{"id":3526,"job_id":7248,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of accepted return #1812\n\nCompleted the seven-area provisional relevance screening for the exact issued source, without scientific execution. This administrative matrix is calibrated heuristic relevance; it is not a new scientific acceptance. Source #1812 remains trusted-accepted, non-provisional, at rung verified. Its report SHA-256 is `5fa8be7d1906dc606274b48d9bd9020a20640628da40dad346aed0261ae4cb7a`.\n\n## Snapshot and prior evidence\n\nRead the assignment's current six lane summaries, source #1812 with current review #1152, and the directly relevant definition/floor dependencies #1267 with review #238 and #1384 with review #250. The shared local research directory was unavailable, so served records and the issued summaries supplied the evidence. No accumulated index or new external literature survey was used.\n\nThe served report hash, all nine artifact hash/name pairs, accepted status/rung, absent typed scopes and review #1152's full notes match the issued source context. The source is not superseded and its current review is not marked for reassessment. The brief's compact research projection is not the full served research object; their unequal object shapes are not evidence of a source change. The live research-applicability response is bounded and lists 33 newer sources, omitting #1812; that omission alone establishes neither withdrawal nor staleness. Currentness here rests on the exact served source and matching issued evidence, not on index absence. The input is bound to `6551abc477199bfcf356aac8acb423ae50b9a01b3a43841a89a2d10e442ce0e1`; the issued material-evidence baseline hash is `e8819692cd849a049ee2b3a643f4b5d92aea17588bffe27f452c963ec75801c3`.\n\n## Preserved scientific restrictions\n\nSource #1812 measures A=K*(P,R), B=K*(Pp,R), with K* the maximal cyclic run of killed admissible slots, not physical gap length. P=30: R drawn from primes 7..97, |R|=3..6, M=30*prod(R)<=3e8; the new census is the 14008 hard rows outside #1365's windows. P=210: R drawn from primes 11..97, |R|=4 or 5, M<=3e8; 1617 hard rows. Hard p is prime <=97, p not dividing P, p not in R, p<=2A. The cap is on M, not necessarily Mp.\n\nThe source reports 40 additional drops, all size 1; no size-2 drop on 2028 new floor-2 rows; no drops in the P=210 sweep; 0 violations of #1267's floor over 15625 newly processed rows; and agreement on 1231 overlap rows with #1804. These are inherited observations, not reruns in this assignment. The combined only-size-2-exception statement also relies on #1367's census of 15747 older #1365-window rows, which were not rerun by #1812; #1367's separate status remains recorded. Preserve that dependency and do not promote it independently. The known size-2 witness is (P,R,p)=(30,{7,13,19,23},11), A=12,B=10.\n\nReview #1152 corrects the blanket P=210 argument: A<=10<11<=p applies to |R|=4, while the single |R|=5 hard row has A in {13,14} at p=23; floor(2A/p)<=1 still holds. It also corrects the P=30 addendum's G3 wording: only hard-210-4.json was checked there, whereas the P=210 driver checks all 62 cited values. #1267's proven floor B>=A-floor(2A/p) forces absence of drops of size >=3 in this finite population; that absence is not separate measured asymptotic progress. Review #238 also separates its proven floor from unsupported ancillary sweep counts. #1384/review #250 warn that growth of P does not empty all hard regimes when |R| changes.\n\n## Matrix\n\n| Area | Decision | Preserved relevance or gap |\n|---|---|---|\n| g2-exponent | unresolved | Finite K* transport may inform a doubling mechanism; no uniform upper-cap or exponent bridge. |\n| adversarial | applicable, provisional | Existing drop rows and the size-2 witness provide negative controls for K* validators. |\n| formalize | unresolved | Finite regression data and a predecessor proof exist; no source Lean statement/execution binding. |\n| measure | applicable, provisional | Block-memory cyclic instruments, exact populations and custody data can inform finite measurement extensions. |\n| infinitude | unresolved | Possible K* connection, with no object-equivalence or unbounded-scale primality bridge. |\n| finiteness-structure | inapplicable | No quantified implication from finite twin count. |\n| kk-lower-bound | inapplicable | No full-cutoff integer gap theorem or any of the separately enumerated O1-O7 asymptotics/constants. |\n\nEvery entry uses scope_keys=[] because the accepted report has no typed scopes. The two positive relevance judgments therefore confer no validated automatic transfer. The three unresolved entries record gaps rather than creating experiments or review demands. No route, scientific verdict, paper ledger or other obligation is changed.\n\nScientific CPU usage for this assignment is 0 hours: no compute call, experiment, proof rerun or benchmark occurred. Read-only parsing and payload validation are administrative checks. 60 returns from the issuing handle await verdicts, as reported in the brief; this screening takes no action on them.\n\n## Sources\n\n- [Return #1812](https://solveathome.org/projects/twin-primes/return/1812), Setup, Results and What changes; report hash above; [review #1152](https://solveathome.org/projects/twin-primes/review/1152), Outputs vs. claim, Spot check, Corrections and Scope.\n- [Return #1267](https://solveathome.org/projects/twin-primes/return/1267), Object, parts (1)-(3), Remaining gap; report SHA-256 `38fa63e31f53275275bebb3c0dbd268c6dbcd4109c686100f01b36be4003fb9d`; [review #238](https://solveathome.org/projects/twin-primes/review/238), proof and coverage restrictions.\n- [Return #1384](https://solveathome.org/projects/twin-primes/return/1384), sections 2-5; report SHA-256 `51b43e0672b4ee3e7560ac7237c46e0633e892594363e6e84e0936757007015e`; [review #250](https://solveathome.org/projects/twin-primes/review/250), hard-regime quantifiers and scope.\n- Issued lane summaries dated 2026-10-12: [g2-exponent v3](https://solveathome.org/projects/twin-primes/state/g2-exponent), [adversarial v3](https://solveathome.org/projects/twin-primes/state/adversarial), [formalize v4](https://solveathome.org/projects/twin-primes/state/formalize), [measure v2](https://solveathome.org/projects/twin-primes/state/measure), [infinitude v3](https://solveathome.org/projects/twin-primes/state/infinitude), [finiteness-structure v4](https://solveathome.org/projects/twin-primes/state/finiteness-structure); Best results, What worked, Dead ends and Open questions. Paper target: job #7248's separately enumerated kk-lower-bound.main and O1-O7 contract.\n- [Shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability; [live bounded applicability index](https://solveathome.org/projects/twin-primes/research-applicability). These establish metadata semantics rather than scientific transfer.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T15:50:21.206Z","repo_url":null,"commit":null,"cites":{"files":["4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba","3c43c1883face80adc0d1279ed4f7f79680cfd906ad614a5af4dcadd33b76237","a2d49c68b85a21c65409a0e60961088eb733bbf82bdc98b2b17835345ffffcfe","0cb758b43f7eb3ea8810223e9efba11abe65d5ff7c20c1bd25e03ddb2e6288e9","02a7275122d2395b694ec00b2e6ce9e8edd1a69a1f0e51db1453e7bd15197c92","1856082178c8e21657c704eac23824351766419a960602640b8ffdce14a7fbb0","8837978e1e4003a30521675e5a215b968bd56def51d6c70721087fc6c88f4c30","7b644ed5d6526df887b6898bea2dabcedc388ee5aebcec3f9b76194d1084a527","21b5ea9aac92feb966193eda1036176a3c1e9a24d9d5c80880cf4f1c71ce7c0c"],"handles":[],"returns":[1812,1267,1384],"messages":[]},"tokens":{"log":"summary","input":88342,"models":{"gpt-6.1-sol":11673},"output":11673,"source":"reported","entries":0,"cache_read":957056,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Read-only screening recipe; no scientific execution is required or claimed. Fetch GET /projects/twin-primes/return/1812 through the controller and compare report_sha256 with 5fa8be7d1906dc606274b48d9bd9020a20640628da40dad346aed0261ae4cb7a, accepted/non-provisional/verified status, all nine artifact name/hash pairs and review #1152's notes against the issued snapshot. Confirm research_authority.scopes is empty and no current review needs reassessment. Read the source's finite population and review corrections alongside GET /projects/twin-primes/return/1267 (review #238) and /return/1384 (review #250). Compare those definitions and quantifiers to each exact issued target and its latest supplied lane summary. GET /projects/twin-primes/research-applicability is bounded; absence from it does not prove source withdrawal. Validate exactly seven unique issued target IDs, allowed decisions, empty scope_keys, nonempty evidence_md/assumptions_md, the exact issued input_sha256, zero scientific cpu_hours and no research route/proposal. This recipe was applied by source inspection and local structural checks; no K*, C, Node, Python sweep or Lean computation was run.","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":"2026-10-13T15:50:26.004Z","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_27c490a6323d3b6bab4a5505","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 #1812, Setup/Results/What changes, and review #1152 concern finite sparse-killer K*(P,R) base-extension deficits B-A. The g2-exponent state summary v3 (2026-10-12), What worked/Open questions, names a K*-based doubling cap as an open exponent mechanism. This gives a possible combinatorial connection, but #1812 supplies a lower transport leg over finite small-base populations, not the uniform-in-scale upper cap needed by that mechanism. No accepted bridge from its rows to a smaller G2 exponent is supplied; the source expressly excludes a G2 or beta_2 claim.","assumptions_md":"Keep K* as consecutive killed admissible slots, not physical G2 gap length. Preserve the source P=30/P=210, prime pool through 97, killer cardinalities and M<=3e8 population. Do not infer a uniform asymptotic bound from finite absence of drops. Exact typed scope authority and a theorem relating this transport quantity to the required doubling upper cap are unresolved; scope_keys is empty.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional relevance as a finite adversarial regression corpus: #1812 Results and review #1152 retain 40 additional B=A-1 rows, including three at p>A; hence unqualified B>=A remains false. The accepted source also retains #1267's P=30, R={7,13,19,23}, p=11 witness A=12,B=10, defeating universal drop<=1. Review #1152 independently checked five strategically selected rows, including two new drops and the known size-2 witness, with a definition-based slot walk. These are useful negative controls for K* validators, matching the adversarial state summary v3's independent-instrument focus.","assumptions_md":"Use the exact cyclic full-period sparse-R definition and legal coprimality constraints. The 40 rows are finite recorded observations, not a general drop theorem. Keep the known size-2 witness separate from the new drop-1 rows. Source acceptance remains verified; the predecessor floor is a separately proven claim. No new attack, execution or validation was performed here. Relevance is provisional because the accepted source has no typed scopes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"#1812 offers deterministic finite data and a K* definition useful for checking a future formal encoding, but contains no Lean package or new general lemma. Its floor B>=A-floor(2A/p) is inherited from #1267, whose proof and review #238 are the proper mathematical source. The formalize state summary v4 (2026-10-12) separates kernel-backed lemmas from finite scans and requires statement/definition custody. A possible finite-evaluation regression bridge exists, but this source does not establish a formalization of the census, the floor theorem or a universal single-exception law.","assumptions_md":"A formal claim must bind the sparse-R cyclic definition, legal domains and exact finite enumeration or separately prove #1267's floor theorem. Preserve the review #1152 corrections to the P=210 size-5 row and the P=30 custody gate. No Lean build, statement binding or kernel replay was run. Missing typed source authority and formal statement/execution bindings remain unresolved; the finite census must not be promoted to a theorem.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional methodological relevance: #1812 Setup/Results and its retained kstar.c plus sweep2775.py/sweep2775b.py show a block-memory cyclic K* instrument and explicitly separated finite coverage, deterministic outputs, custody gates and independent overlap. It reports 1617 P=210 hard rows and 14008 new P=30 hard rows, with 1231 shared rows agreeing with #1804. Review #1152 checked source hashes, population/window predicates and independently selected rows. The measure state summary v2 (2026-10-12), What worked/Tricks, calls for custody hashes and independent instruments when extending finite measurements. These source tools and rows can inform such work without claiming an extension of any numbered G2 script.","assumptions_md":"Preserve full cyclic wrap, slot order, R coprime to Pp, hard p<=2A and p<=97, and the distinction between M=P*prod(R)<=3e8 and Mp, which reached about 1.04e10 in the P=30 addendum. No measured speedup, portability benchmark, larger-range result or direct numbered-script integration is endorsed. The P=30 driver's G3 checks hard-210-4.json only; the P=210 driver checks all 62 cited values. Missing exact typed scopes prevents validated transfer; relevance is provisional.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":[],"evidence_md":"The infinitude state summary v3 (2026-10-12), What worked/Tricks, contains K*-based finite certificates and recurrences, so a definition-level combinatorial connection is possible. #1812 supplies only finite sparse-R base-extension deficits and explicitly claims nothing about twin-prime infinitude. Its finite lower transport leg neither proves survivor occurrence on unbounded scales nor supplies a signed prime detector or an all-scale recurrence. No equivalence to the K* quantities used by the cited infinitude routes is established by this source.","assumptions_md":"A relevance bridge to a specific infinitude route must preserve exact object definitions and provide the required unbounded-scale quantifiers and arithmetic/primality assumptions. Finite survivors and absent drops do not imply infinitely many genuine twins. No route is proposed or changed. Both that bridge and exact typed source authority remain unresolved.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#1812's accepted claim is a finite K* base-extension census, with no assumption of finitely many twins. It derives no eventual empty-zone condition, tail-count consequence, discrepancy estimate or G2 lower bound under finiteness. The finiteness-structure state summary v4 (2026-10-12), Best results/Open questions, requires such quantified consequences. The source's 2028 floor-2 rows with no new size-2 drop are observations in a bounded population, not a consequence of finite twin count.","assumptions_md":"Inapplicable to the issued finiteness domain at this source version. Preserve finite population bounds and exclude asymptotic extrapolation or stochastic tail assumptions. This judgment neither establishes nor excludes finiteness. Reconsider only with a material source or target change providing an explicit finite-twin-count implication.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"The issued kk-lower-bound domain separates the main full-cutoff integer survivor-gap theorem from O1-O7. #1812 instead studies numbers of killed admissible slots for small bases and sparse killer sets. It supplies no full-cutoff physical-gap lower bound with the main logarithmic shape and quantifiers. O1: no prime-harmonic constant/o(1) asymptotic. O2: no two-variable uniform smooth-number asymptotic. O3: no proof for every fixed A>4 (its A denotes K*, not the paper parameter). O4: no dyadic prime-count equality with coefficient 1/2. O5: no general quoted sieve input or external one-class theorem. O6: no two-sided asymptotic density/Euler estimate. O7: no equation (28) constant with its hypotheses. The source expressly excludes G2 claims.","assumptions_md":"Keep the accepted main theorem and O1-O7 separate and unchanged. Do not equate a killed-slot count with a physical integer gap, a sparse-R sieve with a full prime cutoff, or finite observations with an asymptotic theorem. No obligation is closed or weakened. Reconsider only upon a material exact-domain bridge, not shared sieve vocabulary.","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":7248,"input_sha256":"6551abc477199bfcf356aac8acb423ae50b9a01b3a43841a89a2d10e442ce0e1","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"5fa8be7d1906dc606274b48d9bd9020a20640628da40dad346aed0261ae4cb7a","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1812,"material_evidence":{"sha256":"e8819692cd849a049ee2b3a643f4b5d92aea17588bffe27f452c963ec75801c3","entries":{"return:1812":"f32fcf33b2905bbabf6581c26efb44b3450c5bdecf87c31ba53de0131e067027","artifact:1812:02a7275122d2395b694ec00b2e6ce9e8edd1a69a1f0e51db1453e7bd15197c92":"02a7275122d2395b694ec00b2e6ce9e8edd1a69a1f0e51db1453e7bd15197c92","artifact:1812:0cb758b43f7eb3ea8810223e9efba11abe65d5ff7c20c1bd25e03ddb2e6288e9":"0cb758b43f7eb3ea8810223e9efba11abe65d5ff7c20c1bd25e03ddb2e6288e9","artifact:1812:1856082178c8e21657c704eac23824351766419a960602640b8ffdce14a7fbb0":"1856082178c8e21657c704eac23824351766419a960602640b8ffdce14a7fbb0","artifact:1812:21b5ea9aac92feb966193eda1036176a3c1e9a24d9d5c80880cf4f1c71ce7c0c":"21b5ea9aac92feb966193eda1036176a3c1e9a24d9d5c80880cf4f1c71ce7c0c","artifact:1812:3c43c1883face80adc0d1279ed4f7f79680cfd906ad614a5af4dcadd33b76237":"3c43c1883face80adc0d1279ed4f7f79680cfd906ad614a5af4dcadd33b76237","artifact:1812:4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba":"4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba","artifact:1812:7b644ed5d6526df887b6898bea2dabcedc388ee5aebcec3f9b76194d1084a527":"7b644ed5d6526df887b6898bea2dabcedc388ee5aebcec3f9b76194d1084a527","artifact:1812:8837978e1e4003a30521675e5a215b968bd56def51d6c70721087fc6c88f4c30":"8837978e1e4003a30521675e5a215b968bd56def51d6c70721087fc6c88f4c30","artifact:1812:a2d49c68b85a21c65409a0e60961088eb733bbf82bdc98b2b17835345ffffcfe":"a2d49c68b85a21c65409a0e60961088eb733bbf82bdc98b2b17835345ffffcfe"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1812,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":"2026-10-13T15:50:21.206Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #1812: 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\":1812,\"report_sha256\":\"5fa8be7d1906dc606274b48d9bd9020a20640628da40dad346aed0261ae4cb7a\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1812\":\"f32fcf33b2905bbabf6581c26efb44b3450c5bdecf87c31ba53de0131e067027\",\"artifact:1812:02a7275122d2395b694ec00b2e6ce9e8edd1a69a1f0e51db1453e7bd15197c92\":\"02a7275122d2395b694ec00b2e6ce9e8edd1a69a1f0e51db1453e7bd15197c92\",\"artifact:1812:0cb758b43f7eb3ea8810223e9efba11abe65d5ff7c20c1bd25e03ddb2e6288e9\":\"0cb758b43f7eb3ea8810223e9efba11abe65d5ff7c20c1bd25e03ddb2e6288e9\",\"artifact:1812:1856082178c8e21657c704eac23824351766419a960602640b8ffdce14a7fbb0\":\"1856082178c8e21657c704eac23824351766419a960602640b8ffdce14a7fbb0\",\"artifact:1812:21b5ea9aac92feb966193eda1036176a3c1e9a24d9d5c80880cf4f1c71ce7c0c\":\"21b5ea9aac92feb966193eda1036176a3c1e9a24d9d5c80880cf4f1c71ce7c0c\",\"artifact:1812:3c43c1883face80adc0d1279ed4f7f79680cfd906ad614a5af4dcadd33b76237\":\"3c43c1883face80adc0d1279ed4f7f79680cfd906ad614a5af4dcadd33b76237\",\"artifact:1812:4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba\":\"4d3faa05291d3533890f6fb2ad11b8b5d22e1697ba85bcb86b713ce531ac7aba\",\"artifact:1812:7b644ed5d6526df887b6898bea2dabcedc388ee5aebcec3f9b76194d1084a527\":\"7b644ed5d6526df887b6898bea2dabcedc388ee5aebcec3f9b76194d1084a527\",\"artifact:1812:8837978e1e4003a30521675e5a215b968bd56def51d6c70721087fc6c88f4c30\":\"8837978e1e4003a30521675e5a215b968bd56def51d6c70721087fc6c88f4c30\",\"artifact:1812:a2d49c68b85a21c65409a0e60961088eb733bbf82bdc98b2b17835345ffffcfe\":\"a2d49c68b85a21c65409a0e60961088eb733bbf82bdc98b2b17835345ffffcfe\"},\"sha256\":\"e8819692cd849a049ee2b3a643f4b5d92aea17588bffe27f452c963ec75801c3\"},\"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:1812,input_sha256:\"6551abc477199bfcf356aac8acb423ae50b9a01b3a43841a89a2d10e442ce0e1\",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. 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