Third-order coefficient: ν_eld = cℓ^{−1/3} + c₁ℓ^{1/4} + c₂ℓ^{1/3} + …, c₂ by the fold-scale finite part (d = 1, 2, 3; formal in d ≥ 2; Monte Carlo evidence; scientific effect NONE)

.github/workflows/third-order-coefficient.yml

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+name: Third-order coefficient controls
+
+'on':
+  pull_request:
+    paths:
+      - 'frontiers/third_order_coefficient_20261001/**'
+      - '.github/workflows/third-order-coefficient.yml'
+      # merged sources cited in SOURCES.json (cited_only, v1.4.1): a change to any of them re-runs the identity check
+      - 'frontiers/three_fronts_20260924/LIFETIME_REMAINDER.md'
+      - 'reviews/side24_v1_coefficient_claude_20260929/RESULTS.json'
+      - 'coefficients/side24_v1/ENCLOSURE.json'
+      - 'frontiers/cusp_second_order_20261001/PROOF.md'
+      - 'frontiers/remainder_vanishing_20260930/PROOF.md'
+      - 'frontiers/candidate_third_order_20261001/PROOF.md'
+      - 'frontiers/elder_third_order_20261001/PROOF.md'
+      - 'frontiers/third_order_rate_20261001/PROOF.md'
+      - 'frontiers/c2_exact_20261001/NOTE.md'
+      - 'frontiers/c2_finite_jet_transfer_20261001/PROOF.md'
+      - 'frontiers/cusp_coefficient_certified_20261001/NOTE.md'
+      - 'frontiers/far_elder_rate_20260930/PROOF.md'
+      - 'frontiers/elder_cusp_parity_20261002/PROOF.md'
+      - 'frontiers/d1_third_order_law_20261001/PROOF.md'
+      - 'frontiers/candidate_parity_rate_20261001/PROOF.md'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  exact-controls:
+    runs-on: ubuntu-latest
+    timeout-minutes: 30
+    steps:
+      - uses: actions/checkout@11d5960a326750d5838078e36cf38b85af677262
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@a26af69be951a213d495a4c3e4e4022e16d87065
+        with:
+          python-version: '3.11.16'
+      - name: Verify sources, replay both modes, reject mutants
+        env:
+          PYTHONDONTWRITEBYTECODE: '1'
+          GH_TOKEN: ${{ github.token }}
+          GH_REPOSITORY: ${{ github.repository }}
+        run: |
+          set -euo pipefail
+          python -B -S - <<'PY'
+          import base64, hashlib, json, os, pathlib, subprocess, sys, urllib.parse, urllib.request
+          root = pathlib.Path('frontiers/third_order_coefficient_20261001').resolve()
+          manifest = json.loads((root / 'SOURCES.json').read_text())
+          present = sorted(p.name for p in root.iterdir())
+          expected_names = sorted([e['path'] for e in manifest['files']] + ['SOURCES.json'])
+          if present != expected_names:
+              raise ValueError('packet tree differs from manifest: ' + repr(present))
+          for entry in manifest['files']:
+              path = root / entry['path']
+              if path.is_symlink():
+                  raise ValueError('symlink: ' + entry['path'])
+              data = path.read_bytes()
+              if len(data) != entry['bytes'] or hashlib.sha256(data).hexdigest() != entry['sha256']:
+                  raise ValueError('packet file identity mismatch: ' + entry['path'])
+          for entry in manifest['consumed'] + manifest['cited_only']:
+              data = pathlib.Path(entry['path']).read_bytes()
+              framed = b'blob ' + str(len(data)).encode() + b'\0' + data
+              if len(data) != entry['bytes'] or hashlib.sha256(data).hexdigest() != entry['sha256'] or hashlib.sha1(framed).hexdigest() != entry['git_blob']:
+                  raise ValueError('merged source drifted: ' + entry['path'])
+          if manifest.get('consumed_unmerged'):
+              raise ValueError('this packet declares no unmerged dependency')
+          # cited unmerged sources (comparison only) are bound to their recorded commit, path and blob through the
+          # repository API (v1.2, Codex P2 on v1.1): the recorded head must resolve, the recorded path in that head's tree
+          # must be a file with the recorded blob id and size, and the blob's bytes must have the recorded sha256
+          api = 'https://api.github.com/repos/' + os.environ['GH_REPOSITORY']
+          def get_json(url):
+              req = urllib.request.Request(url, headers={'Authorization': 'Bearer ' + os.environ['GH_TOKEN'],
+                                                         'Accept': 'application/vnd.github+json'})
+              with urllib.request.urlopen(req, timeout=60) as resp:
+                  return json.load(resp)
+          for entry in manifest.get('cited_unmerged', []):
+              commit = get_json(api + '/commits/' + entry['head'])
+              if commit.get('sha') != entry['head']:
+                  raise ValueError('recorded head does not resolve: ' + entry['head'])
+              node = get_json(api + '/contents/' + urllib.parse.quote(entry['path']) + '?ref=' + entry['head'])
+              if (node.get('type') != 'file' or node.get('path') != entry['path'] or node.get('sha') != entry['git_blob']
+                      or node.get('size') != entry['bytes']):
+                  raise ValueError('recorded head/path does not map to the recorded blob: ' + entry['path'])
+              blob = get_json(api + '/git/blobs/' + entry['git_blob'])
+              if blob.get('encoding') != 'base64':
+                  raise ValueError('unexpected blob encoding for ' + entry['path'])
+              data = base64.b64decode(blob['content'])
+              framed = b'blob ' + str(len(data)).encode() + b'\0' + data
+              if len(data) != entry['bytes'] or hashlib.sha256(data).hexdigest() != entry['sha256'] or hashlib.sha1(framed).hexdigest() != entry['git_blob']:
+                  raise ValueError('cited unmerged source differs from its pinned blob: ' + entry['path'])
+              print(json.dumps({'cited_unmerged_bound': entry['path'], 'git_blob': entry['git_blob'], 'head': entry['head']}))
+          script = str(root / 'c2_check.py')
+          expected = (root / 'RESULTS.json').read_bytes()
+          for flags in (['-B', '-S'], ['-B', '-O', '-S']):
+              out = subprocess.run([sys.executable, *flags, script], check=True, capture_output=True, timeout=900).stdout
+              if out != expected:
+                  raise RuntimeError('output differs from RESULTS.json under ' + ' '.join(flags))
+              for m in manifest['mutants']:
+                  rc = subprocess.run([sys.executable, *flags, script, '--mutant', m], capture_output=True, timeout=900).returncode
+                  if rc != 1:
+                      raise RuntimeError('mutant ' + m + ' not rejected')
+              rc = subprocess.run([sys.executable, *flags, script, '--mutant', 'M9'], capture_output=True, timeout=900).returncode
+              if rc != 2:
+                  raise RuntimeError('unknown mutant label not rejected with exit 2')
+          print(json.dumps({'scientific_effect': 'NONE', 'mathematical_acceptance': False}))
+          PY
+          git diff --exit-code