Paired bit-output fusion and verified lifetime reuse: conditional κ = 5.96818007e-4

.github/workflows/paired-cube-lifetime.yml

@@ -0,0 +1,23 @@
+name: Paired-cube lifetime certificate
+
+on:
+  pull_request:
+  push:
+  workflow_dispatch:
+
+jobs:
+  exact-witness:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        python: ['3.11', '3.13', '3.14']
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python }}
+      - name: Rebuild both words and check the complete certificate
+        run: python3 -B research/paired-cube-lifetime/verify.py
+      - name: Ensure verification did not change tracked sources
+        run: git diff --exit-code

SOURCES.json

@@ -500,5 +500,58 @@
     ],
     "scope": "Conditional on retained analytic, uniform-recursion and fixed-tape contracts; complete local paired-cube schedule, exact core sharing and scalar charge supplied in the proof.",
     "curation": "Selected paired-coordinate cube only, compact frozen carrier arcs and bit subset, exact suppliers and assembly. Excludes fallback shared_core results, paired-five motifs, other candidate graphs, search screens and PDFs."
+  },
+  "paired_cube_physical_bit_extension": {
+    "contributor": "eumemic",
+    "assistance": "Prepared with Anthropic Claude assistance.",
+    "predecessor_pr": 144,
+    "predecessor_commit": "c8b22bc5c10dba497ac25804e27d9647d818e2ff",
+    "kappa": "5878747/10000000000",
+    "proof": "notes/paired-cube-note.tex",
+    "certificate": "certificates/paired-cube-network.json",
+    "change": "PR144 paired cubes at p=11 with a triple module restricted from a pinned searched complex DAG and a pinned searched pair-disjoint module with merged face-2/edge-02 outputs, physical frame descent and compensated late-read reuse on the complex word (scripts/paired_cube_physical.py), and a paired-cube bit word with partner-pair source mixing and an annealed pair module (research/paired-cube-bit); phase stop 1e-9 as re-instantiated by geckods (PR153, PR158); PR144 checks and assembly otherwise unchanged.",
+    "adopted": [
+      {
+        "pr": 144,
+        "contributor": "icekylinx",
+        "commit": "c8b22bc5c10dba497ac25804e27d9647d818e2ff",
+        "role": "Paired-cube decoder, modules, shared cores, bit ledger, finite bridge and assembly."
+      },
+      {
+        "pr": 131,
+        "contributor": "eumemic",
+        "role": "Physical frame descent and compensated reuse on Cayley covers (method)."
+      },
+      {
+        "pr": 124,
+        "contributor": "jamesyc",
+        "role": "Compensated birth-read reuse."
+      },
+      {
+        "pr": 143,
+        "contributor": "eumemic",
+        "role": "Deadline (late) compensation reads."
+      },
+      {
+        "pr": 128,
+        "contributor": "an664",
+        "role": "Completed-core sharing."
+      },
+      {
+        "pr": 97,
+        "contributor": "Zhihao Chen (jacklightChen)",
+        "role": "Bit-side compile conventions (deferred readouts, plain or lifted frames)."
+      },
+      {
+        "contributor": "Swapnil Jain",
+        "role": "Round-seven bit lineage (PR62 interval strips) from which the bit pair modules are cut."
+      },
+      {
+        "pr": 158,
+        "contributor": "geckods",
+        "role": "Re-instantiated free assembly constants (phase stop, PR153; atom exponent, PR158)."
+      }
+    ],
+    "scope": "Conditional on the retained PR144 analytic, uniform-recursion and fixed-tape contracts."
   }
 }

certificates/paired-cube-complex-input.json

@@ -1,86 +1,82 @@
 {
-  "R": 26417,
-  "W_per_vertex": 29937,
-  "c": 24767,
+  "R": 16011,
+  "W_per_vertex": 18651,
+  "c": 17735,
   "child_histogram": {
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+    "1": 60462,
+    "10": 2250,
+    "11": 1146,
+    "12": 1383,
+    "13": 1095,
+    "14": 3231,
+    "15": 1902,
+    "16": 588,
+    "17": 8448,
+    "18": 8910,
+    "19": 1980,
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+    "21": 0,
+    "22": 0,
+    "3": 24618,
+    "4": 20595,
+    "5": 14559,
+    "54": 2970,
+    "6": 6093,
+    "7": 4881,
+    "8": 4743,
+    "9": 2571
   },
   "copied_centers_already": true,
-  "deficit_per_vertex": 1936,
-  "h": 24,
-  "loss": 528,
-  "m": 72,
-  "matched": 6074,
+  "deficit_per_vertex": 1320,
+  "h": 22,
+  "loss": 440,
+  "m": 66,
+  "matched": 6201,
   "matching_frames": "coordinate",
-  "phase1_operations": 13616,
-  "q": 7724,
-  "rank_per_vertex": 2153528,
+  "phase1_operations": 10150,
+  "q": 4477,
+  "rank_per_vertex": 1229646,
   "remaining_internal_histogram": [
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     0,
     0
   ],
   "selected_rank_histogram": {
-    "20": 4840
+    "18": 2970
   },
-  "selected_roles": 4840,
+  "selected_roles": 2970,
   "source_data_histogram": {
-    "1": 1760,
-    "2": 1760,
-    "20": 1760
+    "1": 1320,
+    "18": 1320,
+    "2": 1320
   },
   "target_data_histogram": {
-    "0": 12760,
-    "1": 5280,
-    "20": 1760
+    "0": 8250,
+    "1": 3960,
+    "18": 1320
   },
-  "total_M_operations": 49424,
-  "untouched_non_source_roles": 15417,
-  "v": 1760
+  "total_M_operations": 32426,
+  "untouched_non_source_roles": 7819,
+  "v": 1320
 }

certificates/paired-cube-input.json

@@ -1,66 +1,57 @@
 {
-  "absorption_gap": "49772927594887408131062764367/500461342287379865539365770570000000000",
-  "assembly_minimum": "23067114022986563163422943/50046134228737986553936577057",
+  "absorption_gap": "37351770714269060570360194191023257/500588566790582931049971823558856690000000000",
+  "assembly_minimum": "29428339087721461768518344114331/50058856679058293104997182355885669",
   "bit_child_multiplicities": {
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-    "10": 474,
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-    "66": 1760,
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+    "1": 120972,
+    "10": 2160,
+    "11": 2016,
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+    "13": 1080,
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+    "60": 5720,
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+    "9": 648
   },
-  "bit_moment_gap": "9683053551624097783276572314019807322107841/67308782636558677514166530014945948467200000000000000",
+  "bit_moment_gap": "34879094578234633698904410970360032171054091/523539292246066669784729944875262279680000000000000000",
   "complex_child_multiplicities": {
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-  "complex_moment_gap": "35983219312333093839004994137969/179068943294158619192045723836257040072704",
-  "kappa": "4609169/10000000000",
-  "row_coefficient": 20445,
+  "complex_group_order": 3525886442745164056544063644145716736004044180364723200424782744512582104634391857878947474919000911664177132185103526533556870749183073596734571342973795793383290849303191539662953799849547227737400544457729391514661713176468240351330298583217125220869576729661326266259024901649005584114421035252391760900092184489369973370724377894349644301151172572225522957784648909234781611948223712944954177723427440753012339451839407462242698998122862136268155486957700758485307238973641035062973415368109606762999662774702118665848434384838590914531021276158042617166069588021894697108433312726842277534281982740181708602162296504975360000000000000000000,
+  "complex_moment_gap": "46965161945076382039329824844403/229279866220935923833050583634816916258816",
+  "kappa": "5878747/10000000000",
+  "row_coefficient": 12320,
   "row_degree": 70000
 }