correspondence: a named section is not a namespace; an extra axiom is a failure

Round-8 review (GPT-5.6, register key `section-prefix-bug`, CRITICAL).
Reproduced here exactly before fixing.

model-correspondence.py treated `namespace`, `section` and `end` as one event
class and pushed a named section onto the fully-qualified-name prefix. Lean
does not: `section Foo` opens a scope for `variable`/`open` and gives `end Foo`
a label; it does not turn `bar` into `Foo.bar`. Given a template reading

    section Foo
    axiom bar : Nat
    end Foo

the scanner reported `Foo.bar`, `--names` handed Phase 2d only `Foo.bar`, Lean
resolved an unrelated `Foo.bar` definition elsewhere in the corpus, and the
verdict came back PROVEN. The axiom the extraction ACTUALLY depends on was
never queried. This survived both the fail-closed rewrite and the new
Lean-semantic phase, in a scanner rewritten that same week specifically to
stop dropping things.

AND THE REASON IT STAYED SILENT, which is the half worth keeping. The real
external did not vanish — it landed in the table as EXTRA, the one verdict
that could not fail. A silent bucket beside a fail-closed parser is a slower
way of dropping things. An extra AXIOM is now EXTRA-AXIOM and stops the
button: the model exists to answer the template, so an assumption nothing
asks for is either a parse we got wrong or an assumption nobody governs.
Extra definitions stay tolerated; helpers in a model file are ordinary.

That gate fired on the real corpora on its first run. Each fork's
hand-maintained gen/CurveField/FunsExternal.lean carried AVX2/AVX512 backend
axioms present in no template, no proof, no cone and no allowlist — dead
assumptions in a pinned trusted-base file, reported as EXTRA and therefore
invisible. extract.sh:16 confirms these files are never overwritten by
extraction, so they were hand-written and are removed here:

    dalek 2, anza 3, risc0 4, betrusted 4

Nothing referenced them, so no certificate's cone changes; the trusted base
simply gets smaller. Table rows 64->62, 51->48, 57->53, 56->52, and Phase 2d
independently resolved 62/48/53/52 externals against the regenerated tables.

GEN-MODEL.sha256 and HARNESS.sha256 both move: the model bytes changed, and
the harness pins the table and the gen manifest themselves.

Certified: round-10 sweep, 2h53m, ten instruments in each of four forks,
40/40 GREEN, 0 failing, 0 resource-limited. A full run was required — the
--audit-only staleness gate correctly refused after a source change.

Registered in formal-verification-control/review-findings.tsv as
`section-prefix-bug` and `dead-model-axioms`.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

verification/GEN-MODEL.sha256

@@ -1,4 +1,4 @@
-7f173f9ead5b88f2b5444130d906d7b4a3c1c44f960845ad236c9aab796e2c82  CurveField/FunsExternal.lean
+69e5aa74675faafdf18702d87780f5b85b0dcffcaf0652d3a01348e3708f5075  CurveField/FunsExternal.lean
 e0aa7f126fe8e4a2dd4ef083f076192a2db98dc4e723f69cf204c3019a87f7c4  CurveField/FunsExternal_Template.lean
 6aebc152991c3b82fd2b7b576d59ab1524d8ff3e9002264dc84a74b379b3ba74  CurveField/Funs.lean
 127b84e0aff8b079f4d74b4f5e898b7f031f740b836a22519069cee99a3e5f2a  CurveField/TypesExternal.lean

verification/HARNESS.sha256

@@ -2,14 +2,14 @@
 6b25b7e261633f4fa703de0be1dfd3c263d043107e3b3225d4c5079a93b6a64d  check-scalar.sh
 b55a405e1af95d28a6d222f4cfc1d1e33428da2650b7a6668ecdda852eea6330  check.sh
 fdd1337f1f44fa73fdb14e6cda001e4e7358513b9c178c517456b24511d96a8e  extract.sh
-52afbe130c5551686f45643a35065729fd5bb8166b5fa3db67b74c60ba3eff62  GEN-MODEL.sha256
+5a5fd8a0e1d29033e00b98fd0d37b860a3754205d7a46d2c5168d68c26b3dc25  GEN-MODEL.sha256
 6033c86eb08b4c2ea0bd7cdbd2cfb5748059179ece3efa9673270dc17a2e38b9  inventory-allowlist-scalar.txt
 80cdd232c9a0f3078b2b712957e34797add5421b51bd695a151bf64a7855687a  inventory-allowlist.txt
 0bb01bc4abaafa8537d460682004d1f336980b28bc4fe1968bcc9c3bc3bc71ba  inventory_gate.sh
 736ea4be712e1b5bcda10ecb466f0dec7008a2a36eabdfd77563976299c43cce  lean-guard
 b982bd1aa56b0648b10516985a2e0f6a9cacff4e1d19b441dadc5b35d69ec732  lift-guard.sh
-7a9c89cf2b96313bd4bcddb534e8d06724bd7250234e670baadf6a9b0d1fbf81  model-correspondence.py
+1942177f13d6ae229d87a3b0b33f7fbb4b2ae20fe1059cc83010e73f6a156427  model-correspondence.py
-6c1503880f38e4b827df32a4854902b66b7b2ea4783f9eb5c44e691a2c293ae1  MODEL-CORRESPONDENCE.txt
+cf86c955dd5b637bc9d673c4222684979f507a4e11e488ab514e654c49f4e569  MODEL-CORRESPONDENCE.txt
 34c102ca7a38719ef8890b8dedd3f07c3f92e10ae4a1ce2c47a7db4d53523354  Proofs/Audit.lean
 dd957bb260df0bd33266418a6594b45720c4754c5687bfab4ecb30ad573a286c  Proofs/InventoryBasic.lean
 859dcb7fcef13e8b49a8b36a496f46e9fc56448410d3bde16c78361215f4bc19  Proofs/InventoryCore.lean

verification/MODEL-CORRESPONDENCE.txt

@@ -44,9 +44,6 @@ CurveField/FunsExternal|subtle.Choice.Insts.CoreOpsBitBitOrChoiceChoice.bitor|MO
 CurveField/FunsExternal|subtle.Choice.unwrap_u8|MODEL
 CurveField/FunsExternal|subtle.ConditionallySelectable.conditional_assign.default|MODEL
 CurveField/FunsExternal|subtle.ConditionallySelectable.conditional_swap.default|MODEL
-CurveField/FunsExternal|backend.vector.scalar_mul.variable_base.spec_avx2.mul|EXTRA
-CurveField/FunsExternal|backend.vector.scalar_mul.vartime_double_base.spec_avx2.mul|EXTRA
-CurveField/FunsExternal|backend.vector.scalar_mul.vartime_triple_base.spec_avx2.mul_128_128_256_prechecked|EXTRA
 CurveField/TypesExternal|ed25519.Signature|MODEL
 CurveField/TypesExternal|subtle.Choice|MODEL
-CORRESPONDENCE-COUNT|51
+CORRESPONDENCE-COUNT|48

verification/gen/CurveField/FunsExternal.lean

@@ -342,28 +342,6 @@ axiom backend.serial.scalar_mul.vartime_triple_base.mul_128_128_256_prechecked
   scalar.Scalar → edwards.EdwardsPoint → scalar.Scalar →
     edwards.EdwardsPoint → scalar.Scalar → Result edwards.EdwardsPoint
 
-/-- [curve25519::backend::vector::scalar_mul::variable_base::spec_avx2::mul]:
-    Source: 'curve25519/solana-ed25519/src/backend/vector/scalar_mul/variable_base.rs', lines 3:0-3:68
-    Visibility: public -/
-axiom backend.vector.scalar_mul.variable_base.spec_avx2.mul
-  : edwards.EdwardsPoint → scalar.Scalar → Result edwards.EdwardsPoint
-
-/-- [curve25519::backend::vector::scalar_mul::vartime_double_base::spec_avx2::mul]:
-    Source: 'curve25519/solana-ed25519/src/backend/vector/scalar_mul/vartime_double_base.rs', lines 14:0-14:68
-    Visibility: public -/
-axiom backend.vector.scalar_mul.vartime_double_base.spec_avx2.mul
-  :
-  scalar.Scalar → edwards.EdwardsPoint → scalar.Scalar → Result
-    edwards.EdwardsPoint
-
-/-- [curve25519::backend::vector::scalar_mul::vartime_triple_base::spec_avx2::mul_128_128_256_prechecked]:
-    Source: 'curve25519/solana-ed25519/src/backend/vector/scalar_mul/vartime_triple_base.rs', lines 10:0-10:68 -/
-axiom
-  backend.vector.scalar_mul.vartime_triple_base.spec_avx2.mul_128_128_256_prechecked
-  :
-  scalar.Scalar → edwards.EdwardsPoint → scalar.Scalar →
-    edwards.EdwardsPoint → scalar.Scalar → Result edwards.EdwardsPoint
-
 /-- [curve25519::backend::scalar_fits_in_128_bits]:
     Source: 'curve25519/solana-ed25519/src/backend.rs', lines 283:0-285:1 -/
 axiom backend.scalar_fits_in_128_bits : scalar.Scalar → Result Bool

verification/model-correspondence.py

@@ -121,7 +121,11 @@ def strip_comments(text):
 
 
 def declared(path):
-    """Fully-qualified names declared in one file.
+    """{fully-qualified name: declaration keyword} for one file.
+
+    Returns a MAPPING, not a set, because the keyword is load-bearing: an
+    `axiom` the template never asks for must stop the button, while an extra
+    `def` is an ordinary helper. Callers that only need names take `set(...)`.
 
     Raises ScanError on any declaration keyword whose name cannot be read.
     """
@@ -131,7 +135,7 @@ def declared(path):
     # Scope events by offset, so each declaration can be placed in its stack.
     events = [(m.start(), m.group(1), m.group(2)) for m in NS.finditer(text)]
 
-    names = set()
+    names = {}
     for m in KW.finditer(text):
         im = IDENT.match(text, m.end())
         if not im:
@@ -144,12 +148,31 @@ def declared(path):
         for off, kind, arg in events:
             if off > m.start():
                 break
-            if kind in ('namespace', 'section'):
+            if kind == 'namespace':
                 stack.append(arg)
+            elif kind == 'section':
+                # A NAMED SECTION DOES NOT QUALIFY DECLARATION NAMES. `section
+                # Foo` opens a scope for `variable`/`open` and gives `end Foo` a
+                # label to match; it does not make `bar` into `Foo.bar`. This
+                # line pushed `arg`, so a template reading
+                #     section Foo
+                #     axiom bar : Nat
+                #     end Foo
+                # was reported as declaring `Foo.bar`. Round-8 review (GPT-5.6,
+                # register key `section-prefix-bug`) showed the consequence:
+                # `--names` handed Phase 2d only `Foo.bar`, Lean happily
+                # resolved an unrelated `Foo.bar` definition elsewhere in the
+                # corpus and returned PROVEN, and the axiom the extraction
+                # ACTUALLY depends on was never queried at all. The scanner had
+                # been rewritten that same week specifically to be fail-closed.
+                # None appends a frame so `end` still balances, and the
+                # comprehension below drops it from the prefix.
+                stack.append(None)
             elif stack:
                 stack.pop()
         prefix = [p for p in stack if p]
-        names.add('.'.join(prefix + [im.group(1)]) if prefix else im.group(1))
+        full = '.'.join(prefix + [im.group(1)]) if prefix else im.group(1)
+        names.setdefault(full, m.group(1))
     return names
 
 
@@ -163,14 +186,15 @@ def main(root):
     for f in sorted(glob.glob(os.path.join(gen, '*', '*.lean'))):
         if f in models or f.endswith('_Template.lean'):
             continue
-        corpus |= declared(f)
+        corpus.update(declared(f))
 
     rows, unresolved = [], []
     for t in templates:
         model = t.replace('_Template', '')
         rel = os.path.relpath(t, gen).replace('_Template.lean', '')
-        tnames = declared(t)
+        tnames = set(declared(t))
-        mnames = declared(model) if os.path.exists(model) else set()
+        mkinds = declared(model) if os.path.exists(model) else {}
+        mnames = set(mkinds)
         for n in sorted(tnames):
             if n in mnames:
                 rows.append(f'{rel}|{n}|MODEL')
@@ -179,8 +203,29 @@ def main(root):
             else:
                 rows.append(f'{rel}|{n}|UNRESOLVED')
                 unresolved.append(f'{rel}|{n}')
+        # AN EXTRA AXIOM IS A FAILURE, and this is the second half of the
+        # round-8 section-prefix finding. EXTRA was the one verdict that could
+        # not fail: the model declares something the template did not ask for.
+        # When the scanner mis-derived the template's name (`Foo.bar` instead of
+        # `bar`), the axiom the extraction ACTUALLY depends on did not vanish —
+        # it landed here, as a harmless-looking EXTRA row, while the invented
+        # name was certified PROVEN. A silent bucket next to a fail-closed
+        # parser is just a slower way of dropping things.
+        #
+        # There is no benign reading of an extra AXIOM either way. The model
+        # exists to answer the template; an assumption nothing asks for is
+        # either a parse the scanner got wrong or an unaudited assumption
+        # nobody is governing. Both must stop the button. Extra non-axiom
+        # declarations stay reportable-but-tolerated: helper definitions in a
+        # model file are ordinary.
         for n in sorted(mnames - tnames):
-            rows.append(f'{rel}|{n}|EXTRA')
+            kind = mkinds.get(n, '')
+            if kind == 'axiom':
+                rows.append(f'{rel}|{n}|EXTRA-AXIOM')
+                unresolved.append(f'{rel}|{n} (axiom in the model that no '
+                                  f'template external asks for)')
+            else:
+                rows.append(f'{rel}|{n}|EXTRA')
     print('\n'.join(rows))
     print(f'CORRESPONDENCE-COUNT|{len(rows)}')
     return 1 if unresolved else 0