Conditional κ = 0.001679754788150048 from fine source-prime padding

.gitattributes

@@ -151,3 +151,6 @@ research/p111-minrank-proof-reconciliation/vendor/pr620/geo.py -text -whitespace
 research/community-batch1099-audit/** -text -whitespace
 research/community-frontier1094-audit/** -text -whitespace
 research/abelian-cayley-metric-scope/** -text
+
+# Preserve the byte-pinned predecessor files and receipts in this package.
+research/fine-prime-padding/** -text -whitespace

.github/workflows/fine-prime-padding.yml

@@ -0,0 +1,59 @@
+name: Fine prime padding composition
+
+on:
+  workflow_dispatch:
+  pull_request:
+    paths:
+      - 'research/fine-prime-padding/**'
+      - 'research/t74-signed554-phase-fusion/**'
+      - '.github/workflows/fine-prime-padding.yml'
+  push:
+    branches: [main, codex/fine-prime-padding-20261014]
+    paths:
+      - 'research/fine-prime-padding/**'
+      - 'research/t74-signed554-phase-fusion/**'
+      - '.github/workflows/fine-prime-padding.yml'
+
+permissions:
+  contents: read
+
+jobs:
+  verify:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 90
+    strategy:
+      fail-fast: false
+      matrix:
+        python: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7, retained repository pin
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7, retained repository pin
+        with:
+          python-version: ${{ matrix.python }}
+      - name: Install retained cold-replay dependencies
+        run: |
+          sudo apt-get update
+          sudo apt-get install -y --no-install-recommends g++ libboost-dev
+          python -m pip install -r research/fine-prime-padding/requirements.txt
+      - name: Fresh supplier admission and fine-prime padding composition
+        env:
+          CXX: g++
+          BOOST_INCLUDE: /usr/include
+        run: >-
+          python -B research/fine-prime-padding/verify.py
+          --work "$RUNNER_TEMP/fine-prime-padding-cold"
+      - name: Require committed sources unchanged
+        if: always()
+        run: git diff --exit-code
+      - uses: actions/upload-artifact@v4
+        if: always()
+        with:
+          name: fine-prime-padding-python-${{ matrix.python }}
+          path: |
+            ${{ runner.temp }}/fine-prime-padding-cold/*.json
+            ${{ runner.temp }}/fine-prime-padding-cold/*.log
+            ${{ runner.temp }}/fine-prime-padding-cold/supplier/*.json
+            ${{ runner.temp }}/fine-prime-padding-cold/supplier/*.log
+            ${{ runner.temp }}/fine-prime-padding-cold/supplier/strict/*.json

.github/workflows/t74-signed554-phase-fusion.yml

@@ -0,0 +1,57 @@
+name: Classical matrix boundary with signed554 T74
+
+on:
+  workflow_dispatch:
+  pull_request:
+    paths:
+      - 'research/t74-signed554-phase-fusion/**'
+      - '.github/workflows/t74-signed554-phase-fusion.yml'
+  push:
+    branches: [main, codex/t74-signed554-phase-fusion-20261014]
+    paths:
+      - 'research/t74-signed554-phase-fusion/**'
+      - '.github/workflows/t74-signed554-phase-fusion.yml'
+
+permissions:
+  contents: read
+
+jobs:
+  verify:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 90
+    strategy:
+      fail-fast: false
+      matrix:
+        python: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7, retained repository pin
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7, retained repository pin
+        with:
+          python-version: ${{ matrix.python }}
+      - name: Install retained cold-replay dependencies
+        run: |
+          sudo apt-get update
+          sudo apt-get install -y --no-install-recommends g++ libboost-dev
+          python -m pip install -r research/t74-signed554-phase-fusion/requirements.txt
+      - name: Fresh ancestry, supplier, owner construction and strict admission
+        env:
+          CXX: g++
+          BOOST_INCLUDE: /usr/include
+        run: >-
+          python -B research/t74-signed554-phase-fusion/verify.py
+          --work "$RUNNER_TEMP/signed554-fusion-cold"
+      - name: Require committed sources unchanged
+        if: always()
+        run: git diff --exit-code
+      - uses: actions/upload-artifact@v4
+        if: always()
+        with:
+          name: signed554-fusion-python-${{ matrix.python }}
+          path: |
+            ${{ runner.temp }}/signed554-fusion-cold/*.json
+            ${{ runner.temp }}/signed554-fusion-cold/*.log
+            ${{ runner.temp }}/signed554-fusion-cold/strict/*.json
+            ${{ runner.temp }}/signed554-fusion-cold/strict/*.log
+            ${{ runner.temp }}/signed554-fusion-cold/strict/global/audit/*.json

research/fine-prime-padding/B.json

@@ -0,0 +1,13 @@
+{
+  "b": "16797549561255445213349999999999999999999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000",
+  "b_above_endpoint": "0.00167975495613",
+  "profile": {
+    "1": 1560432,
+    "2": 336336,
+    "3": 278724,
+    "4": 84912,
+    "5": 54612,
+    "8": 5328,
+    "48": 22748
+  }
+}

research/fine-prime-padding/CLAIM.json

@@ -0,0 +1,17 @@
+{
+  "claim": "conditional integer multiplication exponent saving",
+  "kappa": "0.001679754788150048",
+  "epsilon": "9999999/10000000",
+  "beta": "9999997/10000000",
+  "theta_power": 2,
+  "halo_power": 48,
+  "core_power": 128,
+  "matrix_exponent": "45/16",
+  "supplier_pr": 1699,
+  "outer_predecessors": [
+    1673,
+    1731,
+    1758
+  ],
+  "scope": "Conditional composition with finer source-prime padding, polynomial offline coefficient precision and unchanged O(p)-bit online records. All inherited all-size compiler, common-label, mutable-source, hosting, semantic C1=1, fixed-tape, prime-packing, equal-chunk interchange, exact recovery and analytic hypotheses remain except the explicitly proved source-prime interval/precision/locality replacements. Published prime theorem and the written gauge-free circuit theorem are mathematical inputs. No practical cutoff or unconditional theorem is claimed."
+}

research/fine-prime-padding/EXPECTED-BALANCE.json

@@ -0,0 +1,42 @@
+{
+  "beta": "9999997/10000000",
+  "boundary_constant": "3/32",
+  "cap": "45396482739407502445439027393324999999999999999999999999999999995000001/50000000000000000000000000000000000000000000000000000000000000000000000",
+  "core_power": 128,
+  "cost_powers": {
+    "boundary_algebraic_matrix": "49916012260592497554560972606675000000000000000000000000000000004999999/50000000000000000000000000000000000000000000000000000000000000000000000",
+    "fused_gaussian": "49916007277390047115816417820025000000000000000000000000000000009999997/50000000000000000000000000000000000000000000000000000000000000000000000",
+    "global_coordinate_router": "19966404900877489109573300000000000000000000000000000000000000003/20000000000000000000000000000000000000000000000000000000000000000",
+    "group_bit_router": "199664029109560188463265671280100000000000000000000000000000000029999991/200000000000000000000000000000000000000000000000000000000000000000000000",
+    "group_scans": "1/5000000",
+    "main_transform": "49916012260592497554560972606675000000000000000000000000000000009999999/50000000000000000000000000000000000000000000000000000000000000000000000",
+    "microbox_face_corrections": "-190000001/2500000",
+    "polynomial_products": "1/10000000",
+    "sparse_union_movement": "29603512260592497554560972606675000000000000000000000000000000004999999/50000000000000000000000000000000000000000000000000000000000000000000000"
+  },
+  "epsilon": "9999999/10000000",
+  "gain_over_reported_1758": "9279347748948453466314800026327686526580209199320247542619067215757027414399369818327775017/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+  "group_chirp_guard": "4603524760592497554560972606675000000000000000000000000000000002499999/25000000000000000000000000000000000000000000000000000000000000000000000",
+  "halo_power": 48,
+  "headline": "52492337129689/31250000000000000",
+  "kappa": "16797547881500489087805478664999999999999999999999999999999998000000199999/10000000000000000000000000000000000000000000000000000000000000000000000000000",
+  "ledger_controls": 14,
+  "main_gaussian_gap": "2491601225219372277393325000000000000000000000000000000000000001/25000000000000000000000000000000000000000000000000000000000000000000000",
+  "matrix_exponent": "45/16",
+  "membership_gap": "1/10000000",
+  "normalization_power_gap": "999999999999999999999999999999999999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000",
+  "scope": "Separate exact implementation in one session. The cited prime theorem and written precision, locality and circuit arguments are mathematical inputs; finite tests do not prove the complete multiplication theorem.",
+  "separate_fault_controls": {
+    "epsilon_limit": true,
+    "full_union_key_sort": true,
+    "old_g_union_scan": true,
+    "old_linear_guard": true,
+    "old_per_axis_full_scan": true,
+    "old_theta_chirp_guard": true,
+    "old_two_beta_tag_budget": true,
+    "unsupported_strassen_exponent": true
+  },
+  "status": "PASS_SEPARATE_FINE_PADDING_COST_DERIVATION",
+  "strict_checks": 56,
+  "theta_power": 2
+}