{"id":3644,"job_id":7295,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of accepted return #1878 — provisional consideration\n\nAdministrative relevance judgment only; the source retains its accepted **measured** rung. The screening itself is qualitative (**heuristic**), with no new scientific claim or acceptance.\n\n## Exact source and currentness\nRead the complete served return #1878 and current trusted review #1181 once, starting from the issued latest lane summaries, especially finiteness-structure v4 (2026-10-12, through #1693 with #1878 separately listed). The report SHA-256 is 70f6710dbb7e0ca429fa646acdbae8fcec4d9c885d72b4954a2efa28fd4aa2bc, matching both the served hash and locally hashed UTF-8 report bytes. The seven served artifact identifiers and the review's complete notes match the issued evidence; source accepted/non-provisional, not superseded, review needs_reassessment=false. These are metadata/text checks, not fresh file-byte verification or scientific execution. No typed scopes exist, so every entry uses scope_keys=[]. Missing scope authority remains an unresolved validation condition for every positive entry; none authorizes automatic transfer.\n\nThe live bounded research-applicability index returned 33 sources and did not include #1878. Adding source_return_id=1878 returned the same bounded list; this query did not establish source-specific applicability currentness. Current accepted status and report/review/artifact-metadata equality are instead supported by the served return and issued snapshot. No prior screening was included in the brief. Do not infer withdrawal from omission in a bounded index.\n\n## Preserved scientific scope and corrections\nSeed 2079; N_SUB_RHO=120, N_SUB_LEV=40; H_SUB=0.30..0.54 by 0.03; LOW=[1e13,1e15), HIGH=[1e15,4e18), four and seven anchors. Source novelty is two appended synthetic response points and the formerly missing crossings, not the inherited grid. Review #1181 reports gate maximum relative difference 4.740e-11, 13 unique crossings, 20 pairwise comparisons and four true coded criteria. The LOW crossings are rho1=0.379251, r_dn=0.352366, R=0.490250, R_pool(1.0)=0.487747 and R_pool(2.0)=0.490092. Corresponding proxy errors are 0.077932, 0.046467, 0.151540, 0.103171 and 0.084431. The tightest LOW comparison margin is 0.0311362553.\n\nThe conditional aggregate H=0.3952369916, averaged proxy=0.05958993508, epsilon(1e19)=1.33263291098e-8 and transformed proxy half-band=3.01295499605e-9 are existing instrument outputs, not independently reproduced here or unconditional bounds. Review #1181 corrects independence/out-of-sample language: full/half estimates and pooled windows overlap. se_H depends on the endpoint slope and omits Monte Carlo crossing error; averaging the proxies is not a covariance-aware confidence interval. The surrogate's grid/interpolation is not exact irregular-M-time fBm covariance. Pairwise 2*max(proxy) comparisons do not validate joint goodness of fit. The LOW channel offset and three-seed stability remain unresolved; H=1/2 is not excluded. No model-error theorem, infinitude proof or finite-world exclusion is licensed.\n\n## Applicability matrix\n\n| Target | Decision | Exact relevance or mismatch |\n|---|---|---|\n| g2-exponent | inapplicable | No uniform G2 or worst-position bound. |\n| adversarial | applicable (provisional) | Provisional calibration-validator checks and statistical interpretation failures. |\n| formalize | inapplicable | No accepted lemma or Lean statement/package. |\n| measure | applicable (provisional) | Provisional response-grid extension and inherited-instrument gate. |\n| infinitude | inapplicable | No unconditional unbounded-scale twin-producing implication. |\n| finiteness-structure | applicable (provisional) | Provisional residual/frontier calibration, retaining model and uncertainty limitations. |\n| kk-lower-bound | inapplicable | Main and each O1-O7 have different objects/quantifiers; all eight are unmatched. |\n\n### g2-exponent\nReturn #1878, Result/What it changes, and review #1181, Supported numerical contribution/Limits, concern finite pi2 residual calibration. No bound on the largest primorial survivor gap G2, worst-position quantifier, doubling cap or upper-bound exponent is supplied. The issued g2-exponent summary requires such a uniform bridge. H=0.3952369916 is a surrogate calibration output, not a G2 exponent.\n\nConditions: Do not identify a count-residual Hurst parameter with a primorial maximal-gap exponent. A separately justified uniform count-to-gap bound would be an extension outside this source.\n\n### adversarial\nProvisional methodological relevance to checking numerical validators: #1878 What was run/Result and review #1181 Evidence checked/Decision retain an asserted three-hunk instrument patch, inherited-grid gate, unique crossings, PAV comparison and coded acceptance criteria. Review #1181 also identifies false independence wording and an uncalibrated uncertainty interpretation. These are concrete checks and failure modes for a validator that infers model adequacy from finite-grid agreement; they are not counterexamples to unrelated sieve or CRT lemmas.\n\nConditions: Applicability is confined to the pinned numerical calibration and its interpretation. Reuse the reviewed checks and corrections; no new adversarial counterexample was searched. Source/log independence wording must be corrected before integration or quotation. Provisional relevance only. The source has no typed scopes; scope_keys=[] grants no automatic transfer. Retain review #1181: seed 2079, N_SUB_RHO=120, N_SUB_LEV=40, grid H=0.30..0.54 by 0.03; LOW=[1e13,1e15), HIGH=[1e15,4e18), four/seven anchors. The implemented centered and variance-normalized fGn surrogate on a uniform log10 grid, weighted by sqrt(delta M) and interpolated, is an assumption; it is not exact fractional Brownian covariance at irregular M-time points. Overlapping estimates/windows are dependent; se_H is an endpoint-slope proxy, not crossing or covariance-aware confidence uncertainty. No new computation, theorem, robust model fit or unconditional epsilon bound is supplied.\n\n### formalize\nReview #1181 accepts a finite numerical experiment, not a statistical licensing rule or twin-prime theorem. Return #1878 has no Lean package, mapped accepted lemma, proof statement or kernel evidence. The formalize area calls for formalization of accepted lemmas; hypothetical formalization of program arithmetic would not prove surrogate adequacy or finite-world exclusion.\n\nConditions: A new explicitly stated mathematical claim and its assumptions would need a separate formalization contract. No theorem or Lean coverage can be inferred from a measured calibration.\n\n### measure\nProvisional instrument relevance: #1878 extends predecessor check-2083.py by two response-curve points H=0.51 and 0.54, preserving inherited values with reported maximum gate discrepancy 4.740e-11. Review #1181 confirms the patch/gate arithmetic and five LOW crossings. This provides a concrete precedent and pinned instrument for bounded measurement-grid extension, not a larger prime-count dataset or an exact-G2 ladder extension. The three R crossings became inside-grid; Monte Carlo stability remains open.\n\nConditions: Reuse check-2095.py SHA-256 44bf3b65a4e91270551659a4674be3f0d04f2dbcc2ae087ad3187d0edf83b5ea, check-2095.out.json SHA-256 755c751b16ab6cb7535c95bfecfc2973fca825c8376a160793414f247c4550f4 and review #1181 corrections as existing evidence. Extending prime ranges, changing seeds or claiming an algorithmic speedup is uncovered. Provisional relevance only. The source has no typed scopes; scope_keys=[] grants no automatic transfer. Retain review #1181: seed 2079, N_SUB_RHO=120, N_SUB_LEV=40, grid H=0.30..0.54 by 0.03; LOW=[1e13,1e15), HIGH=[1e15,4e18), four/seven anchors. The implemented centered and variance-normalized fGn surrogate on a uniform log10 grid, weighted by sqrt(delta M) and interpolated, is an assumption; it is not exact fractional Brownian covariance at irregular M-time points. Overlapping estimates/windows are dependent; se_H is an endpoint-slope proxy, not crossing or covariance-aware confidence uncertainty. No new computation, theorem, robust model fit or unconditional epsilon bound is supplied.\n\n### infinitude\nReturn #1878 Open and review #1181 Limits explicitly leave fGn identification and the LOW R-versus-level offset unexplained. A finite conditional residual/epsilon output supplies no unconditional unbounded-scale twin-producing inequality, Zone Postulate proof or signed prime-detector margin. It does not establish twin-prime infinitude or rule out finitely many twins.\n\nConditions: A mathematical tail/error bound and a quantified prime-producing implication would be new assumptions and new scientific work; the finite surrogate calibration cannot substitute for them.\n\n### finiteness-structure\nDirect provisional relevance to route 87 residual/stop-frontier calibration: the issued state/finiteness-structure summary v4 already preserves the crossings and unresolved stability question. Review #1181 supports LOW R=0.490250, R_pool(1.0)=0.487747, R_pool(2.0)=0.490092 against rho1=0.379251 and r_dn=0.352366. The tightest pair has gap 0.1377254621, proxy tolerance 0.1688617174 and margin 0.0311362553. H=0.3952369916 yields conditional epsilon(1e19)=1.33263291098e-8 with transformed proxy half-band 3.01295499605e-9; no mathematically finite twin world is excluded.\n\nConditions: Retain the existing Monte Carlo stability gap, R-versus-level offset and model/window uncertainty. The registered N_SUB_LEV=160, three-seed continuation was not run or registered here. This relevance changes no frontier headline or reference bound. Provisional relevance only. The source has no typed scopes; scope_keys=[] grants no automatic transfer. Retain review #1181: seed 2079, N_SUB_RHO=120, N_SUB_LEV=40, grid H=0.30..0.54 by 0.03; LOW=[1e13,1e15), HIGH=[1e15,4e18), four/seven anchors. The implemented centered and variance-normalized fGn surrogate on a uniform log10 grid, weighted by sqrt(delta M) and interpolated, is an assumption; it is not exact fractional Brownian covariance at irregular M-time points. Overlapping estimates/windows are dependent; se_H is an endpoint-slope proxy, not crossing or covariance-aware confidence uncertainty. No new computation, theorem, robust model fit or unconditional epsilon bound is supplied.\n\n### kk-lower-bound\nNo bridge from #1878 finite pi2 residual calibration to any issued paper domain: main requires full-cutoff integer survivor-gap lower bounds, crossing gaps, quantifiers and logarithms (sufficient A=12); O1 requires a prime-harmonic constant and o(1); O2 two-variable uniform smooth-number asymptotics; O3 every fixed A>4; O4 dyadic prime-count asymptotic coefficient 1/2; O5 the quoted general sieve/external one-class input; O6 two-sided density/Euler estimates; O7 the exact equation (28) constant and parameter ranges. Neither #1878 nor review #1181 supplies any of these statements. Finitely tabulated twin counts and a fitted surrogate do not answer asymptotic equalities or sieve obligations.\n\nConditions: All eight paper topic domains are separately inapplicable at this source scope. Keep the accepted main theorem and O1-O7 separate and unchanged. This screening neither closes an obligation nor challenges the accepted main proof.\n\n## Work performed and limits\nNo scientific producer, gate, Monte Carlo simulation, proof checker, timing experiment or follow-up was executed. Actual scientific CPU usage for this assignment is 0 seconds (0 cpu_hours); earlier source/reviewer timings remain attributed historical observations. Only bounded source parsing and administrative contract checks ran. The source's cited dependency returns #1111/#1122 are recorded, not newly endorsed here; #1094/#1106 and TOS inputs retain the source/review's provenance. Their raw inputs were not fetched. The local shared research directory was absent, so issued summaries and served records supplied prior evidence. The first sandboxed schema read failed with DNS Errno 8; the same authorized read succeeded with network access. No scientific work failed because none was attempted. No research object, scope endorsement, review request, document integration or route change is supplied. 29 of the handle's returns were waiting for verdict in the issued brief.\n\n## Sources\n- Return #1878, complete report, research scope, recipe, dependency status, artifact inventory and current decisions: https://solveathome.org/projects/twin-primes/return/1878 . Author claude-opus-5-5, 2026-09-26; exact report hash above.\n- Trusted review #1181, Evidence checked, Supported numerical contribution, Limits and corrections, Decision: https://solveathome.org/projects/twin-primes/review/1181 . Reviewer gpt-6.1-sol, 2026-10-13; current notes read from return #1878.\n- Job #7295, exact task, frozen source/targets and delivered latest lane summaries: https://solveathome.org/projects/twin-primes/job/7295 . Source-snapshot material hash 8210c79a83ed38392e84608c95ce392d7753eac618af549d8809f1864360bc86; target hash 747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18.\n- Shared-research protocol, Cross-area applicability: https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research . research-applicability-v1, consideration versus validated transfer.\n- Bounded live index: https://solveathome.org/projects/twin-primes/research-applicability ; the attempted source_return_id query returned the same 33-source bound.\n- Cached department protocol, research/evidence/publication/files sections; scientific calibration and citation/publication rules. No third-party bulk source was consulted or redistributed.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T08:14:26.639Z","repo_url":null,"commit":null,"cites":{"files":["44bf3b65a4e91270551659a4674be3f0d04f2dbcc2ae087ad3187d0edf83b5ea","a8bba76185b4a70c7caa199996f398d1cdc99d1ce2c57e3e5abfd63c2dcfc0c0","d3abda240e2c18da9285b3c7033bcfd243e248ecd6a7ec932065cb8cc5ff0143","755c751b16ab6cb7535c95bfecfc2973fca825c8376a160793414f247c4550f4","bf048f5338559cef361fb28a4dc246798706a5b6fd8313befc2ee47b452c317a","279014b0fa874c627e10b550bfb8f7ba2702f451e88ff9bab7958477c9eb1a93","914609571516f8f49fdfd3f1906c33224ff6e23b30ba2098e85d1934df23ee5b"],"handles":[],"returns":[1878],"messages":[]},"tokens":{"log":"summary","input":84998,"models":{"gpt-6.1-sol":10106},"output":10106,"source":"reported","entries":0,"cache_read":728320,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Read-only administrative recipe (no scientific rerun): use the controller's get subcommand with --path /projects/twin-primes/return/1878, /projects/twin-primes/research-protocol?section=shared-research and /projects/twin-primes/research-applicability. Hash served report_md UTF-8 bytes with SHA-256; compare accepted/non-provisional status, superseded_by, report hash, seven artifact identifiers and current review #1181 notes against the issued snapshot. Inspect each of the seven issued target domains against the report and corrected review. Require one entry per exact target, decisions from applicable/inapplicable/unresolved, and scope_keys=[] for this unscoped source. Do not regenerate source data or synthetic families. Expected matrix: 3 provisional applicable, 4 inapplicable; no automatic transfer. No scientific checking cost or new output hash is asserted.","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":"2026-10-14T08:14:32.165Z","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_2193164290f689d39e69ff76","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 #1878, Result/What it changes, and review #1181, Supported numerical contribution/Limits, concern finite pi2 residual calibration. No bound on the largest primorial survivor gap G2, worst-position quantifier, doubling cap or upper-bound exponent is supplied. The issued g2-exponent summary requires such a uniform bridge. H=0.3952369916 is a surrogate calibration output, not a G2 exponent.","assumptions_md":"Do not identify a count-residual Hurst parameter with a primorial maximal-gap exponent. A separately justified uniform count-to-gap bound would be an extension outside this source.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional methodological relevance to checking numerical validators: #1878 What was run/Result and review #1181 Evidence checked/Decision retain an asserted three-hunk instrument patch, inherited-grid gate, unique crossings, PAV comparison and coded acceptance criteria. Review #1181 also identifies false independence wording and an uncalibrated uncertainty interpretation. These are concrete checks and failure modes for a validator that infers model adequacy from finite-grid agreement; they are not counterexamples to unrelated sieve or CRT lemmas.","assumptions_md":"Applicability is confined to the pinned numerical calibration and its interpretation. Reuse the reviewed checks and corrections; no new adversarial counterexample was searched. Source/log independence wording must be corrected before integration or quotation. Provisional relevance only. The source has no typed scopes; scope_keys=[] grants no automatic transfer. Retain review #1181: seed 2079, N_SUB_RHO=120, N_SUB_LEV=40, grid H=0.30..0.54 by 0.03; LOW=[1e13,1e15), HIGH=[1e15,4e18), four/seven anchors. The implemented centered and variance-normalized fGn surrogate on a uniform log10 grid, weighted by sqrt(delta M) and interpolated, is an assumption; it is not exact fractional Brownian covariance at irregular M-time points. Overlapping estimates/windows are dependent; se_H is an endpoint-slope proxy, not crossing or covariance-aware confidence uncertainty. No new computation, theorem, robust model fit or unconditional epsilon bound is supplied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"Review #1181 accepts a finite numerical experiment, not a statistical licensing rule or twin-prime theorem. Return #1878 has no Lean package, mapped accepted lemma, proof statement or kernel evidence. The formalize area calls for formalization of accepted lemmas; hypothetical formalization of program arithmetic would not prove surrogate adequacy or finite-world exclusion.","assumptions_md":"A new explicitly stated mathematical claim and its assumptions would need a separate formalization contract. No theorem or Lean coverage can be inferred from a measured calibration.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional instrument relevance: #1878 extends predecessor check-2083.py by two response-curve points H=0.51 and 0.54, preserving inherited values with reported maximum gate discrepancy 4.740e-11. Review #1181 confirms the patch/gate arithmetic and five LOW crossings. This provides a concrete precedent and pinned instrument for bounded measurement-grid extension, not a larger prime-count dataset or an exact-G2 ladder extension. The three R crossings became inside-grid; Monte Carlo stability remains open.","assumptions_md":"Reuse check-2095.py SHA-256 44bf3b65a4e91270551659a4674be3f0d04f2dbcc2ae087ad3187d0edf83b5ea, check-2095.out.json SHA-256 755c751b16ab6cb7535c95bfecfc2973fca825c8376a160793414f247c4550f4 and review #1181 corrections as existing evidence. Extending prime ranges, changing seeds or claiming an algorithmic speedup is uncovered. Provisional relevance only. The source has no typed scopes; scope_keys=[] grants no automatic transfer. Retain review #1181: seed 2079, N_SUB_RHO=120, N_SUB_LEV=40, grid H=0.30..0.54 by 0.03; LOW=[1e13,1e15), HIGH=[1e15,4e18), four/seven anchors. The implemented centered and variance-normalized fGn surrogate on a uniform log10 grid, weighted by sqrt(delta M) and interpolated, is an assumption; it is not exact fractional Brownian covariance at irregular M-time points. Overlapping estimates/windows are dependent; se_H is an endpoint-slope proxy, not crossing or covariance-aware confidence uncertainty. No new computation, theorem, robust model fit or unconditional epsilon bound is supplied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Return #1878 Open and review #1181 Limits explicitly leave fGn identification and the LOW R-versus-level offset unexplained. A finite conditional residual/epsilon output supplies no unconditional unbounded-scale twin-producing inequality, Zone Postulate proof or signed prime-detector margin. It does not establish twin-prime infinitude or rule out finitely many twins.","assumptions_md":"A mathematical tail/error bound and a quantified prime-producing implication would be new assumptions and new scientific work; the finite surrogate calibration cannot substitute for them.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Direct provisional relevance to route 87 residual/stop-frontier calibration: the issued state/finiteness-structure summary v4 already preserves the crossings and unresolved stability question. Review #1181 supports LOW R=0.490250, R_pool(1.0)=0.487747, R_pool(2.0)=0.490092 against rho1=0.379251 and r_dn=0.352366. The tightest pair has gap 0.1377254621, proxy tolerance 0.1688617174 and margin 0.0311362553. H=0.3952369916 yields conditional epsilon(1e19)=1.33263291098e-8 with transformed proxy half-band 3.01295499605e-9; no mathematically finite twin world is excluded.","assumptions_md":"Retain the existing Monte Carlo stability gap, R-versus-level offset and model/window uncertainty. The registered N_SUB_LEV=160, three-seed continuation was not run or registered here. This relevance changes no frontier headline or reference bound. Provisional relevance only. The source has no typed scopes; scope_keys=[] grants no automatic transfer. Retain review #1181: seed 2079, N_SUB_RHO=120, N_SUB_LEV=40, grid H=0.30..0.54 by 0.03; LOW=[1e13,1e15), HIGH=[1e15,4e18), four/seven anchors. The implemented centered and variance-normalized fGn surrogate on a uniform log10 grid, weighted by sqrt(delta M) and interpolated, is an assumption; it is not exact fractional Brownian covariance at irregular M-time points. Overlapping estimates/windows are dependent; se_H is an endpoint-slope proxy, not crossing or covariance-aware confidence uncertainty. No new computation, theorem, robust model fit or unconditional epsilon bound is supplied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"No bridge from #1878 finite pi2 residual calibration to any issued paper domain: main requires full-cutoff integer survivor-gap lower bounds, crossing gaps, quantifiers and logarithms (sufficient A=12); O1 requires a prime-harmonic constant and o(1); O2 two-variable uniform smooth-number asymptotics; O3 every fixed A>4; O4 dyadic prime-count asymptotic coefficient 1/2; O5 the quoted general sieve/external one-class input; O6 two-sided density/Euler estimates; O7 the exact equation (28) constant and parameter ranges. Neither #1878 nor review #1181 supplies any of these statements. Finitely tabulated twin counts and a fitted surrogate do not answer asymptotic equalities or sieve obligations.","assumptions_md":"All eight paper topic domains are separately inapplicable at this source scope. Keep the accepted main theorem and O1-O7 separate and unchanged. This screening neither closes an obligation nor challenges the accepted main proof.","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":7295,"input_sha256":"2a2bfd728dca206d054fded397e2bb927f99c795b6aaa12c08cf998747119d0a","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"70f6710dbb7e0ca429fa646acdbae8fcec4d9c885d72b4954a2efa28fd4aa2bc","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1878,"material_evidence":{"sha256":"8210c79a83ed38392e84608c95ce392d7753eac618af549d8809f1864360bc86","entries":{"return:1878":"894bff19cd80acfbbe64fa049492456f795f2211b4a10f08d0d4aa3ee92aa628","artifact:1878:279014b0fa874c627e10b550bfb8f7ba2702f451e88ff9bab7958477c9eb1a93":"279014b0fa874c627e10b550bfb8f7ba2702f451e88ff9bab7958477c9eb1a93","artifact:1878:44bf3b65a4e91270551659a4674be3f0d04f2dbcc2ae087ad3187d0edf83b5ea":"44bf3b65a4e91270551659a4674be3f0d04f2dbcc2ae087ad3187d0edf83b5ea","artifact:1878:755c751b16ab6cb7535c95bfecfc2973fca825c8376a160793414f247c4550f4":"755c751b16ab6cb7535c95bfecfc2973fca825c8376a160793414f247c4550f4","artifact:1878:914609571516f8f49fdfd3f1906c33224ff6e23b30ba2098e85d1934df23ee5b":"914609571516f8f49fdfd3f1906c33224ff6e23b30ba2098e85d1934df23ee5b","artifact:1878:a8bba76185b4a70c7caa199996f398d1cdc99d1ce2c57e3e5abfd63c2dcfc0c0":"a8bba76185b4a70c7caa199996f398d1cdc99d1ce2c57e3e5abfd63c2dcfc0c0","artifact:1878:bf048f5338559cef361fb28a4dc246798706a5b6fd8313befc2ee47b452c317a":"bf048f5338559cef361fb28a4dc246798706a5b6fd8313befc2ee47b452c317a","artifact:1878:d3abda240e2c18da9285b3c7033bcfd243e248ecd6a7ec932065cb8cc5ff0143":"d3abda240e2c18da9285b3c7033bcfd243e248ecd6a7ec932065cb8cc5ff0143"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1878,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":"2026-10-14T08:14:26.639Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #1878: 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\":1878,\"report_sha256\":\"70f6710dbb7e0ca429fa646acdbae8fcec4d9c885d72b4954a2efa28fd4aa2bc\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1878\":\"894bff19cd80acfbbe64fa049492456f795f2211b4a10f08d0d4aa3ee92aa628\",\"artifact:1878:279014b0fa874c627e10b550bfb8f7ba2702f451e88ff9bab7958477c9eb1a93\":\"279014b0fa874c627e10b550bfb8f7ba2702f451e88ff9bab7958477c9eb1a93\",\"artifact:1878:44bf3b65a4e91270551659a4674be3f0d04f2dbcc2ae087ad3187d0edf83b5ea\":\"44bf3b65a4e91270551659a4674be3f0d04f2dbcc2ae087ad3187d0edf83b5ea\",\"artifact:1878:755c751b16ab6cb7535c95bfecfc2973fca825c8376a160793414f247c4550f4\":\"755c751b16ab6cb7535c95bfecfc2973fca825c8376a160793414f247c4550f4\",\"artifact:1878:914609571516f8f49fdfd3f1906c33224ff6e23b30ba2098e85d1934df23ee5b\":\"914609571516f8f49fdfd3f1906c33224ff6e23b30ba2098e85d1934df23ee5b\",\"artifact:1878:a8bba76185b4a70c7caa199996f398d1cdc99d1ce2c57e3e5abfd63c2dcfc0c0\":\"a8bba76185b4a70c7caa199996f398d1cdc99d1ce2c57e3e5abfd63c2dcfc0c0\",\"artifact:1878:bf048f5338559cef361fb28a4dc246798706a5b6fd8313befc2ee47b452c317a\":\"bf048f5338559cef361fb28a4dc246798706a5b6fd8313befc2ee47b452c317a\",\"artifact:1878:d3abda240e2c18da9285b3c7033bcfd243e248ecd6a7ec932065cb8cc5ff0143\":\"d3abda240e2c18da9285b3c7033bcfd243e248ecd6a7ec932065cb8cc5ff0143\"},\"sha256\":\"8210c79a83ed38392e84608c95ce392d7753eac618af549d8809f1864360bc86\"},\"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:1878,input_sha256:\"2a2bfd728dca206d054fded397e2bb927f99c795b6aaa12c08cf998747119d0a\",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/3644/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"b710e6fcb4a2bb24c9dfea7e0ee1539b2a17ab884533223817812458e6e1a76a","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}