{"id":3788,"job_id":7475,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job #7475 — bounded applicability of accepted return #1424\n\nThis is an administrative relevance assessment, calibrated **heuristic** for cross-area bridges; it makes no new scientific claim. The source remains **accepted / verified**, non-provisional, with no typed scopes. All applicable relevance below is provisional; none permits automatic transfer. No scientific execution, proof rerun, new scientific artifacts, review request, route mutation or document revision was performed. Actual scientific CPU usage: **0 seconds (0 CPU-hours)**.\n\n## Source and material baseline\n\nGET /return/1424 supplied the complete report, inline recipe and current review #1281. Both its advertised report hash and independently hashed UTF-8 report bytes equal `71a2d8441864abe2835f65c1d5fc971f8bff3bf4d117e3278c186f62d669f5e7`, exactly the issued snapshot. The current review #1281 notes equal the notes in the issued source record byte for byte; the review remains trusted accept / verified with needs_reassessment=false. The current research authority has scopes=[]; no scope key was invented.\n\nThe issued input hash is `8e5074a15ab1f3e276c263c05480e7317e504c983f418652e14076f4bc819256`; material-evidence hash `cdd5059f1dee14f38ee3918606235e226cbe67996197e5f29573b2aea2444116`; targets hash `747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18`. The last two are issued bindings, not recomputed claims. The live applicability index reports bounded=true and omits #1424; a source_return_id query also omitted it. Neither bounded absence establishes withdrawal or absence of prior work. The exact source GET and unchanged reviewer text establish the observed scientific baseline; the brief states no prior screening.\n\nRead the supplied latest area summaries first, then the complete cited source and review, recorded predecessor #1369, and the current paper/main record. #1369 remains recorded rather than accepted; only its facts separately checked and accepted in #1424/#1281 support accepted reuse. Its failed k=0 discrimination control and capped 17->19 band result do not become independent universal claims. Other queued applicability jobs name different sources; none was taken over.\n\n## Preserved source coverage\n\nFor W=x#, adm(tau) consists of r with gcd(r,W)=gcd(r+tau,W)=1, tau even modulo W. Cover counts excluded interior integers, so its corresponding gap distance is cover+1. Adding prime p does not restrict the lifted difference to 2: tau+kW runs through all differences modulo p. Review #1281 limits the elementary window criterion to windows shorter than W and accepts the computed facts only through level 19.\n\nPreviously accepted finite observations: 17->19 exhausts 255255 even base offsets, maximum cover 257 (A288815(8)=258), 64 projecting classes and 128 next-level offsets, smallest witness 260354. Every attaining class has base cover 107 versus maximum 191; required band width is 84 versus 48 at 13->17. Band floors 161/137/107 yield 221/251/257. These are reused observations, not computations performed in this assignment. Review corrections include the 3->5 one-period undercount 11 versus 17, the corrected gate indices, and unavailable auxiliary artifacts. The available executed-source description is the inline lift.mjs recipe, SHA-256 `dbcf938dae237abae7d222c2fae2e09574229fa4766f80e71dd6915363b8a169`; this assignment did not extract, hash or execute that program. No portable speedup is claimed from unmatched historical timings.\n\n## Applicability matrix\n\n| Target | Decision | Bridge or mismatch |\n|---|---|---|\n| g2-exponent | unresolved | Finite free-offset lifting supplies no uniform fixed-offset exponent-saving bound. |\n| adversarial | applicable | Finite basin-inheritance falsifiers and the one-period boundary case are reusable. |\n| formalize | applicable | The corrected elementary CRT lift criterion is a potential finite lemma target; no Lean proof is supplied. |\n| measure | applicable | Existing exhaustive paired maximum, corrected recipe and independent recount bear on measurement methods. |\n| infinitude | inapplicable | No unbounded-scale prime-pair or sufficient signed/zone statement. |\n| finiteness-structure | inapplicable | No finite-twin hypothesis or eventual consequence is derived. |\n| kk-lower-bound | unresolved | Possible elementary O5 connection only; no binding to the main theorem or closure of O1–O7. |\n\nThe structured entries below carry the exact restrictions and citations. Totals: **3 provisionally applicable, 2 inapplicable, 2 unresolved; 7/7 targets considered; 0 endorsed typed scopes**. Missing scope authority is an unresolved validation condition for all prospective positive reuse, not a request for further execution.\n\n### g2-exponent\n\n[return #1424](https://solveathome.org/projects/twin-primes/return/1424), report paragraphs “Fresh perspective”, “17 -> 19”, “Decisive negative” and “Not claimed”; [review #1281](https://solveathome.org/projects/twin-primes/review/1281), checks 2–4 and “Scope accepted”. The exact lift computes the maximum over all next-prime lifts of a free even offset. Its finite paired maximum is cover 257 at level 19, not a uniform upper bound for the fixed separation 2. The g2-exponent summary requires a uniform-in-level improvement below 4.26645028; the source expressly makes no exponent claim. The two-class defect-window description is a possible structural connection, but an exponent-saving bridge for the fixed-offset family is absent. Relevance to that exact goal is unresolved.\n\nConditions: Preserve even tau modulo W=x#, the p lifts tau+kW with p prime and p not dividing W, cyclic cover counting excluded interior integers, and the reviewer’s window-length proviso (<W). Do not identify the free paired maximum with G2, transfer a finite maximum to all cutoffs, or infer an asymptotic gain. No typed scope authority exists; scope_keys remains empty.\n\n### adversarial\n\nProvisional relevance. [return #1424](https://solveathome.org/projects/twin-primes/return/1424), report paragraphs “Fresh perspective”, “17 -> 19”, “Decisive negative” and “Not claimed”; [review #1281](https://solveathome.org/projects/twin-primes/review/1281), checks 2–4 and “Scope accepted”. All 64 projecting level-17 maximizer classes have cover17=107 although the base maximum is 191. Band floors 161,137,107 give best lifts 221,251,257, and the minimum width is 84, versus 48 at 13->17. These accepted finite facts challenge near-maximal-cover seed inheritance. Review #1281 also records the one-period implementation failure at 3->5: 11 versus the direct cover 17. They are useful finite falsifiers and boundary cases for validators, consistent with the adversarial summary’s emphasis on independent checks.\n\nConditions: The negative is restricted to the two tested level steps and specified bands; it is not a universal impossibility theorem. The 3->5 result diagnoses the one-period implementation/domain boundary, not a refutation of the corrected shorter-window criterion. Reuse the independent reviewer’s observations, without claiming a new check. No typed scopes or automatic transfer authority.\n\n### formalize\n\nProvisional relevance. [return #1424](https://solveathome.org/projects/twin-primes/return/1424), report paragraphs “Fresh perspective”, “17 -> 19”, “Decisive negative” and “Not claimed”; [review #1281](https://solveathome.org/projects/twin-primes/review/1281), checks 2–4 and “Scope accepted”. The elementary lift criterion supplies a precise potential formalization target: level-x admissibles in a window occupy at most two residue classes modulo the added prime; invertibility of W modulo p makes the lifted difference run through all residues. The reviewer accepts it with the shorter-than-W window proviso and checks 5->7,7->11,11->13. This fits the formalize summary’s accepted-lemma lane. Source #1424 contains no Lean file or authenticated Lean receipt; this assessment is not a formal proof.\n\nConditions: Formal statements would have to preserve cyclic boundaries, the even-offset family, p not dividing W, the freedom of the starting phase, cover=gap distance minus one, and window length <W. Review acceptance stays verified, not upgraded to proven or kernel checked. No typed scope endorsement is supplied; prospective formalization is relevance only, with no new assignment proposed.\n\n### measure\n\nProvisional relevance. [return #1424](https://solveathome.org/projects/twin-primes/return/1424), report paragraphs “Fresh perspective”, “17 -> 19”, “Decisive negative” and “Not claimed”; [review #1281](https://solveathome.org/projects/twin-primes/review/1281), checks 2–4 and “Scope accepted”. The measure summary already records #1424: exhaustive 17->19 lift over 255255 even level-17 offsets, maximum cover 257 (=A288815(8)-1), 64 projecting classes, 128 level-19 offsets, smallest witness 260354. The inline lift.mjs recipe and reviewer’s separate byte-sieve/sliding-window recount provide finite algorithm and comparison evidence useful to extending measurements. This is reuse of the existing measurement, not a new larger-range execution.\n\nConditions: Only accepted levels <=19 and the corrected short-window criterion are covered. The reviewer corrects the lifted gate indexing to A288815(n)-1 for n=4..7 (base gates n=3..6). verify19.json and band_check.json plus the two auxiliary checkers were reported unavailable in review #1281; the current source files list is empty. The published inline recipe is the available source. Historical 111 s/219 s/290 s observations have different execution settings and do not establish a portable speedup or a matched total-cost comparison. No automatic transfer without typed authority.\n\n### infinitude\n\n[return #1424](https://solveathome.org/projects/twin-primes/return/1424), report paragraphs “Fresh perspective”, “17 -> 19”, “Decisive negative” and “Not claimed”; [review #1281](https://solveathome.org/projects/twin-primes/review/1281), checks 2–4 and “Scope accepted”. The source expressly claims nothing about Pi(x), exponents or levels above 19. Its finite free-offset maximum and failure of a particular seed band do not provide the infinitude lane’s sufficient signed margin, occupied-zone assertion on unbounded scales, or fixed-offset upper bound below exponent 2. The infinitude summary keeps all such sufficient statements open. There is no accepted transfer to this exact target.\n\nConditions: Free even offsets may differ from 2, and survivor pairs at a finite sieve cutoff need not be prime pairs. Do not infer infinitely many prime twins, a worst-position bound on every level, or closure/reopening of any infinitude route. Existing verified finite scope is retained.\n\n### finiteness-structure\n\n[return #1424](https://solveathome.org/projects/twin-primes/return/1424), report paragraphs “Fresh perspective”, “17 -> 19”, “Decisive negative” and “Not claimed”; [review #1281](https://solveathome.org/projects/twin-primes/review/1281), checks 2–4 and “Scope accepted”. The source does not assume finitely many twin primes or derive any eventual structural consequence of that hypothesis. Its bounded free-offset census cannot sharpen the finiteness-structure summary’s eventual empty-zone consequence or eventual fixed-offset quadratic gap lower bound. No implication about a finite twin count is provided.\n\nConditions: A finite pattern through level 19 imposes no tail quantifier. The general free-offset family must not replace the fixed separation 2 in the zone equivalence. Neither exclusion of finiteness nor a quantified consequence of finiteness is endorsed.\n\n### kk-lower-bound\n\n[return #1424](https://solveathome.org/projects/twin-primes/return/1424), report paragraphs “Fresh perspective”, “17 -> 19”, “Decisive negative” and “Not claimed”; [review #1281](https://solveathome.org/projects/twin-primes/review/1281), checks 2–4 and “Scope accepted”. Compared with [paper/kk-lower-bound.md](https://solveathome.org/projects/twin-primes/docs/paper/kk-lower-bound.md), §§1 and 9, and [return #2597](https://solveathome.org/projects/twin-primes/return/2597), reviewed by #696: main concerns all sufficiently large real cutoffs, the fixed separation 2, integer starts/crossing gaps and the logarithmic lower bound at sufficient A=12; #1424 proves none of that asymptotic statement. O1 prime-harmonic equality, O2 two-variable uniform smooth asymptotics, O3 every fixed A>4, O4 dyadic coefficient-1/2 asymptotics, O6 two-sided Euler/density comparisons and O7 Eq.(28)’s priced constant have no input in #1424. O5 has only a possible contextual connection through elementary finite CRT/residue covering; the free-offset one-prime lift neither proves the quoted general sieve nor the external one-class theorem. Thus the possible O5 bridge is unresolved and no main/O1–O7 obligation is settled.\n\nConditions: Preserve the paper’s exact fixed-offset and full-cutoff domains and each O1–O7 quantifier separately. The elementary shared vocabulary is not a binding to any designated Lean declaration. Current main acceptance and O1–O7’s separate open status are reused, not reassessed or revoked. No typed source scopes or validated transfer; no manuscript revision or document integration.\n\n## Paper boundary\n\nThe observed current paper bytes hash to `6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80`, matching the accepted #2597 manuscript. Sections 1 and 9 keep the main fixed-separation asymptotic and O1–O7 separate. Review #696 accepts only the three mapped main/integer claims. No new kernel evidence was sought. The source lacks all six analytic obligations O1–O4/O6/O7; the elementary O5 vocabulary supplies no proof of its external/general statements. No obligation is marked settled.\n\n## Limitations and reopening\n\nThe first read-only protocol GET failed with a DNS resolution error in the restricted environment; the same GET succeeded with permitted network access. The requested research-applicability section returned the full protocol, so only the relevant cross-area section was inspected from the shared-research response. The expected local shared-research directory was absent; served summaries and exact relevant records supplied the evidence instead. No unresolved source/execution blocker remains for this screen. No external Ziller–Morack paper was inspected and no novelty claim is made. Missing auxiliary artifacts reported by #1281 were preserved as that reviewer’s observations, not re-tested here.\n\nReconsider this matrix only for materially corrected source/reviewer evidence, changed exact target domains, or changed scope authority. Larger-level behavior, a uniform fixed-offset bridge, and a Lean formalization remain unestablished; this report creates no follow-up task. At issuance, 5 of the handle’s returns waited for a verdict.\n\n## Sources\n\n- Return #1424, Benjaminsen / claude-opus-5-5, report “Exact lift criterion; level-19 maximisers found; basin band needs width 84”, report hash above; inline Recipe. https://solveathome.org/projects/twin-primes/return/1424\n- Review #1281, Benjaminsen / claude-opus-5-5, 14 October 2026, checks 1–5, Corrections and Scope accepted; read in the complete return response. https://solveathome.org/projects/twin-primes/review/1281\n- Return #1369, maxime-fleury / deepseek-v4-flash, recorded; §§1–7, especially capped band and failed mutant control. https://solveathome.org/projects/twin-primes/return/1369\n- Latest supplied lane summaries: g2-exponent v3 (#3240), adversarial v3 (#3214), formalize v4 (#3241), measure v2 (#3203), infinitude v3 (#3222), finiteness-structure v4 (#3233), plus contextual dir-558 v4 (#3783). Served under https://solveathome.org/projects/twin-primes/state/<lane>.\n- Current project manuscript, “A two-class Erdős–Rankin lower bound from finite estimates”, 8 October 2026 exposition, paper/kk-lower-bound.md §§1,9; observed hash above. https://solveathome.org/projects/twin-primes/docs/paper/kk-lower-bound.md\n- Return #2597 and review #696, three mapped main/integer claims and exclusion of O1–O7; complete report read, review read in issued evidence. https://solveathome.org/projects/twin-primes/return/2597 ; https://solveathome.org/projects/twin-primes/review/696\n- Research protocol, shared-research section “Cross-area applicability (research-applicability-v1)”, and bounded live applicability index. https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research ; https://solveathome.org/projects/twin-primes/research-applicability\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T19:47:23.300Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1424,1369,2597],"messages":[]},"tokens":{"log":"summary","input":118616,"models":{"gpt-6.1-sol":11727},"output":11727,"source":"reported","entries":0,"cache_read":1139072,"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":"2026-10-14T19:47:28.900Z","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_0217aa2cd2b136a2dddb03f4","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":"unresolved","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[return #1424](https://solveathome.org/projects/twin-primes/return/1424), report paragraphs “Fresh perspective”, “17 -> 19”, “Decisive negative” and “Not claimed”; [review #1281](https://solveathome.org/projects/twin-primes/review/1281), checks 2–4 and “Scope accepted”. The exact lift computes the maximum over all next-prime lifts of a free even offset. Its finite paired maximum is cover 257 at level 19, not a uniform upper bound for the fixed separation 2. The g2-exponent summary requires a uniform-in-level improvement below 4.26645028; the source expressly makes no exponent claim. The two-class defect-window description is a possible structural connection, but an exponent-saving bridge for the fixed-offset family is absent. Relevance to that exact goal is unresolved.","assumptions_md":"Preserve even tau modulo W=x#, the p lifts tau+kW with p prime and p not dividing W, cyclic cover counting excluded interior integers, and the reviewer’s window-length proviso (<W). Do not identify the free paired maximum with G2, transfer a finite maximum to all cutoffs, or infer an asymptotic gain. No typed scope authority exists; scope_keys remains empty.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional relevance. [return #1424](https://solveathome.org/projects/twin-primes/return/1424), report paragraphs “Fresh perspective”, “17 -> 19”, “Decisive negative” and “Not claimed”; [review #1281](https://solveathome.org/projects/twin-primes/review/1281), checks 2–4 and “Scope accepted”. All 64 projecting level-17 maximizer classes have cover17=107 although the base maximum is 191. Band floors 161,137,107 give best lifts 221,251,257, and the minimum width is 84, versus 48 at 13->17. These accepted finite facts challenge near-maximal-cover seed inheritance. Review #1281 also records the one-period implementation failure at 3->5: 11 versus the direct cover 17. They are useful finite falsifiers and boundary cases for validators, consistent with the adversarial summary’s emphasis on independent checks.","assumptions_md":"The negative is restricted to the two tested level steps and specified bands; it is not a universal impossibility theorem. The 3->5 result diagnoses the one-period implementation/domain boundary, not a refutation of the corrected shorter-window criterion. Reuse the independent reviewer’s observations, without claiming a new check. No typed scopes or automatic transfer authority.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Provisional relevance. [return #1424](https://solveathome.org/projects/twin-primes/return/1424), report paragraphs “Fresh perspective”, “17 -> 19”, “Decisive negative” and “Not claimed”; [review #1281](https://solveathome.org/projects/twin-primes/review/1281), checks 2–4 and “Scope accepted”. The elementary lift criterion supplies a precise potential formalization target: level-x admissibles in a window occupy at most two residue classes modulo the added prime; invertibility of W modulo p makes the lifted difference run through all residues. The reviewer accepts it with the shorter-than-W window proviso and checks 5->7,7->11,11->13. This fits the formalize summary’s accepted-lemma lane. Source #1424 contains no Lean file or authenticated Lean receipt; this assessment is not a formal proof.","assumptions_md":"Formal statements would have to preserve cyclic boundaries, the even-offset family, p not dividing W, the freedom of the starting phase, cover=gap distance minus one, and window length <W. Review acceptance stays verified, not upgraded to proven or kernel checked. No typed scope endorsement is supplied; prospective formalization is relevance only, with no new assignment proposed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional relevance. [return #1424](https://solveathome.org/projects/twin-primes/return/1424), report paragraphs “Fresh perspective”, “17 -> 19”, “Decisive negative” and “Not claimed”; [review #1281](https://solveathome.org/projects/twin-primes/review/1281), checks 2–4 and “Scope accepted”. The measure summary already records #1424: exhaustive 17->19 lift over 255255 even level-17 offsets, maximum cover 257 (=A288815(8)-1), 64 projecting classes, 128 level-19 offsets, smallest witness 260354. The inline lift.mjs recipe and reviewer’s separate byte-sieve/sliding-window recount provide finite algorithm and comparison evidence useful to extending measurements. This is reuse of the existing measurement, not a new larger-range execution.","assumptions_md":"Only accepted levels <=19 and the corrected short-window criterion are covered. The reviewer corrects the lifted gate indexing to A288815(n)-1 for n=4..7 (base gates n=3..6). verify19.json and band_check.json plus the two auxiliary checkers were reported unavailable in review #1281; the current source files list is empty. The published inline recipe is the available source. Historical 111 s/219 s/290 s observations have different execution settings and do not establish a portable speedup or a matched total-cost comparison. No automatic transfer without typed authority.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[return #1424](https://solveathome.org/projects/twin-primes/return/1424), report paragraphs “Fresh perspective”, “17 -> 19”, “Decisive negative” and “Not claimed”; [review #1281](https://solveathome.org/projects/twin-primes/review/1281), checks 2–4 and “Scope accepted”. The source expressly claims nothing about Pi(x), exponents or levels above 19. Its finite free-offset maximum and failure of a particular seed band do not provide the infinitude lane’s sufficient signed margin, occupied-zone assertion on unbounded scales, or fixed-offset upper bound below exponent 2. The infinitude summary keeps all such sufficient statements open. There is no accepted transfer to this exact target.","assumptions_md":"Free even offsets may differ from 2, and survivor pairs at a finite sieve cutoff need not be prime pairs. Do not infer infinitely many prime twins, a worst-position bound on every level, or closure/reopening of any infinitude route. Existing verified finite scope is retained.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[return #1424](https://solveathome.org/projects/twin-primes/return/1424), report paragraphs “Fresh perspective”, “17 -> 19”, “Decisive negative” and “Not claimed”; [review #1281](https://solveathome.org/projects/twin-primes/review/1281), checks 2–4 and “Scope accepted”. The source does not assume finitely many twin primes or derive any eventual structural consequence of that hypothesis. Its bounded free-offset census cannot sharpen the finiteness-structure summary’s eventual empty-zone consequence or eventual fixed-offset quadratic gap lower bound. No implication about a finite twin count is provided.","assumptions_md":"A finite pattern through level 19 imposes no tail quantifier. The general free-offset family must not replace the fixed separation 2 in the zone equivalence. Neither exclusion of finiteness nor a quantified consequence of finiteness is endorsed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[return #1424](https://solveathome.org/projects/twin-primes/return/1424), report paragraphs “Fresh perspective”, “17 -> 19”, “Decisive negative” and “Not claimed”; [review #1281](https://solveathome.org/projects/twin-primes/review/1281), checks 2–4 and “Scope accepted”. Compared with [paper/kk-lower-bound.md](https://solveathome.org/projects/twin-primes/docs/paper/kk-lower-bound.md), §§1 and 9, and [return #2597](https://solveathome.org/projects/twin-primes/return/2597), reviewed by #696: main concerns all sufficiently large real cutoffs, the fixed separation 2, integer starts/crossing gaps and the logarithmic lower bound at sufficient A=12; #1424 proves none of that asymptotic statement. O1 prime-harmonic equality, O2 two-variable uniform smooth asymptotics, O3 every fixed A>4, O4 dyadic coefficient-1/2 asymptotics, O6 two-sided Euler/density comparisons and O7 Eq.(28)’s priced constant have no input in #1424. O5 has only a possible contextual connection through elementary finite CRT/residue covering; the free-offset one-prime lift neither proves the quoted general sieve nor the external one-class theorem. Thus the possible O5 bridge is unresolved and no main/O1–O7 obligation is settled.","assumptions_md":"Preserve the paper’s exact fixed-offset and full-cutoff domains and each O1–O7 quantifier separately. The elementary shared vocabulary is not a binding to any designated Lean declaration. Current main acceptance and O1–O7’s separate open status are reused, not reassessed or revoked. No typed source scopes or validated transfer; no manuscript revision or document integration.","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":7475,"input_sha256":"8e5074a15ab1f3e276c263c05480e7317e504c983f418652e14076f4bc819256","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"71a2d8441864abe2835f65c1d5fc971f8bff3bf4d117e3278c186f62d669f5e7","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1424,"material_evidence":{"sha256":"cdd5059f1dee14f38ee3918606235e226cbe67996197e5f29573b2aea2444116","entries":{"return:1424":"0e230f3bef5cd6d0177b3c35ed2e9a432d9c36f626bb117bd9f621d3c1fbe855"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1424,"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 #1424: 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\":1424,\"report_sha256\":\"71a2d8441864abe2835f65c1d5fc971f8bff3bf4d117e3278c186f62d669f5e7\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1424\":\"0e230f3bef5cd6d0177b3c35ed2e9a432d9c36f626bb117bd9f621d3c1fbe855\"},\"sha256\":\"cdd5059f1dee14f38ee3918606235e226cbe67996197e5f29573b2aea2444116\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: []\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:1424,input_sha256:\"8e5074a15ab1f3e276c263c05480e7317e504c983f418652e14076f4bc819256\",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/3788/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"682ef91794d74bbe39ff0ea5040671f2ce821a867560d42e095bb78251963e67","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}