mirror of https://github.com/allaunthefox/Research-Stack.git synced 2026-07-31 03:05:21 +00:00

Brandon Schneider dac28c1b52 docs: sync all editor rules, opencode agents, and sorry audit

Editor rules updated (.cursorrules, .clinerules, copilot-instructions, .roo):
- Build: 3571 jobs, 0 errors
- Sorry inventory: 8 across 4 files (all documented)
- Q16_16 compliance, new modules list, FPGA info
- Fixed stale path in copilot-instructions

Opencode agents:
- 3 marked RESOLVED (pist-simulation, qfactor, ssms)
- 2 new agents created (adjugate-matrix, hamiltonian-mechanics)
- 1 updated (hyperbolic-statesurface)

SORRY_AUDIT.md: updated to 8 sorries across 4 files

2026-05-28 17:53:54 -05:00

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description

mode

model

permission

Fix the two sorry blocks in AdjugateMatrix.lean (det_self_inverse_approx and det_self_inverse_exact). Use ONLY when asked to fix AdjugateMatrix sorry or resolve matrix inverse proofs.

subagent

anthropic/claude-sonnet-4-6

edit	bash	read
allow	allow	allow

Fix AdjugateMatrix.lean sorry blocks

Context

Semantics/AdjugateMatrix.lean has two sorry blocks related to the 8×8 matrix inverse correctness:

Sorry 1: `det_self_inverse_approx` (line 296)

theorem det_self_inverse_approx {m : Matrix8} {inv : Matrix8} (ε : Q16_16)
    (h : matrixInverse m = some inv) :
    matrixApproxEq (matrixMultiply m inv) identity8 ε := by
  sorry

Blocker: Q16_16 truncation causes 1 LSB error in division/multiplication. The theorem claims m × inv ≈ I within tolerance ε, but the proof requires formalizing the error propagation through adjugate-based matrix inversion on fixed-point arithmetic.

Path forward:

(a) Prove a bounded-error variant with explicit ε bound derived from Q16_16 division error
(b) Add exact-div precondition (if det divides cleanly)
(c) Port to Mathlib ℚ proof where Laplace cofactor identity has a clean proof

Sorry 2: `det_self_inverse_exact` (line 305)

theorem det_self_inverse_exact {m : Matrix8} {inv : Matrix8}
    (h : matrixInverse m = some inv)
    (h_div_exact : ∀ i j : Fin 8, ((getEntry (adjugate m) j.val i.val).toInt * 65536) % (det8 m).toInt = 0)
    (h_mul_exact : ∀ i j k : Fin 8, ((getEntry m i.val k.val).toInt * (getEntry inv k.val j.val).toInt) % 65536 = 0) :
    matrixMultiply m inv = identity8 := by
  sorry

Blocker: Requires showing that when all Q16_16 division and multiplication operations are exact (no truncation), the adjugate-based inverse satisfies m × inv = I exactly. The h_div_exact and h_mul_exact hypotheses pin down the exactness conditions.

Path forward: This is a pure integer-arithmetic proof under the exactness hypotheses. The Laplace cofactor expansion m × adj(m) = det(m) · I needs to be formalized for 8×8 matrices over ℤ, then the exactness hypotheses lift it to Q16_16.

Note

det_self_inverse (the original single sorry from prior audits) was refactored into these two variants. det_self_inverse_identity (identity matrix case) was proven via computation.

Steps

Read Semantics/AdjugateMatrix.lean lines 270-310
Read Semantics/FixedPoint.lean for Q16_16 arithmetic lemmas
Decide strategy: exact-path (det_self_inverse_exact) is likely easier since hypotheses remove all rounding concerns
Prove det_self_inverse_exact first (integer-arithmetic Laplace expansion)
Then address det_self_inverse_approx (requires error-bound analysis)
Build: lake build Semantics.AdjugateMatrix
Build: lake build Compiler

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