Rare-intensity field-norm tightness and conditional closure of the planar cluster law

.github/workflows/local-cluster-tightness.yml

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+name: Local cluster tightness and conditional closure controls
+
+'on':
+  pull_request:
+    paths:
+      - 'frontiers/local_cluster_tightness_20260929/**'
+      - '.github/workflows/local-cluster-tightness.yml'
+      - 'frontiers/c6_palm_route_20260929/PROOF.md'
+      - 'frontiers/d5_dimension_lift_20260929/PROOF.md'
+      - 'frontiers/remote_window_20260924/PROOF.md'
+      - 'frontiers/remote_collision_20260928/PROOF.md'
+      - 'frontiers/window_multiplicity_laws_20260928/LOCAL_MULTIPLICITY.md'
+      - 'frontiers/c6_rare_cluster_laws_20260929/PROOF.md'
+  push:
+    branches: [main]
+    paths:
+      - 'frontiers/local_cluster_tightness_20260929/**'
+      - '.github/workflows/local-cluster-tightness.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  exact-tightness:
+    runs-on: ubuntu-latest
+    timeout-minutes: 10
+    steps:
+      - uses: actions/checkout@11d5960a326750d5838078e36cf38b85af677262
+        with:
+          fetch-depth: 0
+          persist-credentials: false
+      - uses: actions/setup-python@a26af69be951a213d495a4c3e4e4022e16d87065
+        with:
+          python-version: '3.11.16'
+      - name: Both modes, semantic controls and exact current/historical sources
+        run: |
+          set -euo pipefail
+          python -B -S frontiers/local_cluster_tightness_20260929/verify.py --repo "${GITHUB_WORKSPACE}" --output "${RUNNER_TEMP}/tightness-${GITHUB_RUN_ID}-${GITHUB_RUN_ATTEMPT}"
+          git diff --exit-code

frontiers/local_cluster_tightness_20260929/README.md

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+# Local cluster tightness: source-bound companion to #158
+
+Author-side mathematics, nonauthor review required. Scientific effect NONE.
+
+The direct field-norm lemma proves a rare-intensity bound by inserting K4^p into
+the LANDED Palm regional argument. It does not consume #157's still-new count
+exponential theorem. The deterministic transverse argument is the SAME mechanism
+already written by #158's author; it is credited and byte-bound, not claimed as
+an independent discovery. The new work combines it with strict typed-boundary
+control, a mixed local/remote estimate, and a carefully ordered exhaustion.
+
+Sections6-7 state a CONDITIONAL closure of the planar global count law using
+#158's exact, still-author-side compact-sector theorem. The proposed coefficients
+are nu(1)=alpha1+mu_remote and nu(2)=alpha2, with higher values zero in the scaled
+limit. This is NOT acceptance of #158, finite-r support {1,2}, a spatial Poisson
+limit, or a scientific-register transition. The remote coefficient includes k.
+
+Run all finite controls in both Python modes:
+
+    python -B -S verify.py --output /path/to/new-output
+    python -B -O -S verify.py --output /path/to/other-new-output
+
+Each invocation checks exact packet membership, sizes/SHA256/Git blobs, executes
+12 mathematical and6 synthetic custody tests in EACH Python mode, and rejects8
+semantic variants on the intended assertions. With a complete Git checkout,
+add --repo /path/to/repository to verify all8 actual historical source objects
+and every required current source. C and D are pinned draft-branch sources,
+not required to exist on default main; their exact historical bytes are checked.
+The hosted workflow performs that full-repository check. A packet-only local
+replay explicitly records upstream_verified_count=null, not fictitious custody.
+
+The code verifies finite identities, conservative constants and source guards.
+It does not verify Gaussian analytic estimates, compactness or Kac--Rice.

frontiers/local_cluster_tightness_20260929/RECONNAISSANCE.md

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+# Focused reconnaissance — 29 September 2026
+
+Consensus.search was actually called with Gaussian weighted Kac--Rice, field
+norms, rare events and transverse reduction. It returned the exhausted monthly
+30-search quota with October1 reset. No Consensus result is fabricated.
+
+Direct primary source: Armentano, Azais and Leon, arXiv:2304.07424v3,
+https://arxiv.org/abs/2304.07424v3 and its HTML version. Abstract/version record
+and the main-results introduction were inspected. The tool's exact-heading
+searches for 'Theorem 7.1' and 'Remark 8' did not match the HTML numbering, so no
+fresh full verification of those named statements is claimed. The actual formula
+consumed is the landed project P Lemma5.1 with its canonical kernel and two-measure
+proof. Gass--Stecconi arXiv:2305.17586 and publisher record were read at abstract
+scope only; their ordinary moment-finiteness theorem is not a substitute for the
+rare-intensity estimate N1.
+
+The companion is a targeted response to #158 author comment5900564419. The
+subsequent comment5900634812 identified its already-written deterministic addendum
+D atbfcc67dc, which was fully read and is credited. The alternate constants in
+Section3 are a self-contained corroboration, not a separate discovery or review.
+The existing #153 replica argument is also credited and pinned. This is not an
+exhaustive novelty or priority audit, and no external theorem is silently imported.

frontiers/local_cluster_tightness_20260929/RESULTS.json

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+{
+  "tests_per_mode": 18,
+  "mathematical_tests": 12,
+  "custody_fixture_tests": 6,
+  "semantic_mutants_per_mode": 8,
+  "paired_outputs_identical": 9,
+  "scientific_effect": "NONE",
+  "analytic_acceptance": false
+}

frontiers/local_cluster_tightness_20260929/SOURCE_FILES.json

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+{
+  "schema": 1,
+  "scientific_effect": "NONE",
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+      "git_blob": "c983be24eaa43dab08a95ab19477bf42f78cc7c1"
+    },
+    {
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+      "bytes": 4206,
+      "sha256": "977f1e2bfcb3fc727be4d6d3556275aa07052f3c160136ef5cd33fcc2a5b0c8e",
+      "git_blob": "71a65ccc047c322e62f1498150f48c24ff5565cd"
+    }
+  ]
+}

frontiers/local_cluster_tightness_20260929/SOURCE_MAP.json

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+  "scientific_effect": "NONE",
+  "sources": [
+    {
+      "id": "P",
+      "path": "frontiers/c6_palm_route_20260929/PROOF.md",
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+      "role": "Landed marked Kac-Rice, conditional norm moments and regional bounds.",
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+      "current_required": true,
+      "role": "Planar ten-jet rank and endpoint Taylor identities.",
+      "bytes": 13100
+    },
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+      "role": "Fixed-exclusion factorial O(r^5), including near-coincident witnesses.",
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+    },
+    {
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+      "path": "frontiers/planar_cubic_cluster_20260929/PROOF.md",
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+}

frontiers/local_cluster_tightness_20260929/controls.py

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+"""Exact finite identities for local rare-intensity tightness. No Gaussian checker."""
+from fractions import Fraction as F
+from math import ceil, prod
+
+MUTANT=None
+
+def positive(*xs):
+    if any(F(x)<=0 for x in xs): raise ValueError('positive parameters required')
+
+def reduced_third(A,U,V,W,q):
+    A,U,V,W,q=map(F,(A,U,V,W,q))
+    return A-(2 if MUTANT=='wrong-schur-derivative' else 3)*q*U+3*q*q*V-q**3*W
+
+def hermite_constant(r,k):
+    positive(r,k)
+    return (6 if MUTANT=='half-hermite' else 12)*F(k)
+
+def soft_threshold(R,r,K,k):
+    positive(R,r,K,k);R,r,K,k=map(F,(R,r,K,k))
+    if R<1 or K<k: raise ValueError('R>=1 and K>=k required')
+    return 64*(R+1)**2*r*K**(1 if MUTANT=='linear-norm-threshold' else 2)/k
+
+def model_extra_x(k,lam,a):
+    positive(k,lam)
+    if not a: raise ValueError('nonzero mixed coefficient required')
+    return -12*F(k)*F(lam)/F(a)**2
+
+def norm_tail(r,C,p,M):
+    positive(r,C,M)
+    if type(p) is not int or p<1: raise ValueError('positive integer moment required')
+    return F(C)*F(r)**(0 if MUTANT=='lose-rare-scale' else 3)/F(M)**p
+
+def mixed_power():
+    return 4+1+3-(4 if MUTANT=='normalizer-twice' else 2)
+
+def boundary_volume(J,eps):
+    positive(J,eps)
+    return 2*F(eps)*(2*F(J))**3
+
+def global_rates(a1,a2,remote):
+    positive(a1,a2,remote)
+    return {1:F(a1)+(0 if MUTANT=='omit-remote-singletons' else F(remote)),2:F(a2)}
+
+def factorial_coefficient(rates,p):
+    if type(p) is not int or p<1: raise ValueError('positive integer order required')
+    return sum((mass*prod(n-j for j in range(p)) for n,mass in rates.items() if n>=p),F(0))
+
+def decomposition_error(middle,mixed):
+    if min(F(middle),F(mixed))<0: raise ValueError('nonnegative errors required')
+    return 3*((0 if MUTANT=='ignore-middle-region' else F(middle))+F(mixed))
+
+def nonempty_double(rates):
+    return F(rates[2])/sum(rates.values())
+
+def palm_excess(rates):
+    denom=sum(rates.values()) if MUTANT=='palm-equals-nonempty' else sum(n*p for n,p in rates.items())
+    return sum(n*(n-1)*p for n,p in rates.items())/denom
+
+def absorption_order(loss,target,a):
+    positive(a)
+    return max(0,ceil((F(loss)+F(target))/F(a)))

frontiers/local_cluster_tightness_20260929/custody.py

@@ -0,0 +1,48 @@
+"""Fail-closed current/historical source byte checks; no analytic acceptance."""
+import hashlib,json,pathlib,re,subprocess
+
+def require(ok,message):
+    if not ok:raise ValueError(message)
+
+def identity(b):
+    return {'bytes':len(b),'sha256':hashlib.sha256(b).hexdigest(),'git_blob':hashlib.sha1(f'blob {len(b)}\0'.encode()+b).hexdigest()}
+
+def loads(s):
+    def pairs(items):
+        d={}
+        for k,v in items:
+            require(k not in d,'duplicate JSON key');d[k]=v
+        return d
+    return json.loads(s,object_pairs_hook=pairs,parse_constant=lambda _:(_ for _ in ()).throw(ValueError('nonfinite JSON')))
+
+def safe_path(s):
+    p=pathlib.PurePosixPath(s)
+    require(not p.is_absolute() and str(p)==s and '..' not in p.parts and p.parts,'unsafe path')
+    return p
+
+def unique_paths(entries):
+    paths=[e['path'] for e in entries]
+    require(len(paths)==len(set(paths)),'duplicate source path')
+    for p in paths:safe_path(p)
+
+def read_checked(root,e):
+    root=pathlib.Path(root);rel=safe_path(e['path'])
+    require(not root.is_symlink(),'root symlink forbidden')
+    for i in range(1,len(rel.parts)+1):
+        require(not root.joinpath(*rel.parts[:i]).is_symlink(),'source symlink forbidden')
+    path=root.joinpath(*rel.parts);require(path.is_file(),'missing regular file')
+    b=path.read_bytes();actual=identity(b)
+    require(all(actual[k]==e[k] for k in actual if k in e),'source identity mismatch')
+    require('sha256' in e and 'git_blob' in e,'incomplete identity')
+    return b
+
+def upstream(repo,entries):
+    unique_paths(entries);repo=pathlib.Path(repo)
+    for e in entries:
+        require(re.fullmatch('[0-9a-f]{40}',e['commit']) is not None,'invalid pinned commit')
+        obj=e['commit']+':'+e['path']
+        b=subprocess.check_output(['git','-C',str(repo),'show',obj],stderr=subprocess.PIPE,timeout=20)
+        actual=identity(b)
+        require(all(actual[k]==e[k] for k in actual if k in e),'historical source differs: '+e['id'])
+        if e.get('current_required',True):read_checked(repo,e)
+    return len(entries)