Verify YM C326 stable/marginal power threshold

.github/workflows/ym-c326-stable-marginal-power-threshold.yml

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+name: YM C326 stable/marginal power threshold
+
+on:
+  push:
+    branches:
+      - verification/ym-c326-stable-marginal-power-threshold-20260820
+    paths:
+      - verification/ym-c326-stable-marginal-power-threshold/*.lean
+      - .github/workflows/ym-c326-stable-marginal-power-threshold.yml
+  pull_request:
+    paths:
+      - verification/ym-c326-stable-marginal-power-threshold/*.lean
+      - .github/workflows/ym-c326-stable-marginal-power-threshold.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-c326-stable-marginal-power-threshold/FaizalShabirStableMarginalPowerThreshold.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-c326-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-c326-stable-marginal-power-threshold-axle-receipt
+          if-no-files-found: warn
+          retention-days: 30
+          path: /tmp/ym-c326-axle-receipt.json

verification/ym-c326-stable-marginal-power-threshold/FaizalShabirStableMarginalPowerThreshold.lean

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+import Mathlib
+
+/-!
+# Stable/marginal inverse-coupling power threshold
+
+Finite exponent bookkeeping for C326.
+
+If a stable coordinate has size `K = O(g^p)`, the two stable contributions
+identified by the source audit scale as `g^(p-2)` and `g^(2p-3)` in the
+inverse-coupling increment. Along `g ~ k^(-1/2)`, absolute p-series
+summability requires `(p-2)/2 > 1` and `(2p-3)/2 > 1` respectively.
+
+This file proves only that exponent algebra. It does not formalize an RG
+trajectory, asymptotic freedom, summability of the actual Yang--Mills terms,
+AF/IR identification, a mass gap, or the Clay theorem.
+-/
+
+namespace Millennium.YangMills.FaizalShabirStableMarginalPowerThreshold
+
+theorem first_channel_threshold (p : ℝ) :
+    (1 : ℝ) < (p - 2) / 2 ↔ 4 < p := by
+  constructor <;> intro h <;> linarith
+
+theorem second_channel_threshold (p : ℝ) :
+    (1 : ℝ) < (2 * p - 3) / 2 ↔ (5 : ℝ) / 2 < p := by
+  constructor <;> intro h <;> linarith
+
+theorem p_four_first_channel_is_harmonic :
+    (((4 : ℝ) - 2) / 2) = 1 := by
+  norm_num
+
+theorem p_five_first_channel_exponent :
+    (((5 : ℝ) - 2) / 2) = (3 : ℝ) / 2 := by
+  norm_num
+
+theorem p_five_second_channel_exponent :
+    ((2 * (5 : ℝ) - 3) / 2) = (7 : ℝ) / 2 := by
+  norm_num
+
+#print axioms first_channel_threshold
+#print axioms second_channel_threshold
+#print axioms p_four_first_channel_is_harmonic
+#print axioms p_five_first_channel_exponent
+#print axioms p_five_second_channel_exponent
+
+end Millennium.YangMills.FaizalShabirStableMarginalPowerThreshold