c2 on the finite torus: |c2[K_L] − c2[φ]| ≤ 1.001e-10 for every L ≥ 10 (2.1e-111 for L ≥ 24), every frame, d = 1, 2, 3; Lemma E: no r¹ term for every stationary kernel (scientific effect NONE)

.github/workflows/c2-torus-transfer.yml

@@ -0,0 +1,87 @@
+name: c2 torus transfer (replay)
+
+'on':
+  pull_request:
+    paths:
+      - 'frontiers/c2_torus_transfer_20261001/**'
+      - '.github/workflows/c2-torus-transfer.yml'
+      - 'frontiers/c2_exact_20261001/**'
+      - 'coefficients/side24_v1/PROOF.md'
+      - 'frontiers/candidate_third_order_20261001/PROOF.md'
+      - 'frontiers/cusp_coefficient_certified_20261001/RESULTS.json'
+      - 'frontiers/elder_third_order_20261001/PROOF.md'
+      - 'frontiers/cusp_torus_transfer_20261001/PROOF.md'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  transfer-replay:
+    runs-on: ubuntu-latest
+    timeout-minutes: 45
+    strategy:
+      fail-fast: false
+      matrix:
+        flags: ['-B -S', '-B -O -S']
+    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 byte-identical copies
+        env:
+          PYTHONDONTWRITEBYTECODE: '1'
+        run: |
+          set -euo pipefail
+          python -B -S - <<'PY'
+          import hashlib, json, pathlib
+          root = pathlib.Path('frontiers/c2_torus_transfer_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))
+          def ident(data):
+              return len(data), hashlib.sha256(data).hexdigest(), hashlib.sha1(b'blob %d\0' % len(data) + data).hexdigest()
+          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'])
+              if ident(path.read_bytes()) != (entry['bytes'], entry['sha256'], entry['git_blob']):
+                  raise ValueError('source identity mismatch: ' + entry['path'])
+          pins = json.loads((root / 'SOURCE_MAP.json').read_text())
+          for entry in pins['sources']:
+              if not entry['current_required']:
+                  continue
+              if ident(pathlib.Path(entry['path']).read_bytes()) != (entry['bytes'], entry['sha256'], entry['git_blob']):
+                  raise ValueError('consumed source identity mismatch on this tree: ' + entry['path'])
+          for copy, orig in pins['copies'].items():
+              if (root / copy).read_bytes() != pathlib.Path(orig).read_bytes():
+                  raise ValueError('copy differs from its pinned original: ' + copy)
+          print('manifest, pins and copies verified')
+          PY
+      - name: Ball-arithmetic replay against RESULTS.json, mutants, controls
+        env:
+          PYTHONDONTWRITEBYTECODE: '1'
+          FLAGS: ${{ matrix.flags }}
+        run: |
+          set -euo pipefail
+          cd frontiers/c2_torus_transfer_20261001
+          pids=()
+          for m in no-image no-theta drop-ratio eta-half fp-const; do
+            ( set +e; python $FLAGS transfer.py --mutant "$m" > "/tmp/mutant_$m.log" 2>&1; echo $? > "/tmp/mutant_$m.rc" ) &
+            pids+=($!)
+          done
+          python $FLAGS transfer.py --check
+          python $FLAGS controls.py
+          wait "${pids[@]}"
+          for m in no-image no-theta drop-ratio eta-half fp-const; do
+            rc=$(cat "/tmp/mutant_$m.rc")
+            if [ "$rc" -ne 1 ]; then echo "mutant $m not rejected (rc=$rc)"; cat "/tmp/mutant_$m.log"; exit 1; fi
+            echo "mutant $m rejected"
+          done
+          cd "$GITHUB_WORKSPACE"
+          git diff --exit-code
+          test -z "$(git status --porcelain)"

frontiers/c2_torus_transfer_20261001/README.md

@@ -0,0 +1,19 @@
+# `c2` on the finite torus: transfer for every `L >= 10` (Math-#218 (0.1), against `frontiers/c2_exact_20261001`)
+
+`CL-C2-TORUS-TRANSFER-20261001-v1`. Author-side; scientific effect NONE. See `NOTE.md`.
+
+For the normalized periodic Gaussian kernel `K_L` (SIDE24 is `L = 24`), every orthonormal frame and every real `L >= L0`,
+`|c2[K_L] - c2[phi]| <= eps_d(L0)`:
+
+| `d` | `L >= 10` | `L >= 24` |
+|---|---|---|
+| `1` | `1.41035e-13` | `4.09547e-114` |
+| `2` | `2.09404e-12` | `5.20139e-113` |
+| `3` | `1.00039e-10` | `2.09418e-111` |
+
+Lemma E: for every smooth stationary kernel the fixed-cone surrogate has an even finite-order expansion in `r` at fixed
+`b - k r^3/2`, so it has no `r^1` term and its `r^3` coefficient is `-(k/2) d_b A_0`. For real-analytic kernels, which
+include `phi` and `K_L`, it is exactly `A~(r^2, b - k r^3/2, k)`.
+
+Replay: `python3 -B -S transfer.py --check` (exact rational ball arithmetic, standard library only; about two minutes).
+Controls: `python3 -B -S controls.py`.

frontiers/c2_torus_transfer_20261001/RESULTS.json

@@ -0,0 +1,226 @@
+{
+ "bounds": {
+  "d1_L10": {
+   "Delta0": "4.44080e-15",
+   "Delta_int": "1.68784e-15",
+   "L0": 10,
+   "a_min": "7.50000e-1",
+   "d": 1,
+   "dDelta_w": "6.55138e-14",
+   "e_kappa": "8.05025e-17",
+   "eps": "1.41035e-13",
+   "eta_max": "9.40524e-16",
+   "kappa_up": "8.77514e-2",
+   "max_jet_order": 20,
+   "max_radius_H": "3.13354e-13",
+   "n_monomials_H": 9,
+   "rel": "6.13074e-13",
+   "t_diag": "1.00000e+0",
+   "theta1": "3.85750e-22"
+  },
+  "d1_L12": {
+   "Delta0": "4.54251e-24",
+   "Delta_int": "1.71392e-24",
+   "L0": 12,
+   "a_min": "7.50000e-1",
+   "d": 1,
+   "dDelta_w": "6.62356e-23",
+   "e_kappa": "6.27881e-26",
+   "eps": "1.42699e-22",
+   "eta_max": "7.39127e-25",
+   "kappa_up": "8.77514e-2",
+   "max_jet_order": 20,
+   "max_radius_H": "3.04757e-22",
+   "n_monomials_H": 9,
+   "rel": "6.20309e-22",
+   "t_diag": "1.00000e+0",
+   "theta1": "1.07604e-31"
+  },
+  "d1_L16": {
+   "Delta0": "1.82806e-47",
+   "Delta_int": "6.83459e-48",
+   "L0": 16,
+   "a_min": "7.50000e-1",
+   "d": 1,
+   "dDelta_w": "2.62661e-46",
+   "e_kappa": "1.57599e-49",
+   "eps": "5.66439e-46",
+   "eta_max": "1.87017e-48",
+   "kappa_up": "8.77514e-2",
+   "max_jet_order": 20,
+   "max_radius_H": "1.14804e-45",
+   "n_monomials_H": 9,
+   "rel": "2.46230e-45",
+   "t_diag": "1.00000e+0",
+   "theta1": "5.14442e-56"
+  },
+  "d1_L24": {
+   "Delta0": "1.33798e-115",
+   "Delta_int": "4.96197e-116",
+   "L0": 24,
+   "a_min": "7.50000e-1",
+   "d": 1,
+   "dDelta_w": "1.89740e-114",
+   "e_kappa": "5.56180e-118",
+   "eps": "4.09547e-114",
+   "eta_max": "6.64022e-117",
+   "kappa_up": "8.77514e-2",
+   "max_jet_order": 20,
+   "max_radius_H": "7.90074e-114",
+   "n_monomials_H": 9,
+   "rel": "1.78030e-113",
+   "t_diag": "1.00000e+0",
+   "theta1": "1.67579e-125"
+  },
+  "d2_L10": {
+   "Delta0": "1.13884e-14",
+   "Delta_int": "8.94035e-15",
+   "L0": 10,
+   "a_min": "1.25000e-1",
+   "d": 2,
+   "dDelta_w": "3.18908e-13",
+   "e_kappa": "1.81351e-16",
+   "eps": "2.09404e-12",
+   "eta_max": "1.88105e-15",
+   "kappa_up": "3.93992e-3",
+   "max_jet_order": 20,
+   "max_radius_H": "6.32063e-13",
+   "n_monomials_H": 50,
+   "rel": "9.45285e-12",
+   "t_diag": "5.00000e-1",
+   "theta1": "7.71500e-22"
+  },
+  "d2_L12": {
+   "Delta0": "1.12587e-23",
+   "Delta_int": "8.66171e-24",
+   "L0": 12,
+   "a_min": "1.25000e-1",
+   "d": 2,
+   "dDelta_w": "3.07836e-22",
+   "e_kappa": "1.37156e-25",
+   "eps": "2.02307e-21",
+   "eta_max": "1.47826e-24",
+   "kappa_up": "3.93992e-3",
+   "max_jet_order": 20,
+   "max_radius_H": "6.12547e-22",
+   "n_monomials_H": 50,
+   "rel": "9.13248e-21",
+   "t_diag": "5.00000e-1",
+   "theta1": "2.15208e-31"
+  },
+  "d2_L16": {
+   "Delta0": "4.34211e-47",
+   "Delta_int": "3.25673e-47",
+   "L0": 16,
+   "a_min": "1.25000e-1",
+   "d": 2,
+   "dDelta_w": "1.15187e-45",
+   "e_kappa": "3.32413e-49",
+   "eps": "7.57841e-45",
+   "eta_max": "3.74033e-48",
+   "kappa_up": "3.93992e-3",
+   "max_jet_order": 20,
+   "max_radius_H": "2.30056e-45",
+   "n_monomials_H": 50,
+   "rel": "3.42103e-44",
+   "t_diag": "5.00000e-1",
+   "theta1": "1.02889e-55"
+  },
+  "d2_L24": {
+   "Delta0": "3.06010e-115",
+   "Delta_int": "2.24309e-115",
+   "L0": 24,
+   "a_min": "1.25000e-1",
+   "d": 2,
+   "dDelta_w": "7.89749e-114",
+   "e_kappa": "1.14043e-117",
+   "eps": "5.20139e-113",
+   "eta_max": "1.32805e-116",
+   "kappa_up": "3.93992e-3",
+   "max_jet_order": 20,
+   "max_radius_H": "1.58088e-113",
+   "n_monomials_H": 50,
+   "rel": "2.34800e-112",
+   "t_diag": "5.00000e-1",
+   "theta1": "3.35158e-125"
+  },
+  "d3_L10": {
+   "Delta0": "1.78082e-13",
+   "Delta_int": "2.24526e-13",
+   "L0": 10,
+   "a_min": "9.18862e-2",
+   "d": 3,
+   "dDelta_w": "7.70788e-12",
+   "e_kappa": "3.14352e-16",
+   "eps": "1.00039e-10",
+   "eta_max": "2.82157e-15",
+   "kappa_up": "7.05724e-5",
+   "max_jet_order": 20,
+   "max_radius_H": "1.90639e-12",
+   "n_monomials_H": 1006,
+   "rel": "6.20455e-10",
+   "t_diag": "3.67545e-1",
+   "theta1": "1.15725e-21"
+  },
+  "d3_L12": {
+   "Delta0": "1.71757e-22",
+   "Delta_int": "2.07220e-22",
+   "L0": 12,
+   "a_min": "9.18862e-2",
+   "d": 3,
+   "dDelta_w": "7.08488e-21",
+   "e_kappa": "2.29890e-25",
+   "eps": "9.20576e-20",
+   "eta_max": "2.21738e-24",
+   "kappa_up": "7.05724e-5",
+   "max_jet_order": 20,
+   "max_radius_H": "1.84351e-21",
+   "n_monomials_H": 1006,
+   "rel": "5.70957e-19",
+   "t_diag": "3.67545e-1",
+   "theta1": "3.22812e-31"
+  },
+  "d3_L16": {
+   "Delta0": "6.41933e-46",
+   "Delta_int": "7.32175e-46",
+   "L0": 16,
+   "a_min": "9.18862e-2",
+   "d": 3,
+   "dDelta_w": "2.48771e-44",
+   "e_kappa": "5.34636e-49",
+   "eps": "3.23748e-43",
+   "eta_max": "5.61049e-48",
+   "kappa_up": "7.05724e-5",
+   "max_jet_order": 20,
+   "max_radius_H": "6.91048e-45",
+   "n_monomials_H": 1006,
+   "rel": "2.00794e-42",
+   "t_diag": "3.67545e-1",
+   "theta1": "1.54333e-55"
+  },
+  "d3_L24": {
+   "Delta0": "4.39620e-114",
+   "Delta_int": "4.76136e-114",
+   "L0": 24,
+   "a_min": "9.18862e-2",
+   "d": 3,
+   "dDelta_w": "1.60666e-112",
+   "e_kappa": "1.76946e-117",
+   "eps": "2.09418e-111",
+   "eta_max": "1.99207e-116",
+   "kappa_up": "7.05724e-5",
+   "max_jet_order": 20,
+   "max_radius_H": "4.74408e-113",
+   "n_monomials_H": 1006,
+   "rel": "1.29885e-110",
+   "t_diag": "3.67545e-1",
+   "theta1": "5.02737e-125"
+  }
+ },
+ "object": "CL-C2-TORUS-TRANSFER-20261001-v1",
+ "reference_checks": {
+  "1": true,
+  "2": true,
+  "3": true
+ }
+}

frontiers/c2_torus_transfer_20261001/SOURCE_FILES.json

@@ -0,0 +1,59 @@
+{
+ "object": "CL-C2-TORUS-TRANSFER-20261001-v1",
+ "files": [
+  {
+   "path": "NOTE.md",
+   "bytes": 21673,
+   "sha256": "6d15dccc847d9457ff5d77d6286179fa87505b5d0570fea7996366bb2ba79da3",
+   "git_blob": "5ce5bad2a1073b9b425fc4c5e6eed5527d39eaf2"
+  },
+  {
+   "path": "README.md",
+   "bytes": 998,
+   "sha256": "63a3302d33c7ef56aac23044f743e7e613db9aaf2e448d72ef05e84d5135f46c",
+   "git_blob": "68eec096fc928692852e75117a5bd3ce51551e5e"
+  },
+  {
+   "path": "RESULTS.json",
+   "bytes": 5334,
+   "sha256": "dcfcbb15c16327277e1108f4a159ed6553bb1d0de54a931af28b29957c10398a",
+   "git_blob": "919a567b295b46ccc35b37cea1349c5d6f79fd6a"
+  },
+  {
+   "path": "SOURCE_MAP.json",
+   "bytes": 7513,
+   "sha256": "56fae2a5c2aad309bec346cde15e8df968ea75d48b1ae194f3d1e4d0dc35629a",
+   "git_blob": "5365bc2d8e89f6dd0cb473caa3334f910b70a6bb"
+  },
+  {
+   "path": "ball.py",
+   "bytes": 4495,
+   "sha256": "11cd2788b8fc4ea0b967c04711aeb384d5366f9c88e65975405c7ef48a7ea8ed",
+   "git_blob": "72205f8adf9aa741246d9ca5d7b2d4ba0f014e7a"
+  },
+  {
+   "path": "controls.py",
+   "bytes": 8318,
+   "sha256": "9cce7ab25657f7ccb91d7bc23a0712a5fd85534a942519b0bd7f92a3725ea629",
+   "git_blob": "863023c256c209715d46bd4e0a05395a3c1f3ba8"
+  },
+  {
+   "path": "exact.py",
+   "bytes": 16099,
+   "sha256": "974099926619e7c85aea9fbccb5285e54862909cd079895f16e785583c884d6c",
+   "git_blob": "b06819802d1b90813cd172dc372aaac771ff6720"
+  },
+  {
+   "path": "pseries.py",
+   "bytes": 6782,
+   "sha256": "d1faa96ca7e7df0051fbfe78318a17d0c78d608eb9f1ed2e3a3b83a6598a9994",
+   "git_blob": "fac3c562b33e626d477aefecf2b1e680b0ae5f98"
+  },
+  {
+   "path": "transfer.py",
+   "bytes": 25337,
+   "sha256": "59ebbdeda9111c8390c84986c2fefa7725c5916627d4409777a5abc66a6e9f33",
+   "git_blob": "05dc3fba1d1f1399519569f113911ed043a67fba"
+  }
+ ]
+}