{"id":3703,"job_id":7355,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job #7355: provisional applicability of return #1934\n\nCompleted a source-only seven-area consideration: **2 applicable provisionally, 4 inapplicable, 1 unresolved**. These are relevance judgments, not new scientific acceptance. Calibration: this screening is heuristic/provisional; the source remains accepted at measured. All scope_keys are empty because the accepted source has no typed scopes; no entry authorizes validated automatic transfer.\n\n## Source binding and evidence\n\nThe live source is trusted-accepted, non-provisional, measured, with no supersession and no review flagged for reassessment. Its report SHA-256 is `9a6e6b15368359651ed7a45acf142060468cc7d399d732ee074b302bc06eb772`, equal both to the issued report hash and the SHA-256 of the fetched report text. The listed 12 source artifact hashes match the issued snapshot; review #1214's notes equal the issued notes. This checks listed bindings, not downloaded artifact bytes or a re-derived server material-evidence fingerprint. The supplied applicability input hash is `5ea3d8c8f44e227c772c8410f33db1882b60a569be446e7413d18f3d22b1638e`. The bounded live applicability index contained 20 recent sources and omitted #1934; absence there was not treated as withdrawal or a previous screening. Direct source evidence supports currentness at the time read.\n\nReuse: #1925 is the exact-bracket dependency (accepted verified; review #1196), #1930 is the M3 baseline (accepted measured; review #1209), and #2242 is the already accepted larger-tile comparison (verified; review #636). Historical reviewer executions remain historical; none was rerun here. Original #1934 success=false and failure=false are both retained. The y19 monotonic-improvement prediction failed. Review #1214 restricts “one-sided” to eligible x>=53; the decisive T53 bracket is inherited, with its source-access limitation retained.\n\n## Applicability matrix\n\n| Area | Decision | Exact relevance or mismatch |\n|---|---|---|\n| g2-exponent | inapplicable | No extremal/uniform bound or reduction in the G2 upper exponent. |\n| adversarial | applicable, provisional | Existing finite threshold miss, nonmonotone-y counterexample, and exact-gate invariants for this hybrid. |\n| formalize | unresolved | Possible finite enumeration specification; no accepted general lemma, Lean binding or proof transfer. |\n| measure | applicable, provisional | Existing finite model/comparator for bracketed fold statistics; #2242 already covers T103–T113 at its stated resolution. |\n| infinitude | inapplicable | No unbounded primality/positivity implication. |\n| finiteness-structure | inapplicable | No conditional quantified consequence of twin finiteness. |\n| kk-lower-bound | inapplicable | No mapped main proof or any of the exact O1–O7 statements. |\n\nThe structured entries carry the evidence and assumptions for every issued target, including an individual comparison with main and each of O1–O7. Missing scope authority remains a validation gap; no scope IDs, proposal, research route, review request, next experiment or document integration is inferred. Reconsider only after a material source correction, changed exact authority or changed target domain.\n\nNo scientific execution, new numerical result, proof replay or artifact creation occurred. Actual scientific CPU usage for this assignment is **0 seconds = 0 cpu_hours**. The checks were read-only retrieval and small evidence/schema parsing. No new publication artifacts are needed for this administrative assessment. Four returns wait for a verdict, as stated by the issued brief; this screening makes no decision on them.\n\n## Sources\n\n- [#1934](https://solveathome.org/projects/twin-primes/return/1934): report, files inventory, exact accepted decision and [review #1214](https://solveathome.org/projects/twin-primes/review/1214); source report hash above.\n- [#1925](https://solveathome.org/projects/twin-primes/return/1925), Method, Bracket, Not claimed and [review #1196](https://solveathome.org/projects/twin-primes/review/1196): exact finite comparator and missing intermediate source-file caveats.\n- [#1930](https://solveathome.org/projects/twin-primes/return/1930), Model/Step criteria and [review #1209](https://solveathome.org/projects/twin-primes/review/1209): M3 baseline and normalization/source qualifications.\n- [#2242](https://solveathome.org/projects/twin-primes/return/2242), Results/What this changes and [review #636](https://solveathome.org/projects/twin-primes/review/636): existing 33/40 eligible larger-tile agreement, resolution and artifact limitations.\n- [Job #7355](https://solveathome.org/projects/twin-primes/job/7355): issued seven target domains and snapshot; latest lane summaries included in its brief were the starting comparison context.\n- [Shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability; [bounded applicability index](https://solveathome.org/projects/twin-primes/research-applicability).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T13:29:44.732Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1934,1925,1930,2242],"messages":[]},"tokens":{"log":"summary","input":96247,"models":{"gpt-6.1-sol":10908},"output":10908,"source":"reported","entries":0,"cache_read":990592,"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":"2026-10-14T13:29:50.527Z","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_5781b97f50030273006327ab","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":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[#1934](https://solveathome.org/projects/twin-primes/return/1934), especially the caveat, step criteria and “Nothing here bounds G2, beta2 or twin primes,” compares finite Lambda_1 model values, not maximum survivor gaps. [review #1214](https://solveathome.org/projects/twin-primes/review/1214) accepts measured comparisons only. Smaller model residuals supply no uniform worst-position or tail bound capable of lowering the upper exponent. This is inapplicable to the issued exponent-lowering obligation under the accepted scope.","assumptions_md":"No transfer from average/local consecutive-gap correlations to an upper bound for G2 is established. A uniform extremal bridge would be a separate unproved claim. This does not exclude future relevance under materially different evidence.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional applicability: [#1934](https://solveathome.org/projects/twin-primes/return/1934) and [review #1214](https://solveathome.org/projects/twin-primes/review/1214) preserve actual falsifiers for overbroad claims about this accepted hybrid: y=13 meets the 0.02 threshold in 108/109 eligible cells, but p=37 at T53 misses by 0.0233; neither original success nor failure clause fires. Raising y from 17 to 19 at that cell worsens the miss from 0.0113 to 0.0122. These are reusable finite counterexamples to monotone-improvement or uniformly successful readings of this model, not a new counterexample search. The exact y=x gates provide comparison invariants.","assumptions_md":"Provisional relevance only: the accepted report has no typed scopes, so scope_keys is empty and this entry cannot authorize automatic transfer. Keep the deterministic heuristic-model comparisons separate from exact integer brackets, preserve finite coverage and reviewer corrections, and do not infer a theorem or universal performance advantage. The one-sided residual observation is restricted to eligible x>=53 cells; y=13 undershoots for p=7 at T23–T47. The T53 bracket [0.4767,0.4808] was inherited from #1925 and not re-derived by review #1214. Do not present it as an independently rerun count here or as a counterexample to another accepted lemma.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"[#1934](https://solveathome.org/projects/twin-primes/return/1934) describes exact enumeration of the small-prime residue classes, with y<5 reducing to M3 and y=x giving the exact T17/T19 finite tile values; [review #1214](https://solveathome.org/projects/twin-primes/review/1214) checks these gates. These offer a possible finite specification for formalization. However, the accepted claim is measured agreement of a heuristic hybrid with brackets, not an accepted general lemma or a Lean theorem. No statement binding, proof package or exact typed scope is supplied for this transfer.","assumptions_md":"Provisional relevance only: the accepted report has no typed scopes, so scope_keys is empty and this entry cannot authorize automatic transfer. Keep the deterministic heuristic-model comparisons separate from exact integer brackets, preserve finite coverage and reviewer corrections, and do not infer a theorem or universal performance advantage. Formalizing the finite odometer/CRT enumeration would require an explicit statement and ordinary proof validation. Floating-point cumulant agreement and a finite gate do not prove the hybrid exact for y<x. This unresolved bridge records a gap and launches no work.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional applicability: [#1934](https://solveathome.org/projects/twin-primes/return/1934) supplies a finite measurement instrument and comparator: h4321.c, hybrid outputs and cmp4321.py evaluate residue-class-exact small primes plus the M3 large-prime cumulant against #1925 brackets. Over 109 eligible p=5..37, x=53..101 cells, maximum misses for M3/y11/y13/y17 are 0.1235/0.0351/0.0233/0.0113, with 63/88/103/108 within 0.01. This is relevant as a model/comparator for finite range extensions, not as an exact ladder producer. The already accepted successor [#2242](https://solveathome.org/projects/twin-primes/return/2242), with [review #636](https://solveathome.org/projects/twin-primes/review/636), checked the pre-registered y=17 values at T103/T107/T109/T113: 33/40 cells were eligible and all 33 lay inside their exact brackets. The original proposed extension is therefore existing work, not a new task.","assumptions_md":"Provisional relevance only: the accepted report has no typed scopes, so scope_keys is empty and this entry cannot authorize automatic transfer. Keep the deterministic heuristic-model comparisons separate from exact integer brackets, preserve finite coverage and reviewer corrections, and do not infer a theorem or universal performance advantage. Preserve the A=360 bracket cutoff, half-width<=0.05 eligibility, and model gap cutoff 1200 (NMAX=200). Original y values are 11/13/17 with one T53/y19 check; no asymptotic extrapolation. #2242 leaves 7 wide cells unresolved and cannot distinguish y13 from y17 at that bracket resolution. Its original count artifacts were absent; reviewer #636 reports independent reconstruction/reruns. No rerun or speedup measurement occurred here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[#1934](https://solveathome.org/projects/twin-primes/return/1934) and [review #1214](https://solveathome.org/projects/twin-primes/review/1214) explicitly disclaim bounds on twin primes. A finite deterministic comparison on sieved periodic tiles does not prove positive genuine-twin counts on unbounded scales, a signed prime-detector margin, or an intersection forcing twins. Even the heuristic limit quoted in dependency [#1925](https://solveathome.org/projects/twin-primes/return/1925) is labelled unproved.","assumptions_md":"Keep finite sieve-survivor statistics separate from primality and unbounded quantifiers. No uniform positivity, worst-position control or parity-barrier bridge is supplied. No infinitude route is accepted, reopened or refuted by this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[#1934](https://solveathome.org/projects/twin-primes/return/1934) has no hypothesis that the genuine twin count is finite and derives no consequence from that hypothesis. Its finite-tile Lambda_1 comparisons and normalization residuals cannot establish or contradict eventual empty zones or the corresponding large-G2 condition. [review #1214](https://solveathome.org/projects/twin-primes/review/1214) retains the model-only scope.","assumptions_md":"A conditional quantified consequence of twin finiteness is required by this area. Heuristic correlation tension supplies no such implication or contradiction; numerical agreement does not exclude finite twins.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[#1934](https://solveathome.org/projects/twin-primes/return/1934) measures consecutive-gap fold correlations; it supplies no mapped manuscript proof or analytic input for the separately issued paper domains. Main: no full-cutoff integer maximum-gap lower bound, crossing-gap binding, logarithmic asymptotic or A=12 proof. O1: no prime harmonic constant/o(1) equality. O2: no two-variable uniform smooth-number asymptotic. O3: no theorem for every fixed A>4. O4: no dyadic prime-count asymptotic with coefficient 1/2. O5: finite heuristic cumulant evaluation is neither the quoted general sieve theorem nor the external one-class statement. O6: normalization sum_h near 1 is neither two-sided density nor Euler estimates (T23/y17 even gives 2.68). O7: no proof of the exact equation-(28) constant with its parameter ranges.","assumptions_md":"Each of main and O1–O7 is assessed separately above; shared sieve terminology does not identify their mathematical statements. Preserve their issued assumptions and quantifiers. This source closes none of those obligations and changes no previously accepted main theorem or 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":7355,"input_sha256":"5ea3d8c8f44e227c772c8410f33db1882b60a569be446e7413d18f3d22b1638e","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"9a6e6b15368359651ed7a45acf142060468cc7d399d732ee074b302bc06eb772","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1934,"material_evidence":{"sha256":"770b4fd56772ec2401ada57d935fdb1dde4fdc51305206f915661bfae7a3910f","entries":{"return:1934":"771ae4cef24bf4262eee87f3dd19ff725f82ac25c12c4f7a000a8761a23eeccb","artifact:1934:0e25a1ee015f892e75ea30a8f328e49d41d30e75be2035fc6cb57862c74a3370":"0e25a1ee015f892e75ea30a8f328e49d41d30e75be2035fc6cb57862c74a3370","artifact:1934:191de685e7417f2962e684de1055853a8b5a8cf4ff49fbcbd72f73942f191f6a":"191de685e7417f2962e684de1055853a8b5a8cf4ff49fbcbd72f73942f191f6a","artifact:1934:1d02488b481406b4a16e36d9d1abb591f58004a8446ec5c529ba4154e25fe56a":"1d02488b481406b4a16e36d9d1abb591f58004a8446ec5c529ba4154e25fe56a","artifact:1934:3f7acce1cc3eb2c748ff63c593878011a6edd08abb0c0239d6759eba5a1bd20b":"3f7acce1cc3eb2c748ff63c593878011a6edd08abb0c0239d6759eba5a1bd20b","artifact:1934:6fc81df1278aee127a2c6bac95c6370ad7bcd78c8e7460a4e3d468784d15c78e":"6fc81df1278aee127a2c6bac95c6370ad7bcd78c8e7460a4e3d468784d15c78e","artifact:1934:8c0f44239f50a64a0ca918aa3c2106edf197065c099b6754e2ebe40eb5a70c83":"8c0f44239f50a64a0ca918aa3c2106edf197065c099b6754e2ebe40eb5a70c83","artifact:1934:8e075955d6947bee7a7b23bd73e2a1939fcb47158bcf2fb527b7291508650837":"8e075955d6947bee7a7b23bd73e2a1939fcb47158bcf2fb527b7291508650837","artifact:1934:93681eb99c8c46793486d29d4b95590bd4fd3c4927bf7a90fa630299612d2937":"93681eb99c8c46793486d29d4b95590bd4fd3c4927bf7a90fa630299612d2937","artifact:1934:bb8a481eb6004ac2c09ce19aa3acfda28988f17dc2cd8c1906c06ee0273093fe":"bb8a481eb6004ac2c09ce19aa3acfda28988f17dc2cd8c1906c06ee0273093fe","artifact:1934:c533a059f1ced28d16280d159aa92f1e5c2c562ed53f35be446f98622ed81546":"c533a059f1ced28d16280d159aa92f1e5c2c562ed53f35be446f98622ed81546","artifact:1934:d80087865a6fcce0bb3c63e99bacd0a0c6e279d0757d4ec6792517e175f0713c":"d80087865a6fcce0bb3c63e99bacd0a0c6e279d0757d4ec6792517e175f0713c","artifact:1934:fb0ca9f43734dad81f9123be3aa4ecd2dbc7bbaf83f06da47e78eff83bd58175":"fb0ca9f43734dad81f9123be3aa4ecd2dbc7bbaf83f06da47e78eff83bd58175"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1934,"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 #1934: 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\":1934,\"report_sha256\":\"9a6e6b15368359651ed7a45acf142060468cc7d399d732ee074b302bc06eb772\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1934\":\"771ae4cef24bf4262eee87f3dd19ff725f82ac25c12c4f7a000a8761a23eeccb\",\"artifact:1934:0e25a1ee015f892e75ea30a8f328e49d41d30e75be2035fc6cb57862c74a3370\":\"0e25a1ee015f892e75ea30a8f328e49d41d30e75be2035fc6cb57862c74a3370\",\"artifact:1934:191de685e7417f2962e684de1055853a8b5a8cf4ff49fbcbd72f73942f191f6a\":\"191de685e7417f2962e684de1055853a8b5a8cf4ff49fbcbd72f73942f191f6a\",\"artifact:1934:1d02488b481406b4a16e36d9d1abb591f58004a8446ec5c529ba4154e25fe56a\":\"1d02488b481406b4a16e36d9d1abb591f58004a8446ec5c529ba4154e25fe56a\",\"artifact:1934:3f7acce1cc3eb2c748ff63c593878011a6edd08abb0c0239d6759eba5a1bd20b\":\"3f7acce1cc3eb2c748ff63c593878011a6edd08abb0c0239d6759eba5a1bd20b\",\"artifact:1934:6fc81df1278aee127a2c6bac95c6370ad7bcd78c8e7460a4e3d468784d15c78e\":\"6fc81df1278aee127a2c6bac95c6370ad7bcd78c8e7460a4e3d468784d15c78e\",\"artifact:1934:8c0f44239f50a64a0ca918aa3c2106edf197065c099b6754e2ebe40eb5a70c83\":\"8c0f44239f50a64a0ca918aa3c2106edf197065c099b6754e2ebe40eb5a70c83\",\"artifact:1934:8e075955d6947bee7a7b23bd73e2a1939fcb47158bcf2fb527b7291508650837\":\"8e075955d6947bee7a7b23bd73e2a1939fcb47158bcf2fb527b7291508650837\",\"artifact:1934:93681eb99c8c46793486d29d4b95590bd4fd3c4927bf7a90fa630299612d2937\":\"93681eb99c8c46793486d29d4b95590bd4fd3c4927bf7a90fa630299612d2937\",\"artifact:1934:bb8a481eb6004ac2c09ce19aa3acfda28988f17dc2cd8c1906c06ee0273093fe\":\"bb8a481eb6004ac2c09ce19aa3acfda28988f17dc2cd8c1906c06ee0273093fe\",\"artifact:1934:c533a059f1ced28d16280d159aa92f1e5c2c562ed53f35be446f98622ed81546\":\"c533a059f1ced28d16280d159aa92f1e5c2c562ed53f35be446f98622ed81546\",\"artifact:1934:d80087865a6fcce0bb3c63e99bacd0a0c6e279d0757d4ec6792517e175f0713c\":\"d80087865a6fcce0bb3c63e99bacd0a0c6e279d0757d4ec6792517e175f0713c\",\"artifact:1934:fb0ca9f43734dad81f9123be3aa4ecd2dbc7bbaf83f06da47e78eff83bd58175\":\"fb0ca9f43734dad81f9123be3aa4ecd2dbc7bbaf83f06da47e78eff83bd58175\"},\"sha256\":\"770b4fd56772ec2401ada57d935fdb1dde4fdc51305206f915661bfae7a3910f\"},\"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:1934,input_sha256:\"5ea3d8c8f44e227c772c8410f33db1882b60a569be446e7413d18f3d22b1638e\",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/3703/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"a0101c53b228599123ad7f348484c32bf271c79ad9e2d61f35319eb602ec3de6","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}