Conditional κ = 0.003635302061475 via signed rank-nine caller and causal helper retiming

research/signed-rank9-retimed/README.md

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+# Signed rank-nine caller with a retimed helper
+
+Under the stated conditional supplier contracts, the combined
+certificate gives κ = 0.003635302061475 in T(n) =
+O(n (log n)^(1−κ)). The exact gain over the pinned signed rank-nine
+predecessor κ = 0.003635202569271 is
+24873051/250000000000000 = 0.000000099492204. The gain over
+the verified public comparison in #7105 is 0.000003140551475.
+The independent raw crossing is strictly between
+.00363530206147543231249432214964276 and
+.00363530206147543231249432214964277.
+
+This package transfers #7105's helper-1123 split to the exact
+stronger native word and keeps the signed caller unchanged.
+At cut 43039, role 1123 has row x1123 in chart 242. Its only old
+contact before the suffix is the 242→127 move. Move it instead
+to chart 245, insert −x1123+x1480 into role 843 at that chart,
+and use fresh helper 1480 for the later chart-127 contacts.
+The old suffix maps the perturbation e1123+e843 to e1123.
+The old and fresh helper outputs both have their intended
+identity rows. Old owned labels shift by one, preserving their
+moves, liveness and erasure. The three changed chart pairs
+have all 512 columns and absolute phase independently checked.
+The literal native replay also checks all 1,481 physical outputs.
+
+Per native call, productive ranks change by {1:+1, 8:+1, 9:−1}
+and paid ranks by {1:+1, 4:+1, 5:−1}. The full 18-call invoice
+has 117,130 paid and 23,410 productive requests, rank surplus
+1,520 and zero empty-root credits. The modeled ordinary total is
+847,248,064/10^9, with 152,751,936/10^9 reserve. The paired BIT
+cap is .00376669. The exact grid remains S=1125 and c=1342.
+Both directed prices, compiler and outer inequalities pass.
+
+Run `python3.12 -B research/signed-rank9-retimed/verify.py` from
+the repository root. The package authenticates and extracts
+its pinned sources in a clean directory, regenerates the native
+word, and compares the complete result, grid and route receipts
+byte for byte. It includes a bad-scalar control and proves that
+the predecessor invoice rejects the new claim.
+
+## Open next questions
+
+The bound retains the prior all-column native, owned erasure,
+uniform compiler, fixed-tape precision, analytic recovery, A6,
+exact child, LAMBDA, one-field idle, per-port caller, paired E-free
+BIT and modeled ordinary tariff premises. A complete physical
+fixed-tape realization, rounded provider and the physical #6998
+tariff bridge remain open. Test those interfaces on this combined
+word before supplier admission.
+
+The CrocSwap coupled-helper, signed Clifford and interval work
+and the causal helper split by the #7105 contributors supply the
+predecessors. This package is a compatibility transfer to a
+different, stronger certificate. Codex assisted the transfer,
+implementation, audits and replay.

research/signed-rank9-retimed/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "17469fff78c22941280f04d39dc5a1faee09c840",
+  "files": [
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec",
+      "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81"
+    },
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a",
+      "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa"
+    }
+  ]
+}

research/signed-rank9-retimed/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "p104-side-correction",
+  "base_commit": "17469fff78c22941280f04d39dc5a1faee09c840",
+  "original_card": {
+    "id": "p104-side-correction",
+    "question": "Can joint helper bases and a legal causal split improve the complete P104 productive/paid invoice?",
+    "starting_points": [
+      "docs/research/current-priorities.md",
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md",
+      "research/p104-helper-subspace-splits/README.md",
+      "research/dyadic-helper-channel-capacity/README.md"
+    ],
+    "methods": [
+      "Construct and independently check one source-bound instance of the stated first experiment.",
+      "Seek an exact counterexample or target-specific complete-budget obstruction to that same proposed change."
+    ],
+    "acceptance_gate": "An exact arbitrary-input identity, source/target frame availability and restoration at the chosen cut, plus the complete channel+correction+idle/hosting bill or an explicit favorable bound. The native channel alone is not a supplier. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_selected_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read revision 8, the selected review and live exact-source handoffs. Then follow this card's bounded first_experiment.",
+      "scope": "Source-bound orientation only, not a supplier replay or theorem proof."
+    },
+    "first_experiment": "Start with the selected #5599 emitted word and review pending #5718 distinct input/output bases plus #5717/#5719 coverage before claiming work. Pick one uncovered source word, helper group and cut region. Prove the arbitrary-input relation and legal entry/exit corrections, then compare full target and paid profiles. Reject if completion, owned lifetimes or consumer costs repay the gain. A static pairing rank alone is not a physical split.",
+    "bottleneck_link": "Judge the actual current supplier contract and complete signed target/paid bill; frozen-profile ceilings require an applicability proof.",
+    "allowed_variations": [
+      "One exact source head, helper/cut region or quantified proposition and changed hypothesis; check live handoffs first. Different seeds are not different scopes."
+    ],
+    "scope_change_triggers": [
+      "Changing source head, helper/cut domain, operation alphabet or caller boundary without recording the new scope.",
+      "Treating an archived proposal or local numerical pass as complete supplier admission."
+    ],
+    "overlap_terms": [
+      "P104",
+      "helper basis",
+      "helper split",
+      "5718",
+      "dyadic capacity"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #4133: literal-slot defect",
+        "evidence": "research/p104-literal-slot-defect/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "88666f1dee93fbd85b31fd5d6f91a219e111b5f4",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4136: uniform commutation gap",
+        "evidence": "research/p104-uniform-commutation-gap/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "281ce601a8be9db470de630759179c23e1dfaa88",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4140: uniform encoding gap",
+        "evidence": "research/p104-uniform-encoding-gap/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "de25c6525aa866962309df5d107b32d55e6e5628",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4153: source-chart shortcut exhausts its optimistic allowance",
+        "evidence": "research/p104-source-chart-shortcut/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "9123241fea53df77e51ffe30d9aca1625d4bf3a8",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4154: fiber-tag seam mismatch",
+        "evidence": "research/p104-fiber-tag-seam/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "4ffcdaee5d6255a9cea1fe53a5424435068089d0",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "Selected PR5599: complete helper-subspace construction and independent caller replay; five framework assumptions remain.",
+        "evidence": "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md",
+        "remaining": "The next experiment must identify uncovered source-specific work. Successor archive intake does not transfer this admission.",
+        "status": "reviewed",
+        "source_commit": "09dd0965711ca7eeb169057a420abab1c9052137",
+        "selected_record_sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5"
+      }
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Replay the #7105 causal helper split on the signed rank-nine caller and the stronger coupled native word.",
+  "scope_change_reason": "The two improvements target distinct native and caller roles; strict gain needs a fresh combined certificate.",
+  "bottleneck_link": "Compare the complete signed productive and paid profile on the unchanged complex supplier contract.",
+  "stop_rule": "Require zero exact endpoint failures, all changed chart columns and signed routes, two strict rational price engines, and clean replay.",
+  "outcome": "completed",
+  "evidence": "README.md, RESULT.json and the hash-bound REPLAY.tar.gz.",
+  "author": "ToikY",
+  "ai_assistance": "Substantial OpenAI Codex assistance with exact construction and independent verification.",
+  "open_questions": [
+    {
+      "question": "Can a total physical provider and common-volume tariff bridge admit the retained odd-scalar word?",
+      "why_it_matters": "The exponent retains the source tariff and all-width contracts.",
+      "first_step": "Start from #6998 and audit the source/provider conversion and A6 trace under one tape width model.",
+      "blocked_by": "The fixed-tape conversion and total rounded provider are unresolved."
+    }
+  ]
+}

research/signed-rank9-retimed/VERIFY.json

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+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 600,
+      "checks": "Clean exact native and caller replay, changed maps and absolute phase, precision, dual price gates and negative controls."
+    }
+  ]
+}

research/signed-rank9-retimed/verify.py

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+"""Verify the signed rank-nine caller with the transferred causal helper."""
+from hashlib import sha256
+import os
+from pathlib import Path
+from tempfile import TemporaryDirectory
+import subprocess
+import sys
+import tarfile
+
+ARCHIVE_SHA = "c4f4f616a308839acc909abe72291f2e081aee320a8a7c38dc56a192daba3bf1"
+root = Path(__file__).resolve().parent
+archive = root / "REPLAY.tar.gz"
+assert __debug__ and sys.version_info[:2] == (3, 12)
+assert sha256(archive.read_bytes()).hexdigest() == ARCHIVE_SHA
+with TemporaryDirectory(prefix="croc-retimed-package-") as tmp:
+    source, result = Path(tmp) / "source", Path(tmp) / "result"
+    source.mkdir()
+    with tarfile.open(archive) as bundle:
+        bundle.extractall(source, filter="data")
+    subprocess.run(["bash", str(source / "verify.sh"), str(result)],
+                   check=True, env=os.environ | {"RANK9_PYTHON": sys.executable})
+    assert (result / "RESULT.json").read_bytes() == (root / "RESULT.json").read_bytes()