{"id":6583,"job_id":10790,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of accepted return #5393\n\nJob #10790. Completed one bounded documentary comparison across all seven issued targets. Calibration: verified source/metadata comparison and provisional administrative relevance; no new scientific theorem, measurement, scope endorsement, review verdict, or route change. The underlying source remains accepted at measured, with only its exact finite scope endorsed by review #1878.\n\n## Bound source and currentness\n\nIssued input SHA-256: `e55a0f56a6f8dee7e2c19dca0402079b51085ce0edff38d273bfc67036f04ed6`. The served return's report SHA-256 `7735cbdf2bc84f65ca6f96a25da36bcf8240f5d2a55bdea332eb51765f3e3fc6` equals the issued snapshot and the SHA-256 of its UTF-8 report text. Both scope hashes match exactly. Review #1878's notes and structured assessment equal the issued copies, and the nine artifact-reference hashes equal the issued artifact set. These were metadata/reference checks; the nine artifact bodies were not fetched or independently hashed in this assignment. Source status is accepted, non-provisional, trusted; its review does not need reassessment. The bounded live applicability index was read, but did not list #5393; its omission was not treated as withdrawal or as a complete history. Currentness was checked directly against the served return and its authority fields.\n\n- `u8-windows-29-31-exact`: `75a14f78412e621cc163c6ca7946e70deddffa1279371b3f571f4a0f8f4dff2c`, accepted, review #1878.\n- `tile-window-max-instrument`: `ba7aa6ad2024ddce772cda599e31192b0f5f64162a10bcebe9d398ebeedfa90d`, pending scoped endorsement, no supporting scope review. It is considered without being positively transferred or scientifically endorsed here.\n\n## Matrix and evidence\n\n### g2-exponent — applicable\n\nReturn #5393, Rows and Limits, and trusted review #1878 provide exact finite maxsum thresholds U_8(29)=53 and U_8(31)=65. These are reusable finite inputs to the doubling/maxsum mechanism in the issued g2-exponent summary. Later accepted return #6525 and review #2249 already compose F_31(42)=1926 from these rows with the separate reviewed #6137 census to obtain (M8) for s=31..36. This is concrete reuse of the finite data, not an exponent improvement by #5393. No priority claim is endorsed: #2249 corrects the old M8 starting range to s<=20.\n\nConditions: Transfer only the exact accepted finite scope at s=29,31, beta=8, full cyclic twin-admissible tile and #4093 U/L/B conventions. A bound on K* is an independent premise. #6525 supplies a separate composition only at s=31..36; no all-s bound, D8, or exponent below 4.26645028 follows. Method timings and larger-base correctness are outside this positive entry.\n\n### adversarial — applicable\n\nThe Rows section of #5393 and review #1878 supply accepted comparison values for finite-window validators: F_29(52..54)=2052,2064,2076 at threshold 2064, and F_31(64..66)=2700,2718,2796 at threshold 2784. The equality case distinguishes U_8=53 from L_8=52 at base29 and exposes a possible off-by-one error in any future validator using different conventions. #1878 independently reproduced these values and the closure outputs. No counterexample search or new break was performed here.\n\nConditions: Use as reference data only for the same tile, cyclic seam, window length, and strict versus weak inequalities. An observed validator discrepancy would require its own ordinary evaluation; none is claimed. The dropped-class control and method timings belong to the unendorsed method scope and are not endorsed by this entry.\n\n### formalize — unresolved\n\nThe current formalize summary (version21, return #6566, supplied in the brief) separates measured full-cycle censuses and #6525 from Lean-proven statements. #5393 and #1878 establish finite measured rows, not a Lean theorem, statement binding, proof package or kernel receipt for those rows. The finite definitions and equality case can specify a future formalization target, but a link from executable enumeration and closure rules to a checked Lean statement is absent in the reviewed source.\n\nConditions: Any formal transfer must retain the exact finite domain, cycle wrap, positive gaps and #4093 U/L/B definitions, and supply the existing required statement/execution evidence for its exact declarations. The accepted measured rung cannot be upgraded to proven by this screen. No proof build, new verification package or automatic experiment is requested.\n\n### measure — applicable\n\nThe finite scope in #5393 and its endorsement in #1878 provide exact regression baselines at 29# and 31# for larger-range measurement work, including U_8=53/65, D=214708725/6226553025 and Ghat=258/348. A future instrument can compare at these existing bases before its distinct larger-range claim. The source also declares tile-window-max-instrument, but that method scope remains pending scoped endorsement: #1878 did not independently rerun the dropped-class control or timings. This positive entry deliberately references only the accepted finite scope.\n\nConditions: The transfer is baseline data, not correctness, coverage or speedup at larger bases. The described C implementation has base<=23, m<=256 and at most two lifted primes; the Node description requires positions below 2^53 and m<=256. The source states 37# was not run and would require an implementation change or more work. Historical four-thread timings and projected costs are not newly measured or transferable performance claims.\n\n### infinitude — unresolved\n\nThe issued infinitude summary uses the doubling bridge Ghat(2s)<=maxsum_(K*+1)(T_s). #5393 supplies its finite U_8 thresholds but explicitly makes no K*, M8 or prime conclusion. Accepted #6525/#2249 show a separate finite M8 composition for s=31..36 using #6137; the same review explicitly excludes uniform M8/D8 and s=29,30 or s>=37. No uniform-in-s bridge or prime-producing consequence is provided by the screened source.\n\nConditions: Do not infer infinitude, a subquadratic exponent, or a reopened closed route from finitely many tile rows. The separate K* premise and an appropriate all-s or infinitely-often argument remain outside #5393. The known s=31..36 composition is credited to #6525/#6137, not relabelled as a claim of #5393. This unresolved entry is a recorded scope gap, not a new research assignment.\n\n### finiteness-structure — inapplicable\n\nThe supplied finiteness-structure summary (version5, return #3805, with later entries explicitly separate) asks for consequences of a finite actual twin count; it states that finiteness forces eventual large sieve gaps and that finite calibration does not identify a tail exponent. #5393 studies two complete periodic sieve tiles, without assuming finiteness of actual twins. Neither its finite rows nor its described enumeration method establishes a structural consequence of finiteness or an eventual/infinitely-often statement.\n\nConditions: The finite sieve model must remain distinct from primes and from a hypothesized finite twin count. No probabilistic tail model, extrapolation, or new finiteness implication is introduced. The method scope remains pending endorsement; its possible computational utility elsewhere does not supply the absent finiteness premise or consequence.\n\n### kk-lower-bound — inapplicable\n\nCompared each issued paper topic separately against #5393 and the current paper-source report #6177/review #2108. Main: the fixed-A=12 survivor-gap lower theorem and its three mapped claims are not the finite maxsum enumeration. O1: no prime harmonic constant/o(1) asymptotic. O2: no two-variable uniform smooth-number estimate. O3: no every-fixed-A>4 extension. O4: no dyadic prime-count equality with coefficient 1/2. O5: no general sieve Input S or external one-class asymptotic; #6177 explicitly separates its accepted embedding component from the open external interface, and finite twin-tile maxsum values cannot replace either. O6: no two-sided density/Euler asymptotic. O7: no equation-(28) constant with its required hypotheses or ranges. The method scope changes none of these mismatches.\n\nConditions: Retain the accepted main theorem and each O1-O7 obligation separately. Similar CRT/sieve terminology does not identify domains, quantifiers, constants or proof premises. This is a relevance comparison of source reports and assigned domains, not a manuscript audit or integration. No manuscript/declaration/assumption revision, proof rerun, or change to the main theorem or open obligations is made.\n\n## Prior work, corrections and exclusions\n\nStarted from the latest supplied target summaries and their cited relevant records, without reading an accumulated research index. The shared local research directory was absent; supplied summaries and scoped public controller reads supplied the evidence instead. Read #5393 and #1878 in full. Read the live index's relevant later #6525 with #2249 and assigned paper source #6177 with #2108. #6525's finite reuse relies on #6137; its census was not re-reviewed here. Preserve #2249's correction: the earlier M8 range already reached s=19,20, so #6525 is not accepted as the first datum beyond18. Preserve its census hash-chain caveat and its exclusion of universal results. #1878's advisory beta=4 values were not promoted into the exact beta=8 source scope. No closed route is reopened.\n\nThe seven entries comprise 3 applicable, 2 unresolved and 2 inapplicable judgments. All positive scope_keys name only the exact endorsed finite scope. Applicable means a usable finite input or comparison baseline within the stated conditions; it does not assert achievement of a lane's ultimate goal. Method endorsement and any new larger-domain theorem remain separate. No optional research object, new route, review request, scientific artifact, audit revision, or follow-up assignment is supplied.\n\n## Execution and failures\n\nScientific compute calls=0; actual scientific CPU seconds=0; cpu_hours=0. Scientific inputs, seeds and scientific execution failures are empty. Only source retrieval, text inspection, hashing and JSON/schema checks were performed. No producer, compiler, tile pass, numerical falsifier, Lean build or kernel replay was executed. Historical timings and tests quoted in source reports belong to their original workers and are not this assignment's usage or validation.\n\nTwo initial controller GETs failed with DNS resolution errors in restricted execution. Their attempted JSON parses consequently failed on empty output. The same read-only source/protocol requests succeeded with network-enabled execution; the live index and the two additional relevant source reads also succeeded with HTTP200. The shared local research path lookup failed because the directory was absent. These source-access failures are retained as limitations, not scientific failures. No unresolved source/execution blocker remains.\n\n## Sources\n\n- Return #5393, report Sections Rows, Closure and Limits; recipe; research_authority.scopes; trusted review #1878 and its exact supported scope. `/projects/twin-primes/return/5393`.\n- Return #6525, Composition and Caveats; review #2249 and correction to the prior M8 range. Report SHA-256 `19171c396b7c6e1ba60bddcbe0b85416bbe1b5d8437353b1b1685e706bff5b5e`. `/projects/twin-primes/return/6525`.\n- Return #6177, underlying three-claim calibration and O5/O7 interface limits; review #2108. Report SHA-256 `7dc3164e846c8f3712c48d9a14330a36bb0bc71d71c216ac03dd9518510f571c`. `/projects/twin-primes/return/6177`. The manuscript itself was not fetched or audited.\n- Issued job #10790 complete task/domain contract and latest supplied lane summaries: g2-exponent v4 (#4364), adversarial v14 (#6109), formalize v21 (#6566), measure v10 (#6134), infinitude v4 (#5970), finiteness-structure v5 (#3805). These summaries were used as relevance context with their stated coverage dates and pending additions, not as new source acceptance.\n- `/projects/twin-primes/research-applicability`, bounded live source index; `/projects/twin-primes/research-protocol?section=shared-research`, Cross-area applicability; cached department protocol evidence/publication/files sections.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-29T23:59:22.842Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5393,6525,6177],"messages":[]},"tokens":{"log":"summary","input":89004,"models":{"gpt-6.1-sol":10622},"output":10622,"source":"reported","entries":0,"cache_read":931456,"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":"2026-10-29T23:59:25.822Z","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_ed0a9ffe1398b43af74f7f6d","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":["u8-windows-29-31-exact"],"evidence_md":"Return #5393, Rows and Limits, and trusted review #1878 provide exact finite maxsum thresholds U_8(29)=53 and U_8(31)=65. These are reusable finite inputs to the doubling/maxsum mechanism in the issued g2-exponent summary. Later accepted return #6525 and review #2249 already compose F_31(42)=1926 from these rows with the separate reviewed #6137 census to obtain (M8) for s=31..36. This is concrete reuse of the finite data, not an exponent improvement by #5393. No priority claim is endorsed: #2249 corrects the old M8 starting range to s<=20.","assumptions_md":"Transfer only the exact accepted finite scope at s=29,31, beta=8, full cyclic twin-admissible tile and #4093 U/L/B conventions. A bound on K* is an independent premise. #6525 supplies a separate composition only at s=31..36; no all-s bound, D8, or exponent below 4.26645028 follows. Method timings and larger-base correctness are outside this positive entry.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"adversarial","scope_keys":["u8-windows-29-31-exact"],"evidence_md":"The Rows section of #5393 and review #1878 supply accepted comparison values for finite-window validators: F_29(52..54)=2052,2064,2076 at threshold 2064, and F_31(64..66)=2700,2718,2796 at threshold 2784. The equality case distinguishes U_8=53 from L_8=52 at base29 and exposes a possible off-by-one error in any future validator using different conventions. #1878 independently reproduced these values and the closure outputs. No counterexample search or new break was performed here.","assumptions_md":"Use as reference data only for the same tile, cyclic seam, window length, and strict versus weak inequalities. An observed validator discrepancy would require its own ordinary evaluation; none is claimed. The dropped-class control and method timings belong to the unendorsed method scope and are not endorsed by this entry.","transfer_eligible":true,"provisional_relevance":false},{"decision":"unresolved","target_id":"formalize","scope_keys":["u8-windows-29-31-exact"],"evidence_md":"The current formalize summary (version21, return #6566, supplied in the brief) separates measured full-cycle censuses and #6525 from Lean-proven statements. #5393 and #1878 establish finite measured rows, not a Lean theorem, statement binding, proof package or kernel receipt for those rows. The finite definitions and equality case can specify a future formalization target, but a link from executable enumeration and closure rules to a checked Lean statement is absent in the reviewed source.","assumptions_md":"Any formal transfer must retain the exact finite domain, cycle wrap, positive gaps and #4093 U/L/B definitions, and supply the existing required statement/execution evidence for its exact declarations. The accepted measured rung cannot be upgraded to proven by this screen. No proof build, new verification package or automatic experiment is requested.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":["u8-windows-29-31-exact"],"evidence_md":"The finite scope in #5393 and its endorsement in #1878 provide exact regression baselines at 29# and 31# for larger-range measurement work, including U_8=53/65, D=214708725/6226553025 and Ghat=258/348. A future instrument can compare at these existing bases before its distinct larger-range claim. The source also declares tile-window-max-instrument, but that method scope remains pending scoped endorsement: #1878 did not independently rerun the dropped-class control or timings. This positive entry deliberately references only the accepted finite scope.","assumptions_md":"The transfer is baseline data, not correctness, coverage or speedup at larger bases. The described C implementation has base<=23, m<=256 and at most two lifted primes; the Node description requires positions below 2^53 and m<=256. The source states 37# was not run and would require an implementation change or more work. Historical four-thread timings and projected costs are not newly measured or transferable performance claims.","transfer_eligible":true,"provisional_relevance":false},{"decision":"unresolved","target_id":"infinitude","scope_keys":["u8-windows-29-31-exact"],"evidence_md":"The issued infinitude summary uses the doubling bridge Ghat(2s)<=maxsum_(K*+1)(T_s). #5393 supplies its finite U_8 thresholds but explicitly makes no K*, M8 or prime conclusion. Accepted #6525/#2249 show a separate finite M8 composition for s=31..36 using #6137; the same review explicitly excludes uniform M8/D8 and s=29,30 or s>=37. No uniform-in-s bridge or prime-producing consequence is provided by the screened source.","assumptions_md":"Do not infer infinitude, a subquadratic exponent, or a reopened closed route from finitely many tile rows. The separate K* premise and an appropriate all-s or infinitely-often argument remain outside #5393. The known s=31..36 composition is credited to #6525/#6137, not relabelled as a claim of #5393. This unresolved entry is a recorded scope gap, not a new research assignment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["tile-window-max-instrument","u8-windows-29-31-exact"],"evidence_md":"The supplied finiteness-structure summary (version5, return #3805, with later entries explicitly separate) asks for consequences of a finite actual twin count; it states that finiteness forces eventual large sieve gaps and that finite calibration does not identify a tail exponent. #5393 studies two complete periodic sieve tiles, without assuming finiteness of actual twins. Neither its finite rows nor its described enumeration method establishes a structural consequence of finiteness or an eventual/infinitely-often statement.","assumptions_md":"The finite sieve model must remain distinct from primes and from a hypothesized finite twin count. No probabilistic tail model, extrapolation, or new finiteness implication is introduced. The method scope remains pending endorsement; its possible computational utility elsewhere does not supply the absent finiteness premise or consequence.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["tile-window-max-instrument","u8-windows-29-31-exact"],"evidence_md":"Compared each issued paper topic separately against #5393 and the current paper-source report #6177/review #2108. Main: the fixed-A=12 survivor-gap lower theorem and its three mapped claims are not the finite maxsum enumeration. O1: no prime harmonic constant/o(1) asymptotic. O2: no two-variable uniform smooth-number estimate. O3: no every-fixed-A>4 extension. O4: no dyadic prime-count equality with coefficient 1/2. O5: no general sieve Input S or external one-class asymptotic; #6177 explicitly separates its accepted embedding component from the open external interface, and finite twin-tile maxsum values cannot replace either. O6: no two-sided density/Euler asymptotic. O7: no equation-(28) constant with its required hypotheses or ranges. The method scope changes none of these mismatches.","assumptions_md":"Retain the accepted main theorem and each O1-O7 obligation separately. Similar CRT/sieve terminology does not identify domains, quantifiers, constants or proof premises. This is a relevance comparison of source reports and assigned domains, not a manuscript audit or integration. No manuscript/declaration/assumption revision, proof rerun, or change to the main theorem or open obligations 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":true},"effective":true,"check_job_id":10790,"input_sha256":"e55a0f56a6f8dee7e2c19dca0402079b51085ce0edff38d273bfc67036f04ed6","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["tile-window-max-instrument","ba7aa6ad2024ddce772cda599e31192b0f5f64162a10bcebe9d398ebeedfa90d"],["u8-windows-29-31-exact","75a14f78412e621cc163c6ca7946e70deddffa1279371b3f571f4a0f8f4dff2c"]],"report_sha256":"7735cbdf2bc84f65ca6f96a25da36bcf8240f5d2a55bdea332eb51765f3e3fc6","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5393,"material_evidence":{"sha256":"964756d8ac4830ae11ea8c18f9ebb0f5b92c31a05a03bf5f7ee856b2593b3a5b","entries":{"return:5393":"8356cbae4c588541f7ac051a95cebf8b4a0bcae87f96f08fa76d3751be971db7","review:5393:1:claude-opus-5-5":"e4240e0d63ec73d02c00e9d1c177890cd9a18abdd88dbcb26b0463fd7a91b3ee","artifact:5393:0f6e5e703084b121393fbeff97493012f3b9d2b2b41adf7945f806ddc6b2780b":"0f6e5e703084b121393fbeff97493012f3b9d2b2b41adf7945f806ddc6b2780b","artifact:5393:1c0b236334a37c2345c3791b76a072e8bd5bb0797356e6552ac3fbc7823483a6":"1c0b236334a37c2345c3791b76a072e8bd5bb0797356e6552ac3fbc7823483a6","artifact:5393:1d0f5c4a6e5a18f1e190cc349ca832aaf9b5584acaefe4509dc8544c756d1fae":"1d0f5c4a6e5a18f1e190cc349ca832aaf9b5584acaefe4509dc8544c756d1fae","artifact:5393:45dcf739e7c296a4fbaa221f8d6ced00f1b7a946d844d20f8bf0aa8d9193b507":"45dcf739e7c296a4fbaa221f8d6ced00f1b7a946d844d20f8bf0aa8d9193b507","artifact:5393:467c5f53b4daaa26d88e8e4230b5dbe673620d2f3f584e4998493b07875d9b0e":"467c5f53b4daaa26d88e8e4230b5dbe673620d2f3f584e4998493b07875d9b0e","artifact:5393:6bb9d35c7b268969b8ad32ccfc8ef53564f975539e6d18d8689acb1af06bf38f":"6bb9d35c7b268969b8ad32ccfc8ef53564f975539e6d18d8689acb1af06bf38f","artifact:5393:79244e50d2931fe5180cf90db512c6ae856f56319c93eae33d0d716f81d626f2":"79244e50d2931fe5180cf90db512c6ae856f56319c93eae33d0d716f81d626f2","artifact:5393:e2abe92e3c43061946d2662e12d991a98f39907a2816e5e9875eb95f34410704":"e2abe92e3c43061946d2662e12d991a98f39907a2816e5e9875eb95f34410704","artifact:5393:f5d4a8c7c7c822fff1790875fd10c5423a058b083ee3cb7bc0cc0848c6889cbd":"f5d4a8c7c7c822fff1790875fd10c5423a058b083ee3cb7bc0cc0848c6889cbd"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5393,"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 #5393: 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\":5393,\"report_sha256\":\"7735cbdf2bc84f65ca6f96a25da36bcf8240f5d2a55bdea332eb51765f3e3fc6\",\"scope_hashes\":[[\"tile-window-max-instrument\",\"ba7aa6ad2024ddce772cda599e31192b0f5f64162a10bcebe9d398ebeedfa90d\"],[\"u8-windows-29-31-exact\",\"75a14f78412e621cc163c6ca7946e70deddffa1279371b3f571f4a0f8f4dff2c\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5393\":\"8356cbae4c588541f7ac051a95cebf8b4a0bcae87f96f08fa76d3751be971db7\",\"review:5393:1:claude-opus-5-5\":\"e4240e0d63ec73d02c00e9d1c177890cd9a18abdd88dbcb26b0463fd7a91b3ee\",\"artifact:5393:0f6e5e703084b121393fbeff97493012f3b9d2b2b41adf7945f806ddc6b2780b\":\"0f6e5e703084b121393fbeff97493012f3b9d2b2b41adf7945f806ddc6b2780b\",\"artifact:5393:1c0b236334a37c2345c3791b76a072e8bd5bb0797356e6552ac3fbc7823483a6\":\"1c0b236334a37c2345c3791b76a072e8bd5bb0797356e6552ac3fbc7823483a6\",\"artifact:5393:1d0f5c4a6e5a18f1e190cc349ca832aaf9b5584acaefe4509dc8544c756d1fae\":\"1d0f5c4a6e5a18f1e190cc349ca832aaf9b5584acaefe4509dc8544c756d1fae\",\"artifact:5393:45dcf739e7c296a4fbaa221f8d6ced00f1b7a946d844d20f8bf0aa8d9193b507\":\"45dcf739e7c296a4fbaa221f8d6ced00f1b7a946d844d20f8bf0aa8d9193b507\",\"artifact:5393:467c5f53b4daaa26d88e8e4230b5dbe673620d2f3f584e4998493b07875d9b0e\":\"467c5f53b4daaa26d88e8e4230b5dbe673620d2f3f584e4998493b07875d9b0e\",\"artifact:5393:6bb9d35c7b268969b8ad32ccfc8ef53564f975539e6d18d8689acb1af06bf38f\":\"6bb9d35c7b268969b8ad32ccfc8ef53564f975539e6d18d8689acb1af06bf38f\",\"artifact:5393:79244e50d2931fe5180cf90db512c6ae856f56319c93eae33d0d716f81d626f2\":\"79244e50d2931fe5180cf90db512c6ae856f56319c93eae33d0d716f81d626f2\",\"artifact:5393:e2abe92e3c43061946d2662e12d991a98f39907a2816e5e9875eb95f34410704\":\"e2abe92e3c43061946d2662e12d991a98f39907a2816e5e9875eb95f34410704\",\"artifact:5393:f5d4a8c7c7c822fff1790875fd10c5423a058b083ee3cb7bc0cc0848c6889cbd\":\"f5d4a8c7c7c822fff1790875fd10c5423a058b083ee3cb7bc0cc0848c6889cbd\"},\"sha256\":\"964756d8ac4830ae11ea8c18f9ebb0f5b92c31a05a03bf5f7ee856b2593b3a5b\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"u8-windows-29-31-exact\",\"kind\":\"finite\",\"domain_md\":\"Twin-admissible tile T_s = {r mod s#: gcd(r, s#) = gcd(r+2, s#) = 1} at s = 29, 31 with cyclic gaps; F_s(m) / H_s(m) = max / min sum of m consecutive gaps over the full cycle; Ghat = F_s(1); U_8 = max{m: F(m) ≤ 8·Ghat}, L_8 = max{m: F(m) < 8·Ghat}, B_8 = min{m: F(m) > 8·Ghat} (#4093's conventions).\",\"statement_md\":\"Exact full-cycle rows: F_29(49..59) = 1932, 1968, 2016, 2052, 2064, 2076, 2118, 2160, 2220, 2238, 2280 and F_31(61..71) = 2598, 2628, 2676, 2700, 2718, 2796, 2808, 2838, 2916, 2928, 2940 (Ghat 258 / 348, D 214,708,725 / 6,226,553,025). Hence U_8(29) = 53 (F_29(53) = 8·Ghat, so L_8 = 52, B_8 = 54) and U_8(31) = 65 (L_8 = 65, B_8 = 66). With these as pins, #4093's closure_ec.py returns width 1 at both rungs; with only F_29(53), F_29(54) and F_31(66) it returns [53,53] and [64,65]. Full F and H for m = 1..256 are in job8386-outputs.json.\",\"assumptions_md\":\"Exact integer arithmetic over the whole cycle; two instruments that share no code agree on D, F and H for m = 1..80 at 29# and 31#.\",\"artifact_sha256\":[\"1d0f5c4a6e5a18f1e190cc349ca832aaf9b5584acaefe4509dc8544c756d1fae\",\"45dcf739e7c296a4fbaa221f8d6ced00f1b7a946d844d20f8bf0aa8d9193b507\",\"6bb9d35c7b268969b8ad32ccfc8ef53564f975539e6d18d8689acb1af06bf38f\",\"f5d4a8c7c7c822fff1790875fd10c5423a058b083ee3cb7bc0cc0848c6889cbd\",\"0f6e5e703084b121393fbeff97493012f3b9d2b2b41adf7945f806ddc6b2780b\",\"79244e50d2931fe5180cf90db512c6ae856f56319c93eae33d0d716f81d626f2\",\"467c5f53b4daaa26d88e8e4230b5dbe673620d2f3f584e4998493b07875d9b0e\",\"e2abe92e3c43061946d2662e12d991a98f39907a2816e5e9875eb95f34410704\",\"1c0b236334a37c2345c3791b76a072e8bd5bb0797356e6552ac3fbc7823483a6\"],\"transfer_conditions_md\":\"Exact for s = 29 and 31 only, β = 8 only. It says nothing about Kstar, (M8) or actual twin primes; (M8) needs an independently sourced Kstar(s) ≤ U_8(s) − 1.\",\"scope_sha256\":\"75a14f78412e621cc163c6ca7946e70deddffa1279371b3f571f4a0f8f4dff2c\",\"research_status\":\"accepted\",\"review_ids\":[1878]},{\"key\":\"tile-window-max-instrument\",\"kind\":\"method\",\"domain_md\":\"Twin-admissible tile T_s = {r mod s#: gcd(r, s#) = gcd(r+2, s#) = 1} at s = 29, 31 with cyclic gaps; F_s(m) / H_s(m) = max / min sum of m consecutive gaps over the full cycle; Ghat = F_s(1); U_8 = max{m: F(m) ≤ 8·Ghat}, L_8 = max{m: F(m) < 8·Ghat}, B_8 = min{m: F(m) > 8·Ghat} (#4093's conventions).\",\"statement_md\":\"The CRT-lift enumerator (job8386-fms.c) and the 6k+5 segmented sieve (job8386-ind.mjs) compute exact cyclic window max/min F_s(m), H_s(m) on the twin-admissible tile. They reproduce #2268's served rows (s = 13..19, m ≤ 200), the s = 23 check_n anchors and #4093's 36 pins, agree with each other through 31#, and detect a dropped sieve class. Cost: 31# in 37 s wall (C, 4 threads) or 245 s (Node, 4 workers).\",\"assumptions_md\":\"fms: 32-bit base residues (b ≤ 23), MM = 256, at most two lifted primes per run. ind: positions stay below 2^53 in doubles; window m ≤ 256.\",\"artifact_sha256\":[\"1d0f5c4a6e5a18f1e190cc349ca832aaf9b5584acaefe4509dc8544c756d1fae\",\"45dcf739e7c296a4fbaa221f8d6ced00f1b7a946d844d20f8bf0aa8d9193b507\",\"6bb9d35c7b268969b8ad32ccfc8ef53564f975539e6d18d8689acb1af06bf38f\",\"f5d4a8c7c7c822fff1790875fd10c5423a058b083ee3cb7bc0cc0848c6889cbd\",\"0f6e5e703084b121393fbeff97493012f3b9d2b2b41adf7945f806ddc6b2780b\"],\"transfer_conditions_md\":\"37# needs a third lifted prime in fms (a small edit) or about 37× the 31# sieve time (~3 CPU-h in Node); not run here.\",\"scope_sha256\":\"ba7aa6ad2024ddce772cda599e31192b0f5f64162a10bcebe9d398ebeedfa90d\",\"research_status\":\"pending scoped endorsement\",\"review_ids\":[]}]\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:5393,input_sha256:\"e55a0f56a6f8dee7e2c19dca0402079b51085ce0edff38d273bfc67036f04ed6\",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/6583/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"6e254b6e0b8246fe435c266f267bedcfbbed31f61c6162fa96fdd84d50c12412","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}