Bit operation-frame descent on #168's bit word: conditional κ = 6.105562e-4

.github/workflows/paired-cube-bit-descent-168.yml

@@ -0,0 +1,33 @@
+name: Verify bit frame descent on PR168
+
+on:
+  push:
+    paths:
+      - 'research/paired-cube-bit-descent-168/**'
+      - 'research/paired-cube-bit/**'
+      - 'scripts/paired_cube*.py'
+      - '.github/workflows/paired-cube-bit-descent-168.yml'
+  pull_request:
+    paths:
+      - 'research/paired-cube-bit-descent-168/**'
+      - 'research/paired-cube-bit/**'
+      - 'scripts/paired_cube*.py'
+      - '.github/workflows/paired-cube-bit-descent-168.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  prove:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 20
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97
+        with:
+          python-version: '3.13'
+      - name: Bit word, prime witnesses and exact assembly
+        run: python3 -B research/paired-cube-bit-descent-168/prove.py

SOURCES.json

@@ -500,5 +500,73 @@
     ],
     "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": "6096379/10000000000",
+    "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 a pinned searched pair-disjoint module and a nested-prefix all-but-one module with merged face-2/edge-02 outputs, carrier arcs compiled under PR162's closure conditions, physical frame descent (connected bundles) 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 an annealed pair module and the nested-prefix all-but-one module (research/paired-cube-bit); the balanced prefix (scripts/paired_cube_assembly.py); 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)."
+      },
+      {
+        "pr": 162,
+        "contributor": "DaysSky",
+        "role": "Carrier-arc compilation under the closure conditions (compile_closure, scripts/paired_cube/closure.py) and the first-order pairing rounds of the physical layer."
+      },
+      {
+        "pr": 20,
+        "contributor": "RaD project (hipotures)",
+        "role": "Balanced positional transform: prefix margin 1-eps (references/semantic-bulk/rad20/reports/review-balanced-transform.md)."
+      },
+      {
+        "pr": 34,
+        "contributor": "jamesyc",
+        "role": "Balanced assembly composition, with the parameters of research/copied-fixed/balanced_assembly.py (Chafik Boukhalfa)."
+      }
+    ],
+    "scope": "Conditional on the retained PR144 analytic, uniform-recursion and fixed-tape contracts."
   }
 }

certificates/paired-cube-complex-input.json

@@ -1,86 +1,82 @@
 {
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-  "W_per_vertex": 29937,
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+  "R": 15171,
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   "child_histogram": {
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   "copied_centers_already": true,
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+  "h": 22,
+  "loss": 440,
+  "m": 66,
+  "matched": 7701,
   "matching_frames": "coordinate",
-  "phase1_operations": 13616,
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   "remaining_internal_histogram": [
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     0
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   "selected_rank_histogram": {
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+  "selected_roles": 2970,
   "source_data_histogram": {
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   "target_data_histogram": {
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-  "total_M_operations": 49424,
-  "untouched_non_source_roles": 15417,
-  "v": 1760
+  "total_M_operations": 32246,
+  "untouched_non_source_roles": 6939,
+  "v": 1320
 }

certificates/paired-cube-input.json

@@ -1,66 +1,57 @@
 {
-  "absorption_gap": "49772927594887408131062764367/500461342287379865539365770570000000000",
-  "assembly_minimum": "23067114022986563163422943/50046134228737986553936577057",
+  "absorption_gap": "372330996377054099141/5003050049328499012210000000000",
+  "assembly_minimum": "30500492979985189250098779/50030500493284990122100000000",
   "bit_child_multiplicities": {
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-  "bit_moment_gap": "9683053551624097783276572314019807322107841/67308782636558677514166530014945948467200000000000000",
+  "bit_moment_gap": "4016502088469094059996791856341638641311087/200723811957239366463731927094990471168000000000000000",
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 }