Theorem CU: cusp crossover and the second-order terms — ν_eld = cℓ^{−1/3} + c₁ℓ^{1/4} + o(ℓ^{1/4}), c₁ < 0; ν_cand, ρ_rej to the same order (author-side candidate; depends on #191, #198)

.github/workflows/cusp-second-order.yml

@@ -0,0 +1,99 @@
+name: Cusp second-order exact controls
+
+'on':
+  pull_request:
+    paths:
+      - 'frontiers/cusp_second_order_20261001/**'
+      - '.github/workflows/cusp-second-order.yml'
+      # bound merged sources (consumed in SOURCES.json) and the pinned unmerged dependencies (#191, #198; verified by blob)
+      - 'frontiers/remainder_vanishing_20260930/PROOF.md'
+      - 'frontiers/remainder_rate_20260930/PROOF.md'
+      - 'frontiers/three_fronts_20260924/LIFETIME_REMAINDER.md'
+      - 'frontiers/c7_total_bounded_20260929/PROOF.md'
+      - 'imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md'
+      - 'imports/lifetime_parent_20260925/ERRATUM_CONGRUENCE.md'
+      - 'reviews/d1_section9_borel_repair_20260925/REPAIR.md'
+      - 'reviews/d1_chain_reconciliation_20260928/RECONCILIATION.md'
+      - 'frontiers/fixed_r_inverse_lifetime_20260930/PROOF.md'
+      - 'frontiers/c7_zero_gap_limit_20260929/PROOF.md'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  exact-controls:
+    runs-on: ubuntu-latest
+    timeout-minutes: 10
+    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.request
+          root = pathlib.Path('frontiers/cusp_second_order_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'])
+          # each consumed unmerged dependency (#191, #198) is verified by its pinned blob: from the tree if the dependency
+          # has landed (then it must be byte-identical to the pinned version, else this packet needs rebinding),
+          # otherwise fetched by blob id through the repository API; absence or drift fails the job
+          for entry in manifest.get('consumed_unmerged', []):
+              tree_path = pathlib.Path(entry['path'])
+              if tree_path.exists():
+                  data = tree_path.read_bytes()
+                  where = 'tree'
+              else:
+                  req = urllib.request.Request(
+                      'https://api.github.com/repos/' + os.environ['GH_REPOSITORY'] + '/git/blobs/' + entry['git_blob'],
+                      headers={'Authorization': 'Bearer ' + os.environ['GH_TOKEN'], 'Accept': 'application/vnd.github+json'})
+                  with urllib.request.urlopen(req, timeout=60) as resp:
+                      blob = json.load(resp)
+                  if blob.get('encoding') != 'base64':
+                      raise ValueError('unexpected blob encoding for ' + entry['path'])
+                  data = base64.b64decode(blob['content'])
+                  where = 'blob api'
+              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('consumed unmerged dependency differs from the pinned blob (rebind required): ' + entry['path'] + ' via ' + where)
+              print(json.dumps({'consumed_unmerged_verified': entry['path'], 'git_blob': entry['git_blob'], 'via': where}))
+          script = str(root / 'cusp_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=600).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=600).returncode
+                  if rc != 1:
+                      raise RuntimeError('mutant ' + m + ' not rejected')
+              rc = subprocess.run([sys.executable, *flags, script, '--mutant', 'M9'], capture_output=True, timeout=600).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

frontiers/cusp_second_order_20261001/EXPLORE.json

@@ -0,0 +1,138 @@
+{
+ "X1": {
+  "agree_with_window_1_3": 32,
+  "disagreements": [],
+  "r": 0.01,
+  "random_trials": 40,
+  "targeted_r_0.003": [
+   {
+    "elder": true,
+    "kappa": 0.799,
+    "phi_target": 0.3,
+    "typed": true
+   },
+   {
+    "elder": true,
+    "kappa": 0.61,
+    "phi_target": 0.3,
+    "typed": true
+   },
+   {
+    "elder": true,
+    "kappa": 1.483,
+    "phi_target": 0.32,
+    "typed": true
+   },
+   {
+    "elder": true,
+    "kappa": 2.774,
+    "phi_target": 0.32,
+    "typed": true
+   },
+   {
+    "elder": false,
+    "kappa": 0.419,
+    "phi_target": 0.345,
+    "typed": true
+   },
+   {
+    "elder": false,
+    "kappa": 1.618,
+    "phi_target": 0.345,
+    "typed": true
+   },
+   {
+    "elder": false,
+    "kappa": 1.494,
+    "phi_target": 0.36,
+    "typed": true
+   },
+   {
+    "elder": false,
+    "kappa": 2.471,
+    "phi_target": 0.36,
+    "typed": true
+   },
+   {
+    "elder": true,
+    "kappa": 1.776,
+    "phi_target": -0.3,
+    "typed": true
+   },
+   {
+    "elder": true,
+    "kappa": 0.885,
+    "phi_target": -0.3,
+    "typed": true
+   },
+   {
+    "elder": true,
+    "kappa": 1.088,
+    "phi_target": -0.32,
+    "typed": true
+   },
+   {
+    "elder": true,
+    "kappa": 0.802,
+    "phi_target": -0.32,
+    "typed": true
+   },
+   {
+    "elder": false,
+    "kappa": 0.932,
+    "phi_target": -0.345,
+    "typed": true
+   },
+   {
+    "elder": false,
+    "kappa": 0.484,
+    "phi_target": -0.345,
+    "typed": true
+   },
+   {
+    "elder": false,
+    "kappa": 0.482,
+    "phi_target": -0.36,
+    "typed": true
+   },
+   {
+    "elder": false,
+    "kappa": 1.798,
+    "phi_target": -0.36,
+    "typed": true
+   }
+  ],
+  "typed": 32
+ },
+ "X2": {
+  "d2": {
+   "I_cand": -0.1772744,
+   "J": 0.5518754382,
+   "J_coarse": 0.5518754382,
+   "c": 0.073406919306,
+   "c1": -0.26939883,
+   "c1_over_c": -3.669938,
+   "method": "composite Gauss-Legendre, a = -w^4: 24x12 by 56x12 nodes (coarse: 12x12 by 28x12)",
+   "rejected_coefficient": 0.09212443
+  },
+  "d3": {
+   "I_cand": -0.13940406,
+   "J": 1.363390706,
+   "J_coarse": 1.363390722,
+   "c": 0.041775931841,
+   "c1": -0.21184835,
+   "c1_over_c": -5.071062,
+   "mc_check": {
+    "J": 1.36198,
+    "J_se": 0.00089,
+    "c1": -0.21163,
+    "c1_se": 0.00014,
+    "method": "Monte Carlo on the cone, 8000000 samples, seed 1001, 10 batches"
+   },
+   "method": "cone quadrature: Gauss-Legendre 64 x 64 in (rho, u), trapezoid 9 in theta, Gauss-Laguerre 64 in s (coarse: Laguerre 32)",
+   "rejected_coefficient": 0.0724443
+  }
+ },
+ "not_a_control": true,
+ "object": "CL-CUSP-SECOND-ORDER-20261001-v1.1 exploration"
+}