Small-lifetime doublets: exact shape limit, exponent-one companion tail and moment crossover

.github/workflows/small-lifetime-shape.yml

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+name: Small-lifetime shape and moment crossover checks
+
+'on':
+  pull_request:
+    paths:
+      - 'frontiers/small_lifetime_shape_20260930/**'
+      - '.github/workflows/small-lifetime-shape.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 commits
+        run: |
+          set -euo pipefail
+          git fetch --no-tags origin ae343a1c2a0070476fed4d31a15b6911831edd4d
+          git fetch --no-tags origin 56a7904f9ad7d409c31e23195c0e7eeab230613a
+      - name: Verify both sources, packet and exact controls
+        env:
+          PYTHONDONTWRITEBYTECODE: '1'
+          GIT_NO_REPLACE_OBJECTS: '1'
+        run: |
+          set -euo pipefail
+          python -B -S frontiers/small_lifetime_shape_20260930/verify.py
+          git diff --exit-code

frontiers/small_lifetime_shape_20260930/MANIFEST.json

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+{
+  "schema": 1,
+  "scientific_effect": "NONE",
+  "review_status": "NONAUTHOR_REVIEW_OPEN",
+  "files": [
+    {
+      "path": "PLAN.md",
+      "bytes": 1990,
+      "sha256": "57197b803f766fbb499b8036db59b169a34c0eed4bbe883c69064bff0714bd94",
+      "git_blob": "3a21113120bd24e783ba1a647797f56df5d2ee34"
+    },
+    {
+      "path": "PROOF.md",
+      "bytes": 17932,
+      "sha256": "70aec4a9cf0ea0aed1dae04f7345481a32f42f2707dca89d31a086fd451d9b64",
+      "git_blob": "71906304451abc7a422c65a76b297874bdcb8cfe"
+    },
+    {
+      "path": "README.md",
+      "bytes": 3749,
+      "sha256": "52dd2c3050eb34c46364cdf0ec47d1178650d7116a3be6209b47f59a5ab6bc31",
+      "git_blob": "d0886a4bac606f87731c275fe3243c2a444b168f"
+    },
+    {
+      "path": "RECONNAISSANCE.md",
+      "bytes": 2127,
+      "sha256": "d23d28c62e8a90b25c07d7013d5de2eb8240aa3ef8a8f89f2eb6a98cd96050f1",
+      "git_blob": "533cef3ce59bc1976e32c0c7077c4d8b54d0317c"
+    },
+    {
+      "path": "RESULTS.json",
+      "bytes": 800,
+      "sha256": "a733f8baf3a4d409d8b3bff6768a609e3efd36d235d4c04dc76f6ce208e72e39",
+      "git_blob": "7083aeb451578d29e071303e78451692947e7d2a"
+    },
+    {
+      "path": "SOURCES.json",
+      "bytes": 1118,
+      "sha256": "a594d88ce35716bd3f8ef659cf43ee9267b1d1b186b5b19edc0813f327182651",
+      "git_blob": "bde07b2fc5ed653185713c6d011f0ab2bd441b48"
+    },
+    {
+      "path": "VALIDATION.md",
+      "bytes": 3507,
+      "sha256": "c6035d317c3e5b677f0657113ef5641072e7a0abf97d91f0fc14dd6887ee8940",
+      "git_blob": "1cc9569f49e2ccf27173cbae2cfe1dd1ecc28372"
+    },
+    {
+      "path": "shape.py",
+      "bytes": 8811,
+      "sha256": "fa7d46f74b74ca7ab5e52edb0285e60fc0b6db320cd004e1f6bd3dce16ea9226",
+      "git_blob": "d44da81c9faf7428998cf484290db59d89bbf55f"
+    },
+    {
+      "path": "test_jacobian.py",
+      "bytes": 1849,
+      "sha256": "eb7569f5ec0eb8a4d29cdfe2e0ea2a19e4b7518f44159af02576ae0d45f03682",
+      "git_blob": "4fbd7f0a4f0976c3fa01663f37ec0d1c643dfbf9"
+    },
+    {
+      "path": "test_shape.py",
+      "bytes": 8137,
+      "sha256": "ce20396e5659af4361d4102a528496793df532bd83d00c1b0f5fa5a664a73e7d",
+      "git_blob": "a47c361f0cc820a06e1c6e89b80e7844a9da5051"
+    },
+    {
+      "path": "test_verify.py",
+      "bytes": 6746,
+      "sha256": "5ae0bd70f64e1f481405a2ac3be15d420310a1eda764d0e51e22cc96aa6b63d9",
+      "git_blob": "acc836c2c2719f4788cf1e6651d25e20df7dfb15"
+    },
+    {
+      "path": "verify.py",
+      "bytes": 5379,
+      "sha256": "484320913f4f196c0b4113a6af02e245527542825270ad2ee32ad90caa50d0dd",
+      "git_blob": "3403814d2f27574be63faa5f89d3635f7b6d3316"
+    }
+  ]
+}

frontiers/small_lifetime_shape_20260930/PLAN.md

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+# Small-lifetime recovery and implementation plan
+
+Goal: recover the specific unfinished calculation from the user's interruption
+screenshot, test it and publish an additive conditional consumer. Do not redo
+PR182's fixed-r inverse moment proof, alter PR181 or count source-exposed work
+as independent review. The new direct September30 Continue authorizes this
+foreground work; it does not restart a stopped agent, timer, watch or loop.
+
+Design: start from PR181's explicit normalized shape density and exact companion
+map. Solve the singleton boundary before scaling. Blow up the selected lifetime
+and shape coordinate, derive the normalized limiting law, then compare it against
+the exact finite-cutoff doublet square density. The square corner analysis is
+needed to justify unbounded moments rather than infer them from weak convergence.
+
+Implementation is inline in a new isolated packet directory. A complete local
+upstream checkout could not be obtained, so GitHub Git-data writes are additive
+on a new branch and actual historical-source verification is hosted.
+
+Completed author-side tasks:
+1. Read live main#95 claims, PR181 exact interface and PR182's delivered reviews.
+2. Claim only the unfinished small-lifetime consumer, not an overlapping source.
+3. Write eight failing exact tests; implement shape and ratio algebra.
+4. Expand independent checks, including the direct inner-root square Jacobian.
+5. Write16 hostile Git/inventory tests and observe29 failures before implementation.
+6. Implement verification; run46 tests per mode and all six semantic mutants.
+7. Write full proof, immutable source pins, exact results and bounded reconnaissance.
+
+Publication tasks: authenticate the full remote packet tree against local bytes;
+create an additive PR/workflow; request bounded nonauthor A/B/C reviews; inspect
+current hosted source and existing downstream/formal checks, without anticipating
+success or acceptance. The author will not self-merge or change scientific status.