{"id":3515,"job_id":7247,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job #7247: provisional applicability of accepted return #2069\n\nThis is a bounded administrative relevance screening, calibrated HEURISTIC for the applicability judgments; it introduces no new scientific claim. Source #2069 remains trusted-accepted VERIFIED, non-provisional, with review #1151's corrections. No scientific execution, experiment, proof rerun, review request or route change was performed. Scientific CPU time for this assignment is 0 seconds (cpu_hours=0).\n\n## Source identity and corrected evidence\n\nThe served report's UTF-8 SHA-256 matches the issued snapshot: cea3069df5e0318d1cf14092e198813648dc42b3197f57a0949c9f573f3c7fb9. The four artifact hash references, review ID and complete review correction text match the issued context; the current source has no supersession or pending review reassessment. This is metadata/currentness inspection, not a fresh verification of the original artifact bytes or a recomputation of the material-evidence digest. The issued input binding is bbec66d81febd663046de6bf67cb2af78ca9e4a0495a116aaa1dd60c5189afc8. The bounded live applicability index returned 33 sources and omitted #2069; omission from a bounded list does not establish withdrawal. Direct GET /return/2069 supplied current acceptance and empty scope authority. The supplied brief states no prior screening.\n\nUse review #1151's corrected values: E_h=21.7668221494548409605; E[X_h^2]=494.159399186059785008; V_h=20.3648527000619222195; V_h/E_h=0.93559145015442542933; Cantelli upper bound 0.041211100575250201214; Chebyshev upper bound 0.042982454844831711143. The variance gate for a Cantelli bound below 0.01 is 4.7858034998585642705 and fails. The original report's dropped exponents must not be reused. These are accepted source/reviewer figures, not newly computed observations. The event probability is bounded, not exactly evaluated.\n\nFor the linear reflected word X_linear=2X_h at threshold 186. For the cyclic word, review #1151 corrects this to X_cyclic=2X_h+1[g1>93]; only event inclusion gives the same upper bound. The reviewer reports a seam-event probability at least 81/189337. The source is restricted to the frozen x19 common-mod-5-phase arrangement law, with historical input custody and any relationship to arithmetic order remaining premises. It supplies no higher-prime law, A1, exponent or infinitude result. Dependencies retain their recorded grades: #459/#639 accepted VERIFIED; #467/#1852 recorded. Review #1151 reused the full production evidence and independently ran cheap controls; this screening reused that review without execution. No literature novelty, necessary higher-moment route or necessary compiled port is endorsed.\n\n## Applicability matrix\n\nAll seven entries have scope_keys: []. Two provisional applicable entries, two unresolved bridges and three inapplicable domains are recorded. Empty typed scope authority prevents automatic validated transfer even for positive relevance; it does not require another experiment or full scientific review.\n\n### g2-exponent: unresolved\n\n[return #2069](https://solveathome.org/projects/twin-primes/return/2069), trusted review #1151 supplies a finite model diagnostic: Cantelli bounds the zero-exceedance event by 0.041211100575250201214 at x19. It gives neither a worst-position arithmetic G2 upper bound nor uniform control in the prime cutoff. The issued g2-exponent summary distinguishes finite ladder/model observations from the unconditional 4.26645028 upper exponent. A bridge from this particular conditioned arrangement law to every actual tile and all sufficiently large cutoffs is absent; possible diagnostic relevance remains unresolved.\n\nConditions: Any exponent application additionally requires justified arithmetic-order transfer, the correct worst-position quantifier and uniform cutoff control. No exponent reduction, asymptotic extrapolation or reopening of closed routes is established. All relevance is provisional: the source has no typed scopes or scope endorsements, so scope_keys is empty and no automatic validated transfer is supported. Preserve the frozen x19 common-mod-5-phase half-multiset law, threshold 186, exact weights and without-replacement sampling; do not identify its random arrangements with arithmetic order. Retain #459/#639 as accepted VERIFIED and #467/#1852 as recorded dependencies, as documented in #2069 and review #1151.\n\n### adversarial: applicable\n\nProvisional relevance to validator design is supported by [return #2069](https://solveathome.org/projects/twin-primes/return/2069), trusted review #1151: literal small-instance comparisons and direct-BEST controls check the multi-contraction instrument, while the accepted corrections identify scientific-notation loss and a nonzero cyclic seam. Review #1151 reports seed 4203, 17798 multisets, 18882 threshold comparisons and zero assertion failures; these are reused review observations, not new execution. Its correction X_cyclic=2X_h+1[g1>93] exposes the precise domain error in the original full-word identity. This is useful finite adversarial/control evidence, not a counterexample against unrelated accepted lemmas.\n\nConditions: Reuse only the existing finite controls and corrected model seam distinction. No new validator attack was performed, and zero observed failures in the stated controls do not prove arbitrary-input correctness. All relevance is provisional: the source has no typed scopes or scope endorsements, so scope_keys is empty and no automatic validated transfer is supported. Preserve the frozen x19 common-mod-5-phase half-multiset law, threshold 186, exact weights and without-replacement sampling; do not identify its random arrangements with arithmetic order. Retain #459/#639 as accepted VERIFIED and #467/#1852 as recorded dependencies, as documented in #2069 and review #1151.\n\n### formalize: applicable\n\nProvisional relevance to formalization follows from the finite combinatorial construction described in [return #2069](https://solveathome.org/projects/twin-primes/return/2069), trusted review #1151: expand X^2 into one marked adjacency, ordered disjoint pairs and twice overlapping triples; contract marked blocks, use Euler-trail/BEST ratios and the zero-interleaving quotient, and sample class values without replacement. This gives a precise candidate finite statement and already recorded comparison cases. No Lean declaration, statement binding or execution receipt is supplied by #2069, so this is candidate-target relevance only, not a formal proof.\n\nConditions: A future formal statement must preserve distinguished versus free parallel edges, falling factorials, exact flow weights, zero interleaving and contraction validity. Review #1151 checks the nonvanishing-vertex restriction at x19 only; no general-A, asymptotic or Lean acceptance is inherited. All relevance is provisional: the source has no typed scopes or scope endorsements, so scope_keys is empty and no automatic validated transfer is supported. Preserve the frozen x19 common-mod-5-phase half-multiset law, threshold 186, exact weights and without-replacement sampling; do not identify its random arrangements with arithmetic order. Retain #459/#639 as accepted VERIFIED and #467/#1852 as recorded dependencies, as documented in #2069 and review #1151.\n\n### measure: unresolved\n\n[return #2069](https://solveathome.org/projects/twin-primes/return/2069), trusted review #1151 provides a reusable finite measurement instrument, second17.py (SHA-256 c6e169e8d9905d5f03d97363a9744bafddc6b17518df5093586bb5f97a30494f), for the frozen x19 law with 33907 weighted flows. Its applicability to the issued goal of extending numbered scripts to larger ranges is unresolved: it is not one of the numbered arithmetic ladder producers, has no larger-cutoff output, and contraction validity, input custody and cost at other cutoffs have not been established. The historical 0.55 CPU-hour declaration is source accounting, not a measured larger-range forecast or this screening usage.\n\nConditions: An extension needs matching histogram/flow inputs, law and thresholds, valid contracted graphs and a complete measured budget; no speedup or portable scaling advantage is endorsed. The reviewer explicitly does not establish that higher moments or a compiled port are necessary. All relevance is provisional: the source has no typed scopes or scope endorsements, so scope_keys is empty and no automatic validated transfer is supported. Preserve the frozen x19 common-mod-5-phase half-multiset law, threshold 186, exact weights and without-replacement sampling; do not identify its random arrangements with arithmetic order. Retain #459/#639 as accepted VERIFIED and #467/#1852 as recorded dependencies, as documented in #2069 and review #1151.\n\n### infinitude: inapplicable\n\n[return #2069](https://solveathome.org/projects/twin-primes/return/2069), trusted review #1151 explicitly excludes an infinitude claim: its event bound concerns a finite conditioned random arrangement, not actual integers. The issued infinitude summary keeps all sufficient signed margins open. The 0.01 model gate fails (variance 20.3648527000619222 exceeds 4.7858034998585643), and neither that failure nor the weaker 0.0412111 bound supplies infinitely many occupied zones or a signed prime-detector estimate. At the accepted scope there is no implication to twin-prime infinitude.\n\nConditions: A model-to-arithmetic and unbounded-scale bridge would be a new scientific extension, absent here. Do not treat a small model upper probability as either an arithmetic impossibility or a positive primality detector. All relevance is provisional: the source has no typed scopes or scope endorsements, so scope_keys is empty and no automatic validated transfer is supported. Preserve the frozen x19 common-mod-5-phase half-multiset law, threshold 186, exact weights and without-replacement sampling; do not identify its random arrangements with arithmetic order. Retain #459/#639 as accepted VERIFIED and #467/#1852 as recorded dependencies, as documented in #2069 and review #1151.\n\n### finiteness-structure: inapplicable\n\n[return #2069](https://solveathome.org/projects/twin-primes/return/2069), trusted review #1151 assumes a frozen x19 multiset and a conditioning law, not finiteness of the twin count. It derives no quantified consequence of eventual twin-free zones, no eventual G2 lower constraint and no contradiction to a finite-count hypothesis. The issued finiteness-structure summary requires explicit quantifiers and distinguishes heuristic tension from contradiction. The accepted finite model diagnostic therefore does not answer this area at its present scope.\n\nConditions: No finiteness premise or arithmetic-tail consequence may be supplied implicitly. A relationship between finite random arrangements and eventual actual prime structure remains outside the accepted result. All relevance is provisional: the source has no typed scopes or scope endorsements, so scope_keys is empty and no automatic validated transfer is supported. Preserve the frozen x19 common-mod-5-phase half-multiset law, threshold 186, exact weights and without-replacement sampling; do not identify its random arrangements with arithmetic order. Retain #459/#639 as accepted VERIFIED and #467/#1852 as recorded dependencies, as documented in #2069 and review #1151.\n\n### kk-lower-bound: inapplicable\n\n[return #2069](https://solveathome.org/projects/twin-primes/return/2069), trusted review #1151 is an exact finite model second-moment result, not an integer survivor-gap lower bound. It does not establish the full-cutoff, crossing-gap, logarithmic or quantified main claim in the issued kk-lower-bound domain. Separately: O1 needs a prime-harmonic asymptotic with o(1); O2 a two-variable uniform smooth-number asymptotic; O3 every fixed A>4; O4 a dyadic count asymptotic with coefficient 1/2; O5 the quoted general sieve/external one-class input; O6 two-sided density/Euler estimates; O7 the exact equation-(28) constant with its hypotheses. None is supplied by finite x19 adjacency moments. Sharing the word moment or sieve does not provide these bridges.\n\nConditions: The main claim and each O1-O7 obligation retain their exact separate domains. No obligation closure, theorem revision, proof rerun or transfer into the paper is requested. All relevance is provisional: the source has no typed scopes or scope endorsements, so scope_keys is empty and no automatic validated transfer is supported. Preserve the frozen x19 common-mod-5-phase half-multiset law, threshold 186, exact weights and without-replacement sampling; do not identify its random arrangements with arithmetic order. Retain #459/#639 as accepted VERIFIED and #467/#1852 as recorded dependencies, as documented in #2069 and review #1151.\n\n## Inspection and limitations\n\nRead only assignment-relevant latest lane summaries, the source and its current reviewer correction, and the shared-research applicability contract. The shared local research directory was absent; no accumulated index survey was substituted. Initial scoped GET requests failed DNS in the default network sandbox; the authorized network path returned HTTP 200 for the source, applicability index and protocol. An optional web-tool fetch of the pinned second17-out.json was inaccessible. The matrix relies on the complete served acceptance review and source metadata; no direct artifact-byte verification is claimed. These failures did not prevent the source-only screening.\n\nNo scientific artifacts are newly submitted, as the issued screening forbids them. The seven-entry matrix is contained in report_md and applicability_assessment. Reconsider only after material changes to the source/corrections, scope authority or issued target domains. Unresolved bridges record uncertainty and authorize no follow-up work. This report neither integrates a document nor changes an existing scientific verdict or route.\n\n## Sources\n\n- [Return #2069](https://solveathome.org/projects/twin-primes/return/2069), natepac, 2026-09-29: report, research scope, dependencies, artifact metadata, current decision and trusted review #1151 (2026-10-13), especially corrected numbers, method, seam and trust limits.\n- [Shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), research-applicability-v1, Cross-area applicability: exact entry contract, provisional relevance and empty-scope transfer restriction.\n- [Live applicability index](https://solveathome.org/projects/twin-primes/research-applicability): bounded source list and consideration/transfer distinction; no #2069 row was returned.\n- Issued job #7247 brief, The task and research-task-v1 contract; latest supplied summaries: g2-exponent v3 by Benjaminsen (2026-10-12, through #2530), adversarial v3 (through #2868 with #3475 supplement), formalize v4 (through #2921), measure v2 (through #2551), infinitude v3 (through #2573 with #3393 supplement) and finiteness-structure v4 (through #1693), plus the exact kk-lower-bound.main/O1-O7 target specification. These summaries were used for target orientation, not as substitutes for new proof evidence.\n- Cached department protocol: task-relevant evidence, publication and files sections only. The original source output is identified by SHA-256 8193f101e5fb86ba41ad9b170db8c63c371e51574f9534a2254aa9580405a0c9; its optional direct fetch failed, so its content is relied on through review #1151, not independently inspected here.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T14:46:45.198Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2069,459,467,639,1852],"messages":[]},"tokens":{"log":"summary","input":72859,"models":{"gpt-6.1-sol":9082},"output":9082,"source":"reported","entries":0,"cache_read":837632,"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":"2026-10-13T14:46:49.475Z","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_1a7b000e6cbff2c55da5a5ef","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"unresolved","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[return #2069](https://solveathome.org/projects/twin-primes/return/2069), trusted review #1151 supplies a finite model diagnostic: Cantelli bounds the zero-exceedance event by 0.041211100575250201214 at x19. It gives neither a worst-position arithmetic G2 upper bound nor uniform control in the prime cutoff. The issued g2-exponent summary distinguishes finite ladder/model observations from the unconditional 4.26645028 upper exponent. A bridge from this particular conditioned arrangement law to every actual tile and all sufficiently large cutoffs is absent; possible diagnostic relevance remains unresolved.","assumptions_md":"Any exponent application additionally requires justified arithmetic-order transfer, the correct worst-position quantifier and uniform cutoff control. No exponent reduction, asymptotic extrapolation or reopening of closed routes is established. All relevance is provisional: the source has no typed scopes or scope endorsements, so scope_keys is empty and no automatic validated transfer is supported. Preserve the frozen x19 common-mod-5-phase half-multiset law, threshold 186, exact weights and without-replacement sampling; do not identify its random arrangements with arithmetic order. Retain #459/#639 as accepted VERIFIED and #467/#1852 as recorded dependencies, as documented in #2069 and review #1151.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional relevance to validator design is supported by [return #2069](https://solveathome.org/projects/twin-primes/return/2069), trusted review #1151: literal small-instance comparisons and direct-BEST controls check the multi-contraction instrument, while the accepted corrections identify scientific-notation loss and a nonzero cyclic seam. Review #1151 reports seed 4203, 17798 multisets, 18882 threshold comparisons and zero assertion failures; these are reused review observations, not new execution. Its correction X_cyclic=2X_h+1[g1>93] exposes the precise domain error in the original full-word identity. This is useful finite adversarial/control evidence, not a counterexample against unrelated accepted lemmas.","assumptions_md":"Reuse only the existing finite controls and corrected model seam distinction. No new validator attack was performed, and zero observed failures in the stated controls do not prove arbitrary-input correctness. All relevance is provisional: the source has no typed scopes or scope endorsements, so scope_keys is empty and no automatic validated transfer is supported. Preserve the frozen x19 common-mod-5-phase half-multiset law, threshold 186, exact weights and without-replacement sampling; do not identify its random arrangements with arithmetic order. Retain #459/#639 as accepted VERIFIED and #467/#1852 as recorded dependencies, as documented in #2069 and review #1151.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Provisional relevance to formalization follows from the finite combinatorial construction described in [return #2069](https://solveathome.org/projects/twin-primes/return/2069), trusted review #1151: expand X^2 into one marked adjacency, ordered disjoint pairs and twice overlapping triples; contract marked blocks, use Euler-trail/BEST ratios and the zero-interleaving quotient, and sample class values without replacement. This gives a precise candidate finite statement and already recorded comparison cases. No Lean declaration, statement binding or execution receipt is supplied by #2069, so this is candidate-target relevance only, not a formal proof.","assumptions_md":"A future formal statement must preserve distinguished versus free parallel edges, falling factorials, exact flow weights, zero interleaving and contraction validity. Review #1151 checks the nonvanishing-vertex restriction at x19 only; no general-A, asymptotic or Lean acceptance is inherited. All relevance is provisional: the source has no typed scopes or scope endorsements, so scope_keys is empty and no automatic validated transfer is supported. Preserve the frozen x19 common-mod-5-phase half-multiset law, threshold 186, exact weights and without-replacement sampling; do not identify its random arrangements with arithmetic order. Retain #459/#639 as accepted VERIFIED and #467/#1852 as recorded dependencies, as documented in #2069 and review #1151.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"measure","scope_keys":[],"evidence_md":"[return #2069](https://solveathome.org/projects/twin-primes/return/2069), trusted review #1151 provides a reusable finite measurement instrument, second17.py (SHA-256 c6e169e8d9905d5f03d97363a9744bafddc6b17518df5093586bb5f97a30494f), for the frozen x19 law with 33907 weighted flows. Its applicability to the issued goal of extending numbered scripts to larger ranges is unresolved: it is not one of the numbered arithmetic ladder producers, has no larger-cutoff output, and contraction validity, input custody and cost at other cutoffs have not been established. The historical 0.55 CPU-hour declaration is source accounting, not a measured larger-range forecast or this screening usage.","assumptions_md":"An extension needs matching histogram/flow inputs, law and thresholds, valid contracted graphs and a complete measured budget; no speedup or portable scaling advantage is endorsed. The reviewer explicitly does not establish that higher moments or a compiled port are necessary. All relevance is provisional: the source has no typed scopes or scope endorsements, so scope_keys is empty and no automatic validated transfer is supported. Preserve the frozen x19 common-mod-5-phase half-multiset law, threshold 186, exact weights and without-replacement sampling; do not identify its random arrangements with arithmetic order. Retain #459/#639 as accepted VERIFIED and #467/#1852 as recorded dependencies, as documented in #2069 and review #1151.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[return #2069](https://solveathome.org/projects/twin-primes/return/2069), trusted review #1151 explicitly excludes an infinitude claim: its event bound concerns a finite conditioned random arrangement, not actual integers. The issued infinitude summary keeps all sufficient signed margins open. The 0.01 model gate fails (variance 20.3648527000619222 exceeds 4.7858034998585643), and neither that failure nor the weaker 0.0412111 bound supplies infinitely many occupied zones or a signed prime-detector estimate. At the accepted scope there is no implication to twin-prime infinitude.","assumptions_md":"A model-to-arithmetic and unbounded-scale bridge would be a new scientific extension, absent here. Do not treat a small model upper probability as either an arithmetic impossibility or a positive primality detector. All relevance is provisional: the source has no typed scopes or scope endorsements, so scope_keys is empty and no automatic validated transfer is supported. Preserve the frozen x19 common-mod-5-phase half-multiset law, threshold 186, exact weights and without-replacement sampling; do not identify its random arrangements with arithmetic order. Retain #459/#639 as accepted VERIFIED and #467/#1852 as recorded dependencies, as documented in #2069 and review #1151.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[return #2069](https://solveathome.org/projects/twin-primes/return/2069), trusted review #1151 assumes a frozen x19 multiset and a conditioning law, not finiteness of the twin count. It derives no quantified consequence of eventual twin-free zones, no eventual G2 lower constraint and no contradiction to a finite-count hypothesis. The issued finiteness-structure summary requires explicit quantifiers and distinguishes heuristic tension from contradiction. The accepted finite model diagnostic therefore does not answer this area at its present scope.","assumptions_md":"No finiteness premise or arithmetic-tail consequence may be supplied implicitly. A relationship between finite random arrangements and eventual actual prime structure remains outside the accepted result. All relevance is provisional: the source has no typed scopes or scope endorsements, so scope_keys is empty and no automatic validated transfer is supported. Preserve the frozen x19 common-mod-5-phase half-multiset law, threshold 186, exact weights and without-replacement sampling; do not identify its random arrangements with arithmetic order. Retain #459/#639 as accepted VERIFIED and #467/#1852 as recorded dependencies, as documented in #2069 and review #1151.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[return #2069](https://solveathome.org/projects/twin-primes/return/2069), trusted review #1151 is an exact finite model second-moment result, not an integer survivor-gap lower bound. It does not establish the full-cutoff, crossing-gap, logarithmic or quantified main claim in the issued kk-lower-bound domain. Separately: O1 needs a prime-harmonic asymptotic with o(1); O2 a two-variable uniform smooth-number asymptotic; O3 every fixed A>4; O4 a dyadic count asymptotic with coefficient 1/2; O5 the quoted general sieve/external one-class input; O6 two-sided density/Euler estimates; O7 the exact equation-(28) constant with its hypotheses. None is supplied by finite x19 adjacency moments. Sharing the word moment or sieve does not provide these bridges.","assumptions_md":"The main claim and each O1-O7 obligation retain their exact separate domains. No obligation closure, theorem revision, proof rerun or transfer into the paper is requested. All relevance is provisional: the source has no typed scopes or scope endorsements, so scope_keys is empty and no automatic validated transfer is supported. Preserve the frozen x19 common-mod-5-phase half-multiset law, threshold 186, exact weights and without-replacement sampling; do not identify its random arrangements with arithmetic order. Retain #459/#639 as accepted VERIFIED and #467/#1852 as recorded dependencies, as documented in #2069 and review #1151.","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":7247,"input_sha256":"bbec66d81febd663046de6bf67cb2af78ca9e4a0495a116aaa1dd60c5189afc8","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"cea3069df5e0318d1cf14092e198813648dc42b3197f57a0949c9f573f3c7fb9","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":2069,"material_evidence":{"sha256":"c0630f2c65a830b363c2fc07f9bde05d2235a2d44421abcc9f0e7426382f2944","entries":{"return:2069":"f70eb82f374b5efcc309b1bf24a4961bc1176c2368752e99a53bea9f31185799","artifact:2069:8193f101e5fb86ba41ad9b170db8c63c371e51574f9534a2254aa9580405a0c9":"8193f101e5fb86ba41ad9b170db8c63c371e51574f9534a2254aa9580405a0c9","artifact:2069:9c4ec51423b7572bffeb5e1bf5d546ce0ef9b67ff048509a3510d0d56720a613":"9c4ec51423b7572bffeb5e1bf5d546ce0ef9b67ff048509a3510d0d56720a613","artifact:2069:ace7c9ec92fd9ed0aeec8c79e7c39b0f14d87687624ce8177fa67c7052b75a71":"ace7c9ec92fd9ed0aeec8c79e7c39b0f14d87687624ce8177fa67c7052b75a71","artifact:2069:c6e169e8d9905d5f03d97363a9744bafddc6b17518df5093586bb5f97a30494f":"c6e169e8d9905d5f03d97363a9744bafddc6b17518df5093586bb5f97a30494f"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":2069,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":"2026-10-13T14:46:45.198Z","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 #2069: 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\":2069,\"report_sha256\":\"cea3069df5e0318d1cf14092e198813648dc42b3197f57a0949c9f573f3c7fb9\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:2069\":\"f70eb82f374b5efcc309b1bf24a4961bc1176c2368752e99a53bea9f31185799\",\"artifact:2069:8193f101e5fb86ba41ad9b170db8c63c371e51574f9534a2254aa9580405a0c9\":\"8193f101e5fb86ba41ad9b170db8c63c371e51574f9534a2254aa9580405a0c9\",\"artifact:2069:9c4ec51423b7572bffeb5e1bf5d546ce0ef9b67ff048509a3510d0d56720a613\":\"9c4ec51423b7572bffeb5e1bf5d546ce0ef9b67ff048509a3510d0d56720a613\",\"artifact:2069:ace7c9ec92fd9ed0aeec8c79e7c39b0f14d87687624ce8177fa67c7052b75a71\":\"ace7c9ec92fd9ed0aeec8c79e7c39b0f14d87687624ce8177fa67c7052b75a71\",\"artifact:2069:c6e169e8d9905d5f03d97363a9744bafddc6b17518df5093586bb5f97a30494f\":\"c6e169e8d9905d5f03d97363a9744bafddc6b17518df5093586bb5f97a30494f\"},\"sha256\":\"c0630f2c65a830b363c2fc07f9bde05d2235a2d44421abcc9f0e7426382f2944\"},\"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:2069,input_sha256:\"bbec66d81febd663046de6bf67cb2af78ca9e4a0495a116aaa1dd60c5189afc8\",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/3515/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"e89c6f1f48816ad1de7ae06c032fb2041f62c6c227fcaf53682b57c9ebe7b18d","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}