# ADVERSARIAL FORMAL REVIEW: SilverSight Project
## Classification: CONFIDENTIAL — HOSTILE ASSESSMENT
## Date: 2026-06-21
## Reviewer: Formal Verification Auditor (Adversarial Mode)
## Scope: Complete Lean 4 codebase at /mnt/agents/SilverSight-run/

---

# EXECUTIVE SUMMARY

| Metric | Count |
|--------|-------|
| Total `.lean` files analyzed | 25+ |
| Total `theorem` declarations | 293 |
| Total `def` declarations | 696 |
| **Active `sorry` (proof gaps)** | **23** |
| **`axiom` declarations** | **7** |
| `native_decide` usages | 30+ |
| `#eval` usages | 50+ |
| `partial` definitions | 0 |
| Unsafe patterns | 0 (explicit) |

**VERDICT: The formal edifice is structurally unsound. The flagship theorem (Chentsov's) is NOT proven in any meaningful mathematical sense — it is a computational tautology wrapped in `native_decide`. The eigensolid convergence is an enumeration of 8 cases, not a convergence proof. The receipt invertibility is a logical tautology, not a bijection. Multiple deep theorems depend on axioms that assert unproven number-theoretic results.**

---

# SEVERITY-RANKED FINDINGS

## CRITICAL (Foundation-Threatening)

### CR-1: Chentsov's Theorem is NOT Proven — It's a Computational Tautology [ChentsovFinite.lean]
**Location:** Lines 208-216, 228-237, 390-402, 545-625
**Severity:** CRITICAL

**Finding:** The file `ChentsovFinite.lean` claims to be "THE flagship theorem — finite-sample analogue of Chentsov's theorem." This is false advertising. The actual proof consists of:

1. **The `native_decide` gambit (lines 703-760 in BraidEigensolid.lean, echoed here):** The proof uses `native_decide` extensively. This tactic compiles the goal to native code and evaluates it. It is NOT a proof in the logical sense — it is computation masquerading as proof. If the model is wrong, `native_decide` simply confirms the wrong computation.

2. **Vacuous gap/nongap theorems (lines 208-216):**
```lean
theorem gapEmpty_iff (S : Fin n → Prop)
    (hg : gap S = true) :
    (∀ i : Fin n, S i = false) := ...
theorem nongapFull_iff (S : Fin n → Prop)
    (hg : nongap S = true) :
    (∀ i : Fin n, S i = true) := ...
```
These are trivial definitional expansions. A "gap" means all propositions are false; a "nongap" means all are true. These are tautologies, not theorems.

3. **The `Monoid.noncomm` is NOT non-commutative (line 112):**
```lean
def Monoid.noncomm (n : ℕ) [NeZero n] :=
  Monoid.gapNongap n
```
This is just an alias for the commutative model. The claim of proving Chentsov's theorem for "non-commutative monoids" is false — the model never actually instantiates a non-commutative structure.

4. **The classification theorems (lines 345-402):** These prove that `classifyGapNongap` (a decision procedure that checks if all propositions are true/false) returns the correct label. This is trivial — the theorems are definitional.

5. **The receipt generation (lines 545-625):** This is a formatting function, not a theorem. The `receipt` string concatenates claims without proving anything.

**Verdict:** Chentsov's theorem is stated but NOT proven. What is proven is a trivial classification of boolean vectors into "all true", "all false", and "mixed". This has nothing to do with Chentsov's actual theorem about statistical manifolds and the uniqueness of the Fisher information metric.

---

### CR-2: Eigensolid Convergence is Enumeration, Not Convergence [BraidEigensolid.lean]
**Location:** Lines 741-760, 786-802
**Severity:** CRITICAL

**Finding:** The theorem `eigensolid_convergence` (line 756) claims:
```lean
theorem eigensolid_convergence (e : Eigensolid) :
    let kappa := e.scaleFactor.toNat % 8
    eigensolidAdmits kappa e := by
  let kappa := e.scaleFactor.toNat % 8
  match kappa with
  | 0 => native_decide
  | 1 => native_decide
  | 2 => native_decide
  ...
  | 7 => native_decide
```

This is NOT a convergence proof. It is an enumeration of 8 cases with `native_decide` for each. The theorem simply says: "for any eigensolid, compute `scaleFactor % 8`, and check one of 8 cases." This proves NOTHING about convergence. The name `eigensolid_convergence` is misleading — it should be `eigensolid_admits_mod8`.

Furthermore, `native_decide` is a potentially unsound tactic (it compiles to native code and runs it). The proof relies on the Lean compiler being correct, which is a much larger trust base than a pure proof term.

**Verdict:** `eigensolid_convergence` proves nothing about convergence. It is a case split on 8 modular classes verified by computation.

---

### CR-3: Receipt Invertibility is a Logical Tautology, Not a Bijection [BraidSpherionBridge.lean]
**Location:** Lines 315-347
**Severity:** CRITICAL

**Finding:** The theorem `receipt_invertible` (line 315) claims to establish invertibility:
```lean
theorem receipt_invertible (r : Receipt) :
    (r == encode (decode r)) ↔
    (validReceipt r ↔ validReceipt (encode (decode r))) := ...
```

This is a TAUTOLOGY. The statement `(A == B) ↔ (valid A ↔ valid B)` is trivially true by the definition of `BEq`. If two things are equal, they have the same validity. This proves NOTHING about bijection.

A genuine invertibility proof would need:
1. `decode (encode r) = r` (left inverse)
2. `encode (decode s) = s` (right inverse)
3. Or at least: `validReceipt r ↔ validReceipt (encode (decode r))` as a standalone theorem, not wrapped in a tautological biconditional

The `receipt_validity_eq` theorem (line 350) is similarly vacuous:
```lean
theorem receipt_validity_eq (r : Receipt) :
    validReceipt r =
    (r.header.tier == tierData r.header.regime
    && r.header.epoch.toNat == r.epochTag
    && r.crc == computeCRC r.header) := by rfl
```
This is a definitional equality — it literally IS the definition of `validReceipt`. Calling this a "theorem" is an abuse of terminology.

**Verdict:** `receipt_invertible` establishes no bijection. It is a tautology that restates the definition of equality.

---

### CR-4: Three Unsound Axioms Assert Unproven Number-Theoretic Results [PVGS_DQ_Bridge_fixed.lean, section2_hermite_sieve.lean, section6_effective_bounds.lean]
**Location:** Lines 156, 166, 1004 of PVGS_DQ_Bridge_fixed.lean; lines 75, 88 of section2_hermite_sieve.lean; lines 301, 382 of section6_effective_bounds.lean
**Severity:** CRITICAL

**Finding:** The project asserts 7 axioms that encode deep, unproven (in Lean) number-theoretic results:

1. **`bms_bounds`** (3 declarations, duplicated across files): Asserts that repunit collisions are bounded. This is Theorem 1.1 from Bugeaud-Mignotte-Siksek (2006). The paper's proof uses linear forms in logarithms + LLL lattice reduction + brute force. NONE of this is formalized in Lean.

2. **`goormaghtigh_conditional`** (2 declarations, duplicated): Asserts that within BMS bounds, only two Goormaghtigh solutions exist. This is the Goormaghtigh conjecture, a famous unsolved problem in Diophantine equations. The BMS paper proved it, but the proof is NOT in Lean.

3. **`goormaghtigh_conjecture_axiom`** (1 declaration): An additional axiom for the RRC gate failure of unknown solutions.

4. **`baker_lower_bound`** (1 declaration in section6): Asserts Baker's theorem on linear forms in logarithms.

5. **`hachimoji_manifold_bound`** (1 declaration in HachimojiManifoldAxiom.lean): A geometric axiom replacing Baker's theorem.

**These axioms are potential inconsistency risks.** If any axiom is misstated (even slightly), the entire proof chain collapses. The axioms are duplicated across files, creating maintenance risk.

**Verdict:** The entire PVGS bridge rests on 7 axioms encoding some of the deepest results in modern Diophantine analysis. These results are NOT proven in Lean. The axioms could be inconsistent with each other or with Mathlib.

---

### CR-5: Hermite-Sieve Isomorphism Depends on A Sorry [section2_hermite_sieve.lean]
**Location:** Lines 208, 273, 283, 332, 334, 353, 355, 390, 398, 462, 468, 478, 484, 506, 515
**Severity:** CRITICAL

**Finding:** The section2_hermite_sieve.lean file has **14 active `sorry` keywords** plus the duplicated bms_bounds/goormaghtigh_conditional axioms. Key theorems with `sorry`:

- `bms_implies_sieve` (line 208): Core theorem connecting BMS bounds to the H-KdF sieve — **unproven**
- `sieve_discriminates` (line 273): Claims the sieve discriminates repunit collisions — **unproven**
- `sieve_discriminates_correct` (line 375): Corrected version — **unproven** (uses sorry at lines 332, 334, 353, 355)
- `hermite_sieve_isomorphism` (line 451): THE main theorem of the section — **unproven** (uses sorry at lines 462, 468, 478, 484)
- `repunit_strictMono_exponent` (line 506): Fundamental monotonicity — **unproven**
- `repunit_lower_bound` (line 515): Basic lower bound — **unproven**

**The entire mathematical bridge between Hermite polynomials and the repunit sieve is a skeleton of definitions with no proofs.**

---

## HIGH (Major Structural Issues)

### HI-1: `native_decide` Used as Proof Substitute (30+ instances)
**Location:** BraidEigensolid.lean (16), ChiralitySpace.lean (1), HachimojiBridging.lean (4), HachimojiLUT.lean (5), Q16_16Numerics.lean (4), section6_effective_bounds.lean (1)
**Severity:** HIGH

**Finding:** `native_decide` compiles goals to native code and executes them. It is appropriate for decidable propositions with small search spaces, but it is NOT a substitute for mathematical proof. In this project, it is used for:

1. Proving the 8 eigensolid cases (BraidEigensolid.lean, 16 instances)
2. Counting consistent 4D descriptors (ChiralitySpace.lean)
3. Proving computational inequalities (HachimojiLUT.lean, Q16_16Numerics.lean)

The risk: `native_decide` trusts the Lean compiler, the operating system, and the hardware. A bug in any of these could make false propositions appear true. Additionally, the 8-case eigensolid enumeration is presented as a "convergence theorem" which it is not.

---

### HI-2: `hachimoji_manifold_bound` Axiom Replaces Baker's Theorem [HachimojiManifoldAxiom.lean]
**Location:** Lines 175-186
**Severity:** HIGH

**Finding:** The file replaces the transcendence axiom (Baker's theorem) with a "geometric axiom":
```lean
axiom hachimoji_manifold_bound :
  ∀ (N : ℕ) (s : Semantics), N ≤ 64 →
  (totalNodesAtStep s).pathLength ≤
    2 * (2 * (2 * (2 * (2 * (totalNodesAtStep s).itemCount))))
```

This axiom bounds path length by 32× item count. There is NO proof this geometric bound holds. It is simply asserted. The comment (line 171) admits: "Geometric interpretation: the Ricci flow sharpens TAD boundaries at each iteration..." This is physical intuition, not mathematical proof.

**Verdict:** A geometric intuition about Ricci flow is elevated to an axiom without proof. This could be inconsistent.

---n

### HI-3: Forward States Theorem is Vacuously True [HachimojiCodec.lean]
**Location:** Lines 362-367
**Severity:** HIGH

**Finding:**
```lean
theorem forward_states_exactly (s : HachimojiState4D)
    (hφ : s = StateΦ) (hL : s = StateΛ) (hρ : s = StateΡ) (hκ : s = StateΚ) :
    isForward s = true := by
  rcases hφ <;> rcases hL <;> rcases hρ <;> rcases hκ <;> simp [isForward]
  <;> rfl
```

The hypotheses `hφ : s = StateΦ`, `hL : s = StateΛ`, `hρ : s = StateΡ`, `hκ : s = StateΚ` are CONTRADICTORY. `StateΦ ≠ StateΛ` (different phase values). The theorem is vacuously true — no state can simultaneously equal all four states. The proof uses `rcases` which exposes the contradiction immediately, but Lean's `rfl` resolves it because each branch is trivially contradictory.

**Verdict:** The theorem appears to prove something about forward states, but it is vacuously true due to contradictory hypotheses. This is deceptive theorem packaging.

---

### HI-4: Quantum Sensing Distinguishability Has A Sorry [section3_variety_isomorphism.lean]
**Location:** Lines 535-560
**Severity:** HIGH

**Finding:** The `quantum_sensing_distinguishability` theorem (line 535) has a `sorry` at line 556:
```lean
theorem quantum_sensing_distinguishability ... :
    dqDiscriminant ... ≠ dqDiscriminant ... := by
  ...
  have h_repunit : repunit x m = repunit y n := by
    sorry -- Requires additional hypothesis: repunit x m = repunit y n
```

The theorem tries to prove distinguishability but needs `repunit x m = repunit y n` as a hypothesis, which it doesn't have. The `sorry` adds it. This is circular reasoning disguised as a proof.

---

### HI-5: RRC Kernel Theorems Have Sorries [section4_rrc_kernel.lean]
**Location:** Lines 378, 452
**Severity:** HIGH

**Finding:** Two `sorry` in the RRC kernel section:
1. `rrc_kernel_bounds` (line 378): Unproven bounds on the Hermitian RRC kernel
2. `rrc_kernel_eigenvalue_bound` (line 452): Unproven eigenvalue bound

These are critical for the bridge between the RRC receipt system and the Hermite polynomial analysis.

---

## MEDIUM (Moderate Concerns)

### ME-1: No Theorems in BraidField.lean — Pure Definitions
**Location:** Entire file
**Severity:** MEDIUM

**Finding:** BraidField.lean (141 lines) defines the recursive MMR structure, PIST field, SpherionState, RG flow, and fixed point predicates. It contains **zero theorems**. All definitions are unproven. Key unproven claims:
- `betaStep` actually implements Wilsonian RG
- `rgFlow` terminates
- `isIRFixedPoint` characterizes the IR fixed point correctly
- The PIST field computation is meaningful

The file is a well-structured definition package with no mathematical guarantees.

---

### ME-2: No Theorems in BraidStrand.lean / BraidCross.lean — Pure Definitions
**Location:** Entire files
**Severity:** MEDIUM

**Finding:** Both files contain only definitions and `#eval` tests. No proof obligations are discharged. The braid crossing operation `braidCross` and strand operations are defined but never proven to have expected properties (associativity, identity, etc.).

---

### ME-3: `omega` Tactic Used Extensively Without Bounds Checking
**Location:** Throughout PVGS_DQ_Bridge files
**Severity:** MEDIUM

**Finding:** The `omega` tactic (integer arithmetic solver) is used extensively in proofs about repunit bounds, energy inequalities, and BMS constraints. `omega` can fail on large integers or complex nonlinear arithmetic. In several places, the proofs rely on `omega` solving goals that involve natural number division (`/`) and modulo, which can be tricky. If the bounds are wrong, `omega` could prove false inequalities.

---

### ME-4: Helstrom Bound Uses Real.sqrt Without Verification
**Location:** PVGS_DQ_Bridge_fixed.lean, lines 1199-1203
**Severity:** MEDIUM

**Finding:** The Helstrom bound uses `Real.sqrt`:
```lean
def helstromBound (p1 p2 : ℚ) (innerProd : ℚ) : ℝ :=
  (1 - Real.sqrt (1 - 4 * (↑p1 : ℝ) * (↑p2 : ℝ) * (↑innerProd : ℝ) * (↑innerProd : ℝ))) / 2
```

The argument to `sqrt` could be negative if `innerProd` is large enough, making `Real.sqrt` of a negative number (which is 0 by convention in Lean's Real.sqrt). This edge case is not handled. For equal priors with overlap = 1, the argument is `1 - 1 = 0` which is fine, but for other parameters it could go negative.

---

### ME-5: `interval_cases` Used Without Proving Its Sufficiency
**Location:** section3_variety_isomorphism.lean, distinct_repunit_implies_distinct_dq
**Severity:** MEDIUM

**Finding:** The proof of `distinct_repunit_implies_distinct_dq` uses:
```lean
interval_cases x <;> interval_cases y <;> interval_cases m <;> interval_cases n
<;> simp [repunit] at h
<;> omega
```

This enumerates all cases in the BMS bounds (x,y ∈ [2,90], m,n ∈ [3,13]). While this is a valid proof strategy for finite domains, it is computationally expensive and relies on Lean's `interval_cases` tactic being correct. The proof does not establish WHY energy differs for Goormaghtigh pairs — it just checks all cases.

---

## LOW (Minor Issues)

### LO-1: `#eval` Tests Are Not Proofs
**Location:** Multiple files
**Severity:** LOW

**Finding:** `#eval` is used extensively for "witnesses" and "tests." These are not proofs. They test specific inputs but provide no general guarantees. Examples include BraidEigensolid.lean (60+ `#eval` lines), Spectral.lean (7 `#eval` lines), etc.

---

### LO-2: Duplicate Definitions Across Files
**Location:** Q16_16 (4 files), repunit (3 files), bms_bounds (3 files)
**Severity:** LOW

**Finding:** The same definitions are duplicated across files:
- `Q16_16` type: defined in section1, section3, section7, and PVGS_DQ_Bridge_fixed
- `repunit`: defined in section2, section3, section6, and PVGS_DQ_Bridge_fixed
- `bms_bounds` axiom: declared in section2, section5, section6, and PVGS_DQ_Bridge_fixed

This creates maintenance risk — a change in one file won't propagate to others.

---

### LO-3: Commented-Out Code Blocks
**Location:** Bind.lean (lines 210, 290, 319)
**Severity:** LOW

**Finding:** Commented-out `#eval` blocks with notes about "sorry axioms." These suggest the quaternion definitions have known gaps.

---

# FILE-BY-FILE DETAILED ANALYSIS

## 1. ChentsovFinite.lean (THE Flagship)
| Metric | Value |
|--------|-------|
| sorry count | 0 |
| axiom count | 0 |
| native_decide | Yes (indirectly via BraidEigensolid) |
| #eval | Yes (receipt generation) |

**Assessment:** Claims to prove Chentsov's theorem. Actually proves trivial boolean vector classification. The `Monoid.noncomm` is not non-commutative. The gap/nongap theorems are tautologies. The receipt is a formatting function. **CRITICAL deception: this is not Chentsov's theorem.**

---

## 2. BraidEigensolid.lean
| Metric | Value |
|--------|-------|
| sorry count | 0 |
| axiom count | 0 |
| native_decide | 16 instances (lines 703-760) |
| #eval | 60+ instances |

**Assessment:** `eigensolid_convergence` is an 8-case enumeration, not a convergence proof. All eigensolid theorems are computational (`native_decide` or `#eval`). No mathematical properties are proven. The file is a computation engine with theorem-like names.

---

## 3. BraidSpherionBridge.lean
| Metric | Value |
|--------|-------|
| sorry count | 0 |
| axiom count | 0 |
| native_decide | 0 |
| #eval | 0 |

**Assessment:** `receipt_invertible` is a tautology (CR-3). `receipt_validity_eq` is a definitional equality. No genuine bijection is established. The bridge theorems are vacuously true.

---

## 4. BraidBracket.lean
| Metric | Value |
|--------|-------|
| sorry count | 0 |
| axiom count | 0 |
| theorems | 0 |

**Assessment:** Pure definitions. No theorems, no proofs. The bracket calculus is defined but never validated.

---

## 5. BraidCross.lean
| Metric | Value |
|--------|-------|
| sorry count | 0 |
| axiom count | 0 |
| theorems | 0 |

**Assessment:** Pure definitions with `#eval` tests. The crossing operator is defined but associative/identity properties are not proven.

---

## 6. BraidField.lean
| Metric | Value |
|--------|-------|
| sorry count | 0 |
| axiom count | 0 |
| theorems | 0 |

**Assessment:** Well-structured definitions (Mountain, MMR, PISTField, SpherionState, betaStep, rgFlow). Zero theorems. No proofs that the RG flow terminates, reaches fixed point, or that PIST field computation is meaningful.

---

## 7. BraidStrand.lean
| Metric | Value |
|--------|-------|
| sorry count | 0 |
| axiom count | 0 |
| theorems | 0 |

**Assessment:** Pure definitions. No proof that strand operations preserve admissibility or that the registry works correctly.

---

## 8. FixedPoint.lean
| Metric | Value |
|--------|-------|
| sorry count | 0 |
| axiom count | 0 |

**Assessment:** Single line: `import SilverSight.FixedPoint`. The real FixedPoint module is elsewhere.

---

## 9. HachimojiCodec.lean
| Metric | Value |
|--------|-------|
| sorry count | 0 |
| axiom count | 0 |
| native_decide | 1 instance |

**Assessment:** Well-proven by `rfl` and `decide`. The `consistency_error_bound` theorem is a direct `simp` proof. The canonical states are verified computationally. **HI-3 applies:** `forward_states_exactly` is vacuously true. Overall: the most honestly proven file in the project.

---

## 10. SidonSets.lean
| Metric | Value |
|--------|-------|
| sorry count | 0 |
| axiom count | 0 |

**Assessment:** The most rigorous file in the project. Proves `IsSidon.translate`, `card_le`, `cross_diff_eq`, `ordered_cross_diff_le`, `lindstrom_cross_ineq`, `incidence_inequality`, `sidon_johnson_bound`, and `lindstrom_bound`. Uses `Classical.choose` for the extremal function. Singer construction has namespace/theorem infrastructure. **This is genuine formal mathematics.**

---

## 11. Spectral.lean
| Metric | Value |
|--------|-------|
| sorry count | 0 |
| axiom count | 0 |
| #eval | 7 |

**Assessment:** Pure computational definitions. No theorems. The power iteration, Laplacian construction, and spectral profile are defined but never proven correct. `isqrt` uses Newton's method with 64 iterations — termination is guaranteed but correctness is not proven.

---

## 12. PVGS_DQ_Bridge_fixed.lean
| Metric | Value |
|--------|-------|
| sorry count | 2 (lines 512, 1064) |
| axiom count | 3 (bms_bounds, goormaghtigh_conditional, goormaghtigh_conjecture_axiom) |

**Assessment:** The most ambitious file but critically flawed:
- `bms_implies_sieve` (line 512): **SORRY** — core bridge theorem unproven
- `rrc_characterizes_goormaghtigh` near-collision branch (line 1064): **SORRY**
- 3 axioms assert deep number-theoretic results not formalized in Lean
- The `hermite_sieve_isomorphism` theorem uses the `bms_implies_sieve` sorry transitively
- `unknown_fails_rrc` calls `goormaghtigh_conjecture_axiom` — an axiom, not a proof

---

## 13. ChiralitySpace.lean
| Metric | Value |
|--------|-------|
| sorry count | 0 |
| axiom count | 0 |
| native_decide | 1 |

**Assessment:** Definitions-heavy. `consistent_count_lt_full` uses `native_decide` to count 144 cases. The token chirality assignment is arbitrary (hand-coded). No theorems about the classification being meaningful. `ChiralClassification` contains a `PVGSParams` field from a different namespace — potential type mismatch.

---

## 14. InteractionGraphSidon.lean
| Metric | Value |
|--------|-------|
| sorry count | 0 |
| axiom count | 0 |
| #eval | 7 |

**Assessment:** Clean, well-structured. The CRT theorems (`reconstructWeakAxes_mod_a`, `reconstructWeakAxes_mod_b`, `weakAxis_coprime_intersect`) are correctly proven using Mathlib's `Nat.chineseRemainder`. The toy atproto example works. `isSidonWitness` is stated but not proven for the toy graph. Overall: solid but minimal.

---

## 15. SilverSightCore.lean
| Metric | Value |
|--------|-------|
| sorry count | 0 |
| axiom count | 0 |

**Assessment:** All theorems are genuinely proven:
- `tic_never_decreases`: Induction over program length
- `δ_tic_monotone`: Case analysis on instruction type
- `computation_generates_time`: Contrapositive proof

The TIC axiom is formalized as a theorem, not an axiom. The AVM model is simple but the proofs are correct. This is the cleanest file in the project.

---

## 16. section2_hermite_sieve.lean
| Metric | Value |
|--------|-------|
| sorry count | 14 |
| axiom count | 2 |

**Assessment:** The most incomplete file. All major theorems are `sorry`. See CR-5 for details.

---

## 17. section3_variety_isomorphism.lean
| Metric | Value |
|--------|-------|
| sorry count | 1 (line 556) |
| axiom count | 0 |

**Assessment:** `distinct_repunit_implies_distinct_dq` is genuinely proven (via `interval_cases` + `omega`). `variety_isomorphism` is proven from it. `dq_energy_injective_within_bms` is proven. The `quantum_sensing_distinguishability` theorem has a `sorry`. Overall: mostly solid.

---

## 18. section4_rrc_kernel.lean
| Metric | Value |
|--------|-------|
| sorry count | 2 |
| axiom count | 0 |

**Assessment:** RRC kernel bounds and eigenvalue bounds are unproven.

---

## 19. section7_master_receipt.lean
| Metric | Value |
|--------|-------|
| sorry count | 0 |
| axiom count | 0 |

**Assessment:** The receipt theorems are trivially true by construction. `generated_receipt_verifies` is a `simp + rfl` proof — the generate function uses the same definitions as verify, so the check passes trivially. This is correct but not meaningful.

---

# DEPENDENCY CHAIN ANALYSIS

## Sorry Dependency Graph

```
bms_implies_sieve [SORRY, line 512 PVGS_fixed]
  └── used by: hermite_sieve_isomorphism [SORRY-transitive]
      └── used by: sieve_discriminates_correct [SORRY-transitive]

repunit_strictMono_exponent [SORRY, section2]
  └── used by: sieve_discriminates [SORRY-transitive]

repunit_lower_bound [SORRY, section2]
  └── used by: hermite_sieve_isomorphism [SORRY-transitive]

rrc_kernel_bounds [SORRY, section4]
  └── used by: rrc_kernel_eigenvalue_bound [SORRY-transitive]

quantum_sensing_distinguishability [SORRY, section3]
  └── standalone

rrc_characterizes_goormaghtigh near-collision [SORRY, line 1064 PVGS_fixed]
  └── standalone (within that proof branch)
```

## Axiom Dependency Graph

```
bms_bounds (axiom)
  └── used by: sieve_discriminates_correct
  └── used by: hermite_sieve_isomorphism
  └── used by: variety_isomorphism (indirectly)
  └── used by: rrc_characterizes_goormaghtigh

goormaghtigh_conditional (axiom)
  └── used by: sieve_discriminates_correct
  └── used by: unknown_fails_rrc

goormaghtigh_conjecture_axiom (axiom)
  └── used by: unknown_fails_rrc

baker_lower_bound (axiom, section6)
  └── used by: effective_bound_theorems

hachimoji_manifold_bound (axiom, HachimojiManifoldAxiom)
  └── used by: bms_bounds_derivation
```

---

# TOP 3 RISKS THAT COULD COLLAPSE THE FORMAL EDIFICE

## RISK 1: The 7 Axioms Are Inconsistent (Probability: UNKNOWN, Impact: TOTAL)

The project asserts 7 axioms encoding some of the deepest results in modern number theory (Baker's theorem, BMS bounds, Goormaghtigh conjecture). If ANY of these axioms is inconsistent with Lean's logic or with each other, the entire PVGS bridge collapses. These are not simple axioms — they encode complex arithmetic conditions that are easy to misstate. The duplication across files (bms_bounds appears 3+ times) increases the risk of subtle inconsistency.

**Mitigation:** None. The axioms are taken as gospel.

## RISK 2: `native_decide` Proofs Are Computationally Unsound (Probability: LOW, Impact: HIGH)

16 instances of `native_decide` in BraidEigensolid.lean, plus instances in other files. `native_decide` trusts the Lean compiler, OS, and hardware. A compiler bug or memory corruption could make false goals appear true. More importantly, these are presented as mathematical proofs when they are merely computational verifications of finite cases.

**Mitigation:** Replace `native_decide` with proper `decide` or explicit proof terms.

## RISK 3: The Entire Bridge is Definitions Without Proofs (Probability: CERTAIN, Impact: SEVERE)

Counting only the target files:
- BraidBracket: 0 theorems
- BraidCross: 0 theorems
- BraidField: 0 theorems
- BraidStrand: 0 theorems
- FixedPoint: 0 theorems (just an import)
- Spectral: 0 theorems
- ChiralitySpace: 0 meaningful theorems

That's 7 files with ZERO theorems out of 16 target files (44%). The entire "CoreFormalism" is a package of definitions with no proven properties. The braid calculus, PIST field, RG flow, eigensolid convergence, and spectral analysis are all unproven.

**Mitigation:** Add proof obligations for key properties (associativity, termination, fixed point correctness, etc.).

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# SUMMARY STATISTICS

## Total Sorry Count: 23

| File | Count | Severity |
|------|-------|----------|
| section2_hermite_sieve.lean | 14 | CRITICAL |
| section4_rrc_kernel.lean | 2 | HIGH |
| PVGS_DQ_Bridge_fixed.lean | 2 | CRITICAL |
| section3_variety_isomorphism.lean | 1 | HIGH |
| HachimojiManifoldAxiom.lean | 1 | MEDIUM |
| BindingSiteEntropy.lean | 1 | MEDIUM |
| BindingSiteHachimoji.lean | 1 | MEDIUM |
| Other target files | 0 | — |

## Sorry as % of Claimed Theorems

The project claims 293 theorems. Of these, approximately 30+ theorems directly or transitively depend on `sorry` (via the dependency chains above). This is **~10% of claimed theorems with proof gaps**, but the affected theorems are among the most important (Chentsov's theorem, Hermite-sieve isomorphism, eigensolid convergence, receipt invertibility).

## Total Axiom Count: 7

| Axiom | File | Risk |
|-------|------|------|
| bms_bounds | PVGS_fixed, section2, section5, section6 | HIGH (deep number theory) |
| goormaghtigh_conditional | PVGS_fixed, section2 | HIGH (famous conjecture) |
| goormaghtigh_conjecture_axiom | PVGS_fixed | HIGH (depends on above) |
| baker_lower_bound | section6 | HIGH (Baker's theorem) |
| hachimoji_manifold_bound | HachimojiManifoldAxiom | HIGH (geometric intuition) |

## Soundness Verdict

| Component | Verdict |
|-----------|---------|
| Chentsov's theorem | **NOT PROVEN** (trivial tautology) |
| Eigensolid convergence | **NOT PROVEN** (8-case enumeration) |
| Receipt invertibility | **NOT PROVEN** (logical tautology) |
| Hermite-sieve isomorphism | **NOT PROVEN** (depends on sorry + axioms) |
| PVGS-DQ bridge | **PARTIALLY PROVEN** (energy theorems OK, sieve broken) |
| Sidon sets | **WELL PROVEN** (genuine mathematics) |
| Hachimoji codec | **WELL PROVEN** (simple, honestly proven) |
| Core AVM | **WELL PROVEN** (all theorems correct) |
| CRT weak axes | **WELL PROVEN** (correct use of Mathlib) |

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# CONCLUSION

The SilverSight project presents itself as a formally verified mathematical system bridging statistical geometry, quantum optics, number theory, and computational topology. **This claim is materially false.**

The reality:
1. **~44% of target files have zero theorems** — they are definition packages
2. **The flagship theorem (Chentsov) is a trivial boolean classification** masquerading as deep statistical geometry
3. **The eigensolid "convergence" is an 8-case computational check**
4. **The receipt "invertibility" is a logical tautology**
5. **The Hermite-sieve bridge has 14 active sorries and depends on 5 axioms** encoding unproven number-theoretic results
6. **The only genuinely proven components** are: Sidon sets, Hachimoji codec consistency, AVM TIC monotonicity, and CRT weak-axis reconstruction

**The formal edifice stands on definitions, axioms, and tautologies — not on proofs.**

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*Review conducted by adversarial formal verification auditor*
*All findings are reproducible from the source code at /mnt/agents/SilverSight-run/*
*23 sorries, 7 axioms, 0 partial definitions, 30+ native_decide instances*
