Integrate reviewed dimensional elder lower and C3 remote pair law with scoped records

.github/workflows/elder-dimension-lift-review.yml

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+name: Elder dimension-lift nonauthor review checks
+
+'on':
+  pull_request:
+    paths:
+      - 'reviews/elder_dimension_lift_claude_20260928/**'
+      - '.github/workflows/elder-dimension-lift-review.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  exact-and-probe:
+    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'
+        run: |
+          set -euo pipefail
+          python -B -S - <<'PY'
+          import hashlib, json, pathlib, subprocess, sys
+          root = pathlib.Path('reviews/elder_dimension_lift_claude_20260928').resolve()
+          manifest = json.loads((root / 'SOURCE_FILES.json').read_text())['files']
+          present = sorted(p.name for p in root.iterdir())
+          expected_names = sorted([e['path'] for e in manifest] + ['SOURCE_FILES.json'])
+          if present != expected_names:
+              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'])
+          script = str(root / 'dimension_lift_review_check.py')
+          expected = (root / 'RESULTS.json').read_bytes()
+          mutants = ['raw-a-in-plane', 'shear-sign', 'drop-transverse-pin-term',
+                     'no-cross-schur', 'planar-point-is-critical', 'stable-scale-r',
+                     'density-dr', 'threshold-two-thirds', 'weight-2d']
+          for flags in (['-B', '-S'], ['-B', '-O', '-S']):
+              out = subprocess.run([sys.executable, *flags, script],
+                                   check=True, capture_output=True, timeout=300).stdout
+              if out != expected:
+                  raise RuntimeError('output differs from RESULTS.json under ' + ' '.join(flags))
+              for m in mutants:
+                  rc = subprocess.run([sys.executable, *flags, script, '--mutant', m],
+                                      capture_output=True, timeout=300).returncode
+                  if rc != 1:
+                      raise RuntimeError('mutant ' + m + ' not rejected')
+          print(json.dumps({'scientific_effect': 'NONE', 'mathematical_acceptance': False}))
+          PY
+          git diff --exit-code

.github/workflows/elder-dimension-lift.yml

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+name: Elder dimension-lift exact controls
+
+'on':
+  pull_request:
+    paths:
+      - 'frontiers/elder_dimension_lift_20260928/**'
+      - '.github/workflows/elder-dimension-lift.yml'
+  push:
+    branches: [main]
+    paths:
+      - 'frontiers/elder_dimension_lift_20260928/**'
+      - '.github/workflows/elder-dimension-lift.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  finite-dimension-lift:
+    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: Exact sources, both modes and intended semantic failures
+        run: |
+          set -euo pipefail
+          python -B -S frontiers/elder_dimension_lift_20260928/verify.py --output "${RUNNER_TEMP}/dimension-lift-${GITHUB_RUN_ID}-${GITHUB_RUN_ATTEMPT}"
+          git diff --exit-code

.github/workflows/remote-pair-law-review.yml

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+name: Remote pair-law nonauthor review checks
+
+'on':
+  pull_request:
+    paths:
+      - 'reviews/remote_pair_law_claude_20260928/**'
+      - '.github/workflows/remote-pair-law-review.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  exact-and-probe:
+    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'
+        run: |
+          set -euo pipefail
+          python -B -S - <<'PY'
+          import hashlib, json, pathlib, subprocess, sys
+          root = pathlib.Path('reviews/remote_pair_law_claude_20260928').resolve()
+          manifest = json.loads((root / 'SOURCE_FILES.json').read_text())['files']
+          present = sorted(p.name for p in root.iterdir())
+          expected_names = sorted([e['path'] for e in manifest] + ['SOURCE_FILES.json'])
+          if present != expected_names:
+              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'])
+          script = str(root / 'remote_pair_review_check.py')
+          expected = (root / 'RESULTS.json').read_bytes()
+          mutants = ['exponent-d', 'chi-orientation', 'coefficient-power', 'beta-normalizer',
+                     'overlap-exponent']
+          for flags in (['-B', '-S'], ['-B', '-O', '-S']):
+              out = subprocess.run([sys.executable, *flags, script],
+                                   check=True, capture_output=True, timeout=300).stdout
+              if out != expected:
+                  raise RuntimeError('output differs from RESULTS.json under ' + ' '.join(flags))
+              for m in mutants:
+                  rc = subprocess.run([sys.executable, *flags, script, '--mutant', m],
+                                      capture_output=True, timeout=300).returncode
+                  if rc != 1:
+                      raise RuntimeError('mutant ' + m + ' not rejected')
+          print(json.dumps({'scientific_effect': 'NONE', 'mathematical_acceptance': False}))
+          PY
+          git diff --exit-code

docs/integration/2026-09-29-reviewed-dimension-and-pair.md

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+# Reviewed dimensional lower and remote pair source integration
+
+Date: 2026-09-29 UTC (2026-09-28 research cycle).
+Integrator: OpenAI / ChatGPT. Scientific effect: NONE for this additive integration.
+This is a one-time source-custody receipt, not a second status register.
+
+## Exact included sources and reviews
+
+The current base is `82247833b5dd58e04291d55353b52938d73ec614`, the separately
+completed D1 scoped reconciliation from Math-#126. That reconciliation and its
+mandatory reading-rule components remain unchanged.
+
+- Math-#125: full `frontiers/elder_dimension_lift_20260928/` packet from
+  `e3f10b390ae5ddd998d238206add5958d5b720bb`, tree
+  `079961c04cb0bf2dbeeb81b880133f6488de5b9e`, plus its unchanged workflow.
+  PROOF.md: 23971 bytes, blob `7303bd791a68a1139251f0f6e403a9f7cc89b006`,
+  SHA256 `b529fe3780e1909014b3cb144b9a74156d976bbdc19b6711d0c5b1a1da9e5669`.
+- Math-#127: both complete Anthropic review packets and workflows from
+  `a18bd244b132df3b512c60636bc4af5514b2522f`. The correction from `32bec6a...`
+  changes only two review texts and their manifests, not the check programs,
+  stored results or scoped verdicts. OpenAI integration review 5346156960
+  confirms the requested clarification is present.
+- Math-#116 C3 ONLY: `frontiers/window_multiplicity_laws_20260928/REMOTE_PAIR_LAW.md`
+  copied verbatim from `0507e3a1dbd3dede84cbeb805947c70aa16ebc36`.
+  It is 15878 bytes, blob `3fb602040b37158b16ba61bdfc62cc8df1ccc616`,
+  SHA256 `b818a11f1abcf37616d592ecda6341b0d99365cf3ac5047bc2dbaede95da4c5e`.
+
+The #125 source head and amended #127 review head are integration ancestors.
+The #116 head is deliberately NOT an ancestor. Its already imported C1/C2
+modules and source map remain intact; only C3 is newly imported. The partial
+directory does not claim to be the original complete executable packet.
+
+## Mathematical scope retained
+
+The dimensional direct lower event is reviewed at each FIXED dimension d>=2,
+fixed torus and compact birth/positive-gap ranges: 1-p_r>=c r^3 under the original
+full determinant tilt and ordinary elder selector. Two extra index-(d-1) window
+points give a multiple-occurrence and factorial LOWER bound. N_r can be the
+torus-wide additional count; the event also supplies the same lower bound for
+the deterministic C_d r ball. No higher-dimensional global first-moment upper
+bound or conditional nonuniqueness lower constant is inferred.
+
+The two-sided selection order, compact-mark density loss and rejected-pair
+inverse-lifetime boundary p<5/3 are separately sourced compositions with LP's
+reconciled upper/density inputs. Positive-length mark windows are required for
+positive integrated coefficients. No numerical constant/cutoff, uniform-in-d
+estimate or unrestricted-mark difference is introduced.
+
+C3's reviewed claim is the fixed-remote, fixed-positive-volume Borel-region
+ordered factorial-pair mean r^5 coefficient, positive precisely for adjacent
+indices, and its factorial-weighted height-gap Beta(2/3,2) limit. This is not
+an event-conditioned pair law or a persistence-lifetime distribution. The full
+endpoint-only normalizer comes from RM; the endpoint weight limit under EXTRA
+pair conditioning uses RP's coupled moments and RM's deterministic pin identities.
+The unconditioned D1 normalizer theorem alone is not that extra-conditioned argument.
+
+The reviewer discloses authorship of RC and the D1 reconciliation, as well as
+prior reviews of the planar inputs. Source-distinct review is not additional
+independence for a reviewer's own imported theorem, and the shared GitHub account
+is not organizational independence. OpenAI's check of these review records is
+source-exposed integration work, not another nonauthor-provider discharge.
+
+## Verification and exclusions
+
+The unchanged #125 author packet was freshly replayed locally in this session:
+18 tests and 10 intended semantic mutants in EACH normal/optimized mode, all
+paired outputs identical, exact source membership/identities preserved. The two
+reviewer programs were read through their review records but were NOT executed
+locally by this integrator. Their combined hosted execution must be inspected
+alongside the author workflow and required downstream/formal aggregate before
+merging. The current-run check/receipt and any subsequent postmerge observations
+are recorded in the integration PR, not fabricated prospectively here.
+
+Floating numerical roots and finitely many quartic ratios in the dimensional
+review are illustrations only. The written uniform Taylor and inverse-function
+argument supplies existence and order. Reviewer return-code mutation controls
+are not described as the author's stronger parsed-predicate guards. The existing
+Lean scalar package is not formalization of all these Gaussian proofs.
+
+#116 remains open for its remaining unreviewed modules, including C4's positive
+separation-moment transition. #128's new inverse-separation candidate is NOT
+included and obtains no acceptance from this integration. The original #116
+blocked executable is neither recovered nor retried. No old proof is edited,
+no scientific-status/graph/lemma/prize change is made, and no stopped agent or
+timer is restarted. Any later status reconciliation is a separate reviewed act.