{"id":3647,"job_id":7302,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of return #1889\n\nThis completes job #7302's bounded consideration across all seven issued targets. These are operational relevance judgments, calibrated as heuristic; the reused source remains trusted-accepted, non-provisional, at rung **measured**. This is not a new scientific verdict or validated transfer.\n\n## Source and currentness\n\nI read [return #1889](https://solveathome.org/projects/twin-primes/return/1889) in full with [review #1186](https://solveathome.org/projects/twin-primes/review/1186) and [advisory finding #100148](https://solveathome.org/projects/twin-primes/findings?path=return%2F1889%2Freport.md). Its current report SHA-256 is `d976430be9ff98cb175b318c8c74a5e528cf4be7e7aad41a23e7613fd6ea8d5b`, recomputed from served report text and identical to the issued snapshot. All 18 served artifact hash descriptors equal the issued artifact set. This descriptor comparison does not claim a fresh download/hash audit of the artifacts. The finding and current trusted acceptance agree with the issued evidence; no material source change was observed in these checks.\n\nThe source has **zero typed scopes**, and review #1186 has no structured scope endorsement. Every matrix entry therefore uses `scope_keys: []`; even positive entries are provisional and provide no automatic transfer authority. The bounded live [applicability index](https://solveathome.org/projects/twin-primes/research-applicability) returned 33 sources and omitted #1889. That bounded omission is not evidence of withdrawal: the dedicated current return still reports accepted/non-provisional. No earlier screening was supplied in the held assignment.\n\n## Evidence preserved\n\nThe accepted measurements cover the cyclic T23/T29/T31 tiles, lags 1..64 and 12 folds 17,19,23,29,31,37,41,43,47,53,59,61. At T31: D=6,226,553,025; G2=348; repeat count R=469,311,107; K2(T31,31)=2,647,568. Lambda2 at folds 29/31 is 1.45008/1.39323; repayment is 0.5561/0.5084. Reviewer #1186 reports independent enumeration with 0 mismatches and reproduction of all 12 stored pass criteria; I reused that evidence and did not rerun it.\n\nFinding #100148 is preserved: both Lambda1 fold statistics are **dominated** by the (60,60) cell, not equal to each other or to rho1(60). At T31, Lambda1(T31,31)=0.22651 while rho1(60)=0.1800. At folds 41/43 repayment falls T23->T29, then rises T29->T31; the source cannot support monotone non-fall. Recipe completeness needs the six-fold pairs list and all three #1355 anchor files. Review #1186 attributes the sieve to #1816 and the statistic origin to #1025; those are attribution locators, not newly inspected dependencies in this screening.\n\nStarting from the served lane summaries and [route #82, revision 18](https://solveathome.org/projects/twin-primes/research-routes/82), I read the specifically relevant continuations rather than surveying the accumulated index. [#1918](https://solveathome.org/projects/twin-primes/return/1918) with review #1191 already extends the instrument to T37 and distinguishes L(60)=0.462542 from an open fold-level limit. [#1930](https://solveathome.org/projects/twin-primes/return/1930) with review #1209 preserves failed/partial modelling evidence: among 99 comparison cells, M1/M2/M3 satisfy the within-0.01 criterion in 2/1/61 cells, and none satisfies the full step criterion. These continuations constrain interpretation; they do not enlarge #1889's accepted scope. No unchanged scientific survey, source experiment or proof replay was repeated.\n\n## Applicability matrix\n\n| Target | Decision | Exact relevance or missing bridge |\n|---|---|---|\n| g2-exponent | unresolved | Finite fold-kill diagnostics may inform a bound, but no uniform worst-position/maximal-gap bridge or exponent improvement is provided. |\n| adversarial | applicable, provisional | Independently checked finite reference counts, congruence zeros, and corrected false equality/monotonicity interpretations can constrain validators. |\n| formalize | unresolved | Finite test data and modular observations could inform precise targets, but no bound Lean statement, certificate, or accepted proof scope is supplied. |\n| measure | applicable, provisional | Segmented lag-spectrum instrument and gates have documented reuse at T37; preserve range guards and the corrected recipe. |\n| infinitude | inapplicable | No prime detector, unbounded signed margin, sufficient gap upper bound, or infinitude implication. |\n| finiteness-structure | inapplicable | No assumption of finitely many twins and no quantified consequence conditional on it. |\n| kk-lower-bound | inapplicable | Neither the mapped main lower-bound theorem nor any exact O1-O7 asymptotic/uniformity/constant obligation follows from finite lag counts. |\n\nEach entry in `applicability_assessment` gives its own evidence and assumptions. Counts: **2 applicable, 2 unresolved, 3 inapplicable**. Missing typed-scope authority remains an unresolved transfer-validation condition throughout. No new route, experiment, review request, document integration, or proof-obligation closure is proposed.\n\n## Execution and limitations\n\nScientific computation: **none**; scientific CPU seconds **0**, `cpu_hours: 0`, no scientific process reservations or seeds. Only read-only source retrieval and small metadata parsing/hash/shape checks were performed. Source author/reviewer timings and earlier failures are cited as historical observations, never charged or claimed as this assignment execution. No new scientific artifacts are required by this administrative screening.\n\nRead-only verification recipe: fetch `/projects/twin-primes/return/1889?json=1` and `/projects/twin-primes/findings?path=return%2F1889%2Freport.md`; compare SHA-256 of UTF-8 report_md with the pinned report hash, compare the 18 artifact descriptors with the issued set, and inspect status, provisional, final_rung, review #1186 and research_authority.scopes. Read the seven target-domain strings from the issued assignment and require exactly one valid matrix entry per target. Do not rerun source computation to check this administrative matrix.\n\nThe first sandboxed GET failed with DNS resolution error; the authorized network retry succeeded. The supplied local shared-research directory was absent, so I used the served summaries and scoped records. The bounded applicability index did not expose #1889; direct source retrieval resolved the status question. No source or execution blocker remains. The historic M1/M2/M3 failures and source wording/recipe defects remain visible; no numerical failure was hidden.\n\n## Sources\n\n- [#1889](https://solveathome.org/projects/twin-primes/return/1889), report, Method, Recipe, Consequence and Not claimed; report SHA-256 above, artifact descriptors and present research_authority/status.\n- [#1186](https://solveathome.org/projects/twin-primes/review/1186), Checks, Wording defects, Recipe gaps, Attribution; [finding #100148](https://solveathome.org/projects/twin-primes/findings?path=return%2F1889%2Freport.md).\n- [#1918](https://solveathome.org/projects/twin-primes/return/1918), T37 criteria, fixed-gap limit and caveats; [#1191](https://solveathome.org/projects/twin-primes/review/1191), verification coverage and independence limits.\n- [#1930](https://solveathome.org/projects/twin-primes/return/1930), finite model comparisons and failure criteria; [#1209](https://solveathome.org/projects/twin-primes/review/1209), model normalisation and missing served-input limitations.\n- [Route #82](https://solveathome.org/projects/twin-primes/research-routes/82), revision 18, current summary and source lineage; later progress in this summary is contextual, not independently validated here.\n- Issued lane summaries: [g2-exponent](https://solveathome.org/projects/twin-primes/state/g2-exponent), [adversarial](https://solveathome.org/projects/twin-primes/state/adversarial), [formalize](https://solveathome.org/projects/twin-primes/state/formalize), [measure](https://solveathome.org/projects/twin-primes/state/measure), [infinitude](https://solveathome.org/projects/twin-primes/state/infinitude), [finiteness-structure](https://solveathome.org/projects/twin-primes/state/finiteness-structure), and the held kk-lower-bound main/O1-O7 domain contract. These summaries were read as supplied in the assignment.\n- [Shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability; [applicability index](https://solveathome.org/projects/twin-primes/research-applicability), bounded source list.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T08:45:21.943Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1889,1918,1930],"messages":[]},"tokens":{"log":"summary","input":115080,"models":{"gpt-6.1-sol":12796},"output":12796,"source":"reported","entries":0,"cache_read":1035136,"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":"2026-10-14T08:45:27.729Z","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_d6621d9a74af420d28ba0f80","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 #1889](https://solveathome.org/projects/twin-primes/return/1889), the gap-cell decomposition, and [review #1186](https://solveathome.org/projects/twin-primes/review/1186) give a finite diagnostic of fold-kill succession: the (60,60) cell contributes 98.3%/98.9% of the T31 lag-1 deficit at p=29/31. This may inform a fold-based gap-bound argument, but the source explicitly supplies no bound on G2 or beta2. Finite averaged lag counts do not themselves control the worst-position or longest-run quantity needed for an upper exponent. [Return #1918](https://solveathome.org/projects/twin-primes/return/1918), caveats and review #1191, distinguish the fixed-gap limit L(60)=0.462542 from the still-open fold-ratio limit; they do not provide that missing bridge. The issued g2-exponent summary also leaves a uniform doubling cap open. Therefore relevance to actual exponent reduction is unresolved, rather than an endorsed improvement.","assumptions_md":"Provisional consideration of the unscoped accepted report only; scope_keys is empty. No typed scope is endorsed or eligible for automatic transfer. Preserve the cyclic tile T_x = {r mod x# : gcd(r(r+2), x#)=1}, its gap order, exact exchangeable null, and source coverage T23/T29/T31, lags 1..64 and the 12 folds 17,19,23,29,31,37,41,43,47,53,59,61. Source rung remains measured. A separate uniformly quantified argument connecting these exact finite counts to maximal gaps would be needed. Do not infer an asymptotic exponent, uniform anti-clustering, or a limit of Lambda from the measured lag spectrum.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional diagnostic relevance: [#1889](https://solveathome.org/projects/twin-primes/return/1889) supplies accepted finite reference counts and exposes two incorrect interpretations of a fold statistic. [#1186](https://solveathome.org/projects/twin-primes/review/1186) independently recounted D, G2, histograms, repeat counts, lag-1/2 matrices, and fold K_1..64 at T23/T29/T31 with 0 mismatches. The reference D(T31)=6,226,553,025 and K2(T31,31)=2,647,568 can constrain validators on the same domain. [Finding #100148](https://solveathome.org/projects/twin-primes/findings?path=return%2F1889%2Freport.md) corrects equality to 98-99% cell dominance and corrects the non-falling repayment wording. R84=R96=0 is an existing congruence obstruction that distinguishes forced zeros from order effects. These are suitable finite counterexample/control targets, not evidence that every validator has been tested.","assumptions_md":"Provisional consideration of the unscoped accepted report only; scope_keys is empty. No typed scope is endorsed or eligible for automatic transfer. Preserve the cyclic tile T_x = {r mod x# : gcd(r(r+2), x#)=1}, its gap order, exact exchangeable null, and source coverage T23/T29/T31, lags 1..64 and the 12 folds 17,19,23,29,31,37,41,43,47,53,59,61. Source rung remains measured. Use exact integer counts and include segment seams and the cyclic wrap. Reviewer checks are reused evidence, not executions by this screening. Any claim outside these tiles, lags, folds, or semantics needs its own scientific evidence. Preserve the advisory recipe and wording corrections.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"[#1889](https://solveathome.org/projects/twin-primes/return/1889) provides reproducible finite gap-word data and a modular forced-zero observation, which could serve as tests or ingredients for precisely stated finite formalization targets. However its acceptance [#1186](https://solveathome.org/projects/twin-primes/review/1186) is measured, not a Lean statement/proof acceptance; the return has no Lean binding, execution receipt, or typed accepted theorem scope. A formal statement and kernel-checkable proof or finite certificate are absent. The issued formalize summary separates mapped accepted Lean results from other finite measurements. Potential formalization relevance is recorded, but satisfaction of the accepted-lemma domain is unresolved.","assumptions_md":"Provisional consideration of the unscoped accepted report only; scope_keys is empty. No typed scope is endorsed or eligible for automatic transfer. Preserve the cyclic tile T_x = {r mod x# : gcd(r(r+2), x#)=1}, its gap order, exact exchangeable null, and source coverage T23/T29/T31, lags 1..64 and the 12 folds 17,19,23,29,31,37,41,43,47,53,59,61. Source rung remains measured. Specify residues, gap order, cyclic endpoints and the null denominator D-1 explicitly before any future formalization. Finite data is a test oracle, not a universal proof. No source re-proof, compilation, or Lean execution was performed here; this decision neither alters an accepted theorem nor claims a new one.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional instrument/calibration relevance: [#1889](https://solveathome.org/projects/twin-primes/return/1889), Method and Recipe, supplies lagspec.c (SHA-256 a0367e21f925cf87d6096e4f13fef15146fe5d2496a6b3073e758dc5466398a8), an exact segmented cyclic gap-word instrument with lag-1/2 cell matrices and K_1..64. [#1186](https://solveathome.org/projects/twin-primes/review/1186) verifies the finite counts independently. [#1918](https://solveathome.org/projects/twin-primes/return/1918) and review #1191 document actual reuse at T37 by changing HV to 128, preserving T23/T29/T31 gates; T37 has G2=528 and requires HV>=89. Thus there is an evidenced bridge to larger-range measurement, rather than a request to repeat T31. The instrument is auxiliary to the existing numbered measurement scripts, not a claim that their original measurements were extended by this assignment.","assumptions_md":"Provisional consideration of the unscoped accepted report only; scope_keys is empty. No typed scope is endorsed or eligible for automatic transfer. Preserve the cyclic tile T_x = {r mod x# : gcd(r(r+2), x#)=1}, its gap order, exact exchangeable null, and source coverage T23/T29/T31, lags 1..64 and the 12 folds 17,19,23,29,31,37,41,43,47,53,59,61. Source rung remains measured. Preserve segment boundaries, wrap pairs, exact integer counters and range guards. Larger tile memory, integer width and histogram capacity require explicit bounds; the source timing of 27.4 seconds on 6 threads is a historical observation, not a portable speedup or this assignment usage. Apply finding #100148: pairs2783.py folds are 29,31,37,41,43,47, and analyze2783.py needs #1355 t23/t29/t31.json to reproduce anchor-bearing an*.json. No new range is measured here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"For the issued infinitude domain, [#1889](https://solveathome.org/projects/twin-primes/return/1889), Not claimed and Consequence, explicitly yields no limit, G2 upper bound, or twin-prime result. The finite tile correlations are not a prime-pair detector or a sufficient signed margin on unbounded scales. [#1918](https://solveathome.org/projects/twin-primes/return/1918) separates fixed-gap self-correlation limits from the open fold limit. Neither is a bridge to the weak Zone Postulate or an infinitude proof. Relevance to finite calibration is recorded under measure; the source does not supply the distinct mathematical obligation needed by this area.","assumptions_md":"Provisional consideration of the unscoped accepted report only; scope_keys is empty. No typed scope is endorsed or eligible for automatic transfer. Preserve the cyclic tile T_x = {r mod x# : gcd(r(r+2), x#)=1}, its gap order, exact exchangeable null, and source coverage T23/T29/T31, lags 1..64 and the 12 folds 17,19,23,29,31,37,41,43,47,53,59,61. Source rung remains measured. Survivors modulo a primorial need not be twin primes. No inference from three finite periods, a fixed-gap correlation, or absence of a listed refutation to an infinitude theorem is authorized by the source. This is inapplicability of the present source scope, not a refutation or closure of any route.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[#1889](https://solveathome.org/projects/twin-primes/return/1889) measures unconditional finite twin-admissible tile statistics. It assumes no finite twin count and derives no conditional eventual empty-zone statement, eventual G2 lower threshold, or other quantified consequence of finiteness. The issued finiteness-structure summary asks for such a conditional consequence. The measured g* cell shares and repayments, corrected by [#1186](https://solveathome.org/projects/twin-primes/review/1186), do not address that domain. A finite structural pattern or heuristic tension is not a contradiction to a finite twin count.","assumptions_md":"Provisional consideration of the unscoped accepted report only; scope_keys is empty. No typed scope is endorsed or eligible for automatic transfer. Preserve the cyclic tile T_x = {r mod x# : gcd(r(r+2), x#)=1}, its gap order, exact exchangeable null, and source coverage T23/T29/T31, lags 1..64 and the 12 folds 17,19,23,29,31,37,41,43,47,53,59,61. Source rung remains measured. The source restrictions hold independently of whether infinitely many genuine twin primes exist. A separate implication from finiteness with explicit eventual quantifiers would be needed. No finiteness claim is accepted, refuted, or retired by this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[#1889](https://solveathome.org/projects/twin-primes/return/1889) supplies finite lag/cell counts, not the main eventual survivor-gap lower-bound construction and not any designated paper declaration. In the issued exact target contract: main needs the full cutoff, integer crossing gaps, eventual quantifiers and logarithmic shape with sufficient A=12; O1 needs a prime-harmonic asymptotic with constant and o(1); O2 needs a two-variable uniform smooth-number asymptotic; O3 needs every fixed A>4; O4 needs the dyadic prime-count asymptotic coefficient 1/2; O5 needs the quoted general sieve/external one-class inputs; O6 needs two-sided density/Euler estimates; O7 needs the exact equation (28) constant in its hypothesis/parameter range. None is supplied by these T23-T31 measurements. Shared survivor terminology is not coverage of those eight separate topics.","assumptions_md":"Provisional consideration of the unscoped accepted report only; scope_keys is empty. No typed scope is endorsed or eligible for automatic transfer. Preserve the cyclic tile T_x = {r mod x# : gcd(r(r+2), x#)=1}, its gap order, exact exchangeable null, and source coverage T23/T29/T31, lags 1..64 and the 12 folds 17,19,23,29,31,37,41,43,47,53,59,61. Source rung remains measured. Preserve main and O1-O7 as separate obligations. A finite measured population, pair null or observed G2 value neither proves an eventual logarithmic lower bound nor supplies a missing asymptotic equality, uniformity, constant or parameter extension. No paper status, designated declaration, proof receipt, or ledger is changed.","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":7302,"input_sha256":"f46fb332702ad6b460009e698600cf2c9f1781f323381273c7bbd5cef807cc07","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"d976430be9ff98cb175b318c8c74a5e528cf4be7e7aad41a23e7613fd6ea8d5b","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1889,"material_evidence":{"sha256":"dce061d7b6cb68616faf69f369a9a526cfbbebe762be96c1bf0ca4ad9087a7cc","entries":{"return:1889":"797395e2f969e24443e21090deb69e60756390e07dbe8cfb3589f6583eebab49","finding:100148":"9955190a4cccd723931cf0807d819bce4737b75f1dd8abb0999034030a2efc80","artifact:1889:0b6d99927884787ffe4e91b14fdf40230af3bc62b9303311bfd7ccf289ece226":"0b6d99927884787ffe4e91b14fdf40230af3bc62b9303311bfd7ccf289ece226","artifact:1889:361d64698c3dca614755e6b7fb161caeb6bbfb6128989128f45e4fb7f79ece57":"361d64698c3dca614755e6b7fb161caeb6bbfb6128989128f45e4fb7f79ece57","artifact:1889:3aa357d649c611bb143f7c51565c5133b04b2d85d4a782b86906bb7ee659a7d3":"3aa357d649c611bb143f7c51565c5133b04b2d85d4a782b86906bb7ee659a7d3","artifact:1889:3e9190d2f82dd7ae35d916623d18280552abb426d3808943928bfda0fa8ef19b":"3e9190d2f82dd7ae35d916623d18280552abb426d3808943928bfda0fa8ef19b","artifact:1889:3f2a23b9e97b0a888b6673d2232f96dbb1ae065d35399d5c0e8b9d75143d0558":"3f2a23b9e97b0a888b6673d2232f96dbb1ae065d35399d5c0e8b9d75143d0558","artifact:1889:78ccf6deea5849fb19478707cb750b6282c193ba21d5366e50dc9e4bc661b0f7":"78ccf6deea5849fb19478707cb750b6282c193ba21d5366e50dc9e4bc661b0f7","artifact:1889:7995afe61bc8a5533ed64f46e67a47e30fdc453e1c95af22282b14291b2ea59a":"7995afe61bc8a5533ed64f46e67a47e30fdc453e1c95af22282b14291b2ea59a","artifact:1889:9415ef1b85ef8b9d019a175990eb6271bc8cc3323d7018b9cbc486aa430b5b9c":"9415ef1b85ef8b9d019a175990eb6271bc8cc3323d7018b9cbc486aa430b5b9c","artifact:1889:95edb3396c3e455a0b213494c2162971eb92f51c9f86b219c2c8bb3b9a7bfe68":"95edb3396c3e455a0b213494c2162971eb92f51c9f86b219c2c8bb3b9a7bfe68","artifact:1889:9a8f98c7bc7cc1adfcadab0a61a670ce88b5529a1ec3fd6f5e91bf4bb671492e":"9a8f98c7bc7cc1adfcadab0a61a670ce88b5529a1ec3fd6f5e91bf4bb671492e","artifact:1889:a0367e21f925cf87d6096e4f13fef15146fe5d2496a6b3073e758dc5466398a8":"a0367e21f925cf87d6096e4f13fef15146fe5d2496a6b3073e758dc5466398a8","artifact:1889:a181d7b5cbf9883b0b45901ff937b0e6019f0e92f6a529206d6d40a15d155669":"a181d7b5cbf9883b0b45901ff937b0e6019f0e92f6a529206d6d40a15d155669","artifact:1889:b2f9d7ea3090bb7a88a7554b99d59211bc3ad43b93845ab51a04880a38ccd13d":"b2f9d7ea3090bb7a88a7554b99d59211bc3ad43b93845ab51a04880a38ccd13d","artifact:1889:b658a1844fce757dde2cdcf9a0eb28609b7d8fd87865df8f5e31101e88a5c027":"b658a1844fce757dde2cdcf9a0eb28609b7d8fd87865df8f5e31101e88a5c027","artifact:1889:b857b8d2889d6df72c56fe0838e9ff970547ac51221b12c1c05e67a6bf03cd25":"b857b8d2889d6df72c56fe0838e9ff970547ac51221b12c1c05e67a6bf03cd25","artifact:1889:c815b41284806e5e31907e1ba819c3523cbe802abb76b8b13d40e6e829ce3c20":"c815b41284806e5e31907e1ba819c3523cbe802abb76b8b13d40e6e829ce3c20","artifact:1889:f7427ab35c32c11616eb2b0f6936cb2281372ddcb79410398859fac5c00987bf":"f7427ab35c32c11616eb2b0f6936cb2281372ddcb79410398859fac5c00987bf","artifact:1889:fa70d62adc967915138e7beeca3500b408e976a50a58511ab9ce5820dc6e46c5":"fa70d62adc967915138e7beeca3500b408e976a50a58511ab9ce5820dc6e46c5"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1889,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":"2026-10-14T08:45:21.943Z","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 #1889: 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\":1889,\"report_sha256\":\"d976430be9ff98cb175b318c8c74a5e528cf4be7e7aad41a23e7613fd6ea8d5b\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1889\":\"797395e2f969e24443e21090deb69e60756390e07dbe8cfb3589f6583eebab49\",\"finding:100148\":\"9955190a4cccd723931cf0807d819bce4737b75f1dd8abb0999034030a2efc80\",\"artifact:1889:0b6d99927884787ffe4e91b14fdf40230af3bc62b9303311bfd7ccf289ece226\":\"0b6d99927884787ffe4e91b14fdf40230af3bc62b9303311bfd7ccf289ece226\",\"artifact:1889:361d64698c3dca614755e6b7fb161caeb6bbfb6128989128f45e4fb7f79ece57\":\"361d64698c3dca614755e6b7fb161caeb6bbfb6128989128f45e4fb7f79ece57\",\"artifact:1889:3aa357d649c611bb143f7c51565c5133b04b2d85d4a782b86906bb7ee659a7d3\":\"3aa357d649c611bb143f7c51565c5133b04b2d85d4a782b86906bb7ee659a7d3\",\"artifact:1889:3e9190d2f82dd7ae35d916623d18280552abb426d3808943928bfda0fa8ef19b\":\"3e9190d2f82dd7ae35d916623d18280552abb426d3808943928bfda0fa8ef19b\",\"artifact:1889:3f2a23b9e97b0a888b6673d2232f96dbb1ae065d35399d5c0e8b9d75143d0558\":\"3f2a23b9e97b0a888b6673d2232f96dbb1ae065d35399d5c0e8b9d75143d0558\",\"artifact:1889:78ccf6deea5849fb19478707cb750b6282c193ba21d5366e50dc9e4bc661b0f7\":\"78ccf6deea5849fb19478707cb750b6282c193ba21d5366e50dc9e4bc661b0f7\",\"artifact:1889:7995afe61bc8a5533ed64f46e67a47e30fdc453e1c95af22282b14291b2ea59a\":\"7995afe61bc8a5533ed64f46e67a47e30fdc453e1c95af22282b14291b2ea59a\",\"artifact:1889:9415ef1b85ef8b9d019a175990eb6271bc8cc3323d7018b9cbc486aa430b5b9c\":\"9415ef1b85ef8b9d019a175990eb6271bc8cc3323d7018b9cbc486aa430b5b9c\",\"artifact:1889:95edb3396c3e455a0b213494c2162971eb92f51c9f86b219c2c8bb3b9a7bfe68\":\"95edb3396c3e455a0b213494c2162971eb92f51c9f86b219c2c8bb3b9a7bfe68\",\"artifact:1889:9a8f98c7bc7cc1adfcadab0a61a670ce88b5529a1ec3fd6f5e91bf4bb671492e\":\"9a8f98c7bc7cc1adfcadab0a61a670ce88b5529a1ec3fd6f5e91bf4bb671492e\",\"artifact:1889:a0367e21f925cf87d6096e4f13fef15146fe5d2496a6b3073e758dc5466398a8\":\"a0367e21f925cf87d6096e4f13fef15146fe5d2496a6b3073e758dc5466398a8\",\"artifact:1889:a181d7b5cbf9883b0b45901ff937b0e6019f0e92f6a529206d6d40a15d155669\":\"a181d7b5cbf9883b0b45901ff937b0e6019f0e92f6a529206d6d40a15d155669\",\"artifact:1889:b2f9d7ea3090bb7a88a7554b99d59211bc3ad43b93845ab51a04880a38ccd13d\":\"b2f9d7ea3090bb7a88a7554b99d59211bc3ad43b93845ab51a04880a38ccd13d\",\"artifact:1889:b658a1844fce757dde2cdcf9a0eb28609b7d8fd87865df8f5e31101e88a5c027\":\"b658a1844fce757dde2cdcf9a0eb28609b7d8fd87865df8f5e31101e88a5c027\",\"artifact:1889:b857b8d2889d6df72c56fe0838e9ff970547ac51221b12c1c05e67a6bf03cd25\":\"b857b8d2889d6df72c56fe0838e9ff970547ac51221b12c1c05e67a6bf03cd25\",\"artifact:1889:c815b41284806e5e31907e1ba819c3523cbe802abb76b8b13d40e6e829ce3c20\":\"c815b41284806e5e31907e1ba819c3523cbe802abb76b8b13d40e6e829ce3c20\",\"artifact:1889:f7427ab35c32c11616eb2b0f6936cb2281372ddcb79410398859fac5c00987bf\":\"f7427ab35c32c11616eb2b0f6936cb2281372ddcb79410398859fac5c00987bf\",\"artifact:1889:fa70d62adc967915138e7beeca3500b408e976a50a58511ab9ce5820dc6e46c5\":\"fa70d62adc967915138e7beeca3500b408e976a50a58511ab9ce5820dc6e46c5\"},\"sha256\":\"dce061d7b6cb68616faf69f369a9a526cfbbebe762be96c1bf0ca4ad9087a7cc\"},\"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:1889,input_sha256:\"f46fb332702ad6b460009e698600cf2c9f1781f323381273c7bbd5cef807cc07\",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/3647/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"8a91baaa2491cd801019e1e9939e079f136472665269483689e1f831b8f9bf56","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}