eumemic · Oct 9, 2026 · Oct 9, 2026 · Oct 9, 2026 · Oct 9, 2026 · Oct 9, 2026
diff --git a/SOURCES.json b/SOURCES.json
@@ -500,5 +500,83 @@
     ],
     "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": "6558894/10000000000",
+    "proof": "notes/paired-cube-note.tex",
+    "certificate": "certificates/paired-cube-network.json",
+    "change": "PR144 paired cubes at p=11 with pinned annealed triple, pair and all-but-one modules, the L1 local channel circuit and fused face-2/edge-02/edge-12 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 terminal sinks (research/terminal-sinks); a paired-cube bit word with partner-pair source mixing, an annealed pair module, an annealed all-but-one module, the L1 local-channel association and merged outputs (variant u) (research/paired-cube-bit), with late copies and late-read reuse (scripts/paired_cube_bit_physical.py); the balanced prefix (scripts/paired_cube_assembly.py); phase stop 1e-9 (PR153) and the atom exponent at its toll edge (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": 163,
+        "contributor": "chafreaky",
+        "role": "Same-singleton fusion of the single-target outputs (fold orders here from our own search)."
+      },
+      {
+        "pr": 166,
+        "contributor": "jamesyc",
+        "role": "Terminal-sink lemma (dirty-target substitution of all-eight side roots), audited here by research/terminal-sinks/sinks_gate.py."
+      },
+      {
+        "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."
   }
 }
diff --git a/certificates/paired-cube-bit-physical-input.json b/certificates/paired-cube-bit-physical-input.json
@@ -0,0 +1,99 @@
+{
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+  "checks": {
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+    "gauge_read_window": true,
+    "operation_frames_nondegenerate_and_spanning": true,
+    "pair_chronology": true,
+    "partner_chronology": true,
+    "phase_one_closure": true,
+    "register_contents": true,
+    "role_chains_nested": true,
+    "target_chains_nested_in_read_order": true,
+    "telescoping_deficit": true
+  },
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+    "60": 2200
+  },
+  "deficit_per_vertex": 1936,
+  "f2_replay": {
+    "lanes": 64,
+    "registers": 18028,
+    "rejected_controls": [
+      "alias_onto_live_register",
+      "omitted_recipient_read",
+      "read_before_donor_death"
+    ],
+    "seeds_restored_and_y_plus_x": true
+  },
+  "h": 24,
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+  "local_histogram": {
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+  },
+  "loss": 528,
+  "m": 72,
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+  "pairs": 1760,
+  "physical_R": 18028,
+  "physical_gauge_histogram": {
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+  },
+  "rank_per_vertex": 1549520,
+  "source_data_histogram": {
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+  },
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+}
diff --git a/certificates/paired-cube-complex-input.json b/certificates/paired-cube-complex-input.json
@@ -1,86 +1,82 @@
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   "matching_frames": "coordinate",
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 }