Verify the L300/L301 fixed-cut shared-handoff obstruction (no new κ)

research/shared-crossing-cut9047-20261025/HANDOFF.md

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+Research discussion / PR / artifact:
+This package: shared-crossing-cut9047-20261025. Scoped original-prefix
+verification/proof result; no kappa claim. The PR conversation is the canonical
+submission/status record; a hub pointer can link it without duplicating proof.
+
+Exact commit:
+Base 32890bc5de034ab8fc93ac88ead7279a6a416d04; exact native blob/SHA pins in
+SOURCES.json. The publication commit is the commit containing this package.
+Conceptual #5472 reference head f560065151f924838a80ac720fb4c55c6ffc0201 is credited,
+but no pending-head code is imported or required by replay.
+
+What is established:
+Actual same-version reads9045/9047; exact coframed inventory L19/L300/L301;
+pure e300/e301 outside its rational span even with independent successors;
+explicit null-input/separating witnesses; retained-anchor intersection frame21.
+Complete normal/O evidence and portable replay are supplied. The split target
+credit is unadmitted for this rejected original-cut premise.
+
+What remains uncertain:
+Changed prefixes/helper bases, other cuts/anchors, operator-valued ordinary
+recoding and larger words; caller-domain admissibility; protected suffixes,
+owned returns, phases/raw duals, owned relations and full economic/funding
+admission. No actual paid/target gain, new kappa ceiling or selected update.
+
+Smallest useful next task:
+After overlap review, specify one literal earlier prefix/basis change or relocated
+anchor recipe, its admissible input domain, all target/cost consequences and a
+bounded falsifier. Do not rerun unchanged scalar purification at this cut.
+
+Reproduction command and expected runtime:
+From repository root: python3 -B scripts/research_package.py --package
+research/shared-crossing-cut9047-20261025. Python3.12/stdlib, registered150-second
+timeout; typically seconds. Expected PASS_SHARED_CROSSING_CUT9047_SCALAR_OBSTRUCTION.
+The direct portable command and exact historical evidence are in README.md and
+REVIEW.md; no full caller/phase/compiler replay is claimed.
+
+Predecessor credit:
+Cao Yifan, zxv, GamingPuzzled/Joel Pulikkan, Cinna Davis, Matarener, aliromman,
+Dillon Amburgey, Clear1nsight/Chris R and the retained native/provider/controller
+lineage. Substantial OpenAI Codex assistance; Apache-2.0 for new material.

research/shared-crossing-cut9047-20261025/PROOF.md

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+# Original-prefix shared-crossing obstruction (no new kappa)
+
+Indices are zero-based in the forward program pinned in SOURCES.json. This is
+an exact normalized native-row argument; full phase/raw-dual/caller admission
+is not asserted.
+
+## Actual pair and candidate
+
+Events9045/9047 let L300/L301 read the same historical L19 value at frame21,
+basis[273], without an intervening L19 writer. The first later writer is9060;
+the9060--9063 swap makes later L19 distinct. The proposed joint handoff retires
+the original helpers as pure original coordinates and transfers suffix roles
+to two fresh arbitrary independent successors. It uses an actual pair, not a
+duplicated baseline. Earlier holder rewrites in a larger word remain unprovided.
+
+## Exact available rows and witnesses
+
+Replay all632 persistent columns plus the arbitrary owned entry through9047.
+The only coframed owners are L19,L300,L301, with normalized rows D,R300,R301.
+
+| Row | e300 | e505 | e301 | e226 |
+| --- | ---: | ---: | ---: | ---: |
+| D |0 |0 |0 |0 |
+| R300 |1 |1/4 |0 |0 |
+| R301 |0 |0 |1 |-1 |
+
+Other columns are fully retained in expected/RESULT.json. These four inputs
+all start at frame0 and have empty emitted warp words.
+
+The functionals l300=[e300]-4[e505] and l301=[e301]+[e226] annihilate every
+available row but equal1 on their required targets e300/e301. Neither target
+belongs to that rational span. Equivalently, variations(L300=u,L505=-4u)
+and(L301=u,L226=u), holding other inputs fixed, preserve every available row
+but change the respective pure target byu.
+
+Independent fresh successors cannot enlarge the original-only span: old rows
+contain neither fresh column, so a combination producing an original-only
+target has zero coefficient on each successor basis row. Zero scratch adds no
+span. Exact ranks are3 versus4 after adjoining either target; with successors,
+5 versus6. A span pass would only be necessary, not a reversible recipe; COPY
+is restricted to owned scratch, not arbitrary persistent copying.
+
+## Retained-anchor restriction
+
+The three retained anchor spans are423={0,102,273,375},430={0,85,273,324},
+419={0,51,273,290}. Their intersection is{0,273}=frame21. No larger common
+ascending first-window frame exists under those fixed-anchor assumptions.
+Moving or replacing the anchors is a different untested design.
+
+## Scope and economics
+
+This rejects rational-scalar purification of the ORIGINAL UNMODIFIED prefix
+at cut9047/frame21, even with every actual coframed field, two independent
+successors and zero scratch. It does not rule out changed prefixes/helper bases,
+other cuts/anchors, operator-valued ordinary recoding, new transports or larger
+shared words. The witnesses use the original unrestricted input domain; their
+admissibility under another caller's owned/input restrictions was not checked.
+
+The tentative2H1+2H8-2H9 credit is unadmitted for this premise. No complete
+changed ledger, kappa ceiling or funded kappa is established. Protected suffix,
+owned returns, raw dual, phases, changed owned relations, ordinary/precision/
+stock/tape costs, compiler and outer transfer remain open for any new word.

research/shared-crossing-cut9047-20261025/README.md

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+# Reject original-cut scalar purification for a shared helper crossing
+
+**Scoped feasibility result; no new physical word, paid-profile gain or kappa.**
+
+This package proposes one joint hand-off for the actual L19/L300/L301 slice of
+the #4610 word and rejects immediate purification at original forward cut 9047,
+frame 21. L300 and L301 read the same L19 version at events 9045 and 9047. The
+complete coframed inventory is only those three owners. Their actual helper
+rows contain foreign independent inputs; neither required pure original helper
+coordinate is in the available rational scalar span, even with two independent
+successors and zero scratch.
+
+The exact witnesses are `(L300=u,L505=-4u)` and `(L301=u,L226=u)`, holding other
+inputs fixed: every available row is unchanged while the respective required
+pure output changes by u. [PROOF.md](PROOF.md) gives the coefficient table,
+successor projection argument and retained-anchor restriction. The independent
+checker and complete exact output are [cut9047.py](cut9047.py) and
+[expected/RESULT.json](expected/RESULT.json).
+
+## Source and scope
+
+Base: `32890bc5de034ab8fc93ac88ead7279a6a416d04`. The live native word and its
+Git blob/SHA-256 pins are in [SOURCES.json](SOURCES.json). Catalogue and selected
+record pins are historical provenance. The task is a **changed, negative scope**
+under `complex-new-helper-inventory`, assigned directly by the user. The original
+card's positive complete-supplier acceptance gate is not claimed satisfied;
+[TASK.json](TASK.json) retains its exact card and explains the connection.
+
+This is a fixed-original-prefix normalized native-row result, with rational
+scalar recoding at one cut. Earlier prefix rewrites, new helper bases, other
+cuts/anchors, operator-valued ordinary recoding and larger words are not tested.
+The input witnesses must not be transferred to another caller's restricted or
+owned input domain without checking admissibility there. A complete physical
+phase/raw-dual/caller/compiler/outer result is not supplied. The proposed
+`2H1+2H8-2H9` split receives no credit for this rejected local premise.
+
+Nearest predecessors: [#5472](https://github.com/CrocSwap/integer-mult-bounds/pull/5472)
+(successor hand-off and local re-flag neutrality),
+[#5541](https://github.com/CrocSwap/integer-mult-bounds/pull/5541) (actual-word
+balanced-J verification with coded-main restrictions), and the native/owned
+relation lineage below. Unlike a padded toy example, the tested pair and dirty
+input mixtures are taken from the actual word. This result is not a universal
+obstruction to genuine shared re-flagging.
+
+## Reproduce
+
+Python 3.12, standard library only, from the repository root:
+
+```sh
+python3 -B scripts/research_package.py --package research/shared-crossing-cut9047-20261025 --check-only
+python3 -B scripts/research_package.py --package research/shared-crossing-cut9047-20261025
+```
+
+Direct source-export replay also works when the pinned native input is present:
+
+```sh
+python3 -B research/shared-crossing-cut9047-20261025/verify.py
+```
+
+Expected marker: `PASS_SHARED_CROSSING_CUT9047_SCALAR_OBSTRUCTION`.
+The registered command has a 150-second timeout and invokes serial normal and
+optimized checker subprocesses, each capped at 65 seconds. It compares their
+complete bytes to the frozen exact result with zero scientific exclusions,
+checks source/core hashes, the paper separators, input charts and anchor sets.
+No source evaluator is imported. The child checkers use `-I -B` and import only
+the Python standard library; no project bytecode dependency is used.
+
+The original guarded pair took 0.906 seconds at 81.0625 MiB sampled peak RSS;
+portable/hosted runtime is environment-dependent. [REVIEW.md](REVIEW.md)
+distinguishes that historical run, independent agent review and admission.
+The seven declared core controls include clean/poison span cases, independent
+successors, wrong version, omitted pre-subtraction and dirty successor. The
+duplicate-owner control is a synthetic distinct-label sanity check, not a
+complete target-admission replay. No full changed candidate exists to replay.
+
+## Open next questions
+
+The structured questions in [TASK.json](TASK.json) name their relevance, first
+step and blockers. A later design must either specify an earlier prefix/basis
+rewrite that removes these witnesses, or relocate the anchors with a complete
+transport/restoration bill. Neither is supplied here. Repeating this same cut
+with more scalar coefficients or samples cannot evade the exact span result.
+All research stopped after the one qualification result; this package starts
+no new search or automatic continuation.
+
+## Credit
+
+Cao Yifan: #4610 native word. zxv: productive helpers and native semantics.
+GamingPuzzled/Joel Pulikkan: #5472 hand-off and re-flag analysis. Cinna Davis:
+scalar semantics/compression. Matarener: scoped boundary work. aliromman:
+#5383 owned relations and later audits. Dillon Amburgey and Clear1nsight/Chris R:
+provider/completion and #5413 caller lineage. Retain the further source authors
+credited in those packages.
+
+Prepared by Chris R (Clear1nsight) with substantial OpenAI Codex assistance:
+GPT-6-astra/xhigh paper design; GPT-6.1-sol/high event extraction, independent
+checker/physical and invoice review, source custody and guarded execution.
+Agent independence is not independent human or formal theorem admission.
+New material is Apache-2.0; the native input is not copied or modified.

research/shared-crossing-cut9047-20261025/REVIEW.md

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+# Evidence and independent-review boundary
+
+The designer proposed one actual-pair simultaneous hand-off. A separate physical
+reviewer authored cut9047.py independently, with no predecessor evaluator import.
+A sole executor ran the frozen checker in normal/optimized modes through the
+existing serialized guard. The designer, physical reviewer and independent
+invoice reviewer separately inspected the simple separating witnesses.
+
+Historical checker SHA-256:
+`f5c45a13239ea521140920c016e2436195580f78112a45240adaba314041cd12`.
+Complete scientific output SHA-256:
+`70a30ac467a8d9a2b15e54d88b519258ef5bfff98fed11832a208c31c4fd0c81`.
+Both exact files are retained in this package. The original two modes had
+identical complete stdout, empty stderr and parsed JSON, seven declared controls,
+41 unchanged pinned local inputs, 0.906-second guard time and 81.0625 MiB sampled
+peak. There was no failed scientific attempt. Original workstation paths and
+internal coordination records are not necessary public replay inputs and are
+not included.
+
+The portable wrapper verifies the same source/core/output hashes, serial mode
+outputs and paper witnesses. Packaging replay and hosted CI are separate from
+the historical receipt; actual publication/CI status belongs in the PR. No CI
+success is asserted by this evidence note.
+
+Normal/optimized equality is a reproducibility control, not a second independent
+implementation. Independent agent reasoning/checker authorship is not human
+acceptance. The result is an exact fixed-prefix normalized-row qualification;
+absolute phases, raw inverse transpose, a new word, full caller, compiler/outer
+funding and selected-frontier promotion were not established.
+
+The pre-execution interpretation was limited to the ORIGINAL prefix. Negative
+span does not reject an earlier holder rewrite changing those rows. Neither
+the row result nor anchor restriction proves a new kappa ceiling. Another
+caller's restricted/owned input domain requires a separate witness-admissibility
+argument. See PROOF.md for the full exclusions.

research/shared-crossing-cut9047-20261025/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446",
+      "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602",
+      "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72"
+    },
+    {
+      "path": "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz",
+      "usage": "input",
+      "git_blob": "46d929df83817b85a5387bcdb9745e0627d6366e",
+      "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05"
+    }
+  ]
+}

research/shared-crossing-cut9047-20261025/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "complex-new-helper-inventory",
+  "priority_revision": 7,
+  "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04",
+  "original_card": {
+    "id": "complex-new-helper-inventory",
+    "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/complex-local-word-ceiling/README.md",
+      "research/heterogeneous-owner-assembly/README.md",
+      "certificates/selected-result.json",
+      "research/selected-k8-unrestricted-ends/README.md"
+    ],
+    "methods": [
+      "Propose a changed helper inventory and derive an optimistic exact moment.",
+      "Design a small completed instance and independently verify its endpoint and rank bill."
+    ],
+    "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. 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",
+        "research/complex-local-word-ceiling/verify.py"
+      ],
+      "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+      "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+      "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.",
+    "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.",
+    "allowed_variations": [
+      "Narrow to one changed boundary or helper type with explicit counts.",
+      "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+    ],
+    "scope_change_triggers": [
+      "Mixing only providers already inside the pinned catalogue.",
+      "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.",
+      "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts."
+    ],
+    "overlap_terms": [
+      "helper inventory",
+      "heterogeneous-owner",
+      "mutable leaver"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "User-assigned original-design feasibility: actual L19/L300/L301 shared-crossing paper candidate; exact original-prefix cut9047/frame21 rational scalar recovery and retained-anchor restriction. No successful profile or kappa claim.",
+  "scope_change_reason": "A narrow negative feasibility result for a proposed helper-inventory change, rather than the original card positive complete-supplier acceptance gate; explicit user assignment takes precedence over task selection.",
+  "bottleneck_link": "A shared crossing cannot earn split productive targets unless independent original helper coordinates can be legally purified and all consumers restored. This result closes one actual cut premise, leaving changed prefixes open.",
+  "budget_minutes": 60,
+  "stop_rule": "One actual pair, one frozen normal/optimized qualification request, then stop and re-evaluate; no replacement candidate or larger search.",
+  "outcome": "negative-result",
+  "evidence": "PROOF.md; unchanged independent cut9047.py; expected/RESULT.json; portable verify.py; REVIEW.md; HANDOFF.md",
+  "author": "Chris R (Clear1nsight), with OpenAI Codex assistance",
+  "ai_assistance": "Substantial OpenAI Codex assistance: GPT-6-astra/xhigh paper design; GPT-6.1-sol/high extraction, independently authored checker and physical/invoice review, source custody and guarded execution. Agent independence is not independent human or formal theorem admission.",
+  "open_questions": [
+    {
+      "question": "Can a literal earlier prefix rewrite or helper basis change remove the witnesses while preserving all required outputs?",
+      "why_it_matters": "Original-cut scalar purification fails; a new profile improvement must change an excluded premise.",
+      "first_step": "Specify exact changed prefix events, admissible input domain, target ownership, costs and one bounded falsifier.",
+      "blocked_by": "No such word, full caller/domain transfer or owned-relation proof supplied."
+    },
+    {
+      "question": "Can relocated anchors support a shared frame without consuming the split gain?",
+      "why_it_matters": "The retained anchors intersect only at the existing frame.",
+      "first_step": "Name alternative anchors, historical deadlines and literal paid transport/restoration.",
+      "blocked_by": "New geometry, sharing, full costs and protected endpoints unproved."
+    }
+  ],
+  "original_card_acceptance_gate_met": false
+}