Verify YM C333 first-cumulant color cancellation

.github/workflows/ym-c333-first-cumulant-color-cancellation.yml

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+name: YM C333 first-cumulant color cancellation
+
+on:
+  push:
+    branches:
+      - verification/ym-c333-first-cumulant-color-cancellation-20260820
+    paths:
+      - verification/ym-c333-first-cumulant-color-cancellation/*.lean
+      - .github/workflows/ym-c333-first-cumulant-color-cancellation.yml
+  pull_request:
+    paths:
+      - verification/ym-c333-first-cumulant-color-cancellation/*.lean
+      - .github/workflows/ym-c333-first-cumulant-color-cancellation.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-c333-first-cumulant-color-cancellation/FaizalShabirFirstCumulantColorCancellation.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-c333-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-c333-first-cumulant-color-cancellation-axle-receipt
+          if-no-files-found: warn
+          retention-days: 30
+          path: /tmp/ym-c333-axle-receipt.json

verification/ym-c333-first-cumulant-color-cancellation/FaizalShabirFirstCumulantColorCancellation.lean

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+import Mathlib
+
+namespace Millennium.YangMills.FaizalShabirFirstCumulantColorCancellation
+
+theorem odd_two_point_average_zero
+    (f x : ℝ)
+    (hodd : f (-x) = -f x) :
+    (f x + f (-x)) / 2 = 0 := by
+  rw [hodd]
+  ring
+
+theorem antisymmetric_symmetric_pair_cancels
+    (fij fji cij cji : ℝ)
+    (hf : fji = -fij)
+    (hc : cji = cij) :
+    fij * cij + fji * cji = 0 := by
+  rw [hf, hc]
+  ring
+
+theorem antisymmetric_diagonal_zero
+    (fii : ℝ)
+    (h : fii = -fii) :
+    fii = 0 := by
+  linarith
+
+#print axioms odd_two_point_average_zero
+#print axioms antisymmetric_symmetric_pair_cancels
+#print axioms antisymmetric_diagonal_zero
+
+end Millennium.YangMills.FaizalShabirFirstCumulantColorCancellation