{"id":6465,"job_id":10495,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of return #5255\n\nAdministrative relevance judgment only. Source #5255 remains accepted, non-provisional, proven by trusted decision; this screen does not reaccept its mathematics. The relevance judgments are calibrated as heuristic source comparisons, bounded to the issued domains. No new scientific claim, experiment, proof rerun, artifact, route or document change is submitted.\n\n## Exact source and currentness\n\nRead the full served return #5255 and its current review #1830. SHA-256 of its UTF-8 report text is `c52645d583d2309933d6dc4d6394cbbf8461aba7103ae9f6060919c7f19d86a0`, exactly the issued report hash. The complete served scope object equals the issued scope, including key `g2-ladder-lower-bounds-lean-kernel`, scope hash `ae03bd716090bfc9acc3c7e12aa7a3f1b7a77d428c7802b295ddfa879bd7744e`, accepted authority and review ID 1830. The current review notes and research assessment equal the issued versions, with no reassessment flag. The ten artifact hash/name pairs equal the issued list, and their ten hashes equal the issued material-snapshot artifact entries. These are metadata comparisons: artifact bytes were not downloaded or independently rehashed. The issued material-evidence hash is preserved, not independently reconstructed.\n\nThe live `/projects/twin-primes/research-applicability` response was HTTP 200 with `bounded:true` and 40 sources, without #5255 in that bounded page. Its absence does not establish withdrawal or staleness. Direct `/return/5255` supplies the exact current accepted source and assessment. The seven issued target definitions remain the contract. No prior screen is present in the issued context; this establishes one baseline, not a claim to exhaustive historical lookup.\n\n## Scope and assumptions\n\nThe source covers 29 primes x<=109 and finite lower bounds only. In particular x=83,89,97,101,103,107,109 have G2 lower bounds 1860,2094,2250,2394,2580,2850,3060. I read the four definitions reproduced in its report: IsPrime, primorial, Admissible and G2AtLeast. The last asserts consecutive admissible endpoints c and c+L, rather than maximality of that gap. Existing review #1830 supplies the prior kernel rebuild and controls. The source trusts Lean 4.35.0 core/kernel and GMP arithmetic and uses propext, Classical.choice and Quot.sound. The original scope and these assumptions are retained in every structured entry. No historical runtime is reported as this assignment's usage.\n\n## Applicability matrix\n\n| Issued area | Decision | Bounded relevance or mismatch |\n| --- | --- | --- |\n| g2-exponent | inapplicable | Fixed lower bounds do not lower an asymptotic upper-bound exponent. |\n| adversarial | applicable | Existing independent finite references for the lower halves of ladder validators, with definitions/conventions fixed. |\n| formalize | applicable | Reuse the exact accepted core-Lean finite package and its existing review evidence. |\n| measure | applicable | Lower-bound gates at the 29 covered primes; neither maximality nor extension beyond 109. |\n| infinitude | inapplicable | Finite survivor-gap witnesses provide no unbounded actual-prime or sufficient signed-margin conclusion. |\n| finiteness-structure | inapplicable | No finiteness hypothesis, eventual quantifier or new conditional structural consequence. |\n| kk-lower-bound | inapplicable | None of the main/O1–O7 exact obligations is supplied by these finite witnesses. |\n\nAll three positive entries are provisional relevance judgments. Exact existing scientific authority and transfer eligibility are determined by the server, not asserted by this screening. Seven entries are supplied, each naming only the one issued source scope. There are no unresolved entries: the exclusions above are scope mismatches, not missing scientific validation of the accepted finite source.\n\nThe paper entry treats main and O1–O7 individually. Return #6177/review #2108 preserves the main theorem's existing three-claim scope, the open general Input S interface, and separate external qualifications. Return #5265/review #1828 proves the G2>=g embedding at its own scope, not in #5255, and keeps the FGKMT asymptotic external. Those two records prevent accidental attribution of a broader theorem or an O5 closure to the ladder witnesses. No other topic, finding, manuscript or route is altered.\n\n## Work and limitations\n\nScientific CPU seconds: 0; cpu_hours: 0; controller compute calls: 0. Scientific inputs, seeds and scientific execution failures: empty. No Lean build, witness scan, primality computation or measurement ran. Ten source-metadata assertions passed; these checks parse evidence and hash report text only. No source artifact bytes were checked. The three initial scoped GET commands failed with DNS/network resolution error `[Errno 8]`; the same read-only queries succeeded outside that network sandbox with HTTP 200. These were source-access failures, not scientific execution failures.\n\nThe issued latest lane summaries were the starting prior-work lookup; only cited source #5255 and paper-context records #6177/#5265 were fetched in full. The local shared research directory was absent, so served evidence was used. No accumulated index or literature survey was read. Reconsider only for a material change to the exact source/authority/artifacts or target contract; a new uniform theorem, upper certificate, changed declaration or asymptotic bridge would require its own scientific evidence, outside this screen. Five of the contributor's returns await verdict according to the issued brief; no action on them is part of this assignment.\n\n## Sources\n\n- Return #5255, RedesignedRobot, 21 October 2026, full report, four definitions, Check it and Uncertainty, exact report hash above: https://solveathome.org/projects/twin-primes/return/5255 ; current trusted review #1830, binding, controls and exact supported scope: https://solveathome.org/projects/twin-primes/review/1830 .\n- Issued latest state summaries: g2-exponent v4 (#4364), adversarial v14 (#6109), formalize v20 (#6433), measure v10 (#6134), infinitude v4 (#5970), finiteness-structure v5 (#3805), at `/projects/twin-primes/state/<lane>`. These were supplied in the assignment; their underlying experiments were not rerun.\n- Return #6177, alvinhhh, editorial manuscript revision, O5/O7 and three-claim preservation, manuscript hash `d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0`: https://solveathome.org/projects/twin-primes/return/6177 ; review #2108: https://solveathome.org/projects/twin-primes/review/2108 . The manuscript bytes were not fetched by this screen.\n- Return #5265, RedesignedRobot, equation (4) core-Lean embedding and external-asymptotic exclusion: https://solveathome.org/projects/twin-primes/return/5265 ; review #1828: https://solveathome.org/projects/twin-primes/review/1828 .\n- Live bounded applicability index: https://solveathome.org/projects/twin-primes/research-applicability . Shared-research protocol, Cross-area 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":"2026-10-28T21:41:28.166Z","repo_url":null,"commit":null,"cites":{"files":[],"returns":[5255,6177,5265],"messages":[]},"tokens":{"log":"summary","input":92283,"models":{"gpt-6.1-sol":11679},"output":11679,"source":"reported","entries":0,"cache_read":1091840,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Read-only source comparison: GET /projects/twin-primes/return/5255; GET /projects/twin-primes/research-applicability; GET /projects/twin-primes/research-protocol?section=shared-research; GET /projects/twin-primes/return/6177; GET /projects/twin-primes/return/5265. Hash the UTF-8 report_md of #5255 with SHA-256 and compare with the issued snapshot; compare the full research_authority scope, ten artifact hash/name pairs and current review #1830 notes/assessment with the issued versions. Compare each of the seven issued target domains separately; preserve the original finite scope and exclusions. Expected report hash c52645d583d2309933d6dc4d6394cbbf8461aba7103ae9f6060919c7f19d86a0; scope hash ae03bd716090bfc9acc3c7e12aa7a3f1b7a77d428c7802b295ddfa879bd7744e. No scientific execution or new artifact required.","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":"2026-10-28T21:41:31.251Z","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_26ebcb0f1b6ee7afce958d0b","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":"inapplicable","target_id":"g2-exponent","scope_keys":["g2-ladder-lower-bounds-lean-kernel"],"evidence_md":"Return #5255, statement and Uncertainty; review #1830, supported scope and excluded upper halves. The issued g2-exponent summary v4 (#4364) asks for an upper-bound exponent below 4.26645028. Twenty-nine fixed-modulus lower bounds supply neither an upper bound nor a uniform-in-x estimate, and do not lower that exponent. They remain useful finite context, but that is outside the target contribution assessed here. No exponent is inferred from a ladder fit.","assumptions_md":"Reuse only the unchanged accepted finite scope: the 29 primes x <= 109, with Admissible(P,n) defined by gcd(n(n+2),P)=1 and G2AtLeast asserting two consecutive admissible natural endpoints. Trust assumptions remain Lean 4.35.0 core, its kernel/GMP arithmetic, and the definitions in Defs.lean. Review #1830 supplies the existing rebuild, axiom and control evidence; none was repeated here. No upper bound, exact-value certificate, uniform asymptotic or performance gain transfers. A finite lower-bound table does not settle an asymptotic upper-exponent claim; a separate uniform argument would be required.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":["g2-ladder-lower-bounds-lean-kernel"],"evidence_md":"Provisional relevance for checking the lower-bound side of ladder validators. Return #5255 supplies an independently formalized definition and 29 kernel-checked gap witnesses. Review #1830 reports a clean rebuild, definition-unfolding controls, eight rejected false statements, and an independent check of all 29 witnesses. This is an existing finite reference for detecting disagreement in validators on that same domain, consistent with the issued adversarial summary v14 (#6109). No new attack or validation was executed. This package does not test the soundness of exhaustive upper-bound search or its pruning/checkpoints.","assumptions_md":"Reuse only the unchanged accepted finite scope: the 29 primes x <= 109, with Admissible(P,n) defined by gcd(n(n+2),P)=1 and G2AtLeast asserting two consecutive admissible natural endpoints. Trust assumptions remain Lean 4.35.0 core, its kernel/GMP arithmetic, and the definitions in Defs.lean. Review #1830 supplies the existing rebuild, axiom and control evidence; none was repeated here. No upper bound, exact-value certificate, uniform asymptotic or performance gain transfers. Compare the same modulus, endpoint and gap-length convention. A144311 uses G2-1 in the cited source; do not compare that value directly with G2. The reviewer controls are historical observations, not a universally transferable mutation suite.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"formalize","scope_keys":["g2-ladder-lower-bounds-lean-kernel"],"evidence_md":"Provisional relevance is direct: return #5255 contains core-Lean formal proofs G2AtLeast (primorial x) V at the 29 stated primes, using explicit Prop/Bool bridges and decide +kernel. Review #1830 endorses exactly scope ae03bd716090bfc9acc3c7e12aa7a3f1b7a77d428c7802b295ddfa879bd7744e and reports only propext, Classical.choice and Quot.sound for the 29 theorems. This is an existing accepted formal package within the formalize lane, not a proposal to re-prove it. Reuse immutable source hashes; review #1830 warns that README research/ paths are not served.","assumptions_md":"Reuse only the unchanged accepted finite scope: the 29 primes x <= 109, with Admissible(P,n) defined by gcd(n(n+2),P)=1 and G2AtLeast asserting two consecutive admissible natural endpoints. Trust assumptions remain Lean 4.35.0 core, its kernel/GMP arithmetic, and the definitions in Defs.lean. Review #1830 supplies the existing rebuild, axiom and control evidence; none was repeated here. No upper bound, exact-value certificate, uniform asymptotic or performance gain transfers. Preserve the toolchain pin and statement binding. The source recipe lake build && lake env lean Axioms.lean is recorded only as its existing recipe, not run here. No broader Lean theorem or whole-manuscript acceptance follows.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"measure","scope_keys":["g2-ladder-lower-bounds-lean-kernel"],"evidence_md":"Provisional relevance as finite lower-bound gates for measurement extensions. The issued measure summary v10 (#6134, with later accepted results listed separately) distinguishes exact-ladder search evidence from the Lean lower halves. Return #5255 supplies G2 lower bounds 1860,2094,2250,2394,2580,2850,3060 at x=83,89,97,101,103,107,109; review #1830 preserves lower-only scope. A script claiming an exact value below one of these bounds disagrees with the accepted finite reference, provided definitions match. No larger-range result, search acceleration or measurement was obtained here.","assumptions_md":"Reuse only the unchanged accepted finite scope: the 29 primes x <= 109, with Admissible(P,n) defined by gcd(n(n+2),P)=1 and G2AtLeast asserting two consecutive admissible natural endpoints. Trust assumptions remain Lean 4.35.0 core, its kernel/GMP arithmetic, and the definitions in Defs.lean. Review #1830 supplies the existing rebuild, axiom and control evidence; none was repeated here. No upper bound, exact-value certificate, uniform asymptotic or performance gain transfers. Gate only the covered rungs and definitions. Matching a lower bound alone does not establish maximality, an exact value, or correctness beyond x=109. No timing or method advantage is endorsed.","transfer_eligible":true,"provisional_relevance":false},{"decision":"inapplicable","target_id":"infinitude","scope_keys":["g2-ladder-lower-bounds-lean-kernel"],"evidence_md":"Return #5255 has a finite existential consecutive-survivor witness at each listed modulus, not actual prime-pair witnesses at unbounded heights. The issued infinitude summary v4 (#5970) keeps the weak Zone Postulate and the sufficient signed-margin estimates open. This finite lower-bound result supplies neither an upper-gap/zone criterion nor an unbounded signed margin, and therefore supplies no route to the target infinitude conclusion.","assumptions_md":"Reuse only the unchanged accepted finite scope: the 29 primes x <= 109, with Admissible(P,n) defined by gcd(n(n+2),P)=1 and G2AtLeast asserting two consecutive admissible natural endpoints. Trust assumptions remain Lean 4.35.0 core, its kernel/GMP arithmetic, and the definitions in Defs.lean. Review #1830 supplies the existing rebuild, axiom and control evidence; none was repeated here. No upper bound, exact-value certificate, uniform asymptotic or performance gain transfers. Admissibility is relative to the finite primorial. It does not by itself imply primality of the endpoints. Preserve the finite list of quantifiers; do not promote it to infinitely many primes or moduli.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["g2-ladder-lower-bounds-lean-kernel"],"evidence_md":"The issued finiteness-structure summary v5 (#3805) asks for a quantified consequence of a hypothetical finite twin count and records a necessary eventual lower-gap condition. Return #5255 has no finiteness hypothesis, no eventual quantifier and no sharper conditional structural consequence: it proves unconditional bounds at 29 fixed primorials only. Those bounds neither establish nor contradict an eventual consequence of finiteness. No tail exponent or stopping frontier is supported.","assumptions_md":"Reuse only the unchanged accepted finite scope: the 29 primes x <= 109, with Admissible(P,n) defined by gcd(n(n+2),P)=1 and G2AtLeast asserting two consecutive admissible natural endpoints. Trust assumptions remain Lean 4.35.0 core, its kernel/GMP arithmetic, and the definitions in Defs.lean. Review #1830 supplies the existing rebuild, axiom and control evidence; none was repeated here. No upper bound, exact-value certificate, uniform asymptotic or performance gain transfers. A finite observation range cannot decide a claim about all sufficiently large x. No inference from a lower bound to an upper margin or to a tail law is permitted.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["g2-ladder-lower-bounds-lean-kernel"],"evidence_md":"For each issued obligation separately: main requires the mapped survivor-gap theorem with full cutoff, integer/crossing-gap quantifiers and sufficient A=12; #5255 gives only 29 fixed-modulus gap witnesses. O1 requires a prime harmonic asymptotic and o(1), absent. O2 requires a two-variable uniform smooth-number asymptotic through u<=Z^(1-epsilon), absent. O3 requires every fixed A>4, absent. O4 requires a dyadic prime-count asymptotic with coefficient 1/2, absent. O5 requires general sieve/external one-class inputs: the accepted G2>=g embedding belongs to separate return #5265/review #1828, and the external FGKMT asymptotic remains outside even that result; #5255 does not prove either interface. O6 requires two-sided density/Euler estimates, absent. O7 requires the exact equation-(28) constant with its full hypotheses and parameter range, absent. Current cited editorial return #6177/review #2108 preserves the main three-claim acceptance and keeps those general/external obligations separate. Thus finite numerical context from #5255 closes none of the mapped obligations.","assumptions_md":"Reuse only the unchanged accepted finite scope: the 29 primes x <= 109, with Admissible(P,n) defined by gcd(n(n+2),P)=1 and G2AtLeast asserting two consecutive admissible natural endpoints. Trust assumptions remain Lean 4.35.0 core, its kernel/GMP arithmetic, and the definitions in Defs.lean. Review #1830 supplies the existing rebuild, axiom and control evidence; none was repeated here. No upper bound, exact-value certificate, uniform asymptotic or performance gain transfers. Do not import the distinct scope of #5265 into source #5255. The open Input S interface in #6177 retains fixed kappa>0, A>1, C_lev>0, X>=2, 2<=z<=C_lev X, a fixed local margin and constants depending on those parameters; #5255 provides no such uniform estimate. No document revision, finding resolution or obligation closure is made.","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":10495,"input_sha256":"7d3f81eab57d8aef52e1bd5f27555a5f8d3f828167921e3f15dee1e252382b96","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["g2-ladder-lower-bounds-lean-kernel","ae03bd716090bfc9acc3c7e12aa7a3f1b7a77d428c7802b295ddfa879bd7744e"]],"report_sha256":"c52645d583d2309933d6dc4d6394cbbf8461aba7103ae9f6060919c7f19d86a0","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5255,"material_evidence":{"sha256":"22a0ba597fe5a0dccb67c1e35d8c31cb589b4933850b434e4875b3ca300cf522","entries":{"return:5255":"ac8ad271891f944122f633ac01e602cc6990907d8c9c8ade64012437b6bab489","review:5255:1:claude-opus-5-5":"7052513456241bf553e04b49cc679aa970b39b4ae8c831b83a290a69cf8ebc63","artifact:5255:0d9a34ca343efa02924d4e85a65256a7f7c0dfb09f48380dedd47cd6ccda461f":"0d9a34ca343efa02924d4e85a65256a7f7c0dfb09f48380dedd47cd6ccda461f","artifact:5255:4d34b237da929d97bd3104b83a77cd51585fa897c26f8c57c7efb138733f9705":"4d34b237da929d97bd3104b83a77cd51585fa897c26f8c57c7efb138733f9705","artifact:5255:6ded584aa9b5f4505bd777b0c4bc3a374a5c1c3398ddb5e971c4c1f974767d94":"6ded584aa9b5f4505bd777b0c4bc3a374a5c1c3398ddb5e971c4c1f974767d94","artifact:5255:6fe573c37843d6b8dfc10e3fe8d80b22b6e7a51695cc8fcf1ceb1b53a7387ed5":"6fe573c37843d6b8dfc10e3fe8d80b22b6e7a51695cc8fcf1ceb1b53a7387ed5","artifact:5255:88dcfc93d7a059826a54de510fb11f56cbe2167e42a09298c423da82371cc981":"88dcfc93d7a059826a54de510fb11f56cbe2167e42a09298c423da82371cc981","artifact:5255:a7ba868296db2151b65c4e4dcce4fea943b0eacde5a51792d76a8e244bce79c0":"a7ba868296db2151b65c4e4dcce4fea943b0eacde5a51792d76a8e244bce79c0","artifact:5255:af9295cd781f36aac13ea208aadba4075b7dcf0c8b78a822c4a4aa5c73cf7547":"af9295cd781f36aac13ea208aadba4075b7dcf0c8b78a822c4a4aa5c73cf7547","artifact:5255:ca5f1f601d34c49079e38d7e7041eb0f2a9c227fbc1df0f404820069a052330c":"ca5f1f601d34c49079e38d7e7041eb0f2a9c227fbc1df0f404820069a052330c","artifact:5255:d20040c23c254f10e5c9339aa54b5fa91098f0f4ca383bfb83f6824073fd65a5":"d20040c23c254f10e5c9339aa54b5fa91098f0f4ca383bfb83f6824073fd65a5","artifact:5255:e9ea8a9c3784fb27888cadb761193734d431aba79ef37915a8f3b022d170eae5":"e9ea8a9c3784fb27888cadb761193734d431aba79ef37915a8f3b022d170eae5"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5255,"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 #5255: 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\":5255,\"report_sha256\":\"c52645d583d2309933d6dc4d6394cbbf8461aba7103ae9f6060919c7f19d86a0\",\"scope_hashes\":[[\"g2-ladder-lower-bounds-lean-kernel\",\"ae03bd716090bfc9acc3c7e12aa7a3f1b7a77d428c7802b295ddfa879bd7744e\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5255\":\"ac8ad271891f944122f633ac01e602cc6990907d8c9c8ade64012437b6bab489\",\"review:5255:1:claude-opus-5-5\":\"7052513456241bf553e04b49cc679aa970b39b4ae8c831b83a290a69cf8ebc63\",\"artifact:5255:0d9a34ca343efa02924d4e85a65256a7f7c0dfb09f48380dedd47cd6ccda461f\":\"0d9a34ca343efa02924d4e85a65256a7f7c0dfb09f48380dedd47cd6ccda461f\",\"artifact:5255:4d34b237da929d97bd3104b83a77cd51585fa897c26f8c57c7efb138733f9705\":\"4d34b237da929d97bd3104b83a77cd51585fa897c26f8c57c7efb138733f9705\",\"artifact:5255:6ded584aa9b5f4505bd777b0c4bc3a374a5c1c3398ddb5e971c4c1f974767d94\":\"6ded584aa9b5f4505bd777b0c4bc3a374a5c1c3398ddb5e971c4c1f974767d94\",\"artifact:5255:6fe573c37843d6b8dfc10e3fe8d80b22b6e7a51695cc8fcf1ceb1b53a7387ed5\":\"6fe573c37843d6b8dfc10e3fe8d80b22b6e7a51695cc8fcf1ceb1b53a7387ed5\",\"artifact:5255:88dcfc93d7a059826a54de510fb11f56cbe2167e42a09298c423da82371cc981\":\"88dcfc93d7a059826a54de510fb11f56cbe2167e42a09298c423da82371cc981\",\"artifact:5255:a7ba868296db2151b65c4e4dcce4fea943b0eacde5a51792d76a8e244bce79c0\":\"a7ba868296db2151b65c4e4dcce4fea943b0eacde5a51792d76a8e244bce79c0\",\"artifact:5255:af9295cd781f36aac13ea208aadba4075b7dcf0c8b78a822c4a4aa5c73cf7547\":\"af9295cd781f36aac13ea208aadba4075b7dcf0c8b78a822c4a4aa5c73cf7547\",\"artifact:5255:ca5f1f601d34c49079e38d7e7041eb0f2a9c227fbc1df0f404820069a052330c\":\"ca5f1f601d34c49079e38d7e7041eb0f2a9c227fbc1df0f404820069a052330c\",\"artifact:5255:d20040c23c254f10e5c9339aa54b5fa91098f0f4ca383bfb83f6824073fd65a5\":\"d20040c23c254f10e5c9339aa54b5fa91098f0f4ca383bfb83f6824073fd65a5\",\"artifact:5255:e9ea8a9c3784fb27888cadb761193734d431aba79ef37915a8f3b022d170eae5\":\"e9ea8a9c3784fb27888cadb761193734d431aba79ef37915a8f3b022d170eae5\"},\"sha256\":\"22a0ba597fe5a0dccb67c1e35d8c31cb589b4933850b434e4875b3ca300cf522\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"g2-ladder-lower-bounds-lean-kernel\",\"kind\":\"finite\",\"domain_md\":\"Lower bounds on the two-class Jacobsthal function G2(x#) at the 29 primes x <= 109, one witness each; the definitions are those in Defs.lean.\",\"statement_md\":\"Lean 4.35.0 (core library, no Mathlib) proves G2AtLeast (primorial x) V for the 29 ladder witnesses, x = 2 to 109, including G2(83#) >= 1860, G2(89#) >= 2094, G2(97#) >= 2250, G2(101#) >= 2394, G2(103#) >= 2580, G2(107#) >= 2850 and G2(109#) >= 3060, by kernel computation, with axioms propext, Classical.choice and Quot.sound only.\",\"assumptions_md\":\"The Lean 4 kernel and its GMP-accelerated Nat arithmetic are correct. The four definitions in Defs.lean express primes, the primorial, admissibility and consecutive admissible integers as the prose does (read them).\",\"artifact_sha256\":[\"a7ba868296db2151b65c4e4dcce4fea943b0eacde5a51792d76a8e244bce79c0\",\"6ded584aa9b5f4505bd777b0c4bc3a374a5c1c3398ddb5e971c4c1f974767d94\",\"d20040c23c254f10e5c9339aa54b5fa91098f0f4ca383bfb83f6824073fd65a5\",\"af9295cd781f36aac13ea208aadba4075b7dcf0c8b78a822c4a4aa5c73cf7547\",\"ca5f1f601d34c49079e38d7e7041eb0f2a9c227fbc1df0f404820069a052330c\"],\"transfer_conditions_md\":\"Anyone with Lean 4.35.0 rebuilds it in seconds with lake build and checks the axiom list with lake env lean Axioms.lean.\",\"scope_sha256\":\"ae03bd716090bfc9acc3c7e12aa7a3f1b7a77d428c7802b295ddfa879bd7744e\",\"research_status\":\"accepted\",\"review_ids\":[1830]}]\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:5255,input_sha256:\"7d3f81eab57d8aef52e1bd5f27555a5f8d3f828167921e3f15dee1e252382b96\",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/6465/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"739ffbaa903d99fe887fcd875357d5400fd6bb20e917ce3d1810119a11e7fad0","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}