From 776ae75d640e6a5672e8ea798677a2cd3ae2d53c Mon Sep 17 00:00:00 2001
From: Gonzalo-Mier <gmier94@gmail.com>
Date: Sat, 17 Oct 2026 09:14:29 +0200
Subject: [PATCH] research: release T740 precision35 kappa refinement

---
 .../PRECISION-EDITS.json                      |  30 +
 research/t740-six-skip-precision35/PROOF.md   |  27 +
 research/t740-six-skip-precision35/README.md  |  50 ++
 .../t740-six-skip-precision35/SOURCES.json    | 600 ++++++++++++++++++
 research/t740-six-skip-precision35/TASK.json  |  66 ++
 .../t740-six-skip-precision35/VERIFY.json     | 133 ++++
 .../t740-six-skip-precision35/baseline.py     |  46 ++
 .../evidence/DERIVATION.json                  |  34 +
 .../evidence/OUTER-LEDGER.json                | 575 +++++++++++++++++
 .../evidence/VALIDATION.json                  |  78 +++
 .../t740-six-skip-precision35/reproduce.py    | 194 ++++++
 .../requirements-full.txt                     |   5 +
 research/t740-six-skip-precision35/seal.py    | 151 +++++
 .../t740-six-skip-precision35/test_verify.py  | 107 ++++
 research/t740-six-skip-precision35/verify.py  | 258 ++++++++
 15 files changed, 2354 insertions(+)
 create mode 100644 research/t740-six-skip-precision35/PRECISION-EDITS.json
 create mode 100644 research/t740-six-skip-precision35/PROOF.md
 create mode 100644 research/t740-six-skip-precision35/README.md
 create mode 100644 research/t740-six-skip-precision35/SOURCES.json
 create mode 100644 research/t740-six-skip-precision35/TASK.json
 create mode 100644 research/t740-six-skip-precision35/VERIFY.json
 create mode 100644 research/t740-six-skip-precision35/baseline.py
 create mode 100644 research/t740-six-skip-precision35/evidence/DERIVATION.json
 create mode 100644 research/t740-six-skip-precision35/evidence/OUTER-LEDGER.json
 create mode 100644 research/t740-six-skip-precision35/evidence/VALIDATION.json
 create mode 100644 research/t740-six-skip-precision35/reproduce.py
 create mode 100644 research/t740-six-skip-precision35/requirements-full.txt
 create mode 100644 research/t740-six-skip-precision35/seal.py
 create mode 100644 research/t740-six-skip-precision35/test_verify.py
 create mode 100644 research/t740-six-skip-precision35/verify.py

diff --git a/research/t740-six-skip-precision35/PRECISION-EDITS.json b/research/t740-six-skip-precision35/PRECISION-EDITS.json
new file mode 100644
index 0000000000..98943bc3c4
--- /dev/null
+++ b/research/t740-six-skip-precision35/PRECISION-EDITS.json
@@ -0,0 +1,30 @@
+[
+  {
+    "new": "PRECISION = dict(endpoint_digits=35, grid_digits=24, margin_digits=34, bootstrap_steps=12)",
+    "old": "PRECISION = dict(endpoint_digits=24, grid_digits=18, margin_digits=28, bootstrap_steps=12)"
+  },
+  {
+    "new": "dict(b=str(C-Q(1,10**115)), b_above_endpoint=str(C+Q(1,10**35)),",
+    "old": "dict(b=str(C-Q(1,10**104)), b_above_endpoint=str(C+Q(1,10**24)),"
+  },
+  {
+    "new": "kappa == C-Q(1,10**81)-Q(1,10**57)",
+    "old": "kappa == C-Q(1,10**70)-Q(1,10**46)"
+  },
+  {
+    "new": "Endpoint precision35;",
+    "old": "Endpoint precision24;"
+  },
+  {
+    "new": "kappa=C-10^-81-10^-57 exactly; same fixed-grid-maximum proof at precision35.",
+    "old": "kappa=C-10^-70-10^-46 exactly; same fixed-grid-maximum proof at precision24."
+  },
+  {
+    "new": "b='certified complex_lower - 1e-115 (outer/B.json)'",
+    "old": "b='certified complex_lower - 1e-104 (outer/B.json)'"
+  },
+  {
+    "new": "    patch('code/assemble.py', [(\" if DISCOVER:b=Q(M.certify(H,73,owner['live'],False)['lower']);conservative_b=Q(M.certify(H,73,owner['live'],True)['lower'])\", \" def fine_endpoint(bad):\\n  digits=SPEC['outer_refinement']['endpoint_digits']\\n  seed=Q(M.certify(H,73,owner['live'],bad)['lower'])\\n  if digits<=24:return seed\\n  grid=10**digits;left=int(seed*grid);right=left+10**(digits-24)\\n  while right-left>1:\\n   mid=(left+right)//2\\n   lo,hi=FC.moment('fine_mercator',H,73,owner['live'],Q(mid,grid),bad)\\n   if hi<1:left=mid\\n   elif lo>1:right=mid\\n   else:raise ArithmeticError('fine root enclosure exhausted; no endpoint accepted')\\n  return Q(left,grid)\\n if DISCOVER:b=fine_endpoint(False);conservative_b=fine_endpoint(True)\")])\n    spec['outer_refinement'] = PRECISION",
+    "old": "    spec['outer_refinement'] = PRECISION"
+  }
+]
diff --git a/research/t740-six-skip-precision35/PROOF.md b/research/t740-six-skip-precision35/PROOF.md
new file mode 100644
index 0000000000..987859deaf
--- /dev/null
+++ b/research/t740-six-skip-precision35/PROOF.md
@@ -0,0 +1,27 @@
+# Exact 35-digit endpoint extension of the T740 release
+
+This scoped package tests one exact question: does the unchanged T740 six-skip construction admit the next 35-decimal-grid endpoint above the open PR #3115 claim? The latest public point used here is the exact claim `0.001729737950064278551242895823 - 10^-52 - 10^-76` in [PR #3115](https://github.com/CrocSwap/integer-mult-bounds/pull/3115), head `400bc83669f86917f69b6249cd0356d3a913293c`.
+
+For profile `{1:16376940, 2:4741920, 3:1594737, 4:719280, 5:137085, 8:53280, 48:281903}` at `T=740`, the credited root engine brackets the root in
+
+```text
+[1729737950064278551242895823817348847577393 / 10^45,
+ 864868975032139275621447911908674423788697 / (5*10^44)].
+```
+
+The next candidate endpoint is the lower 35-digit grid point
+
+```text
+C35 = 86486897503213927562144791190867 / (5*10^34)
+    = 0.00172973795006427855124289582381734.
+κ35 = C35 - 10^-57 - 10^-81.
+```
+
+Both retained exact rational moment engines must show `M(C35)<1<M(C35+10^-35)`, and both must reject the unpaid rank-1 and rank-48 child controls. Relative to PR #3115's `C30 - 10^-52 - 10^-76`, the exact κ gain is `40867/(5*10^34) + 10^-52 + 10^-76 - 10^-57 - 10^-81`, slightly above `8.1734e-31`. This is a finer endpoint for the same paid mechanism; it does not claim a structural improvement or new supplier mechanism.
+
+The κ claim is admissible only if the complete unmodified T740 baseline and the complete changed strict supplier/outer release pass. The replay must retain every inherited admission predicate, all 63 positive outer rows, all 17 rejection controls, and the authenticated identical native receipt. A root-only check is not a release.
+
+## Open next questions
+
+- Can the weighted diagonal rank-batching screen in [open PR #3116](https://github.com/CrocSwap/integer-mult-bounds/pull/3116) be turned into a fully charged endpoint with a materially higher κ? Its local ceiling is not a constructed claim; the first step is to exhibit and invoice a physical endpoint, including the separate bit supplier.
+- Which changed paid producer/consumer boundary can lower the local profile enough to exceed the fixed-word ceiling materially? Start with the live normal-7 B-phase/later-A handoff; price the full supplier bill before expanding the construction.
diff --git a/research/t740-six-skip-precision35/README.md b/research/t740-six-skip-precision35/README.md
new file mode 100644
index 0000000000..02619d0ff3
--- /dev/null
+++ b/research/t740-six-skip-precision35/README.md
@@ -0,0 +1,50 @@
+# T740 six-skip 35-digit release candidate
+
+This package tests the exact next 35-digit complex-moment point above the public PR #3115 claim, which was still open when checked on 2026-10-17. The candidate endpoint is `0.00172973795006427855124289582381734`; at endpoint precision 35 the fixed-grid slacks give exact κ `C35 - 10^-57 - 10^-81`. It exceeds #3115 by about `8.1734e-31` if and only if the entire strict outer release accepts it.
+
+This is a precision extension of the same T740 profile, not a changed paid mechanism. The two independent rational moment engines, 35-digit adjacent-point rejection, and unpaid-child rejection are checked locally. These checks do not establish a κ release.
+
+The outer ledger's free gap is `R0 = 10^-(endpoint_digits+80)`, so this endpoint requires the exact interior point `b = C35 - 10^-115`. The package binds both that rational value and its claim text to the declared endpoint precision.
+
+Run the unmodified predecessor release first:
+
+```sh
+python3.12 -B research/t740-six-skip-precision35/baseline.py \
+  --repo FULL_GIT_REPO_WITH_GIT_SOURCES_OBJECTS --work /tmp/t740-precision35-baseline
+```
+
+Create a Python 3.12 environment from `requirements-full.txt` and use its interpreter for every command. The full release invokes child processes through the active interpreter; the system Python may have incompatible scientific packages.
+
+```sh
+python3.12 -m venv .venv
+. .venv/bin/activate
+python -m pip install -r research/t740-six-skip-precision35/requirements-full.txt
+```
+
+Then run the candidate's complete changed admission and outer release in a fresh workspace:
+
+```sh
+python3.12 -B research/t740-six-skip-precision35/reproduce.py \
+  --baseline-work /tmp/t740-precision35-baseline \
+  --work /tmp/t740-precision35-candidate
+```
+
+After both full releases pass, seal only the verified terminal evidence:
+
+```sh
+python3.12 -B research/t740-six-skip-precision35/seal.py \
+  --baseline-work /tmp/t740-precision35-baseline \
+  --work /tmp/t740-precision35-candidate
+```
+
+The package pins its scientific inputs to canonical main `997e6a9ca7b4f95d50e366f61412fd640d72a88a`. `FULL_GIT_REPO_WITH_GIT_SOURCES_OBJECTS` must contain the exact heads listed in the predecessor `GIT-SOURCES.json`; fetch those objects before an offline replay if needed. The full run uses the pinned Python dependencies and native C++ build; runtime metadata and any environment difference must be recorded in sealed evidence. The registered package check validates the sealed exact arithmetic and actual outer ledger but does not rerun native providers.
+
+## Frontier check (2026-10-17)
+
+Direct GitHub pages show PR #3115 still open with the exact claim above and the current open-PR listing extending through #3119. The later visible submissions do not claim a higher exponent: #3116 is a local ceiling screen explicitly without a κ claim, #3117 says the complex side still binds and makes no new κ claim, #3118 is a partial set-level covering investigation, and #3119 says it adds no exponent. The canonical Git fetch and cached overlap refresh both failed here because DNS could not resolve `github.com`; this is a direct-page check rather than a refreshed Git snapshot or an exhaustive immutable overlap audit. Recheck the public frontier before relying on this comparison after 2026-10-17.
+
+## Open next questions
+
+This result is a tiny arithmetic refinement only. A potentially larger route is open PR #3116's weighted diagonal rank-batching screen, whose local ceiling is around κ=0.1006 but which explicitly has no constructed endpoint, physical fusion invoice, or bit-supplier admission. Coordinate with that work before pursuing it; a full charged endpoint is still needed. The parallel B-phase/later-A handoff around normal-7 pivots 363/395 also remains a structural route, subject to a complete supplier bill.
+
+Credit the T740 six-skip and precision30 predecessors and all source lineage they retain. No selected-frontier update, independent human review, formal proof, or hosted CI pass is implied by this local package.
diff --git a/research/t740-six-skip-precision35/SOURCES.json b/research/t740-six-skip-precision35/SOURCES.json
new file mode 100644
index 0000000000..1eaf384ca2
--- /dev/null
+++ b/research/t740-six-skip-precision35/SOURCES.json
@@ -0,0 +1,600 @@
+{
+  "base_commit": "997e6a9ca7b4f95d50e366f61412fd640d72a88a",
+  "files": [
+    {
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "path": "certificates/selected-result.json",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129",
+      "usage": "provenance"
+    },
+    {
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "path": "docs/research/agent-task-catalog.json",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0",
+      "usage": "provenance"
+    },
+    {
+      "git_blob": "6c0f54527d879396f689523bfde19928a9b6157c",
+      "path": "research/complex-local-word-ceiling/ceiling.py",
+      "sha256": "86a1432870b3b21d8454106ec9162fddc0471472d9214c590a1420f2426cedfc",
+      "usage": "input"
+    },
+    {
+      "git_blob": "9544fee4e6ee1f202cee22bfaeaf229ee3b2515e",
+      "path": "research/rank7-joint-endframes/allocation/DISPATCH.json",
+      "sha256": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c",
+      "usage": "input"
+    },
+    {
+      "git_blob": "8d4fd644d60ba2c98106dc770803b647afdf0963",
+      "path": "research/rank7-joint-endframes/allocation/FILL.json.gz",
+      "sha256": "c2136be9434cda511a1a8a44d98f9f72ea5376830a8426674253b4ee351c4c39",
+      "usage": "input"
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+    {
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+      "path": "research/rank7-joint-endframes/allocation/ORDER.json",
+      "sha256": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+      "usage": "input"
+    },
+    {
+      "git_blob": "e1d99e12cfa3ac8375984d85c0b040dc36ea1312",
+      "path": "research/rank7-joint-endframes/allocation/PROVIDERS.json",
+      "sha256": "f2edb7922f3029a5d607437e737775ff3371bca49ebab62e5e2495d16d3bf573",
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+      "path": "research/rank7-joint-endframes/allocation/vendor/PLAN.json.gz",
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+      "usage": "input"
+    },
+    {
+      "git_blob": "114808c32b1799da53524bdc25cea67efb60009e",
+      "path": "research/rank7-joint-endframes/allocation/vendor/TEMPLATE.json.gz",
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+      "path": "research/rank7-joint-endframes/allocation/vendor/independent_owners.py",
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+    },
+    {
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+      "path": "research/rank7-joint-endframes/certificates/RELAX-CAP.json",
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+      "path": "research/rank7-joint-endframes/data/WORD-base.json.gz",
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+      "path": "research/rank7-t740-carrier-skips/VENDOR.json",
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+      "usage": "input"
+    },
+    {
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+      "path": "research/rank7-t740-carrier-skips/VERIFY.json",
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+      "usage": "input"
+    },
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+      "path": "research/rank7-t740-carrier-skips/evidence/ADAPTER-DERIVATION.json",
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+    },
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+      "usage": "input"
+    },
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+      "usage": "input"
+    },
+    {
+      "git_blob": "3b2f8894687405e1d3f16f1f4a6aefe65989cb69",
+      "path": "research/rank7-t740-carrier-skips/evidence/DISCOVERY-STAGES.json",
+      "sha256": "d495fde14c4e91d2bacbc763ac89dbc102094db3b4fa22806c77a77b0ad70b75",
+      "usage": "input"
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+      "sha256": "1396410de482883416fc7f534062ab005b484056b035fdcfa3b5cc065536ba35",
+      "usage": "input"
+    },
+    {
+      "git_blob": "3bd142311aa5e7134deb2aaf6a09fdc6347e6eaa",
+      "path": "research/rank7-t740-carrier-skips/verify.py",
+      "sha256": "4345698b1ae187f3708f9fa01313def62208f3165b799ee86cd9de5db7a9e5dc",
+      "usage": "input"
+    },
+    {
+      "git_blob": "b63351c861dff0c285f7762e36e381786c81f201",
+      "path": "research/rank7-t740-carrier-skips/verify_release.py",
+      "sha256": "9b2ab4c773862d1fc9a62efd1d54505b86f3d23ee30bb354da924f0fd1deff18",
+      "usage": "input"
+    },
+    {
+      "git_blob": "50b74b1d6d26fa11aa801d4207fbd9d067c568e8",
+      "path": "research/rank7-t740-carrier-skips/word_check.py",
+      "sha256": "f525647b903f9b8b2187f45f54cd7596dbec51e0024ed5fee80006adce65842b",
+      "usage": "input"
+    },
+    {
+      "git_blob": "0d96586a00f03058d6dc1d7882ec8fbe6661ed00",
+      "path": "research/two-sided-helper-extraction/tools/audit_moment.py",
+      "sha256": "e7147ccb8c57aa32a2cb227234a6a200a0b9e735eb1a655fd79ab29a4d7c0a00",
+      "usage": "input"
+    },
+    {
+      "git_blob": "dbc974a289a2060dc1f28bcd31414af7a2631d3c",
+      "path": "research/two-sided-helper-extraction/tools/admit_channel408.py",
+      "sha256": "a62c21eac4e0df502cbfb78c88b19a763fd351cde3c11c0588874f84db6992bf",
+      "usage": "input"
+    }
+  ],
+  "schema_version": 1
+}
diff --git a/research/t740-six-skip-precision35/TASK.json b/research/t740-six-skip-precision35/TASK.json
new file mode 100644
index 0000000000..9dbec110bc
--- /dev/null
+++ b/research/t740-six-skip-precision35/TASK.json
@@ -0,0 +1,66 @@
+{
+  "schema_version": 1,
+  "task_id": "uniform-transfer-audit",
+  "priority_revision": 6,
+  "base_commit": "997e6a9ca7b4f95d50e366f61412fd640d72a88a",
+  "original_card": {
+    "id": "uniform-transfer-audit",
+    "question": "Can one exact all-size/compiler, precision, hosting or restoration implication be proved or falsified?",
+    "starting_points": [
+      "certificates/selected-result.json",
+      "docs/audit.md"
+    ],
+    "methods": [
+      "Prove one missing implication with explicit quantified hypotheses.",
+      "Find an exact counterexample at the claimed interface boundary."
+    ],
+    "acceptance_gate": "Identify the proposition and what would change downstream; do not equate a finite replay with a universal proof.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read the selected review scope and choose one exact all-size or precision implication.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Write its quantified inputs and conclusion; find a missing hypothesis or construct a minimal exact adversarial instance.",
+    "bottleneck_link": "Finite supplier improvements are useful only under the retained transfer obligations.",
+    "allowed_variations": [
+      "Choose one tape, precision, hosting or restoration lemma."
+    ],
+    "scope_change_triggers": [
+      "Replacing a quantified obligation with another finite smoke test."
+    ],
+    "overlap_terms": [
+      "uniform transfer",
+      "all-size",
+      "precision"
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Does the complete T740 six-skip release admit a strictly higher exact endpoint than public PR #3115?",
+  "bottleneck_link": "Exact local moments permit a candidate 8.1734e-31 above the latest claimed point; only a complete release decides admissibility.",
+  "budget_minutes": 360,
+  "stop_rule": "Stop on the first failed full outer predicate or source binding; do not reuse projected receipts as a complete release. If the exact candidate passes, seal evidence and continue structural search separately.",
+  "outcome": "completed",
+  "evidence": "PASS_T740_SIX_SKIP_PRECISION35_COMPLETE_RELEASE in evidence/VALIDATION.json: complete unmodified baseline and complete candidate strict release both pass; candidate kappa exceeds the exact open PR #3115 claim; both moment engines, 63 strict rows, 17 outer controls, authenticated native receipt, and sealed terminal receipts pass.",
+  "author": "OpenAI Codex with substantial automated assistance; no independent human review claimed.",
+  "ai_assistance": "Substantial OpenAI Codex assistance for exact precision derivation, authenticated replay continuation, package verification and evidence sealing; no independent human or kernel review claimed.",
+  "open_questions": [
+    {
+      "question": "Can the weighted diagonal rank-batching screen be turned into a fully charged endpoint that materially raises kappa?",
+      "why_it_matters": "Open PR #3116 reports a local ceiling around 0.1006 but explicitly does not construct the changed endpoint, price fusion, or admit the bit supplier.",
+      "first_step": "Coordinate against PR #3116, then exhibit a physical changed endpoint and price its entire complex and bit supplier bills before running the strict release.",
+      "blocked_by": "No complete changed endpoint, physical invoice, or full supplier admission is currently claimed by that screen."
+    },
+    {
+      "question": "Which changed paid boundary can materially beat the fixed-word ceiling?",
+      "why_it_matters": "The endpoint refinement leaves the supplier mechanism and cost profile unchanged.",
+      "first_step": "Return to the #2612 B-phase re-pair/later-A handoff and state the complete producer/consumer bill.",
+      "blocked_by": "New construction and full supplier cost."
+    }
+  ],
+  "scope_change_reason": "The user explicitly assigned a search for a higher kappa and then focused the target on exceeding the latest claimed endpoint. This narrows the catalogue card’s precision-audit scope to one exact T740 endpoint question; it does not claim a universal transfer theorem or change any construction cost."
+}
diff --git a/research/t740-six-skip-precision35/VERIFY.json b/research/t740-six-skip-precision35/VERIFY.json
new file mode 100644
index 0000000000..a8b0ac183f
--- /dev/null
+++ b/research/t740-six-skip-precision35/VERIFY.json
@@ -0,0 +1,133 @@
+{
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "checks": "Exact 35-digit gain over PR #3115 with both credited moment engines, next-point and unpaid-child rejection, mandatory completed-release evidence and every original outer margin/control. Does not rerun native chains.",
+      "timeout_seconds": 180
+    },
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "-O",
+        "-m",
+        "unittest",
+        "discover",
+        "-s",
+        "{package}",
+        "-p",
+        "test_*.py",
+        "-v"
+      ],
+      "checks": "Actual inherited ledger mutants reject wrong points, zero margins and missing controls; strict completion flags reject unfinished or malformed releases under optimized Python.",
+      "timeout_seconds": 60
+    }
+  ],
+  "inputs": [
+    "research/complex-local-word-ceiling/ceiling.py",
+    "research/rank7-joint-endframes/allocation/DISPATCH.json",
+    "research/rank7-joint-endframes/allocation/FILL.json.gz",
+    "research/rank7-joint-endframes/allocation/ORDER.json",
+    "research/rank7-joint-endframes/allocation/PROVIDERS.json",
+    "research/rank7-joint-endframes/allocation/vendor/PLAN.json.gz",
+    "research/rank7-joint-endframes/allocation/vendor/TEMPLATE.json.gz",
+    "research/rank7-joint-endframes/allocation/vendor/independent_owners.py",
+    "research/rank7-joint-endframes/certificates/RELAX-CAP.json",
+    "research/rank7-joint-endframes/data/WORD-base.json.gz",
+    "research/rank7-joint-endframes/data/WORD-extra.json.gz",
+    "research/rank7-joint-endframes/tools/root.py",
+    "research/rank7-t740-carrier-skips/.gitattributes",
+    "research/rank7-t740-carrier-skips/ADAPTED.json",
+    "research/rank7-t740-carrier-skips/ENGINEERING.md",
+    "research/rank7-t740-carrier-skips/GIT-SOURCES.json",
+    "research/rank7-t740-carrier-skips/PINS.json",
+    "research/rank7-t740-carrier-skips/README.md",
+    "research/rank7-t740-carrier-skips/SOURCES.json",
+    "research/rank7-t740-carrier-skips/TASK.json",
+    "research/rank7-t740-carrier-skips/VENDOR.json",
+    "research/rank7-t740-carrier-skips/VERIFY.json",
+    "research/rank7-t740-carrier-skips/evidence/ADAPTER-DERIVATION.json",
+    "research/rank7-t740-carrier-skips/evidence/ADMISSION-RESULT.json",
+    "research/rank7-t740-carrier-skips/evidence/ADMISSION-STAGES.json",
+    "research/rank7-t740-carrier-skips/evidence/ASYNC-AUDIT.json",
+    "research/rank7-t740-carrier-skips/evidence/COMPOSITION-RESULT.json",
+    "research/rank7-t740-carrier-skips/evidence/DECISIONS.tsv",
+    "research/rank7-t740-carrier-skips/evidence/DISCOVERY-INVOICE.json.gz",
+    "research/rank7-t740-carrier-skips/evidence/DISCOVERY-RESULT.json",
+    "research/rank7-t740-carrier-skips/evidence/DISCOVERY-STAGES.json",
+    "research/rank7-t740-carrier-skips/evidence/ENVIRONMENT.json",
+    "research/rank7-t740-carrier-skips/evidence/FINITE.json",
+    "research/rank7-t740-carrier-skips/evidence/GLOBAL-PREFIX.json",
+    "research/rank7-t740-carrier-skips/evidence/INVOICE-PAYLOAD.json",
+    "research/rank7-t740-carrier-skips/evidence/MATERIALIZED.json",
+    "research/rank7-t740-carrier-skips/evidence/NATIVE-LOCAL-REPLAY-base.json",
+    "research/rank7-t740-carrier-skips/evidence/NATIVE-LOCAL-REPLAY-extra.json",
+    "research/rank7-t740-carrier-skips/evidence/NATIVE-RECEIPT.json",
+    "research/rank7-t740-carrier-skips/evidence/OUTER-B.json",
+    "research/rank7-t740-carrier-skips/evidence/OUTER-CLAIM.json",
+    "research/rank7-t740-carrier-skips/evidence/OUTER-INDEPENDENT.json",
+    "research/rank7-t740-carrier-skips/evidence/OUTER-LEDGER.json",
+    "research/rank7-t740-carrier-skips/evidence/OVERLAP.json",
+    "research/rank7-t740-carrier-skips/evidence/PREFLIGHT.json",
+    "research/rank7-t740-carrier-skips/evidence/RECEIPT-CHECK.json",
+    "research/rank7-t740-carrier-skips/evidence/RECIPE.json",
+    "research/rank7-t740-carrier-skips/evidence/RELEASE-RECEIPT.json",
+    "research/rank7-t740-carrier-skips/evidence/STAGES.json",
+    "research/rank7-t740-carrier-skips/evidence/VALIDATION.json",
+    "research/rank7-t740-carrier-skips/evidence/VENDOR-CHECK.json",
+    "research/rank7-t740-carrier-skips/evidence/logs/baseline.log.txt",
+    "research/rank7-t740-carrier-skips/evidence/logs/complete-admission.log.txt",
+    "research/rank7-t740-carrier-skips/evidence/logs/declared-edit-stage.log.txt",
+    "research/rank7-t740-carrier-skips/evidence/logs/derive-closed-adapters.log.txt",
+    "research/rank7-t740-carrier-skips/evidence/logs/export-pr2833.log.txt",
+    "research/rank7-t740-carrier-skips/evidence/logs/export-pr2894.log.txt",
+    "research/rank7-t740-carrier-skips/evidence/logs/finite-generation.log.txt",
+    "research/rank7-t740-carrier-skips/evidence/logs/four-kernel-stage.log.txt",
+    "research/rank7-t740-carrier-skips/evidence/logs/fresh-current-native.log.txt",
+    "research/rank7-t740-carrier-skips/evidence/logs/fresh-retained-bootstrap.log.txt",
+    "research/rank7-t740-carrier-skips/evidence/logs/paired-extension-stage.log.txt",
+    "research/rank7-t740-carrier-skips/evidence/logs/parent-paired-stage.log.txt",
+    "research/rank7-t740-carrier-skips/evidence/logs/preload-stage.log.txt",
+    "research/rank7-t740-carrier-skips/evidence/logs/rank7-overlay-stage.log.txt",
+    "research/rank7-t740-carrier-skips/evidence/logs/registered.log.txt",
+    "research/rank7-t740-carrier-skips/evidence/logs/release-verify.log.txt",
+    "research/rank7-t740-carrier-skips/evidence/logs/source-preflight.log.txt",
+    "research/rank7-t740-carrier-skips/evidence/logs/tests-optimized.log.txt",
+    "research/rank7-t740-carrier-skips/invoice_check.py",
+    "research/rank7-t740-carrier-skips/materialize.py",
+    "research/rank7-t740-carrier-skips/reproduce.py",
+    "research/rank7-t740-carrier-skips/requirements-full.txt",
+    "research/rank7-t740-carrier-skips/test_invoice.py",
+    "research/rank7-t740-carrier-skips/test_verify.py",
+    "research/rank7-t740-carrier-skips/vendor/PR3021-RESULT.json",
+    "research/rank7-t740-carrier-skips/vendor/PR3030-INVOICE.json.gz",
+    "research/rank7-t740-carrier-skips/vendor/pr3018/EXCHANGE.json",
+    "research/rank7-t740-carrier-skips/vendor/pr3021-FINITE.json",
+    "research/rank7-t740-carrier-skips/vendor/pr3021/reproduce.py",
+    "research/rank7-t740-carrier-skips/vendor/pr3021/verify.py",
+    "research/rank7-t740-carrier-skips/vendor/pr3024/EXCHANGE.json",
+    "research/rank7-t740-carrier-skips/vendor/pr3024/cap_proof.py",
+    "research/rank7-t740-carrier-skips/vendor/pr3024/lift.py",
+    "research/rank7-t740-carrier-skips/vendor/pr3042/CLAIM.json",
+    "research/rank7-t740-carrier-skips/vendor/pr3042/CREDITS.md",
+    "research/rank7-t740-carrier-skips/vendor/pr3042/MANIFEST.json",
+    "research/rank7-t740-carrier-skips/vendor/pr3042/NOTICE",
+    "research/rank7-t740-carrier-skips/vendor/pr3042/allocation/PROVIDERS.json",
+    "research/rank7-t740-carrier-skips/vendor/pr3042/edits/EDITS.json",
+    "research/rank7-t740-carrier-skips/vendor/pr3042/edits/FINAL-WORD-base.json.gz",
+    "research/rank7-t740-carrier-skips/vendor/pr3042/edits/FINAL-WORD-extra.json.gz",
+    "research/rank7-t740-carrier-skips/verify.py",
+    "research/rank7-t740-carrier-skips/verify_release.py",
+    "research/rank7-t740-carrier-skips/word_check.py",
+    "research/two-sided-helper-extraction/tools/admit_channel408.py",
+    "research/two-sided-helper-extraction/tools/audit_moment.py"
+  ],
+  "python": "3.12",
+  "requirements": [],
+  "schema_version": 1,
+  "status": "ready"
+}
diff --git a/research/t740-six-skip-precision35/baseline.py b/research/t740-six-skip-precision35/baseline.py
new file mode 100644
index 0000000000..a9eca50ec1
--- /dev/null
+++ b/research/t740-six-skip-precision35/baseline.py
@@ -0,0 +1,46 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Run the unchanged predecessor recipe with a larger outer wall-time allowance.
+
+Only run_stage's resource timeout changes from 1,800 to at least 7,200 seconds.
+Commands, domains, scientific predicates, log binding and final release checks
+are the original PR3054 implementation. Substantial OpenAI Codex assistance.
+"""
+
+import argparse
+import sys
+
+import verify as v
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--repo", type=v.Path, required=True)
+    parser.add_argument("--work", type=v.Path, required=True)
+    a = parser.parse_args()
+    v.need(
+        not a.work.resolve().is_relative_to(v.P),
+        "baseline logs and cache must stay outside the published package",
+    )
+    v.authenticate()
+    parent = v.ROOT / "research/rank7-t740-carrier-skips"
+    sys.path.insert(0, str(parent))
+    source = v.load(parent / "reproduce.py", "credited_baseline_budget")
+    original = source.run_stage
+
+    def run_stage(name, command, work, env, stages, timeout):
+        allowance = max(timeout, 7200) if name == "complete-admission" else timeout
+        return original(name, command, work, env, stages, allowance)
+
+    source.run_stage = run_stage
+    result = source.execute(a.repo.resolve(), a.work.resolve(), False)
+    source.save(a.work.resolve() / "RESULT.json", result)
+    v.need(
+        result["status"] == "PASS_T740_SIX_SKIP_COMPLETE_RELEASE",
+        "complete original baseline",
+    )
+    print(result["status"])
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/t740-six-skip-precision35/evidence/DERIVATION.json b/research/t740-six-skip-precision35/evidence/DERIVATION.json
new file mode 100644
index 0000000000..569dcfc19a
--- /dev/null
+++ b/research/t740-six-skip-precision35/evidence/DERIVATION.json
@@ -0,0 +1,34 @@
+{
+  "candidate_sha256": "74aba0be8fc1f82943882e43a00116e1c66577d1d621aa2f3d748433d540e81b",
+  "reference_sha256": "1893fa959063f48b523ee9d1974aaaa487f80f19b8592c7210969e1d4419723e",
+  "replacements": [
+    {
+      "new": "PRECISION = dict(endpoint_digits=35, grid_digits=24, margin_digits=34, bootstrap_steps=12)",
+      "old": "PRECISION = dict(endpoint_digits=24, grid_digits=18, margin_digits=28, bootstrap_steps=12)"
+    },
+    {
+      "new": "dict(b=str(C-Q(1,10**115)), b_above_endpoint=str(C+Q(1,10**35)),",
+      "old": "dict(b=str(C-Q(1,10**104)), b_above_endpoint=str(C+Q(1,10**24)),"
+    },
+    {
+      "new": "kappa == C-Q(1,10**81)-Q(1,10**57)",
+      "old": "kappa == C-Q(1,10**70)-Q(1,10**46)"
+    },
+    {
+      "new": "Endpoint precision35;",
+      "old": "Endpoint precision24;"
+    },
+    {
+      "new": "kappa=C-10^-81-10^-57 exactly; same fixed-grid-maximum proof at precision35.",
+      "old": "kappa=C-10^-70-10^-46 exactly; same fixed-grid-maximum proof at precision24."
+    },
+    {
+      "new": "b='certified complex_lower - 1e-115 (outer/B.json)'",
+      "old": "b='certified complex_lower - 1e-104 (outer/B.json)'"
+    },
+    {
+      "new": "    patch('code/assemble.py', [(\" if DISCOVER:b=Q(M.certify(H,73,owner['live'],False)['lower']);conservative_b=Q(M.certify(H,73,owner['live'],True)['lower'])\", \" def fine_endpoint(bad):\\n  digits=SPEC['outer_refinement']['endpoint_digits']\\n  seed=Q(M.certify(H,73,owner['live'],bad)['lower'])\\n  if digits<=24:return seed\\n  grid=10**digits;left=int(seed*grid);right=left+10**(digits-24)\\n  while right-left>1:\\n   mid=(left+right)//2\\n   lo,hi=FC.moment('fine_mercator',H,73,owner['live'],Q(mid,grid),bad)\\n   if hi<1:left=mid\\n   elif lo>1:right=mid\\n   else:raise ArithmeticError('fine root enclosure exhausted; no endpoint accepted')\\n  return Q(left,grid)\\n if DISCOVER:b=fine_endpoint(False);conservative_b=fine_endpoint(True)\")])\n    spec['outer_refinement'] = PRECISION",
+      "old": "    spec['outer_refinement'] = PRECISION"
+    }
+  ]
+}
diff --git a/research/t740-six-skip-precision35/evidence/OUTER-LEDGER.json b/research/t740-six-skip-precision35/evidence/OUTER-LEDGER.json
new file mode 100644
index 0000000000..df2c062b3d
--- /dev/null
+++ b/research/t740-six-skip-precision35/evidence/OUTER-LEDGER.json
@@ -0,0 +1,575 @@
+{
+  "status": "PASS_FINE_PRIME_PADDING_EXACT_ARITHMETIC",
+  "scope": "Conditional fine-prime padding composition. Fresh native admission is required by verify.py. The cited prime theorem, written gauge-free theorem and inherited all-size interfaces are not proved by this arithmetic. No independent human review is claimed.",
+  "geometry_changes": {
+    "theta_power": {
+      "rational": "2",
+      "decimal": "2"
+    },
+    "halo_power": 48,
+    "core_power": 128,
+    "matrix_exponent": {
+      "rational": "45/16",
+      "decimal": "2.8125"
+    }
+  },
+  "halo_umbrella": {
+    "umbrella_power": 10,
+    "theta_power": {
+      "rational": "2",
+      "decimal": "2"
+    },
+    "exponent_budget": {
+      "rational": "13/2",
+      "decimal": "6.5"
+    },
+    "margin": {
+      "rational": "7/2",
+      "decimal": "3.5"
+    },
+    "fails_from_theta_power": {
+      "rational": "15/4",
+      "decimal": "3.75"
+    }
+  },
+  "complex_lower_short": {
+    "rational": "17297379500642785512428958238173399999999999999999999999999999999999999999999999999999999999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "decimal": "0.0017297379500642785512428958238173399999999999999999999999999999999999999999999999999999999999999999999999999999999"
+  },
+  "complex_lower_pinned": {
+    "rational": "86486897503213927562144791190867/50000000000000000000000000000000000",
+    "decimal": "0.00172973795006427855124289582381734"
+  },
+  "native_moment": [
+    {
+      "rational": "15095849699286165408966218323953075184689081878165654612508460830896804230335423445462086291546702126476542044483149833016453931196509928375014084652887408433763951525913/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904",
+      "decimal": "0.9999999999999999999999999999999999748951791020136616318002438862696807430442136192313138034369708145588773530329377382827810309480847287199053282447467638164994975690951317681557457558562499511924639575594100718169697194948459161670832"
+    },
+    {
+      "rational": "15095849699286165408966218323953075184689081878165654612508460830896804230335423445462086291546702126476542044483149833016453931196509928375014084652887408433763951525941/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904",
+      "decimal": "0.9999999999999999999999999999999999748951791020136616318002438862696807430442136192313138034369708145588773530329377382827810309480847287199053282447467638164994975690969865825953280491740565519896276730028290123527838086207634860524301"
+    }
+  ],
+  "profile": {
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+          "rational": "7884622874833913417876352727467641104384000000000000000000102400000000000000000000102400000000000000000000000000000041/102400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "76.998270262049935721448757104176182660000000000000000000001000000000000000000000001000000000000000000000000000000000400390625"
+        }
+      }
+    }
+  },
+  "rejecting_controls": {
+    "struct_boundary_radix_union": {
+      "endpoint_equality": {
+        "complex_endpoint": {
+          "rational": "0",
+          "decimal": "0"
+        },
+        "q_below_effective": {
+          "rational": "-1/20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-5E-116"
+        },
+        "q_below_internal": {
+          "rational": "-1/20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-5E-116"
+        },
+        "q_below_leaf": {
+          "rational": "-17297379500642785512428958238173399999999999999999999999999999999999999999999999999999999999999999999999999999999/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-1.7297379500642785512428958238173399999999999999999999999999999999999999999999999999999999999999999999999999999999E-124"
+        },
+        "lambda_above_tau": {
+          "rational": "-1/40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-2.5E-116"
+        },
+        "lambda_above_internal": {
+          "rational": "-1/40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-2.5E-116"
+        },
+        "lambda_prime_above_lambda": {
+          "rational": "-1/40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-2.5E-116"
+        },
+        "lambda_prime_above_leaf": {
+          "rational": "-17297379500642785512428958238173399999999999999999999999999999999999999999999999999999999999999999999999999999999/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-1.7297379500642785512428958238173399999999999999999999999999999999999999999999999999999999999999999999999999999999E-124"
+        }
+      },
+      "zero_layout_slack": {
+        "positive_layout_slack": {
+          "rational": "0",
+          "decimal": "0"
+        }
+      },
+      "old_per_axis_scan": {
+        "old_per_axis_scan_above_kappa": {
+          "rational": "-708500664346328494589090129435582463999999999999999999590399999999999999999999590399999999999999999999999999999959/409600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-0.00172973795006427855124289582381733999999999999999999999899999999999999999999999899999999999999999999999999999999989990234375"
+        }
+      },
+      "full_cell_gauge": {
+        "unrecentered_group_gauge": {
+          "rational": "-20479999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997949/10240000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-1.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999979970703125"
+        }
+      },
+      "full_key_sort": {
+        "unnecessary_full_key_sort_above_kappa": {
+          "rational": "-1215999999999999999999999999999999999999999999999999999997951999999999999999999997951999999999999999999999999999999795154596279763177103004793643882554699999999999999999999999999999999999999999999999999999999999999999999999999999959/2048000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-0.5937499999999999999999999999999999999999999999999999999989999999999999999999999989999999999999999999999999999999998999778302147281138198265593964270286621093749999999999999999999999999999999999999999999999999999999999999999999999799805"
+        }
+      },
+      "old_g_factor_union_row": {
+        "old_g_factor_union_row_above_kappa": {
+          "rational": "-1215999999999999999999999999999999999999999999999999999997951999999999999999999997951999999999999999999999999999999590154596279763177103004793643882554699999999999999999999999999999999999999999999999999999999999999999999999999999959/2048000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-0.5937499999999999999999999999999999999999999999999999999989999999999999999999999989999999999999999999999999999999997998801739647281138198265593964270286621093749999999999999999999999999999999999999999999999999999999999999999999999799805"
+        }
+      },
+      "old_theta_chirp_guard": {
+        "old_theta_chirp_guard": {
+          "rational": "-835542503321731642472945450647177912319999999999999999999999999999999999999999999999999999999999999999999999999999487245403720236822896995206356117445300000000000000000000000000000000000000000000000000000000000000000000000000000041/1024000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-0.8159594759001285571024857916476346799999999999999999999999999999999999999999999999999999999999999999999999999999994992630895705437723603468812071459426757812500000000000000000000000000000000000000000000000000000000000000000000000400391"
+        }
+      },
+      "old_linear_guard": {
+        "old_linear_guard": {
+          "rational": "-1859542503321731642472945450647177912319999999999999999999999999999999999999999999999999999999999999999999999999999179645403720236822896995206356117445300000000000000000000000000000000000000000000000000000000000000000000000000000041/2048000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-0.9079797379500642785512428958238173399999999999999999999999999999999999999999999999999999999999999999999999999999995994362322852718861801734406035729713378906250000000000000000000000000000000000000000000000000000000000000000000000200195"
+        }
+      },
+      "old_union_tag_2beta": {
+        "old_union_tag_2beta": {
+          "rational": "-204799999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999877/204800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993994140625"
+        }
+      },
+      "matrix_below_strassen": {
+        "strassen_integer_power_gap": {
+          "rational": "-423",
+          "decimal": "-423"
+        }
+      },
+      "halo_too_short": {
+        "halo_covers_generic_inverse_radius": {
+          "rational": "-3",
+          "decimal": "-3"
+        }
+      },
+      "core_too_small": {
+        "microbox_halo_volume": {
+          "rational": "-409599999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999877/409600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999969970703125"
+        },
+        "microbox_face_corrections_above_kappa": {
+          "rational": "-307377125166086582123647272532358895615999999999999999999897599999999999999999999897599999999999999999999999999999959/102400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-3.001729737950064278551242895823817339999999999999999999998999999999999999999999998999999999999999999999999999999999599609375"
+        }
+      },
+      "group_equals_dimension": {
+        "group_below_dimension": {
+          "rational": "0",
+          "decimal": "0"
+        },
+        "group_key_fits_record": {
+          "rational": "0",
+          "decimal": "0"
+        },
+        "membership_arithmetic_fits_record": {
+          "rational": "-41/409600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-1.0009765625E-115"
+        }
+      },
+      "epsilon_equals_one": {
+        "epsilon_below_one": {
+          "rational": "0",
+          "decimal": "0"
+        },
+        "global_gamma_power_slack": {
+          "rational": "-1/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-1E-115"
+        },
+        "actual_logarithmic_gamma_guard": {
+          "rational": "0",
+          "decimal": "0"
+        },
+        "source_axis_superpolynomial": {
+          "rational": "0",
+          "decimal": "0"
+        },
+        "gaussian_above_main": {
+          "rational": "-1063788839289531309014380931647664099999999999999999999999999999999999999999999999999999999999999999999999999999877/2048000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-5.1942814418434145947967818928108598632812499999999999999999999999999999999999999999999999999999999999999999999993994140625E-118"
+        }
+      },
+      "epsilon_not_above_r0_slack": {
+        "global_gamma_power_slack": {
+          "rational": "0",
+          "decimal": "0"
+        }
+      },
+      "beta_below_gaussian_window": {
+        "gaussian_above_main": {
+          "rational": "-42862799554460795000350757073905735299999999999999999999999999999999999999999999999999999999999999999999999999971341/2048000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+          "decimal": "-2.092910134495156005876501810249303481445312499999999999999999999999999999999999999999999999999999999999999999998600634765625E-116"
+        }
+      },
+      "beta_above_membership_window": {
+        "membership_arithmetic_fits_record": {
+          "rational": "0",
+          "decimal": "0"
+        }
+      }
+    }
+  },
+  "pr1673_kappa": {
+    "rational": "1677160151714381/1000000000000000000",
+    "decimal": "0.001677160151714381"
+  },
+  "improvement_over_pr1673": {
+    "rational": "52577798349897551242895823817339999999999999999999998999999999999999999999999/1000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "decimal": "0.000052577798349897551242895823817339999999999999999999998999999999999999999999999"
+  },
+  "source_sha256": {
+    "new/SPEC.json": "434b127573943dc2e901373787587c8307fd2047ed3d0523825a825f77ddd96e",
+    "CLAIM.json": "d34333c2664d1a79f9dcd59206a90a9b1c5151c1693483ec49d80337c0ff1eda"
+  }
+}
diff --git a/research/t740-six-skip-precision35/evidence/VALIDATION.json b/research/t740-six-skip-precision35/evidence/VALIDATION.json
new file mode 100644
index 0000000000..be3d8a9faf
--- /dev/null
+++ b/research/t740-six-skip-precision35/evidence/VALIDATION.json
@@ -0,0 +1,78 @@
+{
+  "admission_sha256": "ec9d9862350e79b9dd42b4889ca4b4dc0ab09b17602bb608edd8a08e652ab47a",
+  "baseline_admission_sha256": "5127595fc2ce577435e54f19986e1f8a0aedf59ac803345d87fb3afea6bbce9d",
+  "baseline_complete": true,
+  "baseline_native_receipt_sha256": "efcac8f6f2a992f71537d1567a3c75857f9641a20f0bf93ad5a6b24de987934b",
+  "baseline_package_manifest_sha256": "b1c276654ef4472e854775f23554b56ab6830686b5d921af699038f806d42f6a",
+  "baseline_release_projection": {
+    "kappa_decimal": "0.0017297379500642785512419999999999999999999998999999999999999999999999",
+    "manifest_sha256": "b1c276654ef4472e854775f23554b56ab6830686b5d921af699038f806d42f6a",
+    "status": "PASS_RELEASE"
+  },
+  "baseline_terminal_receipt_sha256": "5d7918368c57210fc18b7b4a2ba594b0445e519edc854097593f606ffeb40290",
+  "candidate_admission_sha256": "ec9d9862350e79b9dd42b4889ca4b4dc0ab09b17602bb608edd8a08e652ab47a",
+  "candidate_checkpoint_scope": "Reused only hash-verified completed discovery (bind, emit, full audit, invoice, assembly, freeze and independent replay), outer ledger and independent arithmetic. The full strict candidate release ran fresh. A prior adapter assertion used the precision-30 slack exponents; its failed attempt and corrected derivation are retained.",
+  "candidate_complete": true,
+  "candidate_native_receipt_sha256": "efcac8f6f2a992f71537d1567a3c75857f9641a20f0bf93ad5a6b24de987934b",
+  "candidate_package_manifest_sha256": "e74d35750e18e6e0281976c7bde578ab02b054b25e09f3137b0d8533fb7ad143",
+  "candidate_release_projection": {
+    "kappa_decimal": "0.001729737950064278551242895823817339999999999999999999998999999999999999999999999",
+    "manifest_sha256": "e74d35750e18e6e0281976c7bde578ab02b054b25e09f3137b0d8533fb7ad143",
+    "status": "PASS_RELEASE"
+  },
+  "candidate_terminal_receipt_sha256": "fad6f99c358f8291a6a86ea10225cf04c3480b5e58dcb2d8e6419e24200412ac",
+  "controller_controls": [
+    "alias two whole owners",
+    "helper on active data family",
+    "owner in private namespace",
+    "wrong residual width",
+    "wrong spectator coordinate",
+    "omit idle remainder",
+    "omit private zero buffers",
+    "private buffer aliases data",
+    "pooled slots exchange invocation time (equal widths)",
+    "pooled slot time shifted",
+    "understate physical reserve",
+    "extra: wrong provider at its invocation",
+    "extra: stale per-call local program hash",
+    "extra: stale serialized provider program",
+    "extra: unbound residual adapter hash",
+    "extra: wrong per-call residual width",
+    "extra: wrong sweep provider",
+    "extra: entering helper width silently restored to nine",
+    "gauge44: wrong provider at its invocation",
+    "gauge44: stale per-call local program hash",
+    "gauge44: stale serialized provider program",
+    "gauge44: unbound residual adapter hash",
+    "gauge44: wrong per-call residual width",
+    "gauge44: wrong sweep provider",
+    "gauge44: entering helper width silently restored to nine"
+  ],
+  "controller_summary_note": "The unchanged supplier summary retains the historical controller=15 field; the actual completed ASYNC-AUDIT lists25 distinct rejected controls. Original source and receipts are unchanged; this evidence reports the actual list.",
+  "controls": {
+    "admission": 139,
+    "bit": 12,
+    "controller": 25,
+    "geometry": 6,
+    "independent_owner": 8
+  },
+  "files": {
+    "DERIVATION.json": "fe23026d1947a24511a950cc66b01dcbdb753fa662cc503052b9dabe3ba0c951",
+    "OUTER-LEDGER.json": "f0bd022cdb122bb0b4415f115d6b599c40c98ebb19f91d5596633e59a87067a5"
+  },
+  "gain": "895823817340000000000099999999999000000000000099999999999/1000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+  "gain_over_latest": "817340000000000000000099999000000000000000000099999/1000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+  "inherited_supplier_summary_controls": {
+    "admission": 139,
+    "bit": 12,
+    "controller": 15,
+    "geometry": 6,
+    "independent_owner": 8
+  },
+  "kappa": "1729737950064278551242895823817339999999999999999999998999999999999999999999999/1000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+  "latest": "17297379500642785512428958229999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000000000",
+  "previous": "17297379500642785512419999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "projection_scope": "Terminal status, exact point and manifest projected from authentic completed receipts; machine timing omitted. Original bytes remain unchanged privately and are SHA256-bound. Registered replay checks finite evidence; reproduce.py performs the full changed release.",
+  "release_sha256": "fad6f99c358f8291a6a86ea10225cf04c3480b5e58dcb2d8e6419e24200412ac",
+  "status": "PASS_T740_SIX_SKIP_PRECISION35_COMPLETE_RELEASE"
+}
diff --git a/research/t740-six-skip-precision35/reproduce.py b/research/t740-six-skip-precision35/reproduce.py
new file mode 100644
index 0000000000..53c766d887
--- /dev/null
+++ b/research/t740-six-skip-precision35/reproduce.py
@@ -0,0 +1,194 @@
+"""Source-bound precision refinement; complete baseline and changed release are mandatory.
+
+Credit Nick Petalas/PR3054, dcharb78/PR3042 and the retained native/outer lineage.
+Substantial OpenAI Codex assistance. Apache-2.0."""
+
+import ast
+import hashlib
+import importlib.util
+import json
+import os
+import subprocess
+import sys
+from fractions import Fraction as Q
+from pathlib import Path
+import argparse
+
+P = Path(__file__).resolve().parent
+ROOT = P.parents[1]
+parser = argparse.ArgumentParser(description=__doc__)
+parser.add_argument("--baseline-work", type=Path, required=True)
+parser.add_argument("--work", type=Path, required=True)
+a = parser.parse_args()
+BASELINE = a.baseline_work.resolve()
+WORK = a.work.resolve()
+PKG = ROOT / "research/rank7-t740-carrier-skips"
+
+
+def need(ok, msg):
+    if not ok:
+        raise ValueError(msg)
+
+
+def read(p):
+    return json.loads(p.read_bytes())
+
+
+def sha(p):
+    return hashlib.sha256(p.read_bytes()).hexdigest()
+
+
+def save(p, x):
+    p.write_text(json.dumps(x, indent=2, sort_keys=True) + "\n")
+
+
+def load(p, name):
+    spec = importlib.util.spec_from_file_location(name, p)
+    m = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(m)
+    return m
+
+
+need(os.name == "posix" and not sys.flags.optimize, "POSIX and assertions required")
+need(not WORK.is_relative_to(P), "replay workspace outside published package")
+binding = load(P / "verify.py", "refinement_source_binding")
+binding.authenticate()
+sys.path.insert(0, str(PKG))
+m = load(PKG / "reproduce.py", "credited_3054_reproduce")
+r = read(BASELINE / "RESULT.json")
+stages = read(BASELINE / "STAGES.json")
+need(
+    r["status"] == "PASS_T740_SIX_SKIP_COMPLETE_RELEASE", "mandatory completed baseline"
+)
+for s in stages:
+    need(
+        s["exit_code"] == 0
+        and sha(BASELINE / (s["stage"] + ".log")) == s["log_sha256"],
+        "baseline stage and exact log",
+    )
+need(
+    m.check_release(BASELINE, BASELINE / "pr3042", r["fill_sha256"], stages) == r,
+    "full source-bound baseline rederived",
+)
+need(not WORK.exists(), "fresh refinement work")
+WORK.mkdir()
+recipe = read(BASELINE / "RECIPE.json")["commands"]
+derive = [c.copy() for n, c in recipe if n == "derive-closed-adapters"]
+need(len(derive) == 1, "one unchanged adapter derivation")
+c = derive[0]
+need(
+    c == binding.expected_command("derive-closed-adapters", BASELINE, sys.executable),
+    "exact source-pinned derivation command; only workspace/interpreter paths relocate",
+)
+c[c.index("--out") + 1] = str(WORK / "adapters-original")
+subprocess.run(c, check=True)
+original = BASELINE / "run/adapters/admit_extension.py"
+reference = WORK / "adapters-original/admit_extension.py"
+need(
+    reference.read_bytes() == original.read_bytes(),
+    "fresh original adapter derivation equality",
+)
+body = reference.read_text()
+edits = read(P / "PRECISION-EDITS.json")
+edits = [x for x in edits if not x["old"].startswith(("COMPARISONS = {", "choices="))]
+need(len(edits) == 7, "only declared precision and matching outer-gap changes")
+for e in edits:
+    need(body.count(e["old"]) == 1, "one exact precision preimage: " + e["old"])
+    body = body.replace(e["old"], e["new"])
+
+
+def checks(t):
+    tree = ast.parse(t)
+    return sum(isinstance(x, ast.Assert) for x in ast.walk(tree)), sum(
+        isinstance(x, ast.Call) and isinstance(x.func, ast.Name) and x.func.id == "need"
+        for x in ast.walk(tree)
+    )
+
+
+need(
+    checks(body) == checks(reference.read_text()),
+    "all assertion and explicit check counts retained",
+)
+adapter = WORK / "admit_precision35.py"
+adapter.write_text(body)
+save(
+    WORK / "DERIVATION.json",
+    dict(
+        reference_sha256=sha(reference),
+        candidate_sha256=sha(adapter),
+        replacements=edits,
+    ),
+)
+command = [c.copy() for n, c in recipe if n == "complete-admission"]
+need(len(command) == 1, "one complete admission command")
+command = command[0]
+need(
+    command == binding.expected_command("complete-admission", BASELINE, sys.executable),
+    "exact source-pinned complete admission command",
+)
+command[:3] = [sys.executable, "-B", str(adapter)]
+command[command.index("--work") + 1] = str(WORK / "candidate")
+sys.path.insert(0, str(P))
+nom = load(P / "verify.py", "refinement_arithmetic").calculate()
+need(Q(r["kappa"]) == Q(nom["previous"]), "exact current comparison point")
+env = dict(
+    os.environ,
+    PYTHONDONTWRITEBYTECODE="1",
+    PYTHONINTMAXSTRDIGITS="0",
+    OPENBLAS_NUM_THREADS="1",
+    OMP_NUM_THREADS="1",
+)
+for k in (
+    "PYTHONOPTIMIZE",
+    "PYTHONPATH",
+    "WITNESS_SPEC",
+    "WITNESS_RECORD",
+    "WITNESS_DISCOVER",
+):
+    env.pop(k, None)
+print("START_FULL_PRECISION35_ADMISSION", flush=True)
+with (WORK / "complete-admission.log").open("w") as log:
+    subprocess.run(command, check=True, env=env, stdout=log, stderr=subprocess.STDOUT)
+a = read(WORK / "candidate/RESULT.json")
+release = read(WORK / "candidate/release/RELEASE-RECEIPT.json")
+need(
+    a["status"] == "PASS_REPLICA_ORDER_FILL_DERIVATIVE_COMPLETE_RELEASE"
+    and release["status"] == "PASS_RELEASE",
+    "complete actual candidate release",
+)
+need(
+    Q(a["kappa"]) == Q(nom["kappa"]) == Q(release["kappa_decimal"]) > Q(r["kappa"]) and Q(a["kappa"]) > Q(nom["latest"]),
+    "actual exact improved released point",
+)
+for k in (
+    "profile",
+    "fill_sha256",
+    "order_sha256",
+    "dispatch_sha256",
+    "source_manifest_sha256",
+    "native_receipt_sha256",
+):
+    need(
+        a[k] == read(BASELINE / "run/candidate/RESULT.json")[k],
+        "unchanged physical/source/native input " + k,
+    )
+need(
+    a["release_receipt_sha256"] == sha(WORK / "candidate/release/RELEASE-RECEIPT.json"),
+    "actual terminal receipt hash",
+)
+save(
+    WORK / "RESULT.json",
+    dict(
+        status="PASS_T740_SIX_SKIP_PRECISION35_COMPLETE_RELEASE",
+        kappa=a["kappa"],
+        previous=r["kappa"],
+        gain=str(Q(a["kappa"]) - Q(r["kappa"])),
+        latest=nom["latest"],
+        gain_over_latest=str(Q(a["kappa"]) - Q(nom["latest"])),
+        baseline_complete=True,
+        candidate_complete=True,
+        admission_sha256=sha(WORK / "candidate/RESULT.json"),
+        release_sha256=sha(WORK / "candidate/release/RELEASE-RECEIPT.json"),
+    ),
+)
+print("PASS_T740_SIX_SKIP_PRECISION35_COMPLETE_RELEASE", a["kappa"], flush=True)
diff --git a/research/t740-six-skip-precision35/requirements-full.txt b/research/t740-six-skip-precision35/requirements-full.txt
new file mode 100644
index 0000000000..1c940743f4
--- /dev/null
+++ b/research/t740-six-skip-precision35/requirements-full.txt
@@ -0,0 +1,5 @@
+numpy==1.26.4
+scipy==1.15.3
+sympy==1.14.0
+mpmath==1.3.0
+gmpy2==2.3.2
diff --git a/research/t740-six-skip-precision35/seal.py b/research/t740-six-skip-precision35/seal.py
new file mode 100644
index 0000000000..427d5ca152
--- /dev/null
+++ b/research/t740-six-skip-precision35/seal.py
@@ -0,0 +1,151 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Derive privacy-preserving evidence only from completed authenticated replays.
+
+Terminal projections omit machine timing; original receipts remain unchanged
+in the external workspace and are committed to by their exact SHA256 digests.
+Substantial OpenAI Codex assistance. Apache-2.0.
+"""
+
+import argparse
+import shutil
+import sys
+
+import verify as v
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--baseline-work", type=v.Path, required=True)
+    parser.add_argument("--work", type=v.Path, required=True)
+    a = parser.parse_args()
+    baseline, work = a.baseline_work.resolve(), a.work.resolve()
+    v.authenticate()
+    sys.path.insert(0, str(v.ROOT / "research/rank7-t740-carrier-skips"))
+    original = v.load(
+        v.ROOT / "research/rank7-t740-carrier-skips/reproduce.py",
+        "credited_baseline_seal",
+    )
+    result = v.read(baseline / "RESULT.json")
+    stages = v.read(baseline / "STAGES.json")
+    for stage in stages:
+        v.need(
+            stage["exit_code"] == 0
+            and v.sha(baseline / (stage["stage"] + ".log")) == stage["log_sha256"],
+            "authentic completed baseline stage",
+        )
+    v.need(
+        original.check_release(
+            baseline, baseline / "pr3042", result["fill_sha256"], stages
+        )
+        == result,
+        "completed baseline fully rederived",
+    )
+    checked = v.read(work / "RESULT.json")
+    v.completion(checked)
+    v.need(
+        v.sha(work / "candidate/RESULT.json") == checked["admission_sha256"]
+        and v.sha(work / "candidate/release/RELEASE-RECEIPT.json")
+        == checked["release_sha256"],
+        "completed refinement result authenticates actual admission and terminal receipt",
+    )
+    derivation = v.read(work / "DERIVATION.json")
+    v.need(
+        derivation["replacements"] == v.read(v.P / "PRECISION-EDITS.json")
+        and derivation["reference_sha256"]
+        == v.sha(baseline / "run/adapters/admit_extension.py")
+        and derivation["candidate_sha256"] == v.sha(work / "admit_precision35.py"),
+        "exact declared source derivation",
+    )
+    arithmetic = v.calculate()
+    for key in ("kappa", "previous", "gain", "latest", "gain_over_latest"):
+        v.need(v.Q(checked[key]) == v.Q(arithmetic[key]), "exact completed refinement")
+    evidence = dict(checked)
+    for key, directory in (
+        ("baseline", baseline / "run/candidate"),
+        ("candidate", work / "candidate"),
+    ):
+        admission = v.read(directory / "RESULT.json")
+        receipt_path = directory / "release/RELEASE-RECEIPT.json"
+        receipt = v.read(receipt_path)
+        v.need(
+            admission["status"]
+            == "PASS_REPLICA_ORDER_FILL_DERIVATIVE_COMPLETE_RELEASE",
+            "actual complete admission",
+        )
+        v.need(
+            admission["release_receipt_sha256"] == v.sha(receipt_path)
+            and admission["package_manifest_sha256"] == receipt["manifest_sha256"],
+            "actual terminal receipt and admitted manifest",
+        )
+        for stage in admission["stages"]:
+            v.need(
+                stage["exit_code"] == 0
+                and v.sha(directory / (stage["name"] + ".log")) == stage["log_sha256"],
+                "all actual admission stages and logs",
+            )
+        evidence[key + "_release_projection"] = {
+            field: receipt[field]
+            for field in ("status", "kappa_decimal", "manifest_sha256")
+        }
+        evidence[key + "_terminal_receipt_sha256"] = v.sha(receipt_path)
+        evidence[key + "_admission_sha256"] = v.sha(directory / "RESULT.json")
+        evidence[key + "_package_manifest_sha256"] = admission[
+            "package_manifest_sha256"
+        ]
+        evidence[key + "_native_receipt_sha256"] = admission["native_receipt_sha256"]
+        if "checkpoint_scope" in admission:
+            evidence[key + "_checkpoint_scope"] = admission["checkpoint_scope"]
+    controls = v.read(work / "candidate/release/verify/RESULT.json")
+    audit = v.read(
+        work / "candidate/release/verify/strict/global/audit/ASYNC-AUDIT.json"
+    )
+    v.need(
+        audit["status"]
+        == "PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS"
+        and audit["mutation_controls_run"] is True,
+        "actual complete controller mutation audit",
+    )
+    names = audit["mutations_rejected"]
+    v.need(len(names) == len(set(names)) == 25, "all25 actual controller controls")
+    baseline_audit = v.read(
+        baseline / "run/candidate/release/verify/strict/global/audit/ASYNC-AUDIT.json"
+    )
+    expected_names = v.read(
+        v.ROOT / "research/rank7-t740-carrier-skips/evidence/ASYNC-AUDIT.json"
+    )["mutations_rejected"]
+    v.need(
+        baseline_audit["mutations_rejected"] == names == expected_names,
+        "both completed releases retain every named original controller control",
+    )
+    evidence["inherited_supplier_summary_controls"] = controls["controls"]
+    evidence["controller_controls"] = names
+    evidence["controls"] = dict(controls["controls"], controller=len(names))
+    evidence["controller_summary_note"] = (
+        "The unchanged supplier summary retains the historical controller=15 field; "
+        "the actual completed ASYNC-AUDIT lists25 distinct rejected controls. "
+        "Original source and receipts are unchanged; this evidence reports the actual list."
+    )
+    evidence["projection_scope"] = (
+        "Terminal status, exact point and manifest projected from authentic completed receipts; "
+        "machine timing omitted. Original bytes remain unchanged privately and are SHA256-bound. "
+        "Registered replay checks finite evidence; reproduce.py performs the full changed release."
+    )
+    out = v.P / "evidence"
+    v.need(not out.exists(), "fresh evidence output")
+    out.mkdir()
+    for source, name in (
+        (work / "candidate/package/outer/LEDGER.json", "OUTER-LEDGER.json"),
+        (work / "DERIVATION.json", "DERIVATION.json"),
+    ):
+        shutil.copyfile(source, out / name)
+    evidence["files"] = {p.name: v.sha(p) for p in out.iterdir()}
+    (out / "VALIDATION.json").write_text(
+        v.json.dumps(evidence, indent=2, sort_keys=True) + "\n"
+    )
+    v.run()
+    print("PASS_SEALED_COMPLETE_REFINEMENT")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/t740-six-skip-precision35/test_verify.py b/research/t740-six-skip-precision35/test_verify.py
new file mode 100644
index 0000000000..d699e1e2fb
--- /dev/null
+++ b/research/t740-six-skip-precision35/test_verify.py
@@ -0,0 +1,107 @@
+"""Reject incomplete releases and damaged actual outer evidence.
+
+Substantial OpenAI Codex assistance. Apache-2.0.
+"""
+
+import copy
+import os
+import subprocess
+import sys
+import tempfile
+import unittest
+
+import verify as v
+
+
+class EvidenceControls(unittest.TestCase):
+    @unittest.skipUnless(os.name == "posix", "full replay uses POSIX process cleanup")
+    def test_cli_refuses_preflight_baseline(self):
+        with tempfile.TemporaryDirectory() as directory:
+            root = v.Path(directory)
+            baseline = root / "baseline"
+            baseline.mkdir()
+            (baseline / "RESULT.json").write_text(
+                v.json.dumps({"status": "PREFLIGHT_ONLY_NOT_A_RELEASE"})
+            )
+            (baseline / "STAGES.json").write_text("[]")
+            output = root / "candidate"
+            result = subprocess.run(
+                [
+                    sys.executable,
+                    "-B",
+                    str(v.P / "reproduce.py"),
+                    "--baseline-work",
+                    str(baseline),
+                    "--work",
+                    str(output),
+                ],
+                capture_output=True,
+                text=True,
+                timeout=30,
+            )
+            self.assertNotEqual(result.returncode, 0)
+            self.assertIn("mandatory completed baseline", result.stderr)
+            self.assertFalse(output.exists())
+
+    def test_original_source_derivation(self):
+        baseline, candidate = v.expected_adapter_hashes()
+        valid = dict(
+            reference_sha256=baseline,
+            candidate_sha256=candidate,
+            replacements=v.read(v.P / "PRECISION-EDITS.json"),
+        )
+        v.check_derivation(valid)
+        for key in ("reference_sha256", "candidate_sha256"):
+            with self.subTest(key=key), self.assertRaises(ValueError):
+                v.check_derivation(dict(valid, **{key: "0" * 64}))
+
+    def test_outer_b_gap_tracks_endpoint_precision(self):
+        edits = v.read(v.P / "PRECISION-EDITS.json")
+        v.check_outer_gap_edit(edits)
+        broken = [dict(e) for e in edits]
+        gap = next(e for e in broken if e["old"].startswith("dict(b=str("))
+        gap["new"] = gap["new"].replace("10**115", "10**110")
+        with self.assertRaises(ValueError):
+            v.check_outer_gap_edit(broken)
+        broken = [dict(e) for e in edits]
+        kappa = next(e for e in broken if e["old"].startswith("kappa == C-Q("))
+        kappa["new"] = kappa["new"].replace("10**81", "10**76")
+        with self.assertRaises(ValueError):
+            v.check_outer_gap_edit(broken)
+
+    def test_incomplete_releases(self):
+        valid = dict(
+            baseline_complete=True,
+            candidate_complete=True,
+            status="PASS_T740_SIX_SKIP_PRECISION35_COMPLETE_RELEASE",
+        )
+        v.completion(valid)
+        for key in ("baseline_complete", "candidate_complete"):
+            for value in (False, 1, "true"):
+                with self.subTest(key=key, value=value):
+                    bad = dict(valid, **{key: value})
+                    with self.assertRaises(ValueError):
+                        v.completion(bad)
+        with self.assertRaises(ValueError):
+            v.completion(dict(valid, status="PREFLIGHT_ONLY_NOT_A_RELEASE"))
+
+    def test_actual_outer_mutants(self):
+        path = v.ROOT / "research/rank7-t740-carrier-skips/evidence/OUTER-LEDGER.json"
+        actual = v.read(path)
+        point = actual["rows"]["struct_boundary_radix_union"]["kappa"]["rational"]
+        v.check_ledger(actual, point)
+        with self.assertRaises(ValueError):
+            v.check_ledger(actual, v.Q(point) + v.Q(1, 10**35))
+        zero = copy.deepcopy(actual)
+        checks = zero["rows"]["struct_boundary_radix_union"]["strict_checks"]
+        checks[next(iter(checks))]["rational"] = "0"
+        with self.assertRaises(ValueError):
+            v.check_ledger(zero, point)
+        missing = copy.deepcopy(actual)
+        missing["rejecting_controls"]["struct_boundary_radix_union"].popitem()
+        with self.assertRaises(ValueError):
+            v.check_ledger(missing, point)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/research/t740-six-skip-precision35/verify.py b/research/t740-six-skip-precision35/verify.py
new file mode 100644
index 0000000000..aacdb0bf17
--- /dev/null
+++ b/research/t740-six-skip-precision35/verify.py
@@ -0,0 +1,258 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Exact arithmetic refinement; finite receipt checks do not rerun native chains.
+
+Credit the PR3054/3042 construction and both retained rational engines.
+Substantial OpenAI Codex assistance. No independent arithmetic invention claimed.
+"""
+
+import hashlib
+import importlib.util
+import json
+import ast
+from fractions import Fraction as Q
+from pathlib import Path
+from pathlib import PurePosixPath
+
+P = Path(__file__).resolve().parent
+ROOT = P.parents[1]
+PROFILE = {
+    1: 16376940,
+    2: 4741920,
+    3: 1594737,
+    4: 719280,
+    5: 137085,
+    8: 53280,
+    48: 281903,
+}
+
+
+def need(ok, msg):
+    if not ok:
+        raise ValueError(msg)
+
+
+def read(p):
+    return json.loads(p.read_bytes())
+
+
+def sha(p):
+    return hashlib.sha256(p.read_bytes()).hexdigest()
+
+
+def load(p, name):
+    spec = importlib.util.spec_from_file_location(name, p)
+    m = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(m)
+    return m
+
+
+def authenticate():
+    for r in read(P / "SOURCES.json")["files"]:
+        if r["usage"] == "input":
+            need(sha(ROOT / r["path"]) == r["sha256"], "source drift: " + r["path"])
+
+
+def check_outer_gap_edit(edits=None):
+    edits = read(P / "PRECISION-EDITS.json") if edits is None else edits
+    precision = next(e for e in edits if e["old"].startswith("PRECISION = dict("))
+    assignment = ast.parse(precision["new"]).body[0]
+    digits = {
+        keyword.arg: ast.literal_eval(keyword.value)
+        for keyword in assignment.value.keywords
+    }["endpoint_digits"]
+    gap_power = digits + 80  # same R0 exponent used by outer/check_ledger.py
+    gap = next(e for e in edits if e["old"].startswith("dict(b=str("))
+    claim = next(e for e in edits if e["old"].startswith("b='certified complex_lower"))
+    need(f"10**{gap_power}" in gap["new"], "B gap must match the outer R0 exponent")
+    need(f"1e-{gap_power}" in claim["new"], "outer claim text must name the exact B gap")
+    kappa = next(e for e in edits if e["old"].startswith("kappa == C-Q("))
+    need(
+        f"10**{digits + 46}" in kappa["new"]
+        and f"10**{digits + 22}" in kappa["new"],
+        "fixed-grid kappa slacks must follow endpoint precision",
+    )
+
+
+def calculate():
+    authenticate()
+    check_outer_gap_edit()
+    root = load(ROOT / "research/rank7-joint-endframes/tools/root.py", "credited_root")
+    other = load(
+        ROOT / "research/two-sided-helper-extraction/tools/audit_moment.py",
+        "credited_other",
+    )
+    lo, hi = root.kappa_from_profile(PROFILE, 740, digits=45)
+    c = Q((lo * 10**35).__floor__(), 10**35)
+    k = c - Q(1, 10**57) - Q(1, 10**81)
+    old = Q(
+        read(ROOT / "research/rank7-t740-carrier-skips/evidence/ADMISSION-RESULT.json")[
+            "kappa"
+        ]
+    )
+    latest = Q("0.001729737950064278551242895823") - Q(1, 10**52) - Q(1, 10**76)
+    need(k > old and k > latest and c <= lo < hi < c + Q(1, 10**35), "strict gain over PR3054 and PR3115; 35-digit root bracket")
+    need(sum(r * n for r, n in PROFILE.items()) == 65088 * 740, "complete rank mass")
+    for engine in (root, other):
+        need(engine.moment(PROFILE, c, 896 * 740)[1] < 1, "accepted endpoint")
+        need(
+            engine.moment(PROFILE, c + Q(1, 10**35), 896 * 740)[0] > 1,
+            "next grid rejected",
+        )
+        for rank in (1, 48):
+            bad = dict(PROFILE)
+            bad[rank] += 1
+            need(engine.moment(bad, c, 896 * 740)[0] > 1, "unpaid child rejected")
+    return {
+        key: str(v)
+        for key, v in dict(
+            kappa=k,
+            previous=old,
+            gain=k - old,
+            latest=latest,
+            gain_over_latest=k-latest,
+            complex_lower=c,
+            root_lower=lo,
+            root_upper=hi,
+        ).items()
+    }
+
+
+def completion(e):
+    need(
+        e["baseline_complete"] is True and e["candidate_complete"] is True,
+        "both actual complete releases required",
+    )
+    need(
+        e["status"] == "PASS_T740_SIX_SKIP_PRECISION35_COMPLETE_RELEASE",
+        "complete refinement",
+    )
+
+
+def expected_adapter_hashes():
+    original = ROOT / "research/two-sided-helper-extraction/tools/admit_channel408.py"
+    record = read(
+        ROOT / "research/rank7-t740-carrier-skips/evidence/ADAPTER-DERIVATION.json"
+    )
+    inherited = record["changes"]["admit_extension.py"]
+    need(sha(original) == inherited["before_sha256"], "original strict source adapter")
+    body = original.read_text()
+    for edit in inherited["replacements"]:
+        need(body.count(edit["old"]) == 1, "inherited exact source preimage")
+        body = body.replace(edit["old"], edit["new"])
+    baseline = hashlib.sha256(body.encode()).hexdigest()
+    need(
+        baseline == inherited["after_sha256"],
+        "complete published adapter reconstructed",
+    )
+    for edit in read(P / "PRECISION-EDITS.json"):
+        need(body.count(edit["old"]) == 1, "exact precision source preimage")
+        body = body.replace(edit["old"], edit["new"])
+    return baseline, hashlib.sha256(body.encode()).hexdigest()
+
+
+def check_derivation(data):
+    baseline, candidate = expected_adapter_hashes()
+    need(
+        data["reference_sha256"] == baseline and data["candidate_sha256"] == candidate,
+        "exact complete source derivation hashes",
+    )
+    need(
+        data["replacements"] == read(P / "PRECISION-EDITS.json"),
+        "exact seven declared precision/outer-gap/selector changes",
+    )
+
+
+def expected_command(stage, baseline, python):
+    recipe = read(ROOT / "research/rank7-t740-carrier-skips/evidence/RECIPE.json")[
+        "commands"
+    ]
+    derive = [command for name, command in recipe if name == "derive-closed-adapters"]
+    selected = [command for name, command in recipe if name == stage]
+    need(len(derive) == len(selected) == 1, "unique source-pinned recipe stage")
+    prefix = str(PurePosixPath(derive[0][2]).parents[2])
+    command = [arg.replace(prefix + "/", str(baseline) + "/") for arg in selected[0]]
+    command[0] = python
+    return command
+
+
+def check_evidence(e, arithmetic):
+    completion(e)
+    for k in ("kappa", "previous", "gain", "latest", "gain_over_latest"):
+        need(Q(e[k]) == Q(arithmetic[k]), "exact evidence " + k)
+    need(
+        e["controls"]
+        == dict(admission=139, bit=12, controller=25, independent_owner=8, geometry=6),
+        "all actual inherited release controls",
+    )
+    need(
+        len(e["controller_controls"]) == len(set(e["controller_controls"])) == 25,
+        "all25 actual controller rejections, not the inherited summary count",
+    )
+    expected_controls = read(
+        ROOT / "research/rank7-t740-carrier-skips/evidence/ASYNC-AUDIT.json"
+    )["mutations_rejected"]
+    need(
+        e["controller_controls"] == expected_controls,
+        "every named original controller control retained",
+    )
+    need(
+        e["inherited_supplier_summary_controls"]
+        == dict(admission=139, bit=12, controller=15, independent_owner=8, geometry=6),
+        "disclosed unchanged inherited supplier summary",
+    )
+    for key, point in (
+        ("baseline", arithmetic["previous"]),
+        ("candidate", arithmetic["kappa"]),
+    ):
+        projection = e[key + "_release_projection"]
+        need(
+            projection["status"] == "PASS_RELEASE"
+            and Q(projection["kappa_decimal"]) == Q(point),
+            "actual complete terminal projection: " + key,
+        )
+        need(
+            projection["manifest_sha256"] == e[key + "_package_manifest_sha256"],
+            "actual admitted manifest: " + key,
+        )
+    need(
+        e["baseline_native_receipt_sha256"] == e["candidate_native_receipt_sha256"],
+        "same authenticated unchanged native receipt",
+    )
+
+
+def check_ledger(ledger, kappa):
+    row = ledger["rows"]["struct_boundary_radix_union"]
+    need(Q(row["kappa"]["rational"]) == Q(kappa), "actual outer point")
+    need(
+        len(row["strict_checks"]) == 63
+        and all(Q(v["rational"]) > 0 for v in row["strict_checks"].values()),
+        "all63 strict rows",
+    )
+    bad = ledger["rejecting_controls"]["struct_boundary_radix_union"]
+    need(
+        len(bad) == 17
+        and all(
+            v and all(Q(x["rational"]) <= 0 for x in v.values()) for v in bad.values()
+        ),
+        "all17 original outer controls",
+    )
+
+
+def run():
+    arithmetic = calculate()
+    e = read(P / "evidence/VALIDATION.json")
+    check_evidence(e, arithmetic)
+    need(
+        set(e["files"]) == {"OUTER-LEDGER.json", "DERIVATION.json"},
+        "complete declared evidence inventory",
+    )
+    for name, h in e["files"].items():
+        need(sha(P / "evidence" / name) == h, "evidence digest " + name)
+    check_derivation(read(P / "evidence/DERIVATION.json"))
+    check_ledger(read(P / "evidence/OUTER-LEDGER.json"), arithmetic["kappa"])
+    print("PASS_T740_SIX_SKIP_PRECISION35", arithmetic["gain"])
+
+
+if __name__ == "__main__":
+    run()