[Draft / negative control] F₂-orthogonal h23 groups fail rational-H bit-core sharing

.github/workflows/pr128-bit-screen.yml

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+name: PR128 restricted bit groups - rational-H negative control
+on:
+  push:
+    branches:
+      - research/pr128-zero-frame-sharing-screen
+  pull_request:
+    paths:
+      - 'research/pr128-zero-frame-sharing-screen/**'
+      - '.github/workflows/pr128-bit-screen.yml'
+  workflow_dispatch:
+permissions:
+  contents: read
+jobs:
+  exact-screen:
+    name: Rational-H counterexample and screened moment (Python ${{ matrix.python-version }})
+    runs-on: ubuntu-24.04
+    timeout-minutes: 15
+    strategy:
+      fail-fast: false
+      matrix:
+        python-version: ['3.11', '3.13', '3.14']
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97
+        with:
+          python-version: ${{ matrix.python-version }}
+      - name: Run exact hypothesis screen (not a physical certificate)
+        run: |
+          python3 research/pr128-zero-frame-sharing-screen/verify_screen.py > /tmp/bit-screen.json
+          python3 -m json.tool /tmp/bit-screen.json > /dev/null
+          python3 - <<'PY'
+          import json
+          r=json.load(open('/tmp/bit-screen.json'))
+          assert r['rational_H_orthogonal_pairs']==0
+          assert r['rational_H_nonorthogonal_pairs']==17514
+          assert r['legal_bit_supplier_certified'] is False
+          assert r['status'].startswith('PASS F2 geometry and formal moment; FAIL PR129')
+          print('PASS negative control: the hypothesized +10.83% bit result is NOT legal')
+          PY
+          cat /tmp/bit-screen.json
+      - name: Check tracked artifacts unchanged
+        run: git diff --exit-code

research/pr128-zero-frame-sharing-screen/README.md

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+# Restricted PR128 bit groups: exact negative control (NOT a new κ)
+
+**Status: disproved candidate.** The restricted h=23 partition **does not
+implement valid completed-core bit sharing** under the rational
+`H = 9I - J` projector geometry of PR #129. The apparent 10.83% increase
+in stopped-bit saving is **only a hypothetical arithmetic screen** of an
+unrealizable child histogram; it is not a verified algorithm, bit supplier,
+or multiplication exponent.
+
+## Source and reproducibility
+
+- Based on [PR #128](https://github.com/CrocSwap/integer-mult-bounds/pull/128),
+  commit `530588a019b4a74f09180680c9e3961bf649ec89`.
+- Compared against [PR #129](https://github.com/CrocSwap/integer-mult-bounds/pull/129),
+  commit `992a442c10d243eee69bbd20f32ba6fa98fb430e`.
+- `pr128-bit-profile.json` pins PR128's existing bit-word histogram,
+  exterior histogram, source and blob SHA.
+- `restricted-groups.json` retains the 87 signed PR128 complex groups,
+  deletes triples containing coordinate 23 and reindexes the 1,771
+  surviving triples.
+- Run `python3 research/pr128-zero-frame-sharing-screen/verify_screen.py`
+  on standard Python without `-O`. Standard library only.
+
+This is a **negative experiment**, not a physical witness.
+
+## What passes
+
+The restricted partition has 83 groups of 21 and four groups of 7;
+every h=23 triple appears exactly once. Each triple indicator has norm
+one mod 2, and each distinct within-group pair has overlap zero mod 2.
+This makes the binary Gram matrix the identity and produces 36,799
+successful ordered Gram tests. The h=23 quadratic phase tests on 277
+weight-0, weight-1 and weight-2 inputs per group are also exact:
+24,099 checks pass. The orthogonal complements have nondegenerate binary
+forms; their Gauss sums are -2 for the 83 rank-two complements and
+-256i for the four rank-16 complements.
+
+A hypothetical paid rank-mass screen would remove the 17,597 zero-start
+roles' old exteriors and insert a rank-46/368 complement for each shared
+role and each of the 87 groups. This yields formal W=49,249,558 and the
+same rank deficit of 1,344,189. The approximate stopped bit moment
+suggests a 10.8253% gain over PR128's bit supplier **if this grouping
+were legally implementable**. It is not.
+
+## Decisive failure: incompatible rational geometry
+
+PR #129 uses the rational inner product `H=9I-J`, not the standard
+binary dot product. For any two triple incidence vectors T,U, its
+Gram entry is
+
+    T^T H U = 9*(|T intersect U| - 1).
+
+The group construction for PR128's **complex** operation requires binary
+intersection parity zero. After restriction to 23 coordinates, distinct
+triples in each group intersect in **zero or two** points. Those intersections
+yield rational Gram entries -9 or +9, respectively, **never zero**.
+
+The exhaustive witness has:
+- 15,012 within-group unordered pairs meeting in zero points;
+- 2,502 within-group unordered pairs meeting in two points;
+- **0 / 17,514 pairs are rational-H-orthogonal.**
+
+For example, `T={0,6,12}` and `U={0,6,18}` are in the first
+group, with intersection size 2 and `T^T H U=9`.
+
+Consequently their rational projectors do **not** annihilate one another.
+The identity `D_A D_B = D_(A+B)` used by completed-core sharing
+requires `AB=BA=0` and cannot be invoked for these blocks.
+**The 87-group allocation, its W, and its improved bit moment cannot
+be certified as a legal bit supplier.**
+
+PR #129 already constructs a different valid rational-H-orthogonal
+161-group sunflower partition, each group having eleven triples.
+Future physical work must start from that valid geometry (or independently
+prove another valid operator composition), not from this restricted
+F2-only complex partition.
+
+## Record and remaining work
+
+PR #129 claims a conditional coupled exponent
+`κ=0.000129186205798`. Beating it by 3% would require
+`κ >= 0.00013306179197194`, with improvements to **both** limiting
+suppliers and a new exact coupled certificate.
+
+No new `κ` is claimed by this repository branch. The experiment is
+preserved as a corruption/negative control to prevent rational-vs-binary
+orthogonality mistakes.
+
+The source construction is by an664 / PR128 contributors, with
+original partition credits to Zhang and Ge. The PR129 rational bit
+construction and its contributors are credited. This negative audit
+was prepared with OpenAI assistance. Retained upstream licenses apply.

research/pr128-zero-frame-sharing-screen/pr128-bit-profile.json

@@ -0,0 +1,88 @@
+{
+  "source": {
+    "repository": "an664/integer-mult-bounds",
+    "ref": "530588a019b4a74f09180680c9e3961bf649ec89",
+    "path": "research/completed-core-sharing/inputs/research/round8-network-opposite-profile.json",
+    "github_blob_sha": "ea5b8aa53d7acba929ba4c74014a8a0f83271400",
+    "attribution": "Zhihao Chen and original PR128/PR104 bit-network contributors"
+  },
+  "m": 529,
+  "v": 1771,
+  "R": 28866,
+  "N": 3136441,
+  "W": 108516254,
+  "deficit": 1344189,
+  "hist": {
+    "1": 235438511,
+    "2": 236428500,
+    "3": 51022510,
+    "4": 43669318,
+    "5": 22488158,
+    "6": 8072218,
+    "7": 3715558,
+    "8": 6694380,
+    "9": 1919764,
+    "10": 1059058,
+    "11": 1423884,
+    "12": 2064986,
+    "13": 995302,
+    "14": 347116,
+    "15": 2387308,
+    "16": 1441594,
+    "17": 4547928,
+    "18": 2266880,
+    "19": 7484246,
+    "20": 8847916,
+    "21": 1466388,
+    "22": 127512,
+    "484": 6272882,
+    "506": 62328574,
+    "507": 7084,
+    "508": 49588,
+    "509": 159390,
+    "510": 449834,
+    "511": 3542,
+    "512": 276276,
+    "513": 17710,
+    "514": 1083852,
+    "515": 127512,
+    "516": 403788,
+    "517": 99176,
+    "518": 1144066,
+    "519": 315238,
+    "520": 378994,
+    "521": 106260,
+    "522": 1583274,
+    "523": 626934,
+    "524": 2854852,
+    "525": 13711082,
+    "526": 4629394,
+    "527": 5653032,
+    "528": 6233920
+  },
+  "exterior_hist": {
+    "506": 62328574,
+    "507": 7084,
+    "508": 49588,
+    "509": 159390,
+    "510": 449834,
+    "511": 3542,
+    "512": 276276,
+    "513": 17710,
+    "514": 1083852,
+    "515": 127512,
+    "516": 403788,
+    "517": 99176,
+    "518": 1144066,
+    "519": 315238,
+    "520": 378994,
+    "521": 106260,
+    "522": 1583274,
+    "523": 626934,
+    "524": 2854852,
+    "525": 13711082,
+    "526": 4629394,
+    "527": 5653032,
+    "528": 6233920
+  }
+}