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PHASE 3 ORCHESTRATION LOG

BOB Quantum Kernel Loop Invariant Formalization

Generated: 2026-07-24
Orchestrator: Haiku (Haiku 4.5)
Project: sov-kernel-monster
Repo: /c/tmp/jacobian-formal/agda/

ROUND 1: STRUCTURAL ANALYSIS (COMPLETE)

Agent Assignments

  • ahmad_bot: EvolutionLoop.agda (state evolution bookkeeping)
  • forge: EulerLoop.agda (amplitude update mechanics)
  • enki: MatrixAccumulationLoop.agda (matrix/gate logic proofs)

Results Summary

Ahmad_bot Finding: EvolutionLoop.agda Line 139

Hole: h_state_valid = ? in evolution_step function

Diagnosis: STRUCTURAL GAP in StepTransition record

The StepTransition record at lines 100-124 lacks a semantic contract for dimensional validity preservation. Quantum state evolution must preserve the Hilbert space dimension (number of basis states), but this constraint is not encoded in the record definition.

Required Fix: Add field to StepTransition record:

state_valid_preserved :
  isValidDim (EvolutionState.state s) →
  isValidDim (EvolutionState.state s')

Location: EvolutionLoop.agda lines 100-124

Why it matters: Without this field, the inductive step cannot prove that an evolved state remains valid. This is not just a proof technicality—it represents a missing semantic requirement from the physics: evolution operators preserve the dimension of the state space.

Enki Finding: MatrixAccumulationLoop.agda Line 101

Hole: h_k_valid = ? in matrix_acc_base function

Diagnosis: PRECONDITION VIOLATION

The predicate taylorTermIndex k max_terms expands to k ≤ max_terms. At k=1 (base case), we need 1 ≤ max_terms, but no precondition guarantees max_terms ≥ 1.

The function signature is:

matrix_acc_base :
  (s : MatrixAccLoopState) →
  MatrixAccLoopState.k s ≡ 1 →
  ...
  MatrixAccLoopState.error_status s ≡ 0 →
  MatrixAccInvariant s 1

Missing precondition:

h_max_terms_pos : MatrixAccContext.max_terms (MatrixAccLoopState.ctx s) ≥ 1 →

Location: MatrixAccumulationLoop.agda lines 87-97

Why it matters: RK4 Taylor series acceleration requires at least one term (the constant term, k=1). While the implementation uses MAX_TERMS=20 in practice, the formal spec doesn't encode this invariant. This is a gap between the implementation contract and the formalization.

Forge Finding: EulerLoop.agda Line 141

Hole: First element of pair in h_i_in_range record field

Diagnosis: DISCHARGEABLE with stdlib support

The hole requires proving 1 ≤ i + 1 given that i ≥ 1 in the inductive case.

Proposed Proof Term:

Data.Nat.Properties.n≤n+m 1 i

This uses the standard library lemma: n ≤ n + m for any naturals n, m.

Alternative (with explicit case handling):

case (EulerInvariant.h_i_in_range inv_i) of λ where
  (inl ⟨ _ , _ ⟩) → Data.Nat.Properties.n≤n+m 1 i
  (inr p) → absurd (¬p refl)

Status: Requires type-checking against actual Agda/Lean 4 stdlib to verify lemma availability.

Location: EulerLoop.agda line 141

Hole Inventory (Round 1 Analysis)

Total holes identified: 15
Holes discharged: 0
Holes blocked (spec gaps): 3
Holes pending analysis: 12

Module Line Function Status Agent
EvolutionLoop.agda 139 evolution_step BLOCKED ahmad_bot
EvolutionLoop.agda 142 evolution_step PENDING ahmad_bot
EvolutionLoop.agda 149 evolution_step PENDING ahmad_bot
EulerLoop.agda 141 euler_step PROPOSED forge
EulerLoop.agda 142 euler_step PENDING forge
EulerLoop.agda 186 euler_exit PENDING forge
MatrixAccumulationLoop.agda 101 matrix_acc_base BLOCKED enki
MatrixAccumulationLoop.agda 156 matrix_acc_step PENDING enki
MatrixAccumulationLoop.agda 159 matrix_acc_step PENDING enki
MatrixAccumulationLoop.agda 195 matrix_acc_exit PENDING enki
MatrixAccumulationLoop.agda 196 matrix_acc_exit PENDING enki
GateApplicationLoop.agda 172 gate_step NOT_ANALYZED —
GateApplicationLoop.agda 185 gate_step NOT_ANALYZED —
GateApplicationLoop.agda 217 gate_exit NOT_ANALYZED —
GateApplicationLoop.agda 218 gate_exit NOT_ANALYZED —

NEXT STEPS

Phase 3.1: Spec Corrections (PRIORITY CRITICAL)

Before proceeding with Round 2, the following spec gaps must be fixed:

  1. EvolutionLoop.agda: Add state_valid_preserved field to StepTransition record

    • Semantic: Evolution preserves Hilbert space dimension
    • Affects: 3 holes in EvolutionLoop (lines 139, 142, 149)

  2. MatrixAccumulationLoop.agda: Add precondition to matrix_acc_base

    • Add parameter: h_max_terms_pos : max_terms ≥ 1
    • Semantic: RK4 requires minimum 1 term
    • Affects: 5 holes in MatrixAccumulationLoop

Phase 3.2: Round 2 Discharge (AFTER SPEC FIXES)

Reassign holes to agents after corrections are applied. Expect:

  • EvolutionLoop holes 139, 142: ahmad_bot (retry)
  • EulerLoop hole 141: forge (verify proposed discharge)
  • MatrixAccumulationLoop hole 101: enki (retry)
  • Additional holes: assign sequentially

Phase 3.3: GateApplicationLoop Analysis (NEW)

Launch full analysis of GateApplicationLoop.agda (4 holes):

  • Similar precondition patterns expected
  • Likely requires gate unitary enforcement preconditions

WORM AUDIT TRAIL

No WORM seals generated in Round 1 (zero successful discharges). Entries logged to /tmp/PHASE_3_WORM_ENTRIES.jsonl for structural findings.

When discharges succeed in subsequent rounds:

PHASE_3_PROOF_DISCHARGE::<module>::<agent>::<blake3_hash_of_proof_term>

ARTIFACTS

  • Full hole inventory: See hole_list.txt in same directory
  • Agent reports: Collected in agent_findings/ subdirectory
  • Spec gaps report: See PHASE_3_DISCHARGE_REPORT.md

End of Round 1 Log