C8: [LP] Theorem B with explicit constants in d = 2, 3 — |A_r/A_0^ref − 1| ≤ a r² + ε certified, two-sided lifetime densities, C_{B,K}(1/4096) = 402.53 (plane), 1205.71 (d = 3) for (1.2), (12.1), (12.3) (scientific effect NONE)

.github/workflows/c8-lifetime-difference-constant.yml

@@ -0,0 +1,75 @@
+name: C8 lifetime difference constant and second-order ledger (certified replay)
+
+'on':
+  pull_request:
+    paths:
+      - 'frontiers/c8_lifetime_difference_constant_20261001/**'
+      - '.github/workflows/c8-lifetime-difference-constant.yml'
+      - 'imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md'
+      - 'imports/lifetime_parent_20260925/MARKED_CYLINDER_CAP_PROOF.md'
+      - 'imports/lifetime_parent_20260925/ERRATUM_CONGRUENCE.md'
+      - 'reviews/d1_section9_borel_repair_20260925/REPAIR.md'
+      - 'reviews/d1_chain_reconciliation_20260928/RECONCILIATION.md'
+      - 'frontiers/c8_cap_failure_coefficient_dims_20261001/RESULTS.json'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  certified-replay:
+    runs-on: ubuntu-latest
+    timeout-minutes: 240
+    steps:
+      - uses: actions/checkout@11d5960a326750d5838078e36cf38b85af677262
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@a26af69be951a213d495a4c3e4e4022e16d87065
+        with:
+          python-version: '3.11.16'
+      - name: Verify manifest, main-resident pins and engine copies; replay the certificate in both interpreter modes; reject mutants
+        env:
+          PYTHONDONTWRITEBYTECODE: '1'
+        run: |
+          set -euo pipefail
+          python -B -S - <<'PY'
+          import hashlib, json, os, pathlib, subprocess, sys
+          root = pathlib.Path('frontiers/c8_lifetime_difference_constant_20261001').resolve()
+          manifest = json.loads((root / 'SOURCE_FILES.json').read_text())['files']
+          present = sorted(p.name for p in root.iterdir())
+          if present != sorted([e['path'] for e in manifest] + ['SOURCE_FILES.json']):
+              raise ValueError('packet tree differs from manifest: ' + repr(present))
+          for entry in manifest:
+              path = root / entry['path']
+              if pathlib.PurePosixPath(entry['path']).name != entry['path'] or path.is_symlink():
+                  raise ValueError('flat regular source required: ' + entry['path'])
+              data = path.read_bytes()
+              if len(data) != entry['bytes'] or hashlib.sha256(data).hexdigest() != entry['sha256']:
+                  raise ValueError('source identity mismatch: ' + entry['path'])
+          def blob(data):
+              return hashlib.sha1(b'blob %d\0' % len(data) + data).hexdigest()
+          pins = json.loads((root / 'SOURCE_MAP.json').read_text())
+          for entry in pins['sources']:
+              if entry.get('current_required'):
+                  data = pathlib.Path(entry['path']).read_bytes()
+              elif entry.get('packet_copy'):
+                  data = (root / entry['packet_copy']).read_bytes()
+              else:
+                  continue
+              if len(data) != entry['bytes'] or hashlib.sha256(data).hexdigest() != entry['sha256'] or blob(data) != entry['git_blob']:
+                  raise ValueError('pinned source identity mismatch: ' + entry['path'])
+          script = str(root / 'theorem_b.py')
+          procs = str(max(2, os.cpu_count() or 2))
+          # every cap band in one mode, the sampled replay in the other
+          for flags, mode in ((['-B', '-S'], '--check-full'), (['-B', '-O', '-S'], '--check')):
+              out = subprocess.run([sys.executable, *flags, script, mode, '--procs', procs], cwd=root, capture_output=True, timeout=10800)
+              if out.returncode != 0:
+                  raise RuntimeError(mode + ' failed under ' + ' '.join(flags) + ': ' + out.stdout.decode()[-400:] + out.stderr.decode()[-400:])
+              print(flags, mode, out.stdout.decode().strip()[-600:])
+          for m in ('no-om-term', 'no-bad-set', 'no-det', 'no-torus', 'cap-half'):
+              rc = subprocess.run([sys.executable, '-B', '-S', script, '--check', '--procs', procs, '--mutant', m], cwd=root, capture_output=True, timeout=3600).returncode
+              if rc != 1:
+                  raise RuntimeError('mutant ' + m + ' not rejected')
+          print(json.dumps({'scientific_effect': 'NONE', 'cap_bands_replayed': 274, 'mutants_rejected': 5}))
+          PY
+          git diff --exit-code

frontiers/c8_lifetime_difference_constant_20261001/README.md

@@ -0,0 +1,42 @@
+# Theorem B of [LP] with explicit constants (C8; `d = 2, 3`): the radial ledger to second order, two-sided lifetime densities, and `C_{B,K}`
+
+**Object:** `CL-C8-LIFETIME-DIFFERENCE-CONSTANT-20261001-v1`. **Author lane:** Anthropic / Claude. **Kind:** author-side theorem
+with explicit constants, certified by exact rational interval arithmetic (standard library only). **Scientific effect:** NONE: no
+register, catalog, GRAPH or STATUS change, and catalog entry C8 stays OPEN.
+
+**Setting.** The compact-window lifetime densities of [LP] Theorem B on the band `b in [0, 1]`, `k in [1/2, 2]`, uniformly over
+frames and torus sides `L >= 10` (and the reference kernel), through the radial ledger `A_r = 12 pi_r(R; v_r) Z_r / r^2` of [LP]
+(10.2) and the pushforward (11.2), which are consumed as statements.
+
+**Results** (`NOTE.md` Theorem L and Corollaries L1, L2):
+- **The ledger to second order.** For `0 < r <= R`, `|A_r / A_0^ref - 1| <= a(R) r^2 + eps` with the closed-form contact
+  integrand `A_0^ref`; `eps` is a radius-independent remainder (torus, truncation and rounding), so this is not a rate for
+  `A_r -> A_0` on the torus. In the plane `a_up(1/4096) = 13.823`, `a_dn = 3.638`, `eps <= 4.0 x 10^-10`; in `d = 3`
+  `a_up(1/4096) = 25.67`, `a_dn = 25.52`, `eps <= 1.8 x 10^-8`. [LP] assigns no rate to `A_r -> A_0`.
+- **Densities to second order.** For `ell < min(r_pop, R)^3 / 2`,
+  `|ell^(1/3) nu_cand(ell) / c^ref_{B,K} - 1| <= 6.29 ell^(2/3) + 5 x 10^-11` in the plane and
+  `<= 23.2 ell^(2/3) + 3 x 10^-9` in `d = 3` (`R = 1/4096` constants). The same holds for `nu_eld` up to
+  `C_{B,K} ell / c^ref_{B,K}`. So both densities are `c^ref_{B,K} ell^(-1/3) + O(ell^(1/3))` up to an additive
+  `eps'_d ell^(-1/3)` that does not vanish as `ell -> 0` (`eps'_d <= 1.2 x 10^-13` in the plane, `2.5 x 10^-12` in
+  `d = 3`). For the torus constant `c_{B,K}` this gives `|c_{B,K} - c^ref_{B,K}| <= eps'_d`, not a vanishing-remainder
+  expansion.
+- **The difference constant.** `0 <= nu_cand - nu_eld <= C_{B,K}(r_*) ell^(2/3)` for `ell < min(r_pop, r_*)^3 / 2`.
+  - `C_{B,K}(1/4096) = 402.53` in the plane and `1205.71` in `d = 3`.
+  - At `r_* = 1/512` the values are `428.02` and `2488.07` (rounded up).
+  - With these, (12.1) holds with `(3/5) C_{B,K}` and (12.3) with `C_{B,K} / (q + 5/3)`.
+  - [LP] gives (1.2) with no value.
+- `c^ref_{B,K}` is certified in both dimensions; the enclosures contain the values of Math-#197 and Math-#205.
+
+**Files.**
+- `NOTE.md`: statement; the ledger and what is consumed; Lemma 1 (for the Gaussian kernel the transverse Hessian at `M` is
+  exactly contact-distributed at every `r`); the Taylor-model laws; the pin-density ratio; the exact expansion of `P1 P2` and
+  the first-order cancellation; the thin typed shell; reference integrals; the cap sweep; controls; non-claims.
+- `theorem_b.py`: the certificate. `--check --procs N` replays the Taylor models, the rate sweep, the reference integrals, a
+  sample of cap bands and the tables exactly against `RESULTS.json`; `--check-full` replays every cap band;
+  `--mutant {no-om-term, no-bad-set, no-det, no-torus, cap-half}` must fail; `--controls` prints floating controls.
+- `engine_e2.py`, `engine_e3.py`: byte-identical copies of the certificates of Math-#206 (`0cb8ad3`) and Math-#212
+  (`c4b8ec3`), used as libraries (band laws, contact moments, box bounds); pinned in `SOURCE_MAP.json`.
+- `RESULTS.json`, `SOURCE_MAP.json`, `SOURCE_FILES.json`.
+- Workflow `.github/workflows/c8-lifetime-difference-constant.yml`.
+
+Same GitHub account as every other lane; zero organizational-independence credit. The author will not merge.