Verify YM C308 entry-reference center decay firewall

.github/workflows/ym-c308-entry-reference-center-decay.yml

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+name: YM C308 entry reference center decay
+
+on:
+  push:
+    branches:
+      - verification/ym-c308-entry-reference-center-decay-20260820
+    paths:
+      - verification/ym-c308-entry-reference-center-decay/*.lean
+      - .github/workflows/ym-c308-entry-reference-center-decay.yml
+  pull_request:
+    paths:
+      - verification/ym-c308-entry-reference-center-decay/*.lean
+      - .github/workflows/ym-c308-entry-reference-center-decay.yml
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  verify:
+    runs-on: ubuntu-22.04
+    timeout-minutes: 20
+    steps:
+      - uses: actions/checkout@v4
+      - name: Verify flattened Lean theorem source
+        shell: bash
+        run: |
+          set -euo pipefail
+          SRC=verification/ym-c308-entry-reference-center-decay/FaizalShabirEntryReferenceCenterFirewall.lean
+          if grep -nE '\b(sorry|admit|sorryAx|axiom|opaque|unsafe|native_decide|Lean\.ofReduceBool)\b' "$SRC"; then exit 1; fi
+          SRC="$SRC" python3 - <<'PY'
+          import hashlib, json, os, pathlib, urllib.request
+          path = pathlib.Path(os.environ['SRC'])
+          source = path.read_text()
+          payload = json.dumps({'content': source,'environment':'lean-4.30.0','ignore_imports':True,'mathlib_options':False,'timeout_seconds':900}).encode()
+          req = urllib.request.Request('https://axle.axiommath.ai/api/v1/check',data=payload,headers={'Content-Type':'application/json'},method='POST')
+          with urllib.request.urlopen(req, timeout=960) as response:
+            result = json.load(response)
+          receipt={'source_path':str(path),'source_sha256':hashlib.sha256(source.encode()).hexdigest(),'axle_environment':'lean-4.30.0','axle_result':result}
+          pathlib.Path('/tmp/ym-c308-axle-receipt.json').write_text(json.dumps(receipt,indent=2))
+          print(json.dumps(receipt,indent=2))
+          lean=result.get('lean_messages',{}); tool=result.get('tool_messages',{})
+          bad=(not result.get('okay') or bool(result.get('failed_declarations',[])) or bool(lean.get('errors',[])) or bool(lean.get('warnings',[])) or bool(tool.get('errors',[])) or bool(tool.get('warnings',[])) or 'sorryAx' in json.dumps(result))
+          if bad: raise SystemExit(1)
+          PY
+      - uses: actions/upload-artifact@v4
+        if: always()
+        with:
+          name: ym-c308-entry-reference-center-decay-axle-receipt
+          if-no-files-found: warn
+          retention-days: 30
+          path: /tmp/ym-c308-axle-receipt.json

verification/ym-c308-entry-reference-center-decay/FaizalShabirEntryReferenceCenterFirewall.lean

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+import Mathlib
+
+namespace Millennium.YangMills.FaizalShabirEntryReferenceCenterFirewall
+
+theorem identity_center_recurrence_constant
+    (g : ℕ → ℝ)
+    (hg0 : g 0 = 1)
+    (hrec : ∀ n, g (n + 1) = g n) :
+    ∀ n, g n = 1 := by
+  intro n
+  induction n with
+  | zero => exact hg0
+  | succ n ih =>
+      rw [hrec n, ih]
+
+theorem identity_center_not_quarter_at_two
+    (g : ℕ → ℝ)
+    (hg0 : g 0 = 1)
+    (hrec : ∀ n, g (n + 1) = g n) :
+    ¬ (|g 2| ≤ (1 : ℝ) / 4) := by
+  have hconst := identity_center_recurrence_constant g hg0 hrec 2
+  rw [hconst, abs_one]
+  norm_num
+
+theorem nonzero_multiplier_product_does_not_imply_center_decay :
+    (1 : ℝ) ≠ 0 ∧ ¬ ((1 : ℝ) ≤ (1 : ℝ) / 4) := by
+  constructor <;> norm_num
+
+#print axioms identity_center_recurrence_constant
+#print axioms identity_center_not_quarter_at_two
+#print axioms nonzero_multiplier_product_does_not_imply_center_decay
+
+end Millennium.YangMills.FaizalShabirEntryReferenceCenterFirewall