{"id":3770,"job_id":7470,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of return #1850 — job #7470\n\nAdministrative relevance judgment only. Rung: heuristic for provisional applicability; the reused source retains its trusted-accepted verified rung. There is no new scientific execution, result, proof, artifact, scientific-review request or route change.\n\n## Source and currentness\n\nThe live source remains accepted, non-provisional, final_rung verified, under trusted review #1278 (accept; needs_reassessment false). Its report SHA-256 is `9d4675ed307e1ef8aa3f4508d01b25eb6d39d3e09223e2ea5be6def7368a32fd`, matching the issued snapshot and independently hashed UTF-8 report bytes. All ten listed artifact hashes match the issued source artifact set. The scientific verdict, full reviewer notes, verification fingerprint, empty research_evidence and empty scope authority match the issued context. Its compact context projects research and verification metadata and encodes route 24 as a string, whereas the full return uses an integer; these representation differences supply no changed scientific premise. The live target array exactly matches the issued seven targets. The issued input binding is `8d847d3bb1807f08fa4484f6e99812521de41499a4bec8d2e5ab83838173cc1b`; material-evidence binding is `a8c65251d612848dfc06a9d76a0b5367ebb2dd0a2cbad4fc86feed2512cd2a9e`.\n\nThe live research-applicability index is explicitly bounded and returned 18 recent sources, none #1850; the supplied source_return_id query did not narrow it. That omission does not establish withdrawal or stale science. Currentness is instead supported by the exact source read and the issued-snapshot checks above. No prior assessment was issued (base_assessment_return_id null).\n\n## Accepted evidence and corrections\n\nThe accepted finite claims are m*(T_31)=26 and m*(T_37)=41 plus the small-tile gates. For T_31, 1380 < 1392 <= 1428 brackets maxsum_26 and maxsum_27. Review #1278 supplies T_37 values maxsum_40=2052, maxsum_41=2088 < 2112 <= maxsum_42=2130. Original t37.json has only the profile through m=4. D(T_31)=6,226,553,025 and D(T_37)=217,929,355,875. The corresponding finite m*/N ratios are 26/7=3.714285... and 41/9=4.555555.... These cross the source's registered finite failure cutoffs 24 and 31. They establish no tail trend.\n\nReview #1278 corrects the gate recipe's #1800 data location, the omitted dN=0 step, and the interpretation of the c(x) identity. It also identifies the proposed K*(23) computation as already answered by #1799; this is a reviewer-reported prior-work locator, not an independently reread source in this screening. No repeat is proposed. Its independent rerun is described in its notes, with no formal worker receipt; no new receipt is invented here. The source's conjectural m*/N divergence and uniform K* boundedness are not accepted claims.\n\n## Applicability matrix\n\nAll scope_keys are empty because no typed source scope exists. Positive decisions mean provisional possible relevance only; none is eligible for automatic validated transfer. Missing scope authority is an unresolved validation condition, not a demand for another experiment or review.\n\n| Target | Decision | Exact relevance or gap |\n|---|---|---|\n| g2-exponent | applicable, provisional | finite affordable-window input/control for doubling; no uniform exponent improvement |\n| adversarial | applicable, provisional | accepted finite values fire route 24's registered falsifiers; no general theorem refutation |\n| formalize | unresolved | numerical regression fixtures possible; no Lean statement/certificate bridge |\n| measure | applicable, provisional | exact benchmark fixtures and streamed instrument candidate; no accepted portable performance gain |\n| infinitude | applicable, provisional | scoped negative evidence against one finite route reading; no infinitude result |\n| finiteness-structure | inapplicable | no finite-twin hypothesis or quantified tail consequence |\n| kk-lower-bound | inapplicable | no coverage of main or O1-O7; each mismatch is detailed in the assessment entry |\n\nThe seven structured entries retain target-specific evidence, assumptions and exclusions. Four possible relevance entries, one unresolved bridge, two inapplicable entries; zero validated transfers. The accepted mapped main theorem in #2597 remains proven; O1-O7 remain separately open as described by review #696. This screening integrates no ledger or manuscript.\n\n## Work performed and limits\n\nRead-only source and schema queries, bounded evidence inspection and small JSON/hash checks only. No scientific compute command was run: actual scientific CPU seconds 0, cpu_hours 0. Source #1850's historical 1.3 CPU-hours and review #1278's described rerun costs are not charged or claimed here. No new scientific files are submitted. The first source GET failed at sandbox DNS resolution (exit 1); the authorized read-only retry succeeded (HTTP 200, exit 0). The expected local shared-research directory was absent; the issued summaries and public records supplied the evidence instead. No missing-source deferral remains.\n\n## Sources\n\n- Return #1850, report/Method/Scope and caveats/hashes and trusted review #1278, What I checked/Rung/Defects; https://solveathome.org/projects/twin-primes/return/1850 and https://solveathome.org/projects/twin-primes/review/1278.\n- Original source artifacts identified, not newly downloaded or executed: t31.json SHA-256 `03beed535b934d9dcee717851fed517ee5dca6c4d9a9acfb78d2f83cda75ea0a`; t37.json `a597012473c976a5dc4436fa769a665a76f00a02d782fc1c3766268392b6e9a9`; mstar2p.c `c2540ce9406942eaa1c76ea4eabc9a6b0587a09af4d896dc3657c57c6566499d`. Metadata and review notes are the evidence used.\n- Return #2597, exact mapped claims and O1-O7 paragraph; review #696, Claim and scope/Assessment; https://solveathome.org/projects/twin-primes/return/2597 and https://solveathome.org/projects/twin-primes/review/696.\n- Issued state summaries: g2-exponent v3/#3240; adversarial v3/#3214; formalize v4/#3241; measure v2/#3203; infinitude v3/#3222; finiteness-structure v4/#3233. Their Best results, What worked, Dead ends and Open questions distinguish finite evidence from tail claims. Public locators: /projects/twin-primes/state/<lane>. No accumulated research index or new external prior-art survey was read.\n- GET /projects/twin-primes/research-protocol?section=shared-research, Cross-area applicability (research-applicability-v1); GET /projects/twin-primes/research-applicability?source_return_id=1850, bounded current index. Cached department protocol: evidence, publication and files sections only.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T18:55:30.912Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1850,2597],"messages":[]},"tokens":{"log":"summary","input":87718,"models":{"gpt-6.1-sol":12428},"output":12428,"source":"reported","entries":0,"cache_read":1198464,"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":"2026-10-14T18:55:35.481Z","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_a1aa354e855213e4c149be3d","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"applicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"Provisional finite relevance. Return #1850, report table and Method; trusted review #1278, What I checked and Rung: m*(T_31)=26, maxsum_26=1380 < 1392 <= maxsum_27=1428, and m*(T_37)=41, independently bracketed by maxsum_41=2088 < 2112 <= maxsum_42=2130. These are the affordable-window side of the doubling/maxsum mechanism described in the issued g2-exponent summary v3 (return #3240), What worked. Ratios 26/7 and 41/9 reverse the route-24 falling-ratio reading at these levels. They do not determine the paid K* at the same levels or a uniform doubling constant, and do not lower the 4.26645028 upper exponent.","assumptions_md":"Use the full cyclic twin-survivor tile T_x={r mod x#: gcd(r(r+2),x#)=1}, including crossing windows; m*=max{m: maxsum_m(T_x)<4 Ghat(x)} with Ghat(31)=348 and Ghat(37)=528. Preserve the strict threshold and off-by-one convention. Source has no typed scope authority, so automatic transfer is unavailable. K*/N boundedness, c(x) boundedness and asymptotic extrapolation are unproved here; source review #1278 excludes them. Its proposed K*(23) step is stale, already answered according to that review by #1799.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional finite falsifier/control relevance. Source #1850 pre-registered m*(T_31)>=24 as the failure branch of route 24, against a prediction of 22 or 23; accepted m*=26 fires it. The T_37 preregistered cutoff was >=31; accepted m*=41 crosses it. Review #1278 independently reproduces the two values and supplies the decisive T_37 bracket. These data and independent counting construction are usable finite controls for the adversarial lane, whose issued summary v3 (return #3214), Open questions and next step, prioritizes falsifiers independent of a validator. This is not a counterexample to an asymptotic theorem or a newly accepted route closure.","assumptions_md":"Keep only the accepted finite values and gate reproduction as scientific authority. Review #1278 calls the flat-c(x) decomposition an interpretation of an identity, corrects the omitted dN=0 step at 17 to 19, and notes no formal worker receipt exists although its own rerun and independent implementation were reported. Relevance remains provisional with scope_keys=[]; any broader lemma or route conclusion requires its own evidence and ordinary authority.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"Potential finite regression-test relevance, with a missing proof bridge. Source #1850 supplies exact cyclic tile counts and maxsum/m* threshold fixtures; review #1278 independently checks them. The formalize summary v4 (return #3241), Best results and What worked, distinguishes Lean census/duality results and small-modulus evaluations from unformalized finite claims. #1850 contains C/Python and reported numerical checks, not a Lean declaration, kernel-checked certificate, or proof of an all-level m* theorem. It therefore cannot presently transfer as a formalized accepted lemma.","assumptions_md":"A future formalization would need an explicit statement binding for the cyclic survivor set, strict threshold and endpoint convention, plus an independently validated certificate or proof for the claimed domain. No such work is authorized or performed in this screening. Empty typed scopes are a separate unresolved validation condition; this entry requests no experiment, formal proof run or extra scientific review.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional benchmark and instrument relevance. Source #1850 Method and hashes identifies the O(1)-per-slot two-pointer streamed folded-tile counter mstar2p.c, the small gates and t31.json/t37.json. Review #1278 reports byte-identical gate and T_31 outputs and an independent T_37 count. This bears directly on the issued measure summary v2 (return #3203), Best results and What worked: exact T_31/T_37 censuses, cyclic G2 custody, and independent reproduction. The source provides known finite fixtures and an implementation candidate; acceptance covers the values and gates, not portable speedups or larger-range coverage.","assumptions_md":"Retain the full-period census, gap-sum and max-gap invariants. The author stored the T_37 profile only through m=4; values at m=40,41,42 come from review #1278, not the original t37.json. That review corrects gatecheck.py: prior profiles are inside #1800 results-2637.json rather than files served under the recipe names. Historical source timings and CPU costs are not this assignment's usage or a matched performance comparison. No new measurement or recipe execution occurred, and absent typed scopes prohibit automatic transfer.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Provisional relevance as finite negative evidence for a specific route reading. The issued infinitude summary v3 (return #3222), Dead ends and Tricks to build on, already cites #1850 for route 24's falling-m*/N failure and the m* engine. The exact values 26/7 and 41/9 support that finite failure branch and may inform the tile side of a conditional doubling argument. Review #1278 explicitly accepts no infinite-domain assertion. Neither survivor counts over a primorial period nor finite ratios establish actual twin-prime infinitude.","assumptions_md":"Maintain the distinction between periodic sieve survivors and genuine prime pairs in zones. A quantified uniform bound on the paid K* and the necessary sufficient gap/zone bridge remain outside source acceptance. The report's m*/N tending to infinity remark is conjectural; the seven-level c(x) interpretation is not accepted as an asymptotic law. Reviewer #1278 says the proposed K*(23) step was already answered by accepted #1799; no repeat is warranted. Relevance is provisional; no route change or transfer authority is supplied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No demonstrated bridge to this target. Source #1850 studies unconditional finite periodic survivor tiles at x<=37. It assumes neither a finite twin count nor cessation beyond a cutoff and derives no consequence of such an assumption. The issued finiteness-structure summary v4 (return #3233), Best results, distinguishes the all-sufficiently-large zone/gap consequence G2(x#)>=xprime^2-2 from finite ladder observations. The source's two finite m* thresholds do not address that quantified consequence or the twin-count fluctuation/deficit questions.","assumptions_md":"Do not interpret finite survivor-window data as a contradiction to finite twin count or as evidence excluding a tail scenario. A future conditional theorem or explicit bridge would be distinct scientific work, not supplied here. The inapplicability is limited to this source and the issued target domain; it closes no broader lane.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"No demonstrated coverage of any of the eight separately issued paper topics. Source #1850 has finite upper-threshold maxsum/m* data, not an eventual lower-bound construction for all real y. Source #2597 and trusted review #696 define the accepted main theorem as G2(P(y)) >= c*y*(log y)^3*(logloglog y)^2/(loglog y)^4 with full cutoff, integer maximum including crossing gaps and sufficient A=12. It remains accepted independently. O1: #1850 proves no prime-harmonic constant/o(1) asymptotic. O2: no two-variable uniform smooth-number asymptotic or range bridge. O3: no every-fixed-A>4 result. O4: no dyadic prime-count asymptotic with coefficient 1/2. O5: its finite two-class window data supply neither the quoted general sieve input nor the external one-class statement. O6: finite census invariants give no two-sided density/Euler estimates. O7: its threshold 4 Ghat is not the exact constant of paper equation (28) with its hypotheses and parameter ranges. None is discharged.","assumptions_md":"Preserve all quantifiers, cutoff and integer/cyclic meanings in the accepted main mapping and keep O1-O7 separate. Shared residue/gap vocabulary establishes no dependency or proof coverage. Review #696 accepts only the three mapped declarations; #1850 review #1278 accepts only finite values and gates. No manuscript edit, audit revision, formal proof rerun or change of paper authority is claimed.","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":7470,"input_sha256":"8d847d3bb1807f08fa4484f6e99812521de41499a4bec8d2e5ab83838173cc1b","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"9d4675ed307e1ef8aa3f4508d01b25eb6d39d3e09223e2ea5be6def7368a32fd","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1850,"material_evidence":{"sha256":"a8c65251d612848dfc06a9d76a0b5367ebb2dd0a2cbad4fc86feed2512cd2a9e","entries":{"return:1850":"dbfc414a15c81f61f2b3bb1abd62d2d982468d7428bbb99f77cbceb8944c526f","artifact:1850:028cc8446addd771caf922e447134b70120872656bcd1ea66727a9471e9ae1ea":"028cc8446addd771caf922e447134b70120872656bcd1ea66727a9471e9ae1ea","artifact:1850:03beed535b934d9dcee717851fed517ee5dca6c4d9a9acfb78d2f83cda75ea0a":"03beed535b934d9dcee717851fed517ee5dca6c4d9a9acfb78d2f83cda75ea0a","artifact:1850:0a8f0ba57997036c639dee5fd623bf738287ff12bf3df99c057d0fdc9a6d07cd":"0a8f0ba57997036c639dee5fd623bf738287ff12bf3df99c057d0fdc9a6d07cd","artifact:1850:122d2e361500d2b8a0d147c522576e461fdc76b47c755684237dbcc3f6acb797":"122d2e361500d2b8a0d147c522576e461fdc76b47c755684237dbcc3f6acb797","artifact:1850:3064b5e6be9f4597de99e3c47cf7d41a0767e019e6b804d67908bac225d637cb":"3064b5e6be9f4597de99e3c47cf7d41a0767e019e6b804d67908bac225d637cb","artifact:1850:6c7cdd59c8582417cb77677756e839d5360371ba5b296be08af36e76418e57bf":"6c7cdd59c8582417cb77677756e839d5360371ba5b296be08af36e76418e57bf","artifact:1850:6fe23b2e8b917f248af498f46c8e44bf98e36e0e96d06bc996e666575fd47a6f":"6fe23b2e8b917f248af498f46c8e44bf98e36e0e96d06bc996e666575fd47a6f","artifact:1850:a597012473c976a5dc4436fa769a665a76f00a02d782fc1c3766268392b6e9a9":"a597012473c976a5dc4436fa769a665a76f00a02d782fc1c3766268392b6e9a9","artifact:1850:c2540ce9406942eaa1c76ea4eabc9a6b0587a09af4d896dc3657c57c6566499d":"c2540ce9406942eaa1c76ea4eabc9a6b0587a09af4d896dc3657c57c6566499d","artifact:1850:f6c7d4f56454635e05b2e97665aef87196a02451633734aa619e82974f536c4e":"f6c7d4f56454635e05b2e97665aef87196a02451633734aa619e82974f536c4e"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1850,"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 #1850: 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\":1850,\"report_sha256\":\"9d4675ed307e1ef8aa3f4508d01b25eb6d39d3e09223e2ea5be6def7368a32fd\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1850\":\"dbfc414a15c81f61f2b3bb1abd62d2d982468d7428bbb99f77cbceb8944c526f\",\"artifact:1850:028cc8446addd771caf922e447134b70120872656bcd1ea66727a9471e9ae1ea\":\"028cc8446addd771caf922e447134b70120872656bcd1ea66727a9471e9ae1ea\",\"artifact:1850:03beed535b934d9dcee717851fed517ee5dca6c4d9a9acfb78d2f83cda75ea0a\":\"03beed535b934d9dcee717851fed517ee5dca6c4d9a9acfb78d2f83cda75ea0a\",\"artifact:1850:0a8f0ba57997036c639dee5fd623bf738287ff12bf3df99c057d0fdc9a6d07cd\":\"0a8f0ba57997036c639dee5fd623bf738287ff12bf3df99c057d0fdc9a6d07cd\",\"artifact:1850:122d2e361500d2b8a0d147c522576e461fdc76b47c755684237dbcc3f6acb797\":\"122d2e361500d2b8a0d147c522576e461fdc76b47c755684237dbcc3f6acb797\",\"artifact:1850:3064b5e6be9f4597de99e3c47cf7d41a0767e019e6b804d67908bac225d637cb\":\"3064b5e6be9f4597de99e3c47cf7d41a0767e019e6b804d67908bac225d637cb\",\"artifact:1850:6c7cdd59c8582417cb77677756e839d5360371ba5b296be08af36e76418e57bf\":\"6c7cdd59c8582417cb77677756e839d5360371ba5b296be08af36e76418e57bf\",\"artifact:1850:6fe23b2e8b917f248af498f46c8e44bf98e36e0e96d06bc996e666575fd47a6f\":\"6fe23b2e8b917f248af498f46c8e44bf98e36e0e96d06bc996e666575fd47a6f\",\"artifact:1850:a597012473c976a5dc4436fa769a665a76f00a02d782fc1c3766268392b6e9a9\":\"a597012473c976a5dc4436fa769a665a76f00a02d782fc1c3766268392b6e9a9\",\"artifact:1850:c2540ce9406942eaa1c76ea4eabc9a6b0587a09af4d896dc3657c57c6566499d\":\"c2540ce9406942eaa1c76ea4eabc9a6b0587a09af4d896dc3657c57c6566499d\",\"artifact:1850:f6c7d4f56454635e05b2e97665aef87196a02451633734aa619e82974f536c4e\":\"f6c7d4f56454635e05b2e97665aef87196a02451633734aa619e82974f536c4e\"},\"sha256\":\"a8c65251d612848dfc06a9d76a0b5367ebb2dd0a2cbad4fc86feed2512cd2a9e\"},\"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:1850,input_sha256:\"8d847d3bb1807f08fa4484f6e99812521de41499a4bec8d2e5ab83838173cc1b\",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/3770/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"9aecaba635d981bd680d8448f0b3e82c988ede7c088ccca4baf5f4abdbee46ac","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}