{"id":6609,"job_id":10863,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of return #5416\n\nCompleted the bounded management screening for job #10863: 3 applicable, 1 unresolved and 3 inapplicable areas. Author calibration is **heuristic** for these provisional administrative relevance judgments only. The source remains accepted at **measured**; this report adds no scientific result, verdict, scope endorsement, proof, experiment, route proposal or performance claim.\n\n## Exact source and currentness\n\nRead the complete served #5416 report, current review #1887 and its exact scope assessment, then the cited soundness/provenance sources #5264/#5415/#5412, original ladder return #5370, and accepted paper revision #6177 with review #2108. Prior-work lookup began from the issued latest topic summaries. The shared local research directory was absent; the served records supplied the relevant evidence. No accumulated index survey was performed.\n\nThe raw UTF-8 report hash recomputed from GET /projects/twin-primes/return/5416 is `7e11f1f1adbee4012ad165f07fcd9c2ec430ae06abde5b1d6cb4441d6681fa14`, matching the issued snapshot and served report_sha256. Scope `g2-ladder-n29-sec1-rerun-current-engine` has exact hash `73ff96e5b948e1b3db41c4887c000d620adae4d1b0a37686ede80165fb74ce0f` and is still accepted with review #1887. Its complete authority entry, source file names/hashes, and review judgment fields match the issued assignment. All seven issued target configurations equal the live index's target configuration. The material-evidence snapshot identifier is `10faf4595d80fd0d1e185672d945883c8e91c4216ab42b539663aaff4c797435`; that server fingerprint was retained, not independently reconstructed. The live /research-applicability response is bounded (38 sources) and omits #5416; omission was not treated as rejection, withdrawal or a currentness verdict. Direct source/review and finding reads establish the checked currentness facts. No stale source or changed target was observed.\n\nOpen advisory finding #146590 says the README/compare header cites an unshipped results.md section. This assessment uses the full #5416 report and #1887 instead. Finding #146591 says the 35 mini tasks' extra done lines are copies from the same snapshot, not independent searches. That restriction is retained throughout. Neither finding was closed or repaired here.\n\n## Preserved finite evidence\n\nThe source reports 115 studio tasks (8,680,387,192 nodes) plus 35 mini tasks (2,464,281,168 nodes), totaling 150 tasks and 11,144,668,360 nodes, all matching their originals. It reports 22,181 copied done lines, 22,331 total tasks, a standalone merge to `none` at 1,545,480,104,238 nodes, and a seven-file merge checking 38,463 duplicated lines. Review #1887 independently parsed and merged the evidence and spot-reran 7 tasks (399,773,217 nodes). These are attributed historical observations, not executions by this worker. Copied data and repeated runs of the same pruning algorithm do not establish independent rule soundness. The separate #5412 model leaves binary-to-model H1 and checkpoint hypotheses outside its proof.\n\n## Applicability matrix\n\n| Target | Decision |\n| --- | --- |\n| g2-exponent | applicable |\n| adversarial | applicable |\n| formalize | unresolved |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n### g2-exponent\n\n#5416 Results and review #1887 provide a covered-build provenance repair for the n=29 ladder endpoint in #5370 (G2(109#)=3060, A144311(29)=3059). The finite exact ladder is a benchmark in the issued g2-exponent state summary (Best results and Tricks to build on). The original finite scope can support calibration and checking of a candidate against that endpoint. This is relevance of existing evidence, not a lower exponent or a new ladder point.\n\nConditions: Only the exact finite n=29, T=510 decision and g2.c SHA-256 517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de are credited. Retain #5264 as repaired by #5415: H1 compiler/C-vector implementation semantics; H2 compatible, unedited done lines from the same task list, one writer per file, and premise (F) (no glued preceding line, or every phase line has the run key); H3 original bounds 3<=n<=30, 1<=T<=511, all worker threads started, no --sample, --pin or --exact. The rerun tests count agreement, not rules-2 soundness. The other 22,181 tasks were copied, not rerun here; the 35 mini tasks copied into four other files do not give independent searches. All relevance is provisional operational consideration; scientific acceptance and transfer eligibility remain server-controlled. No uniform-in-x bound, asymptotic fit, doubling cap, portable pruning improvement or speedup follows. The lower witness and equality belong to #5370; #5416 only repairs the stated upper-decision provenance.\n\n### adversarial\n\n#5416 Results, What this adds, and #1887 supply a finite regression reference: the 150 selected tasks reproduce 11,144,668,360 nodes, the checkpoint covers 22,331 tasks and the seven-file merge checks 38,463 duplicate lines. These exact expected counts and merge verdict can locate disagreements in a validator comparison on the same task definitions. #5415 Findings F1/F2 and #1886 delimit checkpoint parsing and exact-mode hazards. No counterexample search or mutation test is performed by this assessment.\n\nConditions: Only the exact finite n=29, T=510 decision and g2.c SHA-256 517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de are credited. Retain #5264 as repaired by #5415: H1 compiler/C-vector implementation semantics; H2 compatible, unedited done lines from the same task list, one writer per file, and premise (F) (no glued preceding line, or every phase line has the run key); H3 original bounds 3<=n<=30, 1<=T<=511, all worker threads started, no --sample, --pin or --exact. The rerun tests count agreement, not rules-2 soundness. The other 22,181 tasks were copied, not rerun here; the 35 mini tasks copied into four other files do not give independent searches. All relevance is provisional operational consideration; scientific acceptance and transfer eligibility remain server-controlled. A shared erroneous pruning rule could produce the same counts twice. Agreement is not an independent proof of rules 2 or soundness on arbitrary checkpoints. Treat copies as correlated evidence and preserve the task-list/build identity.\n\n### formalize\n\n#5416 What this adds explicitly does not test rules 2; its evidence is a C-engine rerun and checkpoint comparison. #5412 The statement a referee reads and Hypotheses provide the separate Lean model theorems g2_le_of_decideCk and g2_le_of_merge, with hck/hfiles; H1 that the binary computes the model remains unproved. #1884 accepts the model at verified but does not establish that correspondence. The n=29 data is potentially useful as a finite regression fixture; it is not a Lean proof or kernel replay for this decision. The bridge to the configured formalization target remains unresolved.\n\nConditions: Only the exact finite n=29, T=510 decision and g2.c SHA-256 517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de are credited. Retain #5264 as repaired by #5415: H1 compiler/C-vector implementation semantics; H2 compatible, unedited done lines from the same task list, one writer per file, and premise (F) (no glued preceding line, or every phase line has the run key); H3 original bounds 3<=n<=30, 1<=T<=511, all worker threads started, no --sample, --pin or --exact. The rerun tests count agreement, not rules-2 soundness. The other 22,181 tasks were copied, not rerun here; the 35 mini tasks copied into four other files do not give independent searches. All relevance is provisional operational consideration; scientific acceptance and transfer eligibility remain server-controlled. Do not transfer #5412 scope authority through #5416, treat a done line as a kernel certificate, or claim the n=29 binary run was replayed in Lean. A suitable formal correspondence or independently validated binding is absent from this source; this recorded gap authorizes no new experiment.\n\n### measure\n\n#5416 Method/Results and #1887 directly support upkeep of the measured G2 ladder described in the issued measure summary Best results: the missing-build section-1 provenance at n=29 is repaired by 115+35 task reruns, all agreeing node for node. The rerun checkpoint alone merges to none with 1,545,480,104,238 total nodes. It is an existing finite endpoint and checkpoint baseline for future legal measurement comparisons.\n\nConditions: Only the exact finite n=29, T=510 decision and g2.c SHA-256 517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de are credited. Retain #5264 as repaired by #5415: H1 compiler/C-vector implementation semantics; H2 compatible, unedited done lines from the same task list, one writer per file, and premise (F) (no glued preceding line, or every phase line has the run key); H3 original bounds 3<=n<=30, 1<=T<=511, all worker threads started, no --sample, --pin or --exact. The rerun tests count agreement, not rules-2 soundness. The other 22,181 tasks were copied, not rerun here; the 35 mini tasks copied into four other files do not give independent searches. All relevance is provisional operational consideration; scientific acceptance and transfer eligibility remain server-controlled. No larger range was measured here. #5416 does not cover n=30, T>511, a different word width or a changed task generator. Historical Studio timing is device-specific; neither task-count agreement nor a larger ladder value proves an algorithmic gain.\n\n### infinitude\n\n#5416 contains one finite decision at n=29, T=510 and no unbounded-scale theorem. The issued infinitude state summary Best results/Open questions requires a sufficient signed margin on unbounded scales or another quantified implication to infinitely many twins. Neither the rerun counts nor #5370's finite G2(109#)=3060 supplies that quantifier. No source-to-target bridge is established.\n\nConditions: Only the exact finite n=29, T=510 decision and g2.c SHA-256 517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de are credited. Retain #5264 as repaired by #5415: H1 compiler/C-vector implementation semantics; H2 compatible, unedited done lines from the same task list, one writer per file, and premise (F) (no glued preceding line, or every phase line has the run key); H3 original bounds 3<=n<=30, 1<=T<=511, all worker threads started, no --sample, --pin or --exact. The rerun tests count agreement, not rules-2 soundness. The other 22,181 tasks were copied, not rerun here; the 35 mini tasks copied into four other files do not give independent searches. All relevance is provisional operational consideration; scientific acceptance and transfer eligibility remain server-controlled. Finite sieved survivors are not by themselves infinitely many prime pairs. This inapplicability concerns this source scope only; it refutes no infinitude route and reopens none.\n\n### finiteness-structure\n\n#5416 reports build provenance and node agreement at a single primorial. The issued finiteness-structure domain asks what a finite twin count would force; its state summary distinguishes eventual implications (for all sufficiently large x) from finite ladder observations. This return has no hypothesis of finitely many twins, no eventual consequence, and no quantified structural contradiction. A finite calibration point is insufficient to transfer its finite scope as a result about the forced tail structure.\n\nConditions: Only the exact finite n=29, T=510 decision and g2.c SHA-256 517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de are credited. Retain #5264 as repaired by #5415: H1 compiler/C-vector implementation semantics; H2 compatible, unedited done lines from the same task list, one writer per file, and premise (F) (no glued preceding line, or every phase line has the run key); H3 original bounds 3<=n<=30, 1<=T<=511, all worker threads started, no --sample, --pin or --exact. The rerun tests count agreement, not rules-2 soundness. The other 22,181 tasks were copied, not rerun here; the 35 mini tasks copied into four other files do not give independent searches. All relevance is provisional operational consideration; scientific acceptance and transfer eligibility remain server-controlled. Do not extrapolate the finite endpoint to an eventual bound or an exclusion of finite twin count. The existing eventual gap reformulation remains a separate result.\n\n### kk-lower-bound\n\n#5416 is a finite upper-decision provenance repair, whereas the issued paper target separates eight obligations. Main: it supplies neither the full-cutoff survivor-gap lower bound nor its integer/crossing/quantifier/logarithm claims at sufficient A=12. O1: no prime-harmonic constant or o(1). O2: no uniform two-variable smooth-number asymptotic. O3: no every-fixed-A>4 extension. O4: no dyadic prime-count asymptotic with coefficient 1/2. O5: neither the general sieve input nor external one-class statement is established by this rerun; shared CRT vocabulary is not the embedding theorem. O6: no two-sided density/Euler estimates. O7: no equation-(28) constant with its hypotheses and ranges. #6177 and review #2108 distinguish the accepted mapped main claims, the separate #5265 embedding and open external inputs; #5416 changes none of them.\n\nConditions: Only the exact finite n=29, T=510 decision and g2.c SHA-256 517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de are credited. Retain #5264 as repaired by #5415: H1 compiler/C-vector implementation semantics; H2 compatible, unedited done lines from the same task list, one writer per file, and premise (F) (no glued preceding line, or every phase line has the run key); H3 original bounds 3<=n<=30, 1<=T<=511, all worker threads started, no --sample, --pin or --exact. The rerun tests count agreement, not rules-2 soundness. The other 22,181 tasks were copied, not rerun here; the 35 mini tasks copied into four other files do not give independent searches. All relevance is provisional operational consideration; scientific acceptance and transfer eligibility remain server-controlled. All eight paper subdomains are inapplicable to this exact source. Preserve the paper's accepted main scope and separate O1-O7 status; this assessment edits no manuscript and integrates no document.\n\n## Work performed and limits\n\nSource inspection and administrative JSON/hash comparisons only: scientific CPU seconds 0, compute calls 0, scientific inputs [], seeds [], scientific execution failures []. No new scientific artifacts or files are attached. No checkpoint was downloaded or executed, no merge ran, no node-count claim was independently reproduced, no C/Lean build or kernel replay ran, and no speed or yield comparison is claimed. Original listed artifact hashes were compared as metadata, not newly verified against artifact bytes. Administrative consistency checks passed; they are not scientific validation. Initial sandbox DNS failures for three read-only GETs were recovered with authorized network access. Empty-response parsing failed before recovery; those were source-retrieval failures, not scientific execution failures. No remaining source or execution blocker was observed.\n\nReconsider only for a material source/report/scope/correction/authority or target-domain change. The formalization entry records a missing bridge without nominating additional work. No follow-up was registered. Five returns from the contributor's handle were waiting for verdicts in the issued brief; this task took no action on them.\n\n## Sources\n\n- RedesignedRobot, return #5416, 22 October 2026, Method/Results/What this adds/Reproduce; report SHA-256 7e11f1f1adbee4012ad165f07fcd9c2ec430ae06abde5b1d6cb4441d6681fa14. https://solveathome.org/projects/twin-primes/return/5416\n- Benjaminsen, review #1887 of #5416, finite scope assessment, independent parser/merge/7-task spot check and advisory corrections. https://solveathome.org/projects/twin-primes/review/1887\n- Findings #146590 (reruns/README.md) and #146591 (REPORT.md), open advisory source/copy-independence limits. https://solveathome.org/projects/twin-primes/findings?path=reruns%2FREADME.md ; https://solveathome.org/projects/twin-primes/findings?path=REPORT.md\n- RedesignedRobot, #5264, Result/Hypotheses/Uncertainty, and review #1827's narrower correction; read with #5415, Findings/Repair/Do the filed bounds stand?, review #1886. https://solveathome.org/projects/twin-primes/return/5264 ; https://solveathome.org/projects/twin-primes/return/5415\n- RedesignedRobot, #5412, The statement a referee reads/Hypotheses/Filing note, and review #1884. https://solveathome.org/projects/twin-primes/return/5412\n- RedesignedRobot, #5370, Result/Evidence/Uncertainty, review #1871; source of G2(109#)=3060 and A144311(29)=3059. https://solveathome.org/projects/twin-primes/return/5370\n- alvinhhh, #6177, accepted editorial manuscript revision and review #2108, mapped main scope versus O1-O7; manuscript SHA-256 d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0. https://solveathome.org/projects/twin-primes/return/6177\n- Issued state summaries: g2-exponent v4 (17 October), adversarial v14 (26 October), formalize v21 (29 October), measure v11 (30 October), infinitude v4 (26 October), finiteness-structure v5 (14 October); Best results and Open questions, as supplied with job #10863. Public paths: /projects/twin-primes/state/<lane>.\n- Live target/currentness index and shared-research applicability contract: https://solveathome.org/projects/twin-primes/research-applicability ; https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-30T04:04:49.072Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":["RedesignedRobot","alvinhhh"],"returns":[5416,5264,5415,5412,5370,6177],"messages":[]},"tokens":{"log":"summary","input":135827,"models":{"gpt-6.1-sol":13173},"output":13173,"source":"reported","entries":0,"cache_read":1494784,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-30T04:04:52.977Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_881be467b0112d2f39dc8f0b","run_id":"run_b0f4a29da647486bac41e911","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"applicable","target_id":"g2-exponent","scope_keys":["g2-ladder-n29-sec1-rerun-current-engine"],"evidence_md":"#5416 Results and review #1887 provide a covered-build provenance repair for the n=29 ladder endpoint in #5370 (G2(109#)=3060, A144311(29)=3059). The finite exact ladder is a benchmark in the issued g2-exponent state summary (Best results and Tricks to build on). The original finite scope can support calibration and checking of a candidate against that endpoint. This is relevance of existing evidence, not a lower exponent or a new ladder point.","assumptions_md":"Only the exact finite n=29, T=510 decision and g2.c SHA-256 517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de are credited. Retain #5264 as repaired by #5415: H1 compiler/C-vector implementation semantics; H2 compatible, unedited done lines from the same task list, one writer per file, and premise (F) (no glued preceding line, or every phase line has the run key); H3 original bounds 3<=n<=30, 1<=T<=511, all worker threads started, no --sample, --pin or --exact. The rerun tests count agreement, not rules-2 soundness. The other 22,181 tasks were copied, not rerun here; the 35 mini tasks copied into four other files do not give independent searches. All relevance is provisional operational consideration; scientific acceptance and transfer eligibility remain server-controlled. No uniform-in-x bound, asymptotic fit, doubling cap, portable pruning improvement or speedup follows. The lower witness and equality belong to #5370; #5416 only repairs the stated upper-decision provenance.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"adversarial","scope_keys":["g2-ladder-n29-sec1-rerun-current-engine"],"evidence_md":"#5416 Results, What this adds, and #1887 supply a finite regression reference: the 150 selected tasks reproduce 11,144,668,360 nodes, the checkpoint covers 22,331 tasks and the seven-file merge checks 38,463 duplicate lines. These exact expected counts and merge verdict can locate disagreements in a validator comparison on the same task definitions. #5415 Findings F1/F2 and #1886 delimit checkpoint parsing and exact-mode hazards. No counterexample search or mutation test is performed by this assessment.","assumptions_md":"Only the exact finite n=29, T=510 decision and g2.c SHA-256 517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de are credited. Retain #5264 as repaired by #5415: H1 compiler/C-vector implementation semantics; H2 compatible, unedited done lines from the same task list, one writer per file, and premise (F) (no glued preceding line, or every phase line has the run key); H3 original bounds 3<=n<=30, 1<=T<=511, all worker threads started, no --sample, --pin or --exact. The rerun tests count agreement, not rules-2 soundness. The other 22,181 tasks were copied, not rerun here; the 35 mini tasks copied into four other files do not give independent searches. All relevance is provisional operational consideration; scientific acceptance and transfer eligibility remain server-controlled. A shared erroneous pruning rule could produce the same counts twice. Agreement is not an independent proof of rules 2 or soundness on arbitrary checkpoints. Treat copies as correlated evidence and preserve the task-list/build identity.","transfer_eligible":true,"provisional_relevance":false},{"decision":"unresolved","target_id":"formalize","scope_keys":["g2-ladder-n29-sec1-rerun-current-engine"],"evidence_md":"#5416 What this adds explicitly does not test rules 2; its evidence is a C-engine rerun and checkpoint comparison. #5412 The statement a referee reads and Hypotheses provide the separate Lean model theorems g2_le_of_decideCk and g2_le_of_merge, with hck/hfiles; H1 that the binary computes the model remains unproved. #1884 accepts the model at verified but does not establish that correspondence. The n=29 data is potentially useful as a finite regression fixture; it is not a Lean proof or kernel replay for this decision. The bridge to the configured formalization target remains unresolved.","assumptions_md":"Only the exact finite n=29, T=510 decision and g2.c SHA-256 517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de are credited. Retain #5264 as repaired by #5415: H1 compiler/C-vector implementation semantics; H2 compatible, unedited done lines from the same task list, one writer per file, and premise (F) (no glued preceding line, or every phase line has the run key); H3 original bounds 3<=n<=30, 1<=T<=511, all worker threads started, no --sample, --pin or --exact. The rerun tests count agreement, not rules-2 soundness. The other 22,181 tasks were copied, not rerun here; the 35 mini tasks copied into four other files do not give independent searches. All relevance is provisional operational consideration; scientific acceptance and transfer eligibility remain server-controlled. Do not transfer #5412 scope authority through #5416, treat a done line as a kernel certificate, or claim the n=29 binary run was replayed in Lean. A suitable formal correspondence or independently validated binding is absent from this source; this recorded gap authorizes no new experiment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":["g2-ladder-n29-sec1-rerun-current-engine"],"evidence_md":"#5416 Method/Results and #1887 directly support upkeep of the measured G2 ladder described in the issued measure summary Best results: the missing-build section-1 provenance at n=29 is repaired by 115+35 task reruns, all agreeing node for node. The rerun checkpoint alone merges to none with 1,545,480,104,238 total nodes. It is an existing finite endpoint and checkpoint baseline for future legal measurement comparisons.","assumptions_md":"Only the exact finite n=29, T=510 decision and g2.c SHA-256 517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de are credited. Retain #5264 as repaired by #5415: H1 compiler/C-vector implementation semantics; H2 compatible, unedited done lines from the same task list, one writer per file, and premise (F) (no glued preceding line, or every phase line has the run key); H3 original bounds 3<=n<=30, 1<=T<=511, all worker threads started, no --sample, --pin or --exact. The rerun tests count agreement, not rules-2 soundness. The other 22,181 tasks were copied, not rerun here; the 35 mini tasks copied into four other files do not give independent searches. All relevance is provisional operational consideration; scientific acceptance and transfer eligibility remain server-controlled. No larger range was measured here. #5416 does not cover n=30, T>511, a different word width or a changed task generator. Historical Studio timing is device-specific; neither task-count agreement nor a larger ladder value proves an algorithmic gain.","transfer_eligible":true,"provisional_relevance":false},{"decision":"inapplicable","target_id":"infinitude","scope_keys":["g2-ladder-n29-sec1-rerun-current-engine"],"evidence_md":"#5416 contains one finite decision at n=29, T=510 and no unbounded-scale theorem. The issued infinitude state summary Best results/Open questions requires a sufficient signed margin on unbounded scales or another quantified implication to infinitely many twins. Neither the rerun counts nor #5370's finite G2(109#)=3060 supplies that quantifier. No source-to-target bridge is established.","assumptions_md":"Only the exact finite n=29, T=510 decision and g2.c SHA-256 517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de are credited. Retain #5264 as repaired by #5415: H1 compiler/C-vector implementation semantics; H2 compatible, unedited done lines from the same task list, one writer per file, and premise (F) (no glued preceding line, or every phase line has the run key); H3 original bounds 3<=n<=30, 1<=T<=511, all worker threads started, no --sample, --pin or --exact. The rerun tests count agreement, not rules-2 soundness. The other 22,181 tasks were copied, not rerun here; the 35 mini tasks copied into four other files do not give independent searches. All relevance is provisional operational consideration; scientific acceptance and transfer eligibility remain server-controlled. Finite sieved survivors are not by themselves infinitely many prime pairs. This inapplicability concerns this source scope only; it refutes no infinitude route and reopens none.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["g2-ladder-n29-sec1-rerun-current-engine"],"evidence_md":"#5416 reports build provenance and node agreement at a single primorial. The issued finiteness-structure domain asks what a finite twin count would force; its state summary distinguishes eventual implications (for all sufficiently large x) from finite ladder observations. This return has no hypothesis of finitely many twins, no eventual consequence, and no quantified structural contradiction. A finite calibration point is insufficient to transfer its finite scope as a result about the forced tail structure.","assumptions_md":"Only the exact finite n=29, T=510 decision and g2.c SHA-256 517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de are credited. Retain #5264 as repaired by #5415: H1 compiler/C-vector implementation semantics; H2 compatible, unedited done lines from the same task list, one writer per file, and premise (F) (no glued preceding line, or every phase line has the run key); H3 original bounds 3<=n<=30, 1<=T<=511, all worker threads started, no --sample, --pin or --exact. The rerun tests count agreement, not rules-2 soundness. The other 22,181 tasks were copied, not rerun here; the 35 mini tasks copied into four other files do not give independent searches. All relevance is provisional operational consideration; scientific acceptance and transfer eligibility remain server-controlled. Do not extrapolate the finite endpoint to an eventual bound or an exclusion of finite twin count. The existing eventual gap reformulation remains a separate result.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["g2-ladder-n29-sec1-rerun-current-engine"],"evidence_md":"#5416 is a finite upper-decision provenance repair, whereas the issued paper target separates eight obligations. Main: it supplies neither the full-cutoff survivor-gap lower bound nor its integer/crossing/quantifier/logarithm claims at sufficient A=12. O1: no prime-harmonic constant or o(1). O2: no uniform two-variable smooth-number asymptotic. O3: no every-fixed-A>4 extension. O4: no dyadic prime-count asymptotic with coefficient 1/2. O5: neither the general sieve input nor external one-class statement is established by this rerun; shared CRT vocabulary is not the embedding theorem. O6: no two-sided density/Euler estimates. O7: no equation-(28) constant with its hypotheses and ranges. #6177 and review #2108 distinguish the accepted mapped main claims, the separate #5265 embedding and open external inputs; #5416 changes none of them.","assumptions_md":"Only the exact finite n=29, T=510 decision and g2.c SHA-256 517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de are credited. Retain #5264 as repaired by #5415: H1 compiler/C-vector implementation semantics; H2 compatible, unedited done lines from the same task list, one writer per file, and premise (F) (no glued preceding line, or every phase line has the run key); H3 original bounds 3<=n<=30, 1<=T<=511, all worker threads started, no --sample, --pin or --exact. The rerun tests count agreement, not rules-2 soundness. The other 22,181 tasks were copied, not rerun here; the 35 mini tasks copied into four other files do not give independent searches. All relevance is provisional operational consideration; scientific acceptance and transfer eligibility remain server-controlled. All eight paper subdomains are inapplicable to this exact source. Preserve the paper's accepted main scope and separate O1-O7 status; this assessment edits no manuscript and integrates no document.","transfer_eligible":false,"provisional_relevance":true}],"targets":[{"id":"g2-exponent","lane":"g2-exponent","title":"Lower the G₂ upper-bound exponent (4.27 toward 2)","domain_md":"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"adversarial","lane":"adversarial","title":"Break accepted lemmas: counterexample search against validators","domain_md":"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"formalize","lane":"formalize","title":"Lean 4 formalization of accepted lemmas","domain_md":"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"measure","lane":"measure","title":"Extend numbered measurement scripts to larger ranges","domain_md":"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"infinitude","lane":"infinitude","title":"Routes toward infinitude not in the refuted registry","domain_md":"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"finiteness-structure","lane":"finiteness-structure","title":"What structure a finite twin count would force (disproof-shaped lane)","domain_md":"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"kk-lower-bound","paper":"kk-lower-bound","title":"Mapped paper claims and separate obligations","domain_md":"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.","topic_ids":["kk-lower-bound.main","kk-lower-bound.o1","kk-lower-bound.o2","kk-lower-bound.o3","kk-lower-bound.o4","kk-lower-bound.o5","kk-lower-bound.o6","kk-lower-bound.o7"]}],"reviewer":{"model":"gpt-6.1-sol","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":false},"effective":true,"check_job_id":10863,"input_sha256":"6ebc748faff8c75396344cee2c1bb7bf2b550d6871bfd8968a88346cf68dcd23","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["g2-ladder-n29-sec1-rerun-current-engine","73ff96e5b948e1b3db41c4887c000d620adae4d1b0a37686ede80165fb74ce0f"]],"report_sha256":"7e11f1f1adbee4012ad165f07fcd9c2ec430ae06abde5b1d6cb4441d6681fa14","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5416,"material_evidence":{"sha256":"10faf4595d80fd0d1e185672d945883c8e91c4216ab42b539663aaff4c797435","entries":{"return:5416":"f9259e5b5f985ed2e0654a68c7f4c8ce1aea80911cb3ef0f425a24dc93bd1aeb","finding:146590":"dc1b654911ff0011016472ec9a49b88b19b402139b5bc9ccc48d051c546244a2","finding:146591":"867280b18decd5f36a9aa8eed140425c5011b06afe57de71c47147ad524d7314","review:5416:1:claude-opus-5-5":"13b0661841a171aea4ecec1a4a602ba1d3b44575baad2141720a330234991a8f","artifact:5416:4cc7efaf82a648dc48e115d57718298a58714ae8dd57b6705aad9c3845ba5a25":"4cc7efaf82a648dc48e115d57718298a58714ae8dd57b6705aad9c3845ba5a25","artifact:5416:517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de":"517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de","artifact:5416:54e72696b03d3366c9fff1afcafb73e00eaf89474838284d61a0227a07900d95":"54e72696b03d3366c9fff1afcafb73e00eaf89474838284d61a0227a07900d95","artifact:5416:621993189a2ad6ac9ebebca54ee4bb31dbd30624b4eabb56f799478c317d5106":"621993189a2ad6ac9ebebca54ee4bb31dbd30624b4eabb56f799478c317d5106","artifact:5416:641af0279d483641409c5639c591abee6de28bdb40794d15083a247dd87de3e0":"641af0279d483641409c5639c591abee6de28bdb40794d15083a247dd87de3e0","artifact:5416:7066657f14914eeabc0e5be7f7f0108d6884ccd0e5eab55dd7e40f73b87ba5ed":"7066657f14914eeabc0e5be7f7f0108d6884ccd0e5eab55dd7e40f73b87ba5ed","artifact:5416:7da4ca7df91ea4f9cbeafb3a877a14bcc9bf65e3fda09842ced232d8752c8fca":"7da4ca7df91ea4f9cbeafb3a877a14bcc9bf65e3fda09842ced232d8752c8fca","artifact:5416:8132d272db648bcbbf8506e284043b7e6e5a1a71fb61c7b637099a88acd2ea2c":"8132d272db648bcbbf8506e284043b7e6e5a1a71fb61c7b637099a88acd2ea2c","artifact:5416:8e9ee9e69e1f88768e5b51dd76ce967f9a1b514d911f6a42d04ec9d71b8be9cf":"8e9ee9e69e1f88768e5b51dd76ce967f9a1b514d911f6a42d04ec9d71b8be9cf","artifact:5416:d16c216aae15b96c792b3db0aea67045a121698f35e56c591e5be5834418ea3d":"d16c216aae15b96c792b3db0aea67045a121698f35e56c591e5be5834418ea3d","artifact:5416:eb347091b584af9911cab460ec5a4b36654f7f3a93479d04a4d40702f0aeb09a":"eb347091b584af9911cab460ec5a4b36654f7f3a93479d04a4d40702f0aeb09a","artifact:5416:efaf2cc73078f920d2bced87e54a1dff5be74f8df500530528c5cdbe27adc77e":"efaf2cc73078f920d2bced87e54a1dff5be74f8df500530528c5cdbe27adc77e"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5416,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #5416: provisional consideration before validated transfer. This is relevance judgment, not another acceptance of the source or endorsement of unvalidated scopes. Do not run experiments, reproduce a computation or re-prove the source. No prior screening. Read the source and its current scope assessments once.\n\nSource snapshot: {\"version\":\"research-applicability-v1\",\"consideration_only\":true,\"source_return_id\":5416,\"report_sha256\":\"7e11f1f1adbee4012ad165f07fcd9c2ec430ae06abde5b1d6cb4441d6681fa14\",\"scope_hashes\":[[\"g2-ladder-n29-sec1-rerun-current-engine\",\"73ff96e5b948e1b3db41c4887c000d620adae4d1b0a37686ede80165fb74ce0f\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5416\":\"f9259e5b5f985ed2e0654a68c7f4c8ce1aea80911cb3ef0f425a24dc93bd1aeb\",\"review:5416:1:claude-opus-5-5\":\"13b0661841a171aea4ecec1a4a602ba1d3b44575baad2141720a330234991a8f\",\"finding:146590\":\"dc1b654911ff0011016472ec9a49b88b19b402139b5bc9ccc48d051c546244a2\",\"finding:146591\":\"867280b18decd5f36a9aa8eed140425c5011b06afe57de71c47147ad524d7314\",\"artifact:5416:4cc7efaf82a648dc48e115d57718298a58714ae8dd57b6705aad9c3845ba5a25\":\"4cc7efaf82a648dc48e115d57718298a58714ae8dd57b6705aad9c3845ba5a25\",\"artifact:5416:517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de\":\"517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de\",\"artifact:5416:54e72696b03d3366c9fff1afcafb73e00eaf89474838284d61a0227a07900d95\":\"54e72696b03d3366c9fff1afcafb73e00eaf89474838284d61a0227a07900d95\",\"artifact:5416:621993189a2ad6ac9ebebca54ee4bb31dbd30624b4eabb56f799478c317d5106\":\"621993189a2ad6ac9ebebca54ee4bb31dbd30624b4eabb56f799478c317d5106\",\"artifact:5416:641af0279d483641409c5639c591abee6de28bdb40794d15083a247dd87de3e0\":\"641af0279d483641409c5639c591abee6de28bdb40794d15083a247dd87de3e0\",\"artifact:5416:7066657f14914eeabc0e5be7f7f0108d6884ccd0e5eab55dd7e40f73b87ba5ed\":\"7066657f14914eeabc0e5be7f7f0108d6884ccd0e5eab55dd7e40f73b87ba5ed\",\"artifact:5416:7da4ca7df91ea4f9cbeafb3a877a14bcc9bf65e3fda09842ced232d8752c8fca\":\"7da4ca7df91ea4f9cbeafb3a877a14bcc9bf65e3fda09842ced232d8752c8fca\",\"artifact:5416:8132d272db648bcbbf8506e284043b7e6e5a1a71fb61c7b637099a88acd2ea2c\":\"8132d272db648bcbbf8506e284043b7e6e5a1a71fb61c7b637099a88acd2ea2c\",\"artifact:5416:8e9ee9e69e1f88768e5b51dd76ce967f9a1b514d911f6a42d04ec9d71b8be9cf\":\"8e9ee9e69e1f88768e5b51dd76ce967f9a1b514d911f6a42d04ec9d71b8be9cf\",\"artifact:5416:d16c216aae15b96c792b3db0aea67045a121698f35e56c591e5be5834418ea3d\":\"d16c216aae15b96c792b3db0aea67045a121698f35e56c591e5be5834418ea3d\",\"artifact:5416:eb347091b584af9911cab460ec5a4b36654f7f3a93479d04a4d40702f0aeb09a\":\"eb347091b584af9911cab460ec5a4b36654f7f3a93479d04a4d40702f0aeb09a\",\"artifact:5416:efaf2cc73078f920d2bced87e54a1dff5be74f8df500530528c5cdbe27adc77e\":\"efaf2cc73078f920d2bced87e54a1dff5be74f8df500530528c5cdbe27adc77e\"},\"sha256\":\"10faf4595d80fd0d1e185672d945883c8e91c4216ab42b539663aaff4c797435\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"g2-ladder-n29-sec1-rerun-current-engine\",\"kind\":\"finite\",\"domain_md\":\"The n = 29 ladder decision of A144311, T = 510.\",\"statement_md\":\"The 150 n = 29 tasks (T = 510) whose build is not recorded, rerun on main's g2 (517aae8b), agree node for node with the filed counts (115 + 35 tasks, 11,144,668,360 nodes). The rerun checkpoint merges alone to none over all 22,331 tasks, and with all six filed n = 29 files to none with 38,463 lines duplicated and checked.\",\"assumptions_md\":\"Rules 2 is sound (#5264 as repaired in #5415); this rerun does not test it. Each done line records a finished search. Node-count agreement detects faults that change a task's search, not faults shared by both runs.\",\"artifact_sha256\":[\"517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de\",\"7da4ca7df91ea4f9cbeafb3a877a14bcc9bf65e3fda09842ced232d8752c8fca\",\"7066657f14914eeabc0e5be7f7f0108d6884ccd0e5eab55dd7e40f73b87ba5ed\",\"8132d272db648bcbbf8506e284043b7e6e5a1a71fb61c7b637099a88acd2ea2c\",\"d16c216aae15b96c792b3db0aea67045a121698f35e56c591e5be5834418ea3d\",\"621993189a2ad6ac9ebebca54ee4bb31dbd30624b4eabb56f799478c317d5106\",\"efaf2cc73078f920d2bced87e54a1dff5be74f8df500530528c5cdbe27adc77e\",\"eb347091b584af9911cab460ec5a4b36654f7f3a93479d04a4d40702f0aeb09a\"],\"transfer_conditions_md\":\"The attached checkpoint and the six filed n = 29 files reproduce every merge in seconds; any one task reruns with g2 --n 29 --decide 510 and a one-task shard.\",\"scope_sha256\":\"73ff96e5b948e1b3db41c4887c000d620adae4d1b0a37686ede80165fb74ce0f\",\"research_status\":\"accepted\",\"review_ids\":[1887]}]\nConfigured areas: [{\"id\":\"g2-exponent\",\"title\":\"Lower the G₂ upper-bound exponent (4.27 toward 2)\",\"lane\":\"g2-exponent\",\"topic_ids\":[],\"domain_md\":\"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"adversarial\",\"title\":\"Break accepted lemmas: counterexample search against validators\",\"lane\":\"adversarial\",\"topic_ids\":[],\"domain_md\":\"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"formalize\",\"title\":\"Lean 4 formalization of accepted lemmas\",\"lane\":\"formalize\",\"topic_ids\":[],\"domain_md\":\"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"measure\",\"title\":\"Extend numbered measurement scripts to larger ranges\",\"lane\":\"measure\",\"topic_ids\":[],\"domain_md\":\"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"infinitude\",\"title\":\"Routes toward infinitude not in the refuted registry\",\"lane\":\"infinitude\",\"topic_ids\":[],\"domain_md\":\"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"finiteness-structure\",\"title\":\"What structure a finite twin count would force (disproof-shaped lane)\",\"lane\":\"finiteness-structure\",\"topic_ids\":[],\"domain_md\":\"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"kk-lower-bound\",\"title\":\"Mapped paper claims and separate obligations\",\"paper\":\"kk-lower-bound\",\"topic_ids\":[\"kk-lower-bound.main\",\"kk-lower-bound.o1\",\"kk-lower-bound.o2\",\"kk-lower-bound.o3\",\"kk-lower-bound.o4\",\"kk-lower-bound.o5\",\"kk-lower-bound.o6\",\"kk-lower-bound.o7\"],\"domain_md\":\"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.\"}]\n\nFor each area return applicability_assessment:{source_return_id:5416,input_sha256:\"6ebc748faff8c75396344cee2c1bb7bf2b550d6871bfd8968a88346cf68dcd23\",entries:[{target_id,decision:\"applicable|inapplicable|unresolved\",scope_keys:[<declared source keys; [] when the accepted report has no typed scope>],evidence_md,assumptions_md}]}. Cite source evidence and explain the possible bridge or mismatch with each area's exact domain. Missing scope authority is an unresolved validation condition, not a demand for another full review or experiment. Applicability remains provisional unless every referenced scope satisfies the existing exact scientific authority rules; only validated entries can be transferred automatically. Preserve the claim's original scope; an extension is unresolved until ordinary scientific review. An unresolved entry is a recorded gap, not an instruction for a new experiment. Submit no new scientific claims, artifacts, review request or route changes in this administrative screening. Record existing evidence even when every area is inapplicable. GET <project>/research-applicability is the live index; OUTCOMES document integration is separate.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/6609/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"2d57c722d680aceb0a50c7be93342f7c83fd517c05979748cf22015d533bc26e","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}