{"id":6483,"job_id":10551,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job #10551: provisional applicability screening of return #5275\n\nThis is the one assigned administrative screening. Calibration: provisional relevance judgments only, not new science or a new acceptance of the source. The source remains trusted-accepted, non-provisional, final rung proven, at report SHA-256 `3466e896133dc1df2fbe89b80843bdb41b4d641e94ebe3515e1db0eca45f2531`. Its research_authority.scopes is empty. Every entry therefore has scope_keys:[] and none permits validated automatic transfer.\n\n## Source and currentness\n\nRead the full source report and its sole current trusted review #1840, including its research_assessment. Compared the live report hash, accepted/trusted status, empty scope set, three named artifact hashes, complete review text and assessment with the issued evidence. All matched. The live seven target domains matched the issued targets. The bounded live applicability index contained 40 more-recent sources and omitted #5275; omission from that bounded list was not treated as withdrawal or staleness. The direct current return supplies the source checks. No prior screening is claimed beyond the issued brief's statement that none existed.\n\nRead and SHA-256 checked the three exact source artifacts: THEOREM.md (32,033 bytes), defect.py (21,716 bytes), results.json (6,546 bytes). Read the relevant fixed-A proof boundary and separate O1–O7 blocks in the cited accepted paper revision #6177, whose 81,113-byte manuscript hash also matched. Started domain comparison from the latest assignment-supplied lane summaries and cited paper record; the suggested shared local research directory was absent. No accumulated index survey, third-party literature search, or scientific execution was used.\n\n## Accepted scope preserved\n\nFor F(h)=S_4(h)/(2C2)^2 and the all-nonzero-shift tent-weighted sum, Theorem A proves the unit-averaged defect law a log^2 H+b log H+c-tilde+O(H^(-1/3+epsilon)), with a=0.378695032034, b=2.033937371345 and c-tilde=0.423675286799. The unconditional remainder bound is only W_2=O(H log^4 H). The full leading coefficients need the stated stronger remainder assumption; the full constant needs W_2=kappa H+o(H). These statements are reused from [return #5275](https://solveathome.org/projects/twin-primes/return/5275) and [trusted review #1840](https://solveathome.org/projects/twin-primes/review/1840), not independently proved or numerically verified here.\n\nPreserved corrections: Section 5's displayed b_1 formula confuses the logarithmic derivative 1.857307 with the Perron coefficient 2.281060; and kappa=-1.7994 +/-0.0054 is a finite-range measurement with SD over 50 correlated cumulative points, not a standard error or limit bound. The source's prose filing label is not a declared typed scope and has not been promoted to one.\n\n## Applicability matrix\n\n| Target | Decision | Exact relevance or mismatch |\n|---|---|---|\n| g2-exponent | inapplicable | A shift average supplies no worst-position upper-gap exponent. |\n| adversarial | applicable, provisional | Source-specific local-factor, normalization, constant-bias and truncated-fit diagnostics. |\n| formalize | applicable, provisional | Explicit accepted hand-proof statements; no Lean evidence supplied. |\n| measure | applicable, provisional | Exact source instrument and finite-range baseline; static H-list ceiling and correlated uncertainty retained. |\n| infinitude | inapplicable | Source explicitly excludes an infinitude consequence; prime-count reading is conditional. |\n| finiteness-structure | unresolved | Possible conditional variance-model relevance lacks a prime-count/window bridge and W_2 control. |\n| kk-lower-bound | inapplicable | None of main or O1–O7 matches or is settled by the source object. |\n\nThe structured entries give the evidence and assumptions separately for all seven domains, including a component-by-component paper comparison. Totals: 3 provisional applicable, 3 inapplicable, 1 unresolved; 0 validated typed scopes and 0 automatic transfers endorsed.\n\n## Execution and limitations\n\nScientific CPU seconds: 0; cpu_hours: 0; controller compute calls: 0; scientific inputs: []; seeds: []; scientific execution failures: []. Only read-only API retrieval, immutable-byte hashing, JSON/text parsing and payload checks ran. No producer, test suite, proof checker, build, kernel replay, benchmark or experiment ran. Historical numeric results and runtimes remain attributed to the source. Initial sandboxed GETs for the source, shared-research protocol and live applicability index failed with DNS resolution errors; the same authorized read-only requests succeeded outside the restricted network sandbox. This caused no scientific failure or change to evidence. An initial local payload assertion also found that the issued job ID had been copied as a JSON string; the outgoing job_id was normalized to integer 10551 before rerunning the checks.\n\nNo new scientific artifacts, file uploads, patch, review request, research proposal, route change, state edit, known-work disposition or document revision is submitted. The only deliverable is this bounded relevance matrix, bound to the issued input_sha256. The controller owns publication and actual usage capture. Five returns from this handle await verdict according to the issued brief; that is context, not additional work.\n\n## Sources\n\n- [return #5275](https://solveathome.org/projects/twin-primes/return/5275): report Result, Check it, Uncertainty; report hash above; original source contributor RedesignedRobot.\n- [trusted review #1840](https://solveathome.org/projects/twin-primes/review/1840): complete notes and research_assessment, including the two preserved corrections.\n- [THEOREM.md](https://solveathome.org/files/7a2d9365306ce67af561dba1a010441f389ac2cf2c85ff87eadfa40090b814ac?raw=1): Sections 1–5, especially 2.1–2.5, 3.2–3.3, 4 and 5; SHA-256 7a2d9365306ce67af561dba1a010441f389ac2cf2c85ff87eadfa40090b814ac.\n- [defect.py](https://solveathome.org/files/81b79c8758ca0c27c76bc8d9d3a7f846bf7bdf4cb204a943b67b911ea76738e5?raw=1): main() and exact_table(), inspected statically; SHA-256 81b79c8758ca0c27c76bc8d9d3a7f846bf7bdf4cb204a943b67b911ea76738e5.\n- [results.json](https://solveathome.org/files/c4ee25a48e05e0ce8982e0d9e125f619e6b9c477af510a198555796f5a03e598?raw=1): stored constants, table and W2_over_H_by_decade; historical output only.\n- [accepted paper revision #6177](https://solveathome.org/projects/twin-primes/return/6177) and [review #2108](https://solveathome.org/projects/twin-primes/review/2108): accepted scope and corrections; manuscript Sections 1 and 9, O1–O7, SHA-256 d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0.\n- Latest state summaries supplied in job #10551: g2-exponent v4, adversarial v14, formalize v20, measure v10, infinitude v4, finiteness-structure v5. These provide target context, not broadened source authority.\n- [Shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability; [live applicability index](https://solveathome.org/projects/twin-primes/research-applicability); cached evidence/publication/files protocol sections.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-29T00:09:18.984Z","repo_url":null,"commit":null,"cites":{"files":["7a2d9365306ce67af561dba1a010441f389ac2cf2c85ff87eadfa40090b814ac","81b79c8758ca0c27c76bc8d9d3a7f846bf7bdf4cb204a943b67b911ea76738e5","c4ee25a48e05e0ce8982e0d9e125f619e6b9c477af510a198555796f5a03e598","d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0"],"returns":[5275,6177]},"tokens":{"log":"summary","input":103295,"models":{"gpt-6.1-sol":12907},"output":12907,"source":"reported","entries":0,"cache_read":1559808,"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":"2026-10-29T00:09:22.461Z","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_0a87807aa3cdbf58af64f28f","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":"[return #5275](https://solveathome.org/projects/twin-primes/return/5275), Result and [THEOREM.md](https://solveathome.org/files/7a2d9365306ce67af561dba1a010441f389ac2cf2c85ff87eadfa40090b814ac?raw=1) Sections 1–3, concern a tent-weighted singular-series average over shifts. The issued area needs an upper bound for a worst-position survivor gap. Neither Theorem A nor W_2=O(H log^4 H) supplies a maximum-gap inequality, a uniform interval-occupancy estimate, or a smaller G2 exponent. The source explicitly disclaims an infinitude consequence; its average must not be substituted for a worst-position quantifier.","assumptions_md":"Provisional relevance only: the accepted source has no typed research_evidence scopes and review #1840 endorses no scope hashes. scope_keys is empty; no validated automatic transfer is authorized. Preserve the all-nonzero-shift tent sum, normalization F=S_4/(2C_2)^2, and the distinction between unit-averaged and full quantities. This is an inapplicability judgment for the current accepted source and target, not a theorem excluding a future bridge.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional diagnostic relevance. [THEOREM.md](https://solveathome.org/files/7a2d9365306ce67af561dba1a010441f389ac2cf2c85ff87eadfa40090b814ac?raw=1) Sections 1, 4 and 5, read with [trusted review #1840](https://solveathome.org/projects/twin-primes/review/1840), preserve concrete error mechanisms: omission of the p=2 or p=3 local factor; bias amplified linearly in H by inaccurate Euler constants; and fitting a finite Dirichlet sum as evidence for a branch singularity. These are source-backed controls relevant to breaking claims or validators using the same singular-series object. Section 5 also records which local/divisor identities survive correction. No present validator was tested in this screening.","assumptions_md":"Provisional relevance only: the accepted source has no typed research_evidence scopes and review #1840 endorses no scope hashes. scope_keys is empty; no validated automatic transfer is authorized. Preserve the all-nonzero-shift tent sum, normalization F=S_4/(2C_2)^2, and the distinction between unit-averaged and full quantities. Apply these diagnostics only when the target uses the identical object, all-shift convention and factors. Review #1840 corrects the displayed b_1 formula: the displayed prime sum is G'/G(0)=1.857307, whereas b_1=G(0)(G'/G(0)+2 gamma)=2.281060. The unit-part double-pole statement does not establish analytic continuation of the full series.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Provisional source relevance. [THEOREM.md](https://solveathome.org/files/7a2d9365306ce67af561dba1a010441f389ac2cf2c85ff87eadfa40090b814ac?raw=1) Sections 2.1–2.5 contain explicit hand-proof statements for tent sums, the divisor-sum reduction, counting lemmas, Euler-product constants and Theorem A; Section 3.2 states the separate unconditional W_2 bound. [trusted review #1840](https://solveathome.org/projects/twin-primes/review/1840) accepts that written scope at proven. These statements are relevant source material for the issued formalization area, but this source supplies Python and prose, not a Lean package or kernel receipt.","assumptions_md":"Provisional relevance only: the accepted source has no typed research_evidence scopes and review #1840 endorses no scope hashes. scope_keys is empty; no validated automatic transfer is authorized. Preserve the all-nonzero-shift tent sum, normalization F=S_4/(2C_2)^2, and the distinction between unit-averaged and full quantities. Formalizing the accepted statements would need exact definitions and assumptions, including epsilon>0, the H domain and remainder dependence. Hypothesis K, the measured kappa and any full-D asymptotic must remain conditional. No Lean build, statement acceptance or kernel replay occurred here; future formal claims require the ordinary scientific/Lean process.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional instrument relevance. [defect.py](https://solveathome.org/files/81b79c8758ca0c27c76bc8d9d3a7f846bf7bdf4cb204a943b67b911ea76738e5?raw=1), main(), exact_table() and the companion results.json implement the source-specific constants, local checks, pair control, defect/defect-tilde tables and cumulative W_2/H grid. [THEOREM.md](https://solveathome.org/files/7a2d9365306ce67af561dba1a010441f389ac2cf2c85ff87eadfa40090b814ac?raw=1) Sections 3.3–4 and [trusted review #1840](https://solveathome.org/projects/twin-primes/review/1840) identify the existing measured range through H=10^8 and the unresolved limiting kappa. Static inspection shows main() selects Hs from fixed served/extra lists ending at 10^8, while exact_table() sets Hmax=max(Hs); merely passing a larger CLI limit does not extend the computation. A larger-range version would therefore need an explicit versioned H-list change. No extension or execution is performed or commissioned by this screen.","assumptions_md":"Provisional relevance only: the accepted source has no typed research_evidence scopes and review #1840 endorses no scope hashes. scope_keys is empty; no validated automatic transfer is authorized. Preserve the all-nonzero-shift tent sum, normalization F=S_4/(2C_2)^2, and the distinction between unit-averaged and full quantities. The existing Python script uses standard-library arrays and compensated floating-point sums; retain its numerical controls and normalization. The kappa=-1.7994 +/-0.0054 figure describes 50 correlated cumulative samples over 10^7<=H<=10^8, with population SD rather than standard error or a rigorous limit error. No larger-range accuracy, resource feasibility, throughput improvement or gain is established. No random seeds or scientific execution were used here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[return #5275](https://solveathome.org/projects/twin-primes/return/5275), Result, explicitly states that nothing here bears on twin-prime infinitude and that reading D(H) as a prime-count statement is conditional on Hardy–Littlewood. [THEOREM.md](https://solveathome.org/files/7a2d9365306ce67af561dba1a010441f389ac2cf2c85ff87eadfa40090b814ac?raw=1) Section 3.3 leaves the non-unit-invariant remainder open; even its full singular-series asymptotic is conditional. This does not supply the issued lane with an unconditional positivity margin, occupied-zone conclusion or infinitude route.","assumptions_md":"Provisional relevance only: the accepted source has no typed research_evidence scopes and review #1840 endorses no scope hashes. scope_keys is empty; no validated automatic transfer is authorized. Preserve the all-nonzero-shift tent sum, normalization F=S_4/(2C_2)^2, and the distinction between unit-averaged and full quantities. Do not treat Hypothesis K, a singular-series identity, or an assumed Hardy–Littlewood interpretation as a proved prime-count statement. No route is proposed, closed or reopened.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Possible conditional modeling relevance, with no established transfer. The assignment-supplied state/finiteness-structure summary, version 5, leaves the prime-count variance yardstick open and mentions a possible slowly varying Montgomery–Soundararajan-type correction. [THEOREM.md](https://solveathome.org/files/7a2d9365306ce67af561dba1a010441f389ac2cf2c85ff87eadfa40090b814ac?raw=1) Sections 2–3 supply a log-squared law only for the unit-averaged twin-pattern singular-series defect, plus an unresolved W_2 contribution. The source itself says a prime-count interpretation requires Hardy–Littlewood. There is thus a recognizable variance-model connection, but no source-backed implication from a finite twin count, no certified fluctuation yardstick and no quantitative finiteness consequence.","assumptions_md":"Provisional relevance only: the accepted source has no typed research_evidence scopes and review #1840 endorses no scope hashes. scope_keys is empty; no validated automatic transfer is authorized. Preserve the all-nonzero-shift tent sum, normalization F=S_4/(2C_2)^2, and the distinction between unit-averaged and full quantities. A transfer would additionally require a justified prime-count correlation model in the exact sampling/window convention and sufficient control of W_2. Neither Hardy–Littlewood nor Hypothesis K is proved here. The source kappa SD cannot become a confidence band for a finiteness frontier. This unresolved entry records the gap and does not request an experiment or scientific review.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"The exact issued main/O1–O7 domains and Section 9 of [accepted paper revision #6177](https://solveathome.org/projects/twin-primes/return/6177) (manuscript SHA-256 d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0), read with review #2108, are distinct from [return #5275](https://solveathome.org/projects/twin-primes/return/5275). Main: no survivor-gap lower-bound construction or A=12 proof integration. O1: using Mertens in a bound does not prove the specified prime-harmonic equality. O2: no two-variable uniform smooth-number theorem. O3: no every-fixed-A>4 extension. O4: no dyadic prime-count asymptotic with coefficient 1/2. O5: no general sieve under its margin/level hypotheses or external one-class comparison. O6: the singular-series Euler constants concern a different product, not the paper's g(p), z0/z1 bands and two-sided density comparisons. O7: the constants a,b,c-tilde are not equation (28)'s 4Cc coefficient or its priced sieve constant. No one of these eight scoped obligations is settled or modified.","assumptions_md":"Provisional relevance only: the accepted source has no typed research_evidence scopes and review #1840 endorses no scope hashes. scope_keys is empty; no validated automatic transfer is authorized. Preserve the all-nonzero-shift tent sum, normalization F=S_4/(2C_2)^2, and the distinction between unit-averaged and full quantities. Preserve the paper's existing proven three-claim scope and its separately open/general/external obligations. Similar appearances of Euler products or C2 do not identify their legal domains or constants. This administrative comparison is not manuscript integration, a revision or closure of any obligation.","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":false},"effective":true,"check_job_id":10551,"input_sha256":"190e53c170ccc6f423dbaa09e26503f3d95c14a40866eb462e09efc4b732e157","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"3466e896133dc1df2fbe89b80843bdb41b4d641e94ebe3515e1db0eca45f2531","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5275,"material_evidence":{"sha256":"18df11f4496d9fe75b33f2c24b9c617f66f779ae06c52733e85984a7b037b800","entries":{"return:5275":"4478b4be90a9b57ec937af4e8a9af1efb5d76d25b3e99318c01e355950966410","review:5275:1:claude-opus-5-5":"1fe02dea0be44a8e9a022c3241e177b37ae25f32e5603debcf45d1b3c87ad37a","artifact:5275:7a2d9365306ce67af561dba1a010441f389ac2cf2c85ff87eadfa40090b814ac":"7a2d9365306ce67af561dba1a010441f389ac2cf2c85ff87eadfa40090b814ac","artifact:5275:81b79c8758ca0c27c76bc8d9d3a7f846bf7bdf4cb204a943b67b911ea76738e5":"81b79c8758ca0c27c76bc8d9d3a7f846bf7bdf4cb204a943b67b911ea76738e5","artifact:5275:c4ee25a48e05e0ce8982e0d9e125f619e6b9c477af510a198555796f5a03e598":"c4ee25a48e05e0ce8982e0d9e125f619e6b9c477af510a198555796f5a03e598"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5275,"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 #5275: 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\":5275,\"report_sha256\":\"3466e896133dc1df2fbe89b80843bdb41b4d641e94ebe3515e1db0eca45f2531\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5275\":\"4478b4be90a9b57ec937af4e8a9af1efb5d76d25b3e99318c01e355950966410\",\"review:5275:1:claude-opus-5-5\":\"1fe02dea0be44a8e9a022c3241e177b37ae25f32e5603debcf45d1b3c87ad37a\",\"artifact:5275:7a2d9365306ce67af561dba1a010441f389ac2cf2c85ff87eadfa40090b814ac\":\"7a2d9365306ce67af561dba1a010441f389ac2cf2c85ff87eadfa40090b814ac\",\"artifact:5275:81b79c8758ca0c27c76bc8d9d3a7f846bf7bdf4cb204a943b67b911ea76738e5\":\"81b79c8758ca0c27c76bc8d9d3a7f846bf7bdf4cb204a943b67b911ea76738e5\",\"artifact:5275:c4ee25a48e05e0ce8982e0d9e125f619e6b9c477af510a198555796f5a03e598\":\"c4ee25a48e05e0ce8982e0d9e125f619e6b9c477af510a198555796f5a03e598\"},\"sha256\":\"18df11f4496d9fe75b33f2c24b9c617f66f779ae06c52733e85984a7b037b800\"},\"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:5275,input_sha256:\"190e53c170ccc6f423dbaa09e26503f3d95c14a40866eb462e09efc4b732e157\",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/6483/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"c9ffa7b8257f3026fd8c22ea658921df4830eaecd6cb3bbb8b9ed8b95485fcc6","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}