Static44 packing ceiling: less than 0.000399% kappa headroom

.gitattributes

@@ -43,3 +43,7 @@ research/e8-complex-gauge-kernel/** -text -whitespace
 research/e8-lemma-a-lean/** -text -whitespace
 research/e8-lemma-g-lean/** -text -whitespace
 research/community-formal-20261012-audit/** -text -whitespace
+
+# Exact scoped static44 packing certificate and independent receipts.
+research/static44-packing-ceiling/** -text -whitespace
+research/static44-packing-ceiling-validation/** -text -whitespace

.github/workflows/static44-packing-ceiling.yml

@@ -0,0 +1,32 @@
+name: Static44 exact packing ceiling
+on:
+  push:
+    paths:
+      - 'research/static44-packing-ceiling/**'
+      - '.github/workflows/static44-packing-ceiling.yml'
+  pull_request:
+    paths:
+      - 'research/static44-packing-ceiling/**'
+      - '.github/workflows/static44-packing-ceiling.yml'
+  workflow_dispatch:
+permissions:
+  contents: read
+jobs:
+  verify:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 5
+    strategy:
+      fail-fast: false
+      matrix:
+        python-version: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97
+        with:
+          python-version: ${{ matrix.python-version }}
+      - name: Verify both exact duals and rejection controls
+        run: python -B research/static44-packing-ceiling/verify.py "$RUNNER_TEMP/static44-packing-ceiling.json"
+      - name: Require unchanged tracked sources
+        run: git diff --exit-code

research/static44-packing-ceiling-validation/CROSS-PLATFORM.json

@@ -0,0 +1,9 @@
+{
+  "status": "PASS_BYTE_IDENTICAL_COMPLETE_RECEIPTS",
+  "platforms": [
+    "macOS arm64 Python 3.14.8",
+    "Linux aarch64 Python 3.11.15"
+  ],
+  "receipt_sha256": "bef2bf8d8b93a5373db8117248394e69e2ed577e4940e92c6c5f6267b633cd70",
+  "package_manifest_sha256": "ce9d4419a8b2941ba0887dd27411c44077bf26879e830643f7aea70cf9e47503"
+}

research/static44-packing-ceiling-validation/README.md

@@ -0,0 +1,7 @@
+# Independent verification receipts
+
+The complete package passed using macOS arm64/Python 3.14.8 and Linux
+aarch64/Python 3.11.15. Both runs used only the standard library. Their entire
+JSON receipts are byte-identical, including both exact interval/dual margins,
+all pattern checks, both rejection controls and the package manifest hash.
+CI is separate and is not claimed green by these receipts.

research/static44-packing-ceiling-validation/linux-python311.json

@@ -0,0 +1,48 @@
+{
+  "status": "PASS_EXACT_STATIC44_POOLED_HOSTING_CEILING",
+  "excluded_b": "1593251957517/1000000000000000",
+  "current_admitted_b": "31864911873350496687/20000000000000000000000",
+  "strict_kappa_ceiling": "1593251957517/1001593251957517",
+  "current_composed_kappa": "397677800014309/250000000000000000",
+  "kappa_headroom_upper": "1588431607148135139889247/250398312989379250000000000000000",
+  "relative_kappa_headroom_percent_upper": "158843160714813513988924700/398311400947642851864860110753",
+  "stock": {
+    "16": 3584,
+    "8": 5376,
+    "32": 3584,
+    "48": 3584
+  },
+  "helper_widths": {
+    "9": 292,
+    "8": 156,
+    "5": 56
+  },
+  "demands": {
+    "5": 4032,
+    "8": 11232,
+    "9": 21024
+  },
+  "patterns_checked": 145,
+  "moment_engines": {
+    "mercator": {
+      "minimum_pattern_slack": "1/100000000000000000000",
+      "local_excess_lower": "21140593396223135953906832552890247523214783536240703507721555436441192626953125/13654704984662271147909857662387020959275168646931586482961066094099431424",
+      "dual_objective": "9530393696685161049826055929050807445184549170211281202953974874805588894672480465895743891/162776768024710072850106449870908510199489219748158293759358717132800000000000000000000",
+      "strict_excess_lower": "3437770789862432253190368897338495516562218179777666790139458108539277122659962759/3906642432593041748402554796901804244787741273955799050224609211187200000000000000000000",
+      "moment_minus_one_lower": "3437770789862432253190368897338495516562218179777666790139458108539277122659962759/1283039594713037548128035358103647015451321452848448654435942400000000000000000000000000000000000"
+    },
+    "base_two": {
+      "minimum_pattern_slack": "20347046494217742549806547672838900387454821410489124841761521281106427096999/2034709600308875910626330623386356377493615246851978671991983964160000000000000000000000000000000",
+      "local_excess_lower": "4848107152408127057387688105681270377649626277/3131391425937500000000000000000000000000",
+      "dual_objective": "9530393696685161049826055929050807445184549170211281202953974874805588894672480465895743891/162776768024710072850106449870908510199489219748158293759358717132800000000000000000000",
+      "strict_excess_lower": "20982487731093776313209552308417510801328205455089525616015104803886439663559018501722549/23844253128619639577652311992808863798753303674046625062406062080000000000000000000000000000000",
+      "moment_minus_one_lower": "20982487731093776313209552308417510801328205455089525616015104803886439663559018501722549/7831052213824692066211153308738079928291756914358207119360000000000000000000000000000000000000000000000"
+    }
+  },
+  "negative_controls": [
+    "current_admitted_b",
+    "inflated_stock_dual"
+  ],
+  "manifest_sha256": "ce9d4419a8b2941ba0887dd27411c44077bf26879e830643f7aea70cf9e47503",
+  "scope": "All fractional pooled whole-helper packings of this fixed local word, idle-child stock, nine-stage chain, eight replicas and helper widths. Chronology, owner identity and integer restrictions are relaxed. Other local words, stage chains, widths or compiler/outer architectures are not bounded."
+}

research/static44-packing-ceiling-validation/macos-python314.json

@@ -0,0 +1,48 @@
+{
+  "status": "PASS_EXACT_STATIC44_POOLED_HOSTING_CEILING",
+  "excluded_b": "1593251957517/1000000000000000",
+  "current_admitted_b": "31864911873350496687/20000000000000000000000",
+  "strict_kappa_ceiling": "1593251957517/1001593251957517",
+  "current_composed_kappa": "397677800014309/250000000000000000",
+  "kappa_headroom_upper": "1588431607148135139889247/250398312989379250000000000000000",
+  "relative_kappa_headroom_percent_upper": "158843160714813513988924700/398311400947642851864860110753",
+  "stock": {
+    "16": 3584,
+    "8": 5376,
+    "32": 3584,
+    "48": 3584
+  },
+  "helper_widths": {
+    "9": 292,
+    "8": 156,
+    "5": 56
+  },
+  "demands": {
+    "5": 4032,
+    "8": 11232,
+    "9": 21024
+  },
+  "patterns_checked": 145,
+  "moment_engines": {
+    "mercator": {
+      "minimum_pattern_slack": "1/100000000000000000000",
+      "local_excess_lower": "21140593396223135953906832552890247523214783536240703507721555436441192626953125/13654704984662271147909857662387020959275168646931586482961066094099431424",
+      "dual_objective": "9530393696685161049826055929050807445184549170211281202953974874805588894672480465895743891/162776768024710072850106449870908510199489219748158293759358717132800000000000000000000",
+      "strict_excess_lower": "3437770789862432253190368897338495516562218179777666790139458108539277122659962759/3906642432593041748402554796901804244787741273955799050224609211187200000000000000000000",
+      "moment_minus_one_lower": "3437770789862432253190368897338495516562218179777666790139458108539277122659962759/1283039594713037548128035358103647015451321452848448654435942400000000000000000000000000000000000"
+    },
+    "base_two": {
+      "minimum_pattern_slack": "20347046494217742549806547672838900387454821410489124841761521281106427096999/2034709600308875910626330623386356377493615246851978671991983964160000000000000000000000000000000",
+      "local_excess_lower": "4848107152408127057387688105681270377649626277/3131391425937500000000000000000000000000",
+      "dual_objective": "9530393696685161049826055929050807445184549170211281202953974874805588894672480465895743891/162776768024710072850106449870908510199489219748158293759358717132800000000000000000000",
+      "strict_excess_lower": "20982487731093776313209552308417510801328205455089525616015104803886439663559018501722549/23844253128619639577652311992808863798753303674046625062406062080000000000000000000000000000000",
+      "moment_minus_one_lower": "20982487731093776313209552308417510801328205455089525616015104803886439663559018501722549/7831052213824692066211153308738079928291756914358207119360000000000000000000000000000000000000000000000"
+    }
+  },
+  "negative_controls": [
+    "current_admitted_b",
+    "inflated_stock_dual"
+  ],
+  "manifest_sha256": "ce9d4419a8b2941ba0887dd27411c44077bf26879e830643f7aea70cf9e47503",
+  "scope": "All fractional pooled whole-helper packings of this fixed local word, idle-child stock, nine-stage chain, eight replicas and helper widths. Chronology, owner identity and integer restrictions are relaxed. Other local words, stage chains, widths or compiler/outer architectures are not bounded."
+}

research/static44-packing-ceiling/CERTIFICATE.json

@@ -0,0 +1,13 @@
+{
+  "excluded_b": "1593251957517/1000000000000000",
+  "dual": [
+    "1159414936640430059330462179261511384581206599102713283120543068094957725638359245042654471/125012557842977335948881753500857735833207720766585569607187494757990400000000000000000000",
+    "2318829873283164971988217906679184253746337572867493152947851815442934289442437325042654471/125012557842977335948881753500857735833207720766585569607187494757990400000000000000000000",
+    "1943441799180566052578162798685443161579219588483422203801769244374593538716498125042654471/125012557842977335948881753500857735833207720766585569607187494757990400000000000000000000",
+    "2516643747598956163026288651309469013630730117317870594961393098503011022804777165042654471/125012557842977335948881753500857735833207720766585569607187494757990400000000000000000000",
+    "-92272544327/10000000000",
+    "-92743877627/10000000000",
+    "-21062393899/10000000000"
+  ],
+  "discovery": "Floating LP nominated this vector; all proof inequalities are independently rechecked over exact rational intervals. No optimizer is imported by verify.py."
+}