Research note: sharp off-target proper-star puncture threshold

.github/workflows/global-star-puncture.yml

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+name: Global proper-star puncture evidence
+
+on:
+  workflow_dispatch:
+  pull_request:
+    paths:
+      - 'research/global-star-puncture/**'
+      - '.github/workflows/global-star-puncture.yml'
+  push:
+    branches: [main, research/seed43-decoder]
+    paths:
+      - 'research/global-star-puncture/**'
+      - '.github/workflows/global-star-puncture.yml'
+
+permissions:
+  contents: read
+
+jobs:
+  replay:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 10
+    strategy:
+      fail-fast: false
+      matrix:
+        python: ['3.11', '3.13']
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # repository baseline pin
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # repository baseline pin
+        with:
+          python-version: ${{ matrix.python }}
+      - name: Exact receipt and failure detection
+        run: |
+          python -I -O -B research/global-star-puncture/verify.py
+          python -I -O -B research/global-star-puncture/test_verify.py
+          python -B scripts/verify_selected_result.py
+      - name: Require checkout unchanged
+        run: test -z "$(git status --porcelain)"

research/global-star-puncture/CLAIM.json

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+{
+  "assignment_seed": 43,
+  "randomness": "OS System.Security.Cryptography.RandomNumberGenerator; unbiased UInt32 rejection then modulo 100",
+  "track": "structural decoder research",
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "started_utc": "2026-10-13T04:30:04Z",
+  "expected_finish_utc": "2026-10-13T05:10:04Z",
+  "verification_reserve_starts_utc": "2026-10-13T05:00:04Z",
+  "coordination": "Only open issue #650 asks for Discussions; no pinned sprint coordination issue exists. Claim recorded locally.",
+  "object": "Paired power-of-two k-port decoder, arbitrary off-target stars of degree below k, target-dependent overlap-class corrections, target-retaining punctures",
+  "method": "Exact F2 incidence-code dual labels and bounded meet-in-middle minimum-support search; attempt a combinatorial lower-bound proof",
+  "initial_domain": [
+    [
+      5,
+      4
+    ],
+    [
+      6,
+      4
+    ]
+  ],
+  "seed_diversification": "Seed 43 selects k=4 and primary p=k+(seed mod 3)=5; target index 43 modulo family size",
+  "deliverable": "One scoped structural decoder note, exact portable verifier, receipt, negative controls and handoff; no kappa claim",
+  "candidates": [
+    {
+      "task": "Extend PR669's target-local puncture result to arbitrary off-target stars",
+      "decision": "selected; explicitly left open by predecessor, new coefficient/support class"
+    },
+    {
+      "task": "Price a non-B_K stage schedule with fewer idle bridge splits",
+      "decision": "deferred; physical and boundary recurrence would exceed this bounded session"
+    },
+    {
+      "task": "Resolve PR620's unfinished extra-total E8 pairing-rank search",
+      "decision": "deferred; more solver time without a new mechanism does not justify reopening it"
+    }
+  ],
+  "predecessors": [
+    {
+      "pr": 669,
+      "head": "308f1e6ec3bb0b6ec0584cf7bfe219addc219b1e"
+    },
+    {
+      "pr": 231,
+      "head": "3c11e696a2fb2c454585d72710de27cd6bd3be68"
+    }
+  ],
+  "overlap": "Read selected review, PR ledger and PR620/631/669/703 plus structural PR search; no matching off-target puncture result found. PR669 comments refreshed immediately before local claim.",
+  "status": "completed",
+  "result": "Proved d(C_p,k)=2(p-k+1) for all k>=2; global proper-star one-target puncture threshold2(p-k)+1 at power-of-two k; exact nonlocal sharp witness",
+  "result_url": "https://github.com/lukemansoor/integer-mult-bounds/tree/research/seed43-decoder/research/global-star-puncture",
+  "finished_utc": "2026-10-13T04:50:00Z",
+  "overlap_refresh": "Refreshed through PR721 and read669/715/717 descriptions; no matching off-target paired-port puncture result"
+}

research/global-star-puncture/NOTICE.md

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+# Attribution and license
+
+Copyright 2026 Luke Mansoor. New files are under the repository Apache-2.0 license.
+
+Prepared by Luke Mansoor (@lukemansoor), with substantial OpenAI Codex assistance in research, proof development, implementation, verification and writing. Separate Codex workers developed the restriction proof, built an independent list-valued verifier and audited the proof and implementation. This is independent AI review, not independent human peer review or proof-assistant verification.
+
+Joel Pulikkan / GamingPuzzled's PR231 supplies the symmetric paired-port decoder and binomial parity obstruction, following icekylinx's PR144 paired-cube work and eumemic's paired-cube bit identity. That source discloses Anthropic Claude assistance. Sam Sung / the-missionary-company's PR669 supplies the full-family obstruction for arbitrary global stars and the sharp target-local puncture theorem; it discloses substantial OpenAI Codex assistance. Its all-parameter local result and unpunctured global result are predecessor work, not claimed as new here. The new theorem closes its explicitly open off-target puncture class using a different restriction and generalized-cube argument. No predecessor code or text is copied into either implementation.
+
+The accepted construction is contextual only: Chafik Boukhalfa's PR626 allocation on Jeremy Kothe's PR622/623 K-triangle providers, with eumemic's PR543 bit supplier. GamingPuzzled's PR620, DreamingOfClouds' format/cold-helper work, Rohan Arun's recurrence correction and the cumulative OpenAI/community lineage remain credited through the maintainer review and original notices. The contribution does not rebuild or replace those constructions.
+
+PR631 studies E8 root-line punctures; PR703 studies asymmetric Hurwitz copy floors. They use different geometries and are neither prerequisites nor priority competitors for the theorem here. Original repository source attribution and license files are unchanged. Source commits, blob IDs and SHA-256 hashes are recorded in SOURCES.json.