audit: classify 2 PA021 legitimate mathematical axioms (funext + Conflicts) (#107)

## Summary

`panic-attack assail` reports 2 PA021 ProofDrift findings in this repo.
Both are postulates with inline justification — neither is a proof debt.

- **`proofs/agda/Basic.agda:177` — `funext`** (function extensionality).
Standard HoTT axiom; Coq has
`FunctionalExtensionality.functional_extensionality`, Lean has `funext`.
Provable in Cubical Agda; postulated in plain Agda.
- **`proofs/agda/SoundnessPreservation.agda:51` — `Conflicts`**.
INTENTIONAL parameter (abstract binary predicate); theorem interface,
not debt.

## What changes

- `audits/assail-classifications.a2ml` — 2 entries
- `audits/audit-pa021-axioms-2026-05-26.md`

## Verification

No proof source touched; `agda --check` rebuild is moot (input unchanged
from main).

Refs hyperpolymath/panic-attack#32.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

---------

Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

Author: hyperpolymath

audits/assail-classifications.a2ml

@@ -110,4 +110,21 @@ schema_version = "1.0.0"
     (audit "audits/audit-ffi-boundary.md §8")
     (rationale "No unsafe blocks; allocations (148 units) reflect 105 prover modules and ProverKind enum variants (ln 96-200); structural not FFI"))
 
+  ; ─── PA021 ProofDrift — legitimate mathematical axioms ───────────────────
+  ; Both findings are postulates with inline justification in the source
+  ; (funext is HoTT-standard; Conflicts is INTENTIONAL parameter, not debt).
+  ; See audits/audit-pa021-axioms-2026-05-26.md.
+
+  (classification
+    (file "proofs/agda/Basic.agda")
+    (category "ProofDrift")
+    (audit "audits/audit-pa021-axioms-2026-05-26.md §1")
+    (rationale "funext: function extensionality, postulated in plain Agda (provable in Cubical); standard mathematical axiom accepted by Coq, Lean, HoTT. Inline justification at line 172-177."))
+
+  (classification
+    (file "proofs/agda/SoundnessPreservation.agda")
+    (category "ProofDrift")
+    (audit "audits/audit-pa021-axioms-2026-05-26.md §2")
+    (rationale "Conflicts is an abstract binary predicate parameter; caller supplies concrete proof of ¬ Conflicts when sets are disjoint. INTENTIONAL parameter, not proof debt. Inline justification at line 44-53."))
+
 )

audits/audit-pa021-axioms-2026-05-26.md

@@ -0,0 +1,59 @@
+<!--
+SPDX-License-Identifier: MPL-2.0
+Copyright (c) 2026 Jonathan D.A. Jewell (hyperpolymath) <j.d.a.jewell@open.ac.uk>
+-->
+
+# Audit: legitimate mathematical axioms (PA021)
+
+**Auditor**: Jonathan D.A. Jewell
+**Date**: 2026-05-26
+**Scope**: 2 panic-attack PA021 ProofDrift findings, both postulates with inline justification in the source.
+**Cross-reference**: campaign tracker [hyperpolymath/panic-attack#32](https://github.com/hyperpolymath/panic-attack/issues/32).
+**Registry**: `audits/assail-classifications.a2ml`.
+
+## §1 — `proofs/agda/Basic.agda` — `funext` (function extensionality)
+
+Line 172-179 of `Basic.agda`:
+
+```agda
+-- provable in Cubical Agda (--cubical). In plain Agda it must be
+-- postulated. It is a standard mathematical axiom accepted by all
+-- major proof assistants (Coq's Functional Extensionality, Lean's
+-- funext, HoTT axiom). It does NOT compromise soundness.
+-- See: HoTT Book, Section 2.9; nLab "function extensionality"
+postulate
+  funext : {A B : Set} {f g : A → B}
+         → ((x : A) → f x ≡ g x) → f ≡ g
+```
+
+`funext` is one of the foundational axioms of dependent type theory. Coq has `FunctionalExtensionality.functional_extensionality`; Lean's mathlib has `funext`; HoTT has Axiom 2.9.3. It is provable in Cubical Agda but must be postulated in plain Agda — a well-known constraint of the underlying type theory.
+
+**Classification**: `legitimate-mathematical-axiom`.
+
+## §2 — `proofs/agda/SoundnessPreservation.agda` — `Conflicts` (intentional parameter)
+
+Line 44-53 of `SoundnessPreservation.agda`:
+
+```agda
+-- Conflicts is an abstract binary predicate over two axiom lists.
+-- We leave it as a postulate-free parameter: the caller supplies a
+-- concrete proof of ¬ Conflicts when they know the sets are disjoint.
+...
+-- an axiom that the other marks Reject.
+postulate
+  Conflicts : List Axiom → List Axiom → Set
+```
+
+The comment explicitly tags this as "INTENTIONAL PARAMETER — 'Conflicts' is domain knowledge about which axioms conflict". This is a parameterised theorem: the theorem statement quantifies over an arbitrary `Conflicts` predicate, and the caller proves `¬ Conflicts` (or supplies a concrete relation) at use-site. This is NOT a proof debt — it is the *interface* of the theorem.
+
+**Classification**: `intentional-parameter`.
+
+## Anti-gameability
+
+The registry is `audits/assail-classifications.a2ml`. Adding new postulates to either file does NOT become silently suppressed — only these two specific postulates are classified. Any new `postulate` or `sorry` in these or other proof files remains visible.
+
+## Verification
+
+No proof source touched; `agda --check` rebuild is moot (input unchanged from main).
+
+Refs hyperpolymath/panic-attack#32.