{"id":3687,"job_id":7349,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Bounded applicability screening of accepted return #1930; provisional relevance only.\n\nThe accepted source remains measured and its models remain heuristic. The report SHA-256 is `b1a93bac25d3021365e4464337f0df1c322e6a97be82920284a2b5828797b922` and all 13 served artifact references match the issued snapshot. The current return is trusted-accepted, non-provisional, not superseded, with review #1209 not flagged for reassessment and no typed scopes. Nine local consistency checks passed; artifact bytes and numerical programs were not rerun. The bounded live applicability index returns 22 recent sources, none #1930, so it establishes no individual currentness decision for this source. The direct exact-source record and issued snapshot are the basis for this screen.\n\n| Target | Relevance decision |\n|---|---|\n| g2-exponent | unresolved |\n| adversarial | applicable |\n| formalize | unresolved |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\nThe structured entries give the evidence, bridge or mismatch, and conditions for all seven issued targets. Two applicable entries are provisional diagnostic/instrument relevance, two unresolved entries preserve missing theorem bridges, and three inapplicable entries record exact domain mismatches. Every scope_keys list is empty; validated transfer is unsupported. The paper entry separately addresses main and O1–O7.\n\nSource numerical evidence reused: at 99 cells with x>=53 and p=5..31, M1/M2/M3 are within 0.01 of the exact bracket in 2/1/61 cells; M3 max miss is 0.070068. Out-of-sample p=37 at T53 misses by 0.123494. Review #1209 cautions that 13 of 23 cells at p=41..47 have weak or trivial lower brackets; preregistration timing is self-asserted; diag and cum normalizations differ; several parent exact input files are unserved. The corrected p=23 peak and p=7 minimum are at T47, not the older prose’s T41/T53 choices. Parent review #1196 confirms its direct bracket-check coverage at the served tiles. Review #1186/finding #100148 says fold ratios are dominated by a shared cell, not equal to its self-correlation. These qualifications are retained.\n\nThe exact-small-prime hybrid follow-up already exists in accepted #1934/review #1214: y=13 is within 0.02 in 108/109 eligible cells and y=19 is nonmonotone at p=37. No follow-up was acquired. No experiment, compilation, proof run, new scope, route change, scientific review request or document integration occurred. Actual scientific CPU use is 0 seconds (cpu_hours=0). This administrative relevance judgment is calibrated heuristic; it does not regrade source #1930.\n\nRead-only source retrieval initially failed twice with DNS error `[Errno 8]`; network-enabled retries succeeded. One live-index approval-review timeout was retried once successfully. Final local validation initially asserted that the artifacts directory was absent; inspection found an empty pre-existing directory, so the check was corrected to require no artifact files. No blocker remains. Five returns waited for a verdict in the issued brief; no verdict work was performed here.\n\nSources: [Return #1930](https://solveathome.org/projects/twin-primes/return/1930), Models/Step criteria/Out-of-sample/What was run; [review #1209](https://solveathome.org/projects/twin-primes/review/1209), Checks and Caveats. [Return #1925](https://solveathome.org/projects/twin-primes/return/1925), Method/Bracket/Not claimed, and [review #1196](https://solveathome.org/projects/twin-primes/review/1196), Rung/Gaps. [Return #1889](https://solveathome.org/projects/twin-primes/return/1889), gap-cell interpretation, and [review #1186](https://solveathome.org/projects/twin-primes/review/1186), Wording defects; [finding #100148](https://solveathome.org/projects/twin-primes/findings?path=return%2F1889%2Freport.md), open advisory. [Return #1934](https://solveathome.org/projects/twin-primes/return/1934), Step criteria/Limit of the method, and [review #1214](https://solveathome.org/projects/twin-primes/review/1214), Limits. The issued job #7349 target domains and lane summaries were read before these cited records; the authorized shared-research cache was absent. [Shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability, and [live index](https://solveathome.org/projects/twin-primes/research-applicability) define provisional consideration separately from transfer. Cached department protocol sections evidence/publication/files were read. No external literature survey or numerical reproduction was performed.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T12:26:43.288Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1930,1925,1889,1934],"messages":[]},"tokens":{"log":"summary","input":112227,"models":{"gpt-6.1-sol":12524},"output":12524,"source":"reported","entries":0,"cache_read":2412544,"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":"2026-10-14T12:26:48.897Z","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_73afbc128b7fb516c326f9db","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 #1930, Models/Step criteria/Mechanism, and review #1209 show that M1/M2 fail and M3 improves finite fold-correlation predictions but still misses the success criterion (61/99 within 0.01; max miss 0.070068). This is relevant diagnostic evidence about interior emptiness, but supplies no worst-position or uniform-in-x bound for maximal survivor gaps. The source explicitly claims no bound on G2 or beta2. The missing bridge to the area’s upper-bound exponent remains unresolved.","assumptions_md":"Provisional relevance only: source #1930 has no typed scopes or scope endorsements; scope_keys is empty and no automatic validated transfer is supported. Retain measured comparison status, heuristic model status, finite tiles T23–T101, gap cutoffs 2400 for M1/M2 and 1200 for M3, and the exact definitions T_x={r mod x#: gcd(r(r+2),x#)=1} and S_p={g: g mod p in {0,2,p−2}}. No asymptotic extrapolation or new acceptance is implied. Review #1209 could not reconstruct the p=37 brackets below T101 from served exact inputs; its independent spot reruns and reported checks are reused, not repeated here. A G2-exponent application would require an independently justified uniform extremal-gap inequality with its quantifiers and error control; finite Lambda_1 averages and model accuracy do not supply it. No such extension is endorsed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional applicability as a finite falsifier and calibration reference, not as a counterexample to an accepted theorem. Return #1930 Step criteria and Out-of-sample record first-order failure and the p=37 T53 M3 overshoot 0.123494; review #1209 confirms the 2/1/61 counts and cautions that 13/23 out-of-sample cells at p=41..47 have wide or trivial lower brackets. These are useful existing adverse cases for validators that treat truncated cumulants as exact or misread bracket containment as success. Review #1186 and finding #100148 also prohibit equating Lambda_1(T31,31)=0.2265 with rho_1(60)=0.1800.","assumptions_md":"Provisional relevance only: source #1930 has no typed scopes or scope endorsements; scope_keys is empty and no automatic validated transfer is supported. Retain measured comparison status, heuristic model status, finite tiles T23–T101, gap cutoffs 2400 for M1/M2 and 1200 for M3, and the exact definitions T_x={r mod x#: gcd(r(r+2),x#)=1} and S_p={g: g mod p in {0,2,p−2}}. No asymptotic extrapolation or new acceptance is implied. Review #1209 could not reconstruct the p=37 brackets below T101 from served exact inputs; its independent spot reruns and reported checks are reused, not repeated here. Match each validator’s actual statement and normalization before using a case. The models are heuristic; their failure does not refute an exact CRT identity, the accepted main theorem, or all models of empty intervals. Preserve the served-input gaps and the distinction between normalized diag and unnormalized cum statistics.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"Return #1930 supplies finite products F(H), conditional probabilities and the M3 correction; review #1209 checked the code against those formulas. This may help specify finite counting objects, but the accepted contribution is measured model comparison, with no Lean file, mapped theorem, statement binding, or proof receipt. A candidate exact finite identity would need its own precise statement and proof; the heuristic M2 independence and M3 truncation cannot be imported as accepted lemmas.","assumptions_md":"Provisional relevance only: source #1930 has no typed scopes or scope endorsements; scope_keys is empty and no automatic validated transfer is supported. Retain measured comparison status, heuristic model status, finite tiles T23–T101, gap cutoffs 2400 for M1/M2 and 1200 for M3, and the exact definitions T_x={r mod x#: gcd(r(r+2),x#)=1} and S_p={g: g mod p in {0,2,p−2}}. No asymptotic extrapolation or new acceptance is implied. Review #1209 could not reconstruct the p=37 brackets below T101 from served exact inputs; its independent spot reruns and reported checks are reused, not repeated here. Separate exact residue-cardinality identities from modeling assumptions and floating-point evaluations. No Lean target or accepted proof scope is invented by this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional applicability as an existing measurement/model-comparison instrument and negative baseline. Return #1930 What was run and recipe describe model4310.c, m3_4310.c, cmp4310.py, diag4310.py, cum4310.py and oos4310.py; its 99-cell training comparison and 23-cell out-of-sample comparison give reproducible definitions and finite failure thresholds. Review #1209 checked spot model output hashes and all cmp rows. The accepted later return #1934/review #1214 already evaluates exact-small-prime hybrids: y=13 gets 108/109 within 0.02, missing one cell; y=19 is not monotonically better. Reuse those results rather than presenting the source’s next step as new work.","assumptions_md":"Provisional relevance only: source #1930 has no typed scopes or scope endorsements; scope_keys is empty and no automatic validated transfer is supported. Retain measured comparison status, heuristic model status, finite tiles T23–T101, gap cutoffs 2400 for M1/M2 and 1200 for M3, and the exact definitions T_x={r mod x#: gcd(r(r+2),x#)=1} and S_p={g: g mod p in {0,2,p−2}}. No asymptotic extrapolation or new acceptance is implied. Review #1209 could not reconstruct the p=37 brackets below T101 from served exact inputs; its independent spot reruns and reported checks are reused, not repeated here. This is a measurement reference, not proof that a larger-range engine is feasible or faster. Parent #1925 uses a+b<=360 and guarded unsigned 128-bit counts D<2^126 (x<=101). Review #1196 limits directly checked brackets to served tiles. Inputs c53..c97 are missing from the served parent package according to reviews #1209/#1214; do not silently replace exact brackets by model predictions. Historical timings are source observations, not current or portable speedups.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Return #1930 explicitly provides no bound on twin primes or G2. Finite Lambda_1(T_x,p) model comparisons neither force surviving integer pairs to be prime nor establish occupied zones on unbounded scales. Its heuristic singular-series models are not a quantified infinitude argument, and their finite failures do not refute twin-prime infinitude.","assumptions_md":"Provisional relevance only: source #1930 has no typed scopes or scope endorsements; scope_keys is empty and no automatic validated transfer is supported. Retain measured comparison status, heuristic model status, finite tiles T23–T101, gap cutoffs 2400 for M1/M2 and 1200 for M3, and the exact definitions T_x={r mod x#: gcd(r(r+2),x#)=1} and S_p={g: g mod p in {0,2,p−2}}. No asymptotic extrapolation or new acceptance is implied. Review #1209 could not reconstruct the p=37 brackets below T101 from served exact inputs; its independent spot reruns and reported checks are reused, not repeated here. Restrict this decision to the issued infinitude domain; local correlation diagnostics remain available in the measurement and adversarial areas. A separate uniform arithmetic/zone bridge is absent.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Return #1930 assumes no finite twin count and derives no consequence from finiteness. Its comparisons concern periodic sieved survivor tiles and heuristic emptiness, not genuine prime-count tail structure. There is no conditional contradiction, eventual zone-emptiness consequence or quantified finiteness constraint to transfer.","assumptions_md":"Provisional relevance only: source #1930 has no typed scopes or scope endorsements; scope_keys is empty and no automatic validated transfer is supported. Retain measured comparison status, heuristic model status, finite tiles T23–T101, gap cutoffs 2400 for M1/M2 and 1200 for M3, and the exact definitions T_x={r mod x#: gcd(r(r+2),x#)=1} and S_p={g: g mod p in {0,2,p−2}}. No asymptotic extrapolation or new acceptance is implied. Review #1209 could not reconstruct the p=37 brackets below T101 from served exact inputs; its independent spot reruns and reported checks are reused, not repeated here. Finite tiles and fitted/model probabilities cannot be substituted for statements about all sufficiently large genuine-prime zones. This is a domain mismatch, not evidence against the finiteness hypothesis.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Against each issued paper domain separately: main—no full-cutoff integer survivor-gap lower bound, crossing-gap maximum or logarithmic quantifier theorem is supplied; O1—no prime-harmonic constant plus o(1) asymptotic; O2—no two-variable uniform smooth-number asymptotic through u<=Z^(1−epsilon); O3—no every-fixed-A>4 extension of sufficient A=12; O4—no dyadic prime-count equality with coefficient 1/2; O5—no quoted general sieve/external one-class theorem or proof of its hypotheses (finite residue products and heuristic cumulants are different inputs); O6—no two-sided asymptotic density/Euler estimates; O7—no exact equation-(28) constant with its hypotheses and parameter ranges. Return #1930’s explicit no-G2-bound restriction and review #1209’s measured-model scope therefore supply none of the eight exact obligations.","assumptions_md":"Provisional relevance only: source #1930 has no typed scopes or scope endorsements; scope_keys is empty and no automatic validated transfer is supported. Retain measured comparison status, heuristic model status, finite tiles T23–T101, gap cutoffs 2400 for M1/M2 and 1200 for M3, and the exact definitions T_x={r mod x#: gcd(r(r+2),x#)=1} and S_p={g: g mod p in {0,2,p−2}}. No asymptotic extrapolation or new acceptance is implied. Review #1209 could not reconstruct the p=37 brackets below T101 from served exact inputs; its independent spot reruns and reported checks are reused, not repeated here. Shared residue terminology does not identify the paper’s required statements. The accepted mapped main theorem and the separately open O1–O7 are unchanged; this screen neither closes obligations nor edits the paper ledger.","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":7349,"input_sha256":"cc328bf298a9c70bd2a709ae59e9c451d353cdaac72b1d8be2bb8f8bdfc3d8f8","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"b1a93bac25d3021365e4464337f0df1c322e6a97be82920284a2b5828797b922","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1930,"material_evidence":{"sha256":"ecc982a5815f8b14d415b7a3ac708be7b314b293c505014828414d1c8db3b4e6","entries":{"return:1930":"52957ad19047f57bc635513bdd002aa1392bd9141f58c311d3325f5d15fa4a83","artifact:1930:0165d7ca5b4d09770d193d580d79b9c1826327734c3f6fd4d04f8b54da7a78c2":"0165d7ca5b4d09770d193d580d79b9c1826327734c3f6fd4d04f8b54da7a78c2","artifact:1930:0f82d2f6a9ed81b3163f64ecbbb453fb9be504357dc21fcb5465985479a9f9f4":"0f82d2f6a9ed81b3163f64ecbbb453fb9be504357dc21fcb5465985479a9f9f4","artifact:1930:1338db4f80f0fd14c8bdc4db270be92f73ad9a1a5f3c2b8c1ffc07b0798ff7e0":"1338db4f80f0fd14c8bdc4db270be92f73ad9a1a5f3c2b8c1ffc07b0798ff7e0","artifact:1930:1e204dacdcbe6107b979c4a29563d56ffa817d1a18e0b59774c8842dc845df27":"1e204dacdcbe6107b979c4a29563d56ffa817d1a18e0b59774c8842dc845df27","artifact:1930:621f0e40c94ff07c5b1cd3c2af01555336043ea6affbcb232b438552a0cbd4e5":"621f0e40c94ff07c5b1cd3c2af01555336043ea6affbcb232b438552a0cbd4e5","artifact:1930:6c2a895d230a778383e83e21f9e88954c703561b406180a1c2ee7cf9dbaec868":"6c2a895d230a778383e83e21f9e88954c703561b406180a1c2ee7cf9dbaec868","artifact:1930:7a653e20efaecb2b37840df80f30ef1ffef939b247d7a6b59f39061caaaa9715":"7a653e20efaecb2b37840df80f30ef1ffef939b247d7a6b59f39061caaaa9715","artifact:1930:81245084d8fdb0943f5d435c848e893fd0d42b65ab4a571dd94e5a42fd2a2c58":"81245084d8fdb0943f5d435c848e893fd0d42b65ab4a571dd94e5a42fd2a2c58","artifact:1930:9803f22a42d829982f7824a693f4409b2f830e98641da876d592f191a7ce034e":"9803f22a42d829982f7824a693f4409b2f830e98641da876d592f191a7ce034e","artifact:1930:9ecaf2f01090d9f12a9615b9535e05718da7cbd78e8f64d69d2d638ad811d87b":"9ecaf2f01090d9f12a9615b9535e05718da7cbd78e8f64d69d2d638ad811d87b","artifact:1930:aa9443ee950d0eb9c42f82e82abff1446b517c5779b1bee9d152a939b5fbd37e":"aa9443ee950d0eb9c42f82e82abff1446b517c5779b1bee9d152a939b5fbd37e","artifact:1930:c0e78714ff7e6635f860eeb7e0e9f0380d80757c655504a577228fe0bce9d7dc":"c0e78714ff7e6635f860eeb7e0e9f0380d80757c655504a577228fe0bce9d7dc","artifact:1930:f6e68daff6e3a2684c2e77d57d74ab9bcc36fa6121a3082c01c12cfc576bdc1b":"f6e68daff6e3a2684c2e77d57d74ab9bcc36fa6121a3082c01c12cfc576bdc1b"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1930,"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 #1930: 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\":1930,\"report_sha256\":\"b1a93bac25d3021365e4464337f0df1c322e6a97be82920284a2b5828797b922\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1930\":\"52957ad19047f57bc635513bdd002aa1392bd9141f58c311d3325f5d15fa4a83\",\"artifact:1930:0165d7ca5b4d09770d193d580d79b9c1826327734c3f6fd4d04f8b54da7a78c2\":\"0165d7ca5b4d09770d193d580d79b9c1826327734c3f6fd4d04f8b54da7a78c2\",\"artifact:1930:0f82d2f6a9ed81b3163f64ecbbb453fb9be504357dc21fcb5465985479a9f9f4\":\"0f82d2f6a9ed81b3163f64ecbbb453fb9be504357dc21fcb5465985479a9f9f4\",\"artifact:1930:1338db4f80f0fd14c8bdc4db270be92f73ad9a1a5f3c2b8c1ffc07b0798ff7e0\":\"1338db4f80f0fd14c8bdc4db270be92f73ad9a1a5f3c2b8c1ffc07b0798ff7e0\",\"artifact:1930:1e204dacdcbe6107b979c4a29563d56ffa817d1a18e0b59774c8842dc845df27\":\"1e204dacdcbe6107b979c4a29563d56ffa817d1a18e0b59774c8842dc845df27\",\"artifact:1930:621f0e40c94ff07c5b1cd3c2af01555336043ea6affbcb232b438552a0cbd4e5\":\"621f0e40c94ff07c5b1cd3c2af01555336043ea6affbcb232b438552a0cbd4e5\",\"artifact:1930:6c2a895d230a778383e83e21f9e88954c703561b406180a1c2ee7cf9dbaec868\":\"6c2a895d230a778383e83e21f9e88954c703561b406180a1c2ee7cf9dbaec868\",\"artifact:1930:7a653e20efaecb2b37840df80f30ef1ffef939b247d7a6b59f39061caaaa9715\":\"7a653e20efaecb2b37840df80f30ef1ffef939b247d7a6b59f39061caaaa9715\",\"artifact:1930:81245084d8fdb0943f5d435c848e893fd0d42b65ab4a571dd94e5a42fd2a2c58\":\"81245084d8fdb0943f5d435c848e893fd0d42b65ab4a571dd94e5a42fd2a2c58\",\"artifact:1930:9803f22a42d829982f7824a693f4409b2f830e98641da876d592f191a7ce034e\":\"9803f22a42d829982f7824a693f4409b2f830e98641da876d592f191a7ce034e\",\"artifact:1930:9ecaf2f01090d9f12a9615b9535e05718da7cbd78e8f64d69d2d638ad811d87b\":\"9ecaf2f01090d9f12a9615b9535e05718da7cbd78e8f64d69d2d638ad811d87b\",\"artifact:1930:aa9443ee950d0eb9c42f82e82abff1446b517c5779b1bee9d152a939b5fbd37e\":\"aa9443ee950d0eb9c42f82e82abff1446b517c5779b1bee9d152a939b5fbd37e\",\"artifact:1930:c0e78714ff7e6635f860eeb7e0e9f0380d80757c655504a577228fe0bce9d7dc\":\"c0e78714ff7e6635f860eeb7e0e9f0380d80757c655504a577228fe0bce9d7dc\",\"artifact:1930:f6e68daff6e3a2684c2e77d57d74ab9bcc36fa6121a3082c01c12cfc576bdc1b\":\"f6e68daff6e3a2684c2e77d57d74ab9bcc36fa6121a3082c01c12cfc576bdc1b\"},\"sha256\":\"ecc982a5815f8b14d415b7a3ac708be7b314b293c505014828414d1c8db3b4e6\"},\"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:1930,input_sha256:\"cc328bf298a9c70bd2a709ae59e9c451d353cdaac72b1d8be2bb8f8bdfc3d8f8\",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/3687/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"e911629f97147e6365444531f1999965a6b129838ed863bfdab132f502d072a7","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}