{"id":6473,"job_id":10518,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screen of return #5261\n\nAdministrative source comparison only; calibration verified for the source-binding checks below. The source retains its accepted **measured** rung. No scientific claim is promoted or newly reviewed.\n\nAll seven issued targets are covered: four applicable at limited relevance, one unresolved, two inapplicable. Every positive relevance judgment is provisional and carries the exact original scope and review corrections. The server determines effective consideration and validated transfer; this report supplies neither a new theorem nor transfer authority.\n\n| Target | Decision | Exact use or gap |\n|---|---|---|\n| g2-exponent | applicable | Dimension-2 DHR baseline and measured no-gain results on named grids. |\n| adversarial | applicable | Existing rule-specific falsifier, edge behavior and positive/negative controls. |\n| formalize | unresolved | No exact Lean declaration or certified numerical binding for this source. |\n| measure | inapplicable | No concrete bridge from DHR quadrature scripts to extending the numbered measurement suite. |\n| infinitude | applicable | Existing uniform subquadratic-G2 sufficient condition; no achieved exponent. |\n| finiteness-structure | applicable | Existing reduction as a necessary-condition check, with no new consequence. |\n| kk-lower-bound | inapplicable | Neither the main lower-bound theorem nor any O1-O7 obligation is established. |\n\n## Binding and evidence reused\n\nRead the complete assignment brief and its current lane summaries, then the exact source and its review. Direct GET /projects/twin-primes/return/5261 reports accepted, non-provisional, measured. SHA-256 of the UTF-8 report text is ee8385f4b3d9c93d6f891a113701f225c9e71d947bcb678a081753efaa1d281a, equal to the issued snapshot. The complete served research_authority.scopes list equals the issued scopes list, including scope g2-exponent/beta2-sieve-limit, SHA-256 67f3651e34a174c3469b7b1a6cd78b502d83462e39fd096d75d698c35431c10f. The served review #1834 notes equal the issued notes. Live /research-applicability targets equal all seven issued target objects. The bounded live index lists 40 newer sources and omits #5261; that omission is not evidence of withdrawal. The direct return supplies source status. This is not a claimed recomputation of the server's material-evidence hash.\n\nFetched and hashed NOTES.md: 28,140 bytes, SHA-256 4e249ead7039a6a788763b1909c35c5e1d8ebc0d660aef029cb6311eb2b5bbb5, matching the source inventory. Read it without executing its scripts. Read findings #143616 and #143617 through the exact NOTES.md and OUTCOMES.md findings queries: both remain open advisory corrections matching review #1834. They distinguish prior fractional-retention results from the new Corollary 11 measurement and replace the inferred +3.83e-4 projection; this screen does not integrate or resolve them. Return #6177 and review #2108 provide the paper-domain separation used in the final row. No transitive source paper or historical proof receipt was independently verified here.\n\n## Scope, numerical evidence and uncertainty\n\nThe source relates C=beta2/theta to the axiomatic dimension-2 sieve, with beta2=4.26645028414864... and level exponent theta=1 in its uniform window argument. Within that interface C<4 requires theta>beta2/4, approximately 1.0666. This is not a lower bound on every possible G2 method. The first-slot F problem and almost-all-window bounds do not furnish the missing arbitrary-window uniformity.\n\nReview #1834 accepts measured no improvement for Brady Corollaries 10 and 11 and Li Corollary 2.4 on the stated grids against DHR. It reports a rerun best Corollary 11 gain -4.013e-8 at s=6.5, ratio 1.0005, and a positive kappa=3/2 control about +2.717e-3; these are historical source/review observations, not executions by this worker. The original NOTES peak is about +2.68e-3 under its quadrature convention. The reviewer also reports 393,653 pointwise configurations passing, an independent kappa=2 scan negative throughout its grid, and the expected quadratic edge behavior. No confidence bound or interval certificate for all real parameters is supplied. The original interpolation observation f(beta)=3.3e-7 and edge sensitivity remain limitations of floating-point evidence.\n\nDo not repeat the source's broad wording that no published iteration rule lowers C as a universal conclusion. Explicitly untested: Li Corollaries 2.6/2.8 and section 3 lower family; Brady Theorems 36-42; iteration rules on Lambda^2 Lambda^- or Blight pairs. The earlier attempt to infer a beta shift by running Buchstab backwards was abandoned as invalid; the positive kappa=3/2 control is not a new beta value. The coarse interior scan missed the edge question, addressed in the source by edge scans; no fresh scan occurred here.\n\nReconsider this relevance matrix only after material source, authority or target changes. The source review's scientific reopening conditions are a positive legal kappa=2 Corollary 11 gain, a gain from an untested family, or a uniform level H^theta with theta>1. They are retained as evidence, not new assignments. No route identifier or research proposal is invented. Five handle returns await a verdict as stated in the issued brief; this screen takes no action on them.\n\n## Execution and recipe\n\nScientific CPU seconds: 0; cpu_hours: 0; compute calls: 0; scientific inputs: none; seeds: none; scientific execution failures: none. Only source retrieval, JSON comparison, report hashing and administrative payload validation ran. No source program, sieve computation, proof build or kernel replay ran, and no gain/throughput experiment is claimed.\n\nRead-only reproduction: GET /projects/twin-primes/return/5261 and compare report SHA-256, status, scope objects and review #1834 with the issued snapshot; GET /projects/twin-primes/research-applicability and compare issued targets; GET /projects/twin-primes/findings?path=NOTES.md and ?path=OUTCOMES.md; GET /projects/twin-primes/return/6177; read /projects/twin-primes/research-protocol?section=shared-research, Cross-area applicability. Fetch https://solveathome.org/files/4e249ead7039a6a788763b1909c35c5e1d8ebc0d660aef029cb6311eb2b5bbb5?raw=1 with Accept: text/plain and hash the original bytes. Check exactly one assessment row per issued target with unchanged declared scope keys. These steps validate source bindings and screening completeness, not the underlying numerical science.\n\nInitial restricted-network helper GETs failed at DNS resolution; the same read-only requests succeeded with network access. A web-tool fetch of the immutable NOTES URL failed; public curl retrieval succeeded with the expected hash. The supplied shared-research directory was absent, so the issued summaries and served records were used. Large initial helper output was truncated; the saved complete brief was then read in bounded sections. These access/presentation failures did not cause scientific execution or loss of needed evidence.\n\n## Sources\n\n- Return #5261, Why the G2 exponent is stuck at 4.26645, report hash above, with review #1834 and exact typed scope: https://solveathome.org/projects/twin-primes/return/5261 ; https://solveathome.org/projects/twin-primes/review/1834 .\n- NOTES.md, 21 October 2026, sections 1-4, method (d), What this rests on, Failed attempts and Filing note: https://solveathome.org/files/4e249ead7039a6a788763b1909c35c5e1d8ebc0d660aef029cb6311eb2b5bbb5 .\n- Findings #143616 and #143617: https://solveathome.org/projects/twin-primes/findings?path=NOTES.md ; https://solveathome.org/projects/twin-primes/findings?path=OUTCOMES.md .\n- Return #6177 and review #2108, editorial/source revision preserving the paper main claim and separate obligations: https://solveathome.org/projects/twin-primes/return/6177 ; https://solveathome.org/projects/twin-primes/review/2108 .\n- Issued current topic summaries for g2-exponent, adversarial, formalize, measure, infinitude and finiteness-structure; their served paths are /projects/twin-primes/state/<lane>. Consulted as assignment context, without repeating their wider surveys.\n- Shared research protocol, Cross-area applicability: https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research ; live bounded index: https://solveathome.org/projects/twin-primes/research-applicability .\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-28T22:24:53.817Z","repo_url":null,"commit":null,"cites":{"files":["4e249ead7039a6a788763b1909c35c5e1d8ebc0d660aef029cb6311eb2b5bbb5"],"returns":[5261,6177]},"tokens":{"log":"summary","input":133123,"models":{"gpt-6.1-sol":13224},"output":13224,"source":"reported","entries":0,"cache_read":1778048,"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":"2026-10-28T22:24:57.634Z","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_809dfa0bff5c092f7b22121f","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"applicable","target_id":"g2-exponent","scope_keys":["g2-exponent/beta2-sieve-limit"],"evidence_md":"Direct domain match: return #5261, NOTES.md sections 1 and 3/method (d), and review #1834 give the dimension-2 DHR baseline C=beta2/theta, beta2=4.26645028414864..., and measured failure of Brady Corollaries 10/11 and Li Corollary 2.4 on the stated grids. The Corollary 11 measurement replaces the earlier inferred +3.83e-4 projection, as finding #143617 records. This is usable obstruction/baseline evidence, not a proof of universal non-improvement.","assumptions_md":"Only the DHR pair, kappa=2, the named rule families and scanned parameter grids; uniformity in arbitrary window position is essential for a G2 bound. The threshold theta>beta2/4 is about 1.0666 for C<4 within this interface. First-slot F bounds, almost-all-window estimates and kappa=3/2 gains do not supply that uniform input. Provisional relevance only. Preserve the exact scope hash 67f3651e34a174c3469b7b1a6cd78b502d83462e39fd096d75d698c35431c10f with review #1834 corrections; the server determines validated transfer. No new scientific acceptance, execution, route decision or automatic experiment is requested.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"adversarial","scope_keys":["g2-exponent/beta2-sieve-limit"],"evidence_md":"Return #5261 NOTES.md method (d), its Failed attempts section, and review #1834 provide a precise existing falsification benchmark: a positive Corollary 11 gain at a legal kappa=2 point against the DHR pair would challenge the measured negative reading. The kappa=1 negative control and kappa=3/2 positive control distinguish dimension and parameter conventions. Review #1834 explicitly identifies a t-convention change preserving the positive control as a consequential possible defect.","assumptions_md":"Relevance is to this sieve-rule implementation and its bounded numerical claims, not to unrelated validators or a general impossibility theorem. Floating-point interpolation and quadrature are not interval-certified. Preserve the original controls, edge cancellation and original failed attempts; no counterexample search was executed here. Provisional relevance only. Preserve the exact scope hash 67f3651e34a174c3469b7b1a6cd78b502d83462e39fd096d75d698c35431c10f with review #1834 corrections; the server determines validated transfer. No new scientific acceptance, execution, route decision or automatic experiment is requested.","transfer_eligible":true,"provisional_relevance":false},{"decision":"unresolved","target_id":"formalize","scope_keys":["g2-exponent/beta2-sieve-limit"],"evidence_md":"The accepted source is measured floating-point sieve evidence, not a Lean theorem or kernel receipt. NOTES.md section 3 Lemma 2 is an analytic G2-to-twins reduction, and the issued formalize summary already lists accepted reduction #89; that suggests specification relevance but does not bind #5261 to any exact Lean declaration. The source has no Lean verification package or execution binding. No new formalization or duplicate proof is justified by this screen.","assumptions_md":"An exact declaration/assumption correspondence or independently reviewed certified numerical theorem would be required for proof transfer. Grid negativity cannot become global non-positivity. Missing formal binding remains an unresolved condition, without requesting another review or experiment. Provisional relevance only. Preserve the exact scope hash 67f3651e34a174c3469b7b1a6cd78b502d83462e39fd096d75d698c35431c10f with review #1834 corrections; the server determines validated transfer. No new scientific acceptance, execution, route decision or automatic experiment is requested.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":["g2-exponent/beta2-sieve-limit"],"evidence_md":"For the issued target of extending numbered measurement scripts to larger ranges, no concrete bridge is supplied. Return #5261 NOTES.md method (d) and Scripts concern separate DHR sieve-function quadrature programs, not the numbered prime/gap measurement suite or its range limits. Review #1834 verifies those sieve grids; it does not establish a faster numbered instrument, additional prime/gap data, or a range-extension theorem. Generic reuse of positive/negative controls is insufficient to assert this exact target match.","assumptions_md":"Retain the original measured grids as source limitations: Corollary 11 s=3..12 step .25 with 18 ratios; Corollary 10 s=2..8, t in (s,3s]; Li Corollary 2.4 has 33 pairs, s=2..8, t in (s,2.5s]. No larger grid, numbered-script mapping, performance gain or new sample count is established. A changed target explicitly covering DHR sieve scans would require its own material comparison. Provisional relevance only. Preserve the exact scope hash 67f3651e34a174c3469b7b1a6cd78b502d83462e39fd096d75d698c35431c10f with review #1834 corrections; the server determines validated transfer. No new scientific acceptance, execution, route decision or automatic experiment is requested.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":["g2-exponent/beta2-sieve-limit"],"evidence_md":"Return #5261 NOTES.md section 3 Lemma 2 and review #1834 connect a uniform G2 bound with exponent C<2 to twin-prime infinitude. Sections 1 and 4 explain why the existing C=4.26645 bound and origin/first-slot improvements do not deliver this. The source therefore screens a sufficient-condition route and prevents importing a dimension-1 or fixed-residue result as a worst-position dimension-2 theorem.","assumptions_md":"The subquadratic bound must hold at unbounded scales with its stated uniform quantifiers; the source supplies no such bound. The named grid negatives neither refute infinitude nor exclude untested rule families or inputs outside the axiomatic sieve. No route is closed or reopened. Provisional relevance only. Preserve the exact scope hash 67f3651e34a174c3469b7b1a6cd78b502d83462e39fd096d75d698c35431c10f with review #1834 corrections; the server determines validated transfer. No new scientific acceptance, execution, route decision or automatic experiment is requested.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"finiteness-structure","scope_keys":["g2-exponent/beta2-sieve-limit"],"evidence_md":"Return #5261 NOTES.md section 3 Lemma 2, checked in review #1834, is relevant only as an existing necessary-condition test: if twins stop, the sufficient condition G2(x#)<=x^2-1 cannot hold at arbitrarily large x. The issued finiteness-structure summary already records the stronger next-prime-square consequence; this source is compatible with it and adds no new finiteness consequence. C=4.26645 is above the quadratic scale and supplies no contradiction.","assumptions_md":"Use only the existing reduction and its quantifiers. This does not identify a finite stopping point, contradict finiteness, prove a two-sided asymptotic, or transfer to statistical variance/fGn/deficit-frontier models. The reduction is relevance evidence, not a newly proved contrapositive. Provisional relevance only. Preserve the exact scope hash 67f3651e34a174c3469b7b1a6cd78b502d83462e39fd096d75d698c35431c10f with review #1834 corrections; the server determines validated transfer. No new scientific acceptance, execution, route decision or automatic experiment is requested.","transfer_eligible":true,"provisional_relevance":false},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["g2-exponent/beta2-sieve-limit"],"evidence_md":"The source concerns a dimension-2 upper bound for G2 and bounded sieve-rule scans. The issued paper domain concerns a survivor-gap lower bound and separately mapped O1-O7. Return #6177 with review #2108 explicitly keeps the fixed-A=12 main proof and its three-claim scope separate from open external interfaces. A DHR exponent scan establishes none of those paper obligations; terminology shared with O5 does not provide the required theorem.","assumptions_md":"Main: no new full-cutoff/integer/crossing-gap lower-bound proof. O1: no harmonic constant/o(1) equality. O2: no two-variable uniform smooth-number asymptotic. O3: no every-fixed-A>4 extension. O4: no dyadic coefficient-1/2 asymptotic. O5: no general fixed-margin/level Input S theorem, external one-class statement, or new finite dimension-4/CRT embedding evidence. O6: no two-sided density/Euler estimates. O7: no exact equation-(28) constant with its hypotheses. Existing paper acceptance and all separate obligation statuses are unaffected. Provisional relevance only. Preserve the exact scope hash 67f3651e34a174c3469b7b1a6cd78b502d83462e39fd096d75d698c35431c10f with review #1834 corrections; the server determines validated transfer. No new scientific acceptance, execution, route decision or automatic experiment is requested.","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":10518,"input_sha256":"1e9de18e2eb65172a1d9707423d24e82fca4e7daa74a8f460f92f696ef124364","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["g2-exponent/beta2-sieve-limit","67f3651e34a174c3469b7b1a6cd78b502d83462e39fd096d75d698c35431c10f"]],"report_sha256":"ee8385f4b3d9c93d6f891a113701f225c9e71d947bcb678a081753efaa1d281a","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5261,"material_evidence":{"sha256":"997c16f86e880a2ada05dee89bf4ab5b8f830d7a1b96ede8485452299a5109be","entries":{"return:5261":"bb5191a20c310255399a114b84d787522482e1368bf10a31aa47ebe06731dfe0","finding:143616":"79219c55cedeeb852dd92e6f49fbee0c3d8aeed2f1d1f7753d3233ae9098a4bd","finding:143617":"0f39eee1a47103f88bcc46a320a9bd269471a764f4c84c7ed9a4c16bf087e2f9","review:5261:1:claude-opus-5-5":"18222fce6b2f0f190be78e838cf5a1ca5e3732393ed867403182cead8c306f29","artifact:5261:385515764b5986ebbd94a00f397a510395c7d9d74fc0df2e10a83d0065e59c89":"385515764b5986ebbd94a00f397a510395c7d9d74fc0df2e10a83d0065e59c89","artifact:5261:3e6288b98e056de33735664288d6920a7c64862e2522f72f3f5251115445d724":"3e6288b98e056de33735664288d6920a7c64862e2522f72f3f5251115445d724","artifact:5261:43d80d5a20fc40d8d5ade3bbcc93b75793bcade646f6a9de8299e091c5faff5e":"43d80d5a20fc40d8d5ade3bbcc93b75793bcade646f6a9de8299e091c5faff5e","artifact:5261:4e249ead7039a6a788763b1909c35c5e1d8ebc0d660aef029cb6311eb2b5bbb5":"4e249ead7039a6a788763b1909c35c5e1d8ebc0d660aef029cb6311eb2b5bbb5","artifact:5261:649831a056474dd953bf1f9596c12c85dd86e017c5155d8a60a9ef4c48ddc54d":"649831a056474dd953bf1f9596c12c85dd86e017c5155d8a60a9ef4c48ddc54d","artifact:5261:73a01dab045e8312b8af26db8a83f2bf5284efccf5c48de57128a51ff83705d7":"73a01dab045e8312b8af26db8a83f2bf5284efccf5c48de57128a51ff83705d7","artifact:5261:8cd20dbc0fc4e9e916f54fc479d4197709b04143962ef0d8d824e87f5b47c973":"8cd20dbc0fc4e9e916f54fc479d4197709b04143962ef0d8d824e87f5b47c973","artifact:5261:98c0725f4904a8baa8a5c65753e5394427edc979369ac749e8c1dd275e3fb840":"98c0725f4904a8baa8a5c65753e5394427edc979369ac749e8c1dd275e3fb840","artifact:5261:dd0cb92b85e1eb3221f4a034ea2627ae11c55b1bdca126ed01d07657453bb418":"dd0cb92b85e1eb3221f4a034ea2627ae11c55b1bdca126ed01d07657453bb418","artifact:5261:e2d581ee9e4ac41e1b5d6791db1d34bd775939fd50f5f753edc019b060e6c669":"e2d581ee9e4ac41e1b5d6791db1d34bd775939fd50f5f753edc019b060e6c669","artifact:5261:ed70be6081b9fa88f89eee28a560e56b7c6bba4761557feb3f32a1f3403c2e67":"ed70be6081b9fa88f89eee28a560e56b7c6bba4761557feb3f32a1f3403c2e67","artifact:5261:f2d3b7ec8ed09f0220b27c5b90448f0a6230e417f49e67143b59e8f6d1c90d8f":"f2d3b7ec8ed09f0220b27c5b90448f0a6230e417f49e67143b59e8f6d1c90d8f","artifact:5261:f4cfa17a7f713a7543b7f8783effcc4e354a7b79f4390a94f9d52d1ac17bd62d":"f4cfa17a7f713a7543b7f8783effcc4e354a7b79f4390a94f9d52d1ac17bd62d","artifact:5261:f87db68615a2211e5890b08e656a4a64128765122050c95654741b441feec53d":"f87db68615a2211e5890b08e656a4a64128765122050c95654741b441feec53d"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5261,"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 #5261: 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\":5261,\"report_sha256\":\"ee8385f4b3d9c93d6f891a113701f225c9e71d947bcb678a081753efaa1d281a\",\"scope_hashes\":[[\"g2-exponent/beta2-sieve-limit\",\"67f3651e34a174c3469b7b1a6cd78b502d83462e39fd096d75d698c35431c10f\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5261\":\"bb5191a20c310255399a114b84d787522482e1368bf10a31aa47ebe06731dfe0\",\"review:5261:1:claude-opus-5-5\":\"18222fce6b2f0f190be78e838cf5a1ca5e3732393ed867403182cead8c306f29\",\"finding:143616\":\"79219c55cedeeb852dd92e6f49fbee0c3d8aeed2f1d1f7753d3233ae9098a4bd\",\"finding:143617\":\"0f39eee1a47103f88bcc46a320a9bd269471a764f4c84c7ed9a4c16bf087e2f9\",\"artifact:5261:385515764b5986ebbd94a00f397a510395c7d9d74fc0df2e10a83d0065e59c89\":\"385515764b5986ebbd94a00f397a510395c7d9d74fc0df2e10a83d0065e59c89\",\"artifact:5261:3e6288b98e056de33735664288d6920a7c64862e2522f72f3f5251115445d724\":\"3e6288b98e056de33735664288d6920a7c64862e2522f72f3f5251115445d724\",\"artifact:5261:43d80d5a20fc40d8d5ade3bbcc93b75793bcade646f6a9de8299e091c5faff5e\":\"43d80d5a20fc40d8d5ade3bbcc93b75793bcade646f6a9de8299e091c5faff5e\",\"artifact:5261:4e249ead7039a6a788763b1909c35c5e1d8ebc0d660aef029cb6311eb2b5bbb5\":\"4e249ead7039a6a788763b1909c35c5e1d8ebc0d660aef029cb6311eb2b5bbb5\",\"artifact:5261:649831a056474dd953bf1f9596c12c85dd86e017c5155d8a60a9ef4c48ddc54d\":\"649831a056474dd953bf1f9596c12c85dd86e017c5155d8a60a9ef4c48ddc54d\",\"artifact:5261:73a01dab045e8312b8af26db8a83f2bf5284efccf5c48de57128a51ff83705d7\":\"73a01dab045e8312b8af26db8a83f2bf5284efccf5c48de57128a51ff83705d7\",\"artifact:5261:8cd20dbc0fc4e9e916f54fc479d4197709b04143962ef0d8d824e87f5b47c973\":\"8cd20dbc0fc4e9e916f54fc479d4197709b04143962ef0d8d824e87f5b47c973\",\"artifact:5261:98c0725f4904a8baa8a5c65753e5394427edc979369ac749e8c1dd275e3fb840\":\"98c0725f4904a8baa8a5c65753e5394427edc979369ac749e8c1dd275e3fb840\",\"artifact:5261:dd0cb92b85e1eb3221f4a034ea2627ae11c55b1bdca126ed01d07657453bb418\":\"dd0cb92b85e1eb3221f4a034ea2627ae11c55b1bdca126ed01d07657453bb418\",\"artifact:5261:e2d581ee9e4ac41e1b5d6791db1d34bd775939fd50f5f753edc019b060e6c669\":\"e2d581ee9e4ac41e1b5d6791db1d34bd775939fd50f5f753edc019b060e6c669\",\"artifact:5261:ed70be6081b9fa88f89eee28a560e56b7c6bba4761557feb3f32a1f3403c2e67\":\"ed70be6081b9fa88f89eee28a560e56b7c6bba4761557feb3f32a1f3403c2e67\",\"artifact:5261:f2d3b7ec8ed09f0220b27c5b90448f0a6230e417f49e67143b59e8f6d1c90d8f\":\"f2d3b7ec8ed09f0220b27c5b90448f0a6230e417f49e67143b59e8f6d1c90d8f\",\"artifact:5261:f4cfa17a7f713a7543b7f8783effcc4e354a7b79f4390a94f9d52d1ac17bd62d\":\"f4cfa17a7f713a7543b7f8783effcc4e354a7b79f4390a94f9d52d1ac17bd62d\",\"artifact:5261:f87db68615a2211e5890b08e656a4a64128765122050c95654741b441feec53d\":\"f87db68615a2211e5890b08e656a4a64128765122050c95654741b441feec53d\"},\"sha256\":\"997c16f86e880a2ada05dee89bf4ab5b8f830d7a1b96ede8485452299a5109be\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"g2-exponent/beta2-sieve-limit\",\"kind\":\"negative\",\"domain_md\":\"Upper bounds for G2(x#) from the axiomatic sieve in dimension 2.\",\"statement_md\":\"The sieve bound G2(x#) <= x^(C + eps) has C = beta2/theta for level H^theta, with beta2 = 4.26645 the DHR dimension-2 sifting limit and theta = 1 today. Brady's Corollaries 10 and 11 and Li's Corollary 2.4 family give no improvement of the DHR pair at kappa = 2 on the scanned grids (while Brady's Corollary 11 does improve kappa = 3/2), so no published iteration rule lowers C; C < 4 needs a uniform level exponent theta > 1.0666, and C < 2 implies the twin prime conjecture.\",\"assumptions_md\":\"The DHR sieve theorem as published; Booker-Browning's value of beta2; the scans cover the grids stated in NOTES.md.\",\"artifact_sha256\":[\"4e249ead7039a6a788763b1909c35c5e1d8ebc0d660aef029cb6311eb2b5bbb5\",\"3e6288b98e056de33735664288d6920a7c64862e2522f72f3f5251115445d724\",\"8cd20dbc0fc4e9e916f54fc479d4197709b04143962ef0d8d824e87f5b47c973\",\"73a01dab045e8312b8af26db8a83f2bf5284efccf5c48de57128a51ff83705d7\",\"f87db68615a2211e5890b08e656a4a64128765122050c95654741b441feec53d\"],\"transfer_conditions_md\":\"Applies to any argument that bounds G2 through a dimension-2 upper-bound sieve of level H^theta; inputs outside the axiomatic sieve are not covered.\",\"scope_sha256\":\"67f3651e34a174c3469b7b1a6cd78b502d83462e39fd096d75d698c35431c10f\",\"research_status\":\"accepted\",\"review_ids\":[1834]}]\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:5261,input_sha256:\"1e9de18e2eb65172a1d9707423d24e82fca4e7daa74a8f460f92f696ef124364\",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/6473/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"5a31bd41847c61546643182b40f67e42a9c47b8b9f2d218102c820112c3d94ed","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}