Microscopic radial rates: all-even tail expansion, sharp Pareto error and signed-mark separation

.github/workflows/radial-rate.yml

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+name: Microscopic radial-rate checks
+
+'on':
+  pull_request:
+    paths:
+      - 'frontiers/radial_rate_20260930/**'
+      - '.github/workflows/radial-rate.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  exact-and-source:
+    runs-on: ubuntu-latest
+    timeout-minutes: 10
+    steps:
+      - uses: actions/checkout@11d5960a326750d5838078e36cf38b85af677262
+        with:
+          persist-credentials: false
+          fetch-depth: 0
+      - uses: actions/setup-python@a26af69be951a213d495a4c3e4e4022e16d87065
+        with:
+          python-version: '3.11.16'
+      - name: Fetch exact public source objects
+        run: |
+          set -euo pipefail
+          git fetch --no-tags origin 80059a97cd8eb32d1a17a0ad9cb22cb2a0d7b337
+          git fetch --no-tags origin 382c0f9ff2281f43651ddbdf2e9b36dd52e2c6bf
+          git fetch --no-tags origin 7a1cb09a9d58d179393e6d29146252f714b9c9bf
+      - name: Verify sources, packet and both Python modes
+        env:
+          PYTHONDONTWRITEBYTECODE: '1'
+          GIT_NO_REPLACE_OBJECTS: '1'
+        run: |
+          set -euo pipefail
+          python -B -S frontiers/radial_rate_20260930/verify.py
+          git diff --exit-code

frontiers/radial_rate_20260930/MANIFEST.json

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+{
+  "schema": 1,
+  "scientific_effect": "NONE",
+  "review_status": "NONAUTHOR_REVIEW_OPEN",
+  "files": [
+    {
+      "path": "PLAN.md",
+      "bytes": 1772,
+      "sha256": "3a436b2f58a3b79bcb5471474d94fff7c07f5f4dce838525fed117cbb5d446db",
+      "git_blob": "db61274a4ce7f2e9e6c4b75303a285230f44d5db"
+    },
+    {
+      "path": "PROOF.md",
+      "bytes": 15755,
+      "sha256": "a3693664900e23e1e763d88a0b5609936a6f31d844cbe6f18c7d0379b94ba710",
+      "git_blob": "65f24b1f9a7b80522a2ee059f5f6877c9f970f0d"
+    },
+    {
+      "path": "README.md",
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+      "git_blob": "cc0e2f5a45c76aa60a3782002321f0c47d0f3b17"
+    },
+    {
+      "path": "RECONNAISSANCE.md",
+      "bytes": 2002,
+      "sha256": "54118b87d9a0dbe78ed9f2162ad413d1a9bfc1c1122c53855274b300751ede2b",
+      "git_blob": "3eb935b8d3fa2c10e8220c71c5243488beb25e31"
+    },
+    {
+      "path": "RESULTS.json",
+      "bytes": 438,
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+      "git_blob": "c7494046e449f30a6346572b2760cca6c1c62afb"
+    },
+    {
+      "path": "SOURCES.json",
+      "bytes": 1396,
+      "sha256": "22b3064a278faff1d915dfb658e9d7e41ec5c4ee69f31e944d47a699a82f8a07",
+      "git_blob": "37f3dc7b5583bf2f4f0a8d1bb1fd5bd39ff12838"
+    },
+    {
+      "path": "VALIDATION.md",
+      "bytes": 2898,
+      "sha256": "b14b2fb0576c7c7fd1a03baf3d7f479d901f186d0ef0a49dac5156805908409d",
+      "git_blob": "5a4a11b112723aaf9a67c1aeaafa3a216e5f17e8"
+    },
+    {
+      "path": "rate.py",
+      "bytes": 6344,
+      "sha256": "e96be67c1703780dcd48113fa55809d98b87f0e498da132b162c9640d300577e",
+      "git_blob": "d213a2762e10a07f3290f9ae1b4dd9f8f73e5667"
+    },
+    {
+      "path": "test_rate.py",
+      "bytes": 7286,
+      "sha256": "f2a096b91de1978dbaa6c1301ac1013d454cadcf96aa705fb66df3c43f53324f",
+      "git_blob": "4074549e593ad0f02f6931c6df211e25a02d84ea"
+    },
+    {
+      "path": "test_verify.py",
+      "bytes": 5792,
+      "sha256": "1e8f2790b5861b520463ab1d44b87c29dd43ba46b652c46992889ecd001bd4c7",
+      "git_blob": "258288f8efa9039782432daf6dde77e2b594ef39"
+    },
+    {
+      "path": "verify.py",
+      "bytes": 5169,
+      "sha256": "7f7006a1f3ba74964a00023dd418624612980e19f8e40a3506245ae43966119c",
+      "git_blob": "d5789cbe7b94b6243b55a62491ecd19bdeb9cbe0"
+    }
+  ]
+}

frontiers/radial_rate_20260930/PLAN.md

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+# Inverse-radius expansion: execution plan
+
+Goal: derive quantitative radius-tail and mark-law results from the exact R11
+integral of the already-formed limiting microscopic POINT intensity. The original
+Gaussian-field limit r->0 is taken first. No whole-cluster maximum or finite-r
+rate is to be inferred.
+
+Design: reciprocal radius z=1/Z makes the physical cutoff an interval with
+explicit endpoints. Map it to [-1,1], prove a smooth even integrated function of
+1/t using Gaussian derivative domination, and compute its first two coefficients.
+Deduce radial and fixed latent-mark total-variation rates, keeping the sign-
+retaining law separate. Preserve the complete original anisotropic covariance,
+Haar factors and full normalizer. No original source or peer branch is edited.
+
+Execution: isolated new runtime directory and new additive GitHub branch.
+Dylan's repeated autonomy instruction authorizes foreground work; no timers or
+background agents are restarted. No subagent tool is available here.
+
+1. Read source R11-R13, exact Gaussian/spectral interface and current peer claims.
+2. Write and observe failing tests for exact shape integrals and endpoint series.
+3. Implement standard-library rational controls; test both signs and parity.
+4. Write complete domination and coefficient proof, plus all scope exclusions.
+5. Verify exact historical source identities, packet inventory and both Python
+   modes; include hostile Git fixtures and semantic mutants.
+6. Publish a new source-bound candidate and request nonauthor analytic review.
+
+Separate supporting task: bounded nonauthor review of PR173 Route C; accept the
+conditional count implication and repair its inadmissible fixed-R substitution
+by a diagonal argument. No graph execution or parent revalidation.