Price whole-bridge carriers and constrain the shortened quotient (no new κ)

research/p104-block-bridge-carriers/COROLLARY-SOURCES.json

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+      "commit": "b269b953f1e06583551470b088d4632a282e149c",
+      "path": "research/noidle-root-defect/PROOF.md",
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+      "url": "https://github.com/CubeJerry/integer-mult-bounds/blob/b269b953f1e06583551470b088d4632a282e149c/research/noidle-root-defect/PROOF.md"
+    },
+    {
+      "role": "quotient_proof",
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+      "url": "https://github.com/CubeJerry/integer-mult-bounds/blob/cda67c44abe75022a3048714b7e7270097564bdf/research/p104-block-bridge-carriers/PROOF.md"
+    },
+    {
+      "role": "known_cap_two_proof",
+      "repository": "CrocSwap/integer-mult-bounds",
+      "pull_request": 6398,
+      "commit": "dee2663ba0918be86993fd9d63c8d64b020f4c83",
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+      "usage": "Known Section2 theorem, independently rederived here; no code import."
+    }
+  ],
+  "external_code_imported": false,
+  "claim": "Applies the known at-most-two rank-two support theorem for shortest roots in even dimension at least four to the exact eighteen-full-query quotient."
+}

research/p104-block-bridge-carriers/EXPECTED.json

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+{
+  "status": "PASS",
+  "claim": "No new kappa",
+  "source_head": "51f54e3c31f2f3a3e056a483b3ed66ae916ad06a",
+  "kappa": "16859/5000000",
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+    [
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+  ],
+  "source_complete_margin": [
+    "53223698408019/500000000000000000",
+    "53223698425787/500000000000000000"
+  ],
+  "full_span_per_port_loss_lower": "417979705566714323/1000000000000000000",
+  "quotient": {
+    "stage_idempotence_defect_rank": 1,
+    "stages": 18,
+    "pair_commutator_rank": 2,
+    "pairs": 153
+  },
+  "dense_masks": {
+    "cases": 81,
+    "dual_column_inequalities": 13851,
+    "best": {
+      "a": 8,
+      "b": 9,
+      "complete_gain_upper": "-21065220134325490533/500000000000000000"
+    },
+    "old_central_capacity": 14,
+    "block_central_capacity": 15
+  },
+  "controls": [
+    "reversed bridge order rejected",
+    "whole-block carrier separates new and old contracts",
+    "minus-leg-only transport rejected by neutral specialization",
+    "image-only transport rejected by full projector test",
+    "unpaired nullspace dimension rejected",
+    "native-only annihilation rejected by bridge closure",
+    "positive inequality multiplier rejected",
+    "overstated dual price rejected"
+  ]
+}

research/p104-block-bridge-carriers/NOTICE

@@ -0,0 +1,21 @@
+Whole-bridge carriers and complete invoice obstruction
+Jerry Chen / @CubeJerry, with substantial OpenAI GPT-6 Astra Pro assistance.
+Apache-2.0.
+
+The independent eigenspace/capacity and quotient-interface review was carried
+out by a separate concurrent OpenAI GPT-6 Astra Pro reasoning agent. It used a
+nullspace/pairing construction rather than the author's cyclic-closure code.
+
+The retained chain root is by DreamingOfClouds with Claude Opus 5.5 (Anthropic)
+via Claude Code, from CrocSwap/integer-mult-bounds#6833 at
+51f54e3c31f2f3a3e056a483b3ed66ae916ad06a. Its own NOTICE and LICENSE are retained
+unchanged. The source notice credits thu-nmrc's common idle fusion (#6716),
+zxv's two-pair root (#6726), the native word of #6824, Ali Romman's helper-basis
+mechanism, and Jerry Chen's native helper retirement work. Only the source
+formulas, profile, proof and notices needed here are retained; this package
+neither reproduces nor re-admits the complete predecessor supplier.
+
+Background structural precedents are CrocSwap/integer-mult-bounds#6840,
+CrocSwap/integer-mult-bounds#6841, CrocSwap/integer-mult-bounds#6844, and
+CrocSwap/integer-mult-bounds#6845. This package changes the pointwise bridge
+annihilation premise and does not claim ownership of those prior obstructions.