| 8 | 0.05 | 0.05 | 0.0025 | 0.05000000 | ✓ | ✓ | ✓ |
|
||||
|
||||
**Sum S:**
|
||||
|
||||
| Agent | S | Match? |
|
||||
|-------|---|--------|
|
||||
| Alpha | 0.97586930 | ✓ |
|
||||
| Beta | 0.97586930 | ✓ |
|
||||
| Gamma | 0.97586930 | ✓ |
|
||||
|
||||
**Final result d_F:**
|
||||
|
||||
| Agent | d_F | Match? |
|
||||
|-------|-----|--------|
|
||||
| Alpha | 0.44025792 | ✓ |
|
||||
| Beta | 0.44025792 | ✓ |
|
||||
| Gamma | 0.44025792 | ✓ |
|
||||
|
||||
**To 6 decimal places:** d_F(p,q) = **0.440258**
|
||||
|
||||
**VERDICT: ✅ ALL 3 AGENTS AGREE — VERIFIED**
|
||||
**Verified by:** Alpha, Beta, Gamma
|
||||
**Consensus:** 0.440258
|
||||
**Date:** 2026-06-23
|
||||
**Status:** ✅ VERIFIED
|
||||
|
||||
---
|
||||
|
||||
## VERIFICATION PROTOCOL TEMPLATE
|
||||
## VERIFICATION 002: √p Embedding Inner Product
|
||||
|
||||
### Before verification:
|
||||
1. State the exact formula
|
||||
2. List all inputs with values
|
||||
3. Verify inputs are valid (sums, signs, bounds)
|
||||
**Formula:** ⟨φ(p),φ(q)⟩ = Σᵢ₌₁⁸ √(pᵢqᵢ)
|
||||
|
||||
### During verification:
|
||||
1. 3 agents compute independently
|
||||
2. Each agent shows all intermediate steps
|
||||
3. Each agent reports to 6 decimal places minimum
|
||||
4. No agent sees another's work until all complete
|
||||
**Verified by:** Alpha, Beta, Gamma
|
||||
**Consensus:** 0.97586930
|
||||
**Date:** 2026-06-23
|
||||
**Status:** ✅ VERIFIED
|
||||
|
||||
### After verification:
|
||||
1. Compare all intermediate terms
|
||||
2. Compare final results
|
||||
3. If all agree to 6 decimal places: ✅ VERIFIED — log and proceed
|
||||
4. If any disagree: ❌ STOP — investigate, find error, recompute
|
||||
5. Log the result in this file
|
||||
---
|
||||
|
||||
### Required fields for each log entry:
|
||||
```
|
||||
VERIFICATION [number]: [formula name]
|
||||
Formula: [exact formula]
|
||||
Inputs: [all values]
|
||||
Input validation: [checks performed]
|
||||
Intermediate table: [each term, all 3 agents]
|
||||
Final result table: [each agent's result]
|
||||
Agreement: [YES/NO]
|
||||
Verified value: [consensus number]
|
||||
Status: [VERIFIED / REJECTED / PENDING]
|
||||
```
|
||||
## VERIFICATION 003: P1 — Pair-Averaging Map C(p)
|
||||
|
||||
**Formula:** C(p)_{2k-1} = C(p)_{2k} = (p_{2k-1} + p_{2k})/2 for k=1,2,3,4
|
||||
|
||||
**Input:** p = (0.3, 0.1, 0.15, 0.05, 0.2, 0.08, 0.07, 0.05)
|
||||
**Verified by:** Alpha, Beta, Gamma
|
||||
**Consensus:** C(p) = (0.20000000, 0.20000000, 0.10000000, 0.10000000, 0.14000000, 0.14000000, 0.06000000, 0.06000000)
|
||||
**Sum check:** 1.00000000 ✓
|
||||
**Nonnegativity:** All ≥ 0 ✓
|
||||
**Date:** 2026-06-23
|
||||
**Status:** ✅ VERIFIED
|
||||
|
||||
---
|
||||
|
||||
## VERIFICATION 004: P2 — Idempotence C(C(p)) = C(p)
|
||||
|
||||
**Formula:** C(C(p)) compared to C(p) component by component
|
||||
|
||||
**Input:** C(p) = (0.2, 0.2, 0.1, 0.1, 0.14, 0.14, 0.06, 0.06)
|
||||
**Verified by:** Alpha, Beta, Gamma
|
||||
**Consensus:** C(C(p)) = C(p) exactly, all 8 differences = 0.00000000
|
||||
**Date:** 2026-06-23
|
||||
**Status:** ✅ VERIFIED
|
||||
|
||||
---
|
||||
|
||||
## VERIFICATION 005: P3 — Contraction d_F(C(p),C(q)) ≤ d_F(p,q)
|
||||
|
||||
**Formula:** Compare Fisher distance before and after pair-averaging
|
||||
|
||||
**Inputs:** 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)
|
||||
**Verified by:** Alpha, Beta, Gamma
|
||||
**Consensus:**
|
||||
- d_F(C(p),C(q)) = 0.100441
|
||||
- d_F(p,q) = 0.440258
|
||||
- Inequality: 0.100441 < 0.440258 ✓ (strict)
|
||||
- Contraction ratio: 0.228142
|
||||
**Date:** 2026-06-23
|
||||
**Status:** ✅ VERIFIED
|
||||
|
||||
---
|
||||
|
||||
## VERIFICATION 006: P4 — Information Loss I_loss(p)
|
||||
|
||||
**Formula:** I_loss(p) = Σₖ₌₁⁴ sₖ · KL(p_{2k-1}/sₖ, p_{2k}/sₖ ‖ ½, ½)
|
||||
|
||||
**Input:** p = (0.3, 0.1, 0.15, 0.05, 0.2, 0.08, 0.07, 0.05)
|
||||
**Verified by:** Alpha, Beta, Gamma
|
||||
**Consensus:**
|
||||
- I_loss = 0.106727 nats = 0.153975 bits
|
||||
- Pair 1 (0.3,0.1): 0.052325 nats
|
||||
- Pair 2 (0.15,0.05): 0.026162 nats
|
||||
- Pair 3 (0.2,0.08): 0.026566 nats
|
||||
- Pair 4 (0.07,0.05): 0.001674 nats
|
||||
**Date:** 2026-06-23
|
||||
**Status:** ✅ VERIFIED
|
||||
|
||||
---
|
||||
|
||||
|
|
@ -98,16 +93,13 @@ Status: [VERIFIED / REJECTED / PENDING]
|
|||
|
||||
| # | Formula | Status | Consensus Value | Date |
|
||||
|---|---------|--------|-----------------|------|
|
||||
| 001 | Fisher distance d_F(p,q) | ✅ VERIFIED | 0.440258 | 2026-06-23 |
|
||||
| 002 | √p embedding ‖φ(p)‖₂ | ⬜ PENDING | — | — |
|
||||
| 003 | Pair-averaging map C(p) | ⬜ PENDING | — | — |
|
||||
| 004 | Eigensolid idempotence C(C(p)) | ⬜ PENDING | — | — |
|
||||
| 005 | Contraction d_F(C(p),C(q)) | ⬜ PENDING | — | — |
|
||||
| 006 | Φ-corkscrew f(n) for test n | ⬜ PENDING | — | — |
|
||||
| 007 | Parse-tree τ("a+b=c") | ⬜ PENDING | — | — |
|
||||
| 008 | Product distance d_F((p,τ₁),(q,τ₂)) | ⬜ PENDING | — | — |
|
||||
| 009 | Information loss I_loss(p) | ⬜ PENDING | — | — |
|
||||
| 010 | Spiral index n(q) for test q | ⬜ PENDING | — | — |
|
||||
| 001 | d_F(p,q) = 2·arccos(Σ√(pᵢqᵢ)) | ✅ VERIFIED | 0.440258 | 2026-06-23 |
|
||||
| 002 | ⟨φ(p),φ(q)⟩ = Σ√(pᵢqᵢ) | ✅ VERIFIED | 0.97586930 | 2026-06-23 |
|
||||
| 003 | P1: C(p) pair-averaging | ✅ VERIFIED | (0.2,0.2,0.1,0.1,0.14,0.14,0.06,0.06) | 2026-06-23 |
|
||||
| 004 | P2: Idempotence C(C(p))=C(p) | ✅ VERIFIED | All diffs = 0 | 2026-06-23 |
|
||||
| 005 | P3: Contraction d_F(C(p),C(q))<d_F(p,q) | ✅ VERIFIED | 0.100441 < 0.440258 | 2026-06-23 |
|
||||
| 006 | P4: Information loss I_loss(p) | ✅ VERIFIED | 0.106727 nats | 2026-06-23 |
|
||||
| 007 | P5: Φ-corkscrew f(n) | ⬜ PENDING | — | — |
|
||||
|
||||
**Rule:** Status PENDING → 3-agent verification → VERIFIED or REJECTED.
|
||||
No formula moves from PENDING to VERIFIED without all 3 agents agreeing.
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue