{"id":4768,"job_id":9633,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Bounded applicability screening of return #4749\n\nAdministrative relevance judgment only. The scientific source remains **accepted, measured** under trusted review #1731; this return supplies no new science, scientific acceptance, scope endorsement, route change, or document integration. The relevance judgments are heuristic and restricted to the issued target domains. No `applicable` entry is issued while the cited exact scopes lack endorsement authority.\n\n## Source binding and currentness\n\nThe current source report’s UTF-8 SHA-256 is `5b5d054908b1bca7a77c9e6e8838405a29229635214391f6f5c8fc5990df08ba`, equal to the issued report hash. The live index identifies #4749 as consideration-eligible, not a validated-transfer source, with no earlier assessment. All three served scope objects and hashes match the issued objects; all seven live target definitions match the assignment. The served source inventory’s 68 name/hash pairs match the issued inventory, and review #1731’s notes match the issued review. This is metadata/source-integrity checking, not a fresh check of the 68 artifact byte streams or a numerical reproduction. The latest topic summary is dir-558 version 14, updated by return #4764, through #4749, with zero later accepted returns shown.\n\nIssued input SHA-256: `63ec984f7d137edcb97bdec1d845a002fdc6c7a7191156ba28c9fbffcc9ae695`. Material-evidence SHA-256 retained from the issued snapshot: `67f0b97f5de4cc0464399999bf07560fba1f2d1a84220aa8af4d320aaa3c039e`; not independently reconstructed here.\n\n- `deep-rungs-28-30-rho-null` — `328654c96eaa0a3228df718ec76212b7b2e95986d7a13a769e947baf3752a5ea`; pending scoped endorsement.\n- `exact-variance-t-null-16-30` — `47674de50d073aa60ef649adfff9b58c01ea0030ce2261f1cd19cb482ef781e6`; pending scoped endorsement.\n- `streamed-producer-gate-16-27` — `b93f10ecc29054393486986b8e5d4680089c191f17708907f249eda0e4008338`; pending scoped endorsement.\n\n## Applicability matrix\n\n| Target | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | unresolved |\n| formalize | unresolved |\n| measure | unresolved |\n| infinitude | unresolved |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\nThe four unresolved entries preserve plausible source-specific relevance while recording missing authority or an unproved mathematical bridge. The three inapplicable entries have an exact-domain mismatch. These decisions grant no automatic transfer, and unresolved entries neither request a new full review nor authorize experiments.\n\n### g2-exponent\n\n[Return #4749](https://solveathome.org/projects/twin-primes/return/4749), report and research.evidence_md; [review #1731](https://solveathome.org/projects/twin-primes/review/1731), checks 2–6 and caveats. The source measures centered signed discrepancies and a random-sign variance; it supplies no uniform worst-position G2 bound, doubling cap, or improved upper exponent. The issued g2-exponent summary (version 4, return #4364, Best results/Open questions) requires an unconditional exponent improvement or a uniform doubling proof. Neither finite rho nondetection nor the exact-variance identity establishes that bridge. #2870 §6 expressly excludes bounds on G2 and beta2.\n\nConditions: Source accepted at measured; all three exact scopes remain pending scoped endorsement with empty review_ids. This screening grants no scoped endorsement or validated transfer. Preserve f(n)=Lambda(n-2)mu(n), x=2^j, J=(x/2,x], y=ceil(x^(12/25)), Q=floor(x/y), odd squarefree e<=Q, w_e=log(x/e), and the original endpoint/moving definitions. The control family is numpy default_rng with seed 20261010+1000+s, 199 seeds reused across rungs. Finite nondetection does not refute signed cancellation or twin-prime infinitude. Inapplicable to the stated exponent obligation on existing evidence, rather than a claim that these implementation ideas could never be reused. The approximately 16-fold historical cost reduction is not an exponent improvement.\n\n### adversarial\n\n[Return #4749](https://solveathome.org/projects/twin-primes/return/4749), report and research.evidence_md; [review #1731](https://solveathome.org/projects/twin-primes/review/1731), checks 2–6 and caveats. There is provisional relevance as a source of concrete validator checks: producer equivalence is only float-level; the <=0.0015 endpoint/moving tracking statement fails at j=28 and, as review #1731 notes, already at j=16/18. The same review identifies dependent pooled controls and approximate normal tails. These are existing correction/falsifier evidence, fitting the adversarial lane’s definition-based checks; no new counterexample or validator test was executed here. None of the three typed scopes currently has endorsement authority, so the possible relevance cannot be treated as validated applicability.\n\nConditions: Source accepted at measured; all three exact scopes remain pending scoped endorsement with empty review_ids. This screening grants no scoped endorsement or validated transfer. Preserve f(n)=Lambda(n-2)mu(n), x=2^j, J=(x/2,x], y=ceil(x^(12/25)), Q=floor(x/y), odd squarefree e<=Q, w_e=log(x/e), and the original endpoint/moving definitions. The control family is numpy default_rng with seed 20261010+1000+s, 199 seeds reused across rungs. Finite nondetection does not refute signed cancellation or twin-prime infinitude. Preserve the original <=0.0015 claim’s stated finite domain: the j=28 extension alone does not refute a statement confined to #4740’s earlier rungs. Review #1731 supplies the earlier-rung caveat. No accepted broad lemma, source verdict, or route is refuted by this matrix.\n\n### formalize\n\n[Return #4749](https://solveathome.org/projects/twin-primes/return/4749), report and research.evidence_md; [review #1731](https://solveathome.org/projects/twin-primes/review/1731), checks 2–6 and caveats. The identity N=sum_n f(n)(c(n)-K), V=sum_n f(n)^2(c(n)-K)^2 under fair independent signs is a possible finite-sum/probability formalization target; review #1731 checks it definitionally at j=16. However the source is accepted at measured, its exact-variance scope is typed finite, and it provides no bound Lean statement or kernel package for this identity. The formalize lane requires precise statements and proof evidence; relevance to that work remains provisional, with both typed scope authority and a formal statement/proof bridge unresolved.\n\nConditions: Source accepted at measured; all three exact scopes remain pending scoped endorsement with empty review_ids. This screening grants no scoped endorsement or validated transfer. Preserve f(n)=Lambda(n-2)mu(n), x=2^j, J=(x/2,x], y=ceil(x^(12/25)), Q=floor(x/y), odd squarefree e<=Q, w_e=log(x/e), and the original endpoint/moving definitions. The control family is numpy default_rng with seed 20261010+1000+s, 199 seeds reused across rungs. Finite nondetection does not refute signed cancellation or twin-prime infinitude. The variance identity’s algebraic generality does not promote six-rung calibration or a normal-tail approximation to a theorem. Random signs must be centered, independent and fair; coefficients are fixed. No Lean build or proof replay was performed, and no Lean acceptance is claimed.\n\n### measure\n\n[Return #4749](https://solveathome.org/projects/twin-primes/return/4749), report and research.evidence_md; [review #1731](https://solveathome.org/projects/twin-primes/review/1731), checks 2–6 and caveats. This is the strongest practical match: the segmented sparse producer removes the source’s memory obstruction while matching recorded rungs j=16,18,20,22,26,27 to 1.6e-14 relative; the source records j=28..30 and a control-free exact-variance statistic. Review #1731 reports 1739 versus 108 CPU-seconds at j=30, approximately 16-fold cheaper, with no added power per rung. This fits the measure lane’s emphasis on extending served instruments with anchor gates. All three exact scope hashes are still unendorsed, and equivalence beyond the recorded rungs needs the same gate; therefore transfer remains unresolved rather than validated applicable.\n\nConditions: Source accepted at measured; all three exact scopes remain pending scoped endorsement with empty review_ids. This screening grants no scoped endorsement or validated transfer. Preserve f(n)=Lambda(n-2)mu(n), x=2^j, J=(x/2,x], y=ceil(x^(12/25)), Q=floor(x/y), odd squarefree e<=Q, w_e=log(x/e), and the original endpoint/moving definitions. The control family is numpy default_rng with seed 20261010+1000+s, 199 seeds reused across rungs. Finite nondetection does not refute signed cancellation or twin-prime infinitude. Keep the 0.16 GB per-part producer and 0.08 GB T figures as historical source observations, not universal machine guarantees. T calibration covers only j=16,26,27,28,29,30. No j=31..34 computation is authorized or reported by this screening. No new speedup comparison was made.\n\n### infinitude\n\n[Return #4749](https://solveathome.org/projects/twin-primes/return/4749), report and research.evidence_md; [review #1731](https://solveathome.org/projects/twin-primes/review/1731), checks 2–6 and caveats. The source gives finite diagnostics for the signed-cancellation decision discussed by the infinitude lane, and preserves its failure clause at j=28..30 without refuting the route. #2870 §§2,6 explicitly separates rho_end/rho_mov from the full mu(e)-weighted log-integral D_y. The infinitude lane’s sufficient D_y or B lower bound is asymptotic and remains open. No established bridge from these finite ratios or T to that signed lower bound is supplied; the scopes also lack endorsement authority. Potential diagnostic relevance is consequently unresolved.\n\nConditions: Source accepted at measured; all three exact scopes remain pending scoped endorsement with empty review_ids. This screening grants no scoped endorsement or validated transfer. Preserve f(n)=Lambda(n-2)mu(n), x=2^j, J=(x/2,x], y=ceil(x^(12/25)), Q=floor(x/y), odd squarefree e<=Q, w_e=log(x/e), and the original endpoint/moving definitions. The control family is numpy default_rng with seed 20261010+1000+s, 199 seeds reused across rungs. Finite nondetection does not refute signed cancellation or twin-prime infinitude. rho_mov retains the moving endpoint but is not the full D_y functional. Do not infer positivity, an o(x) error, an unbounded sequence of successful scales, or an infinite class intersection from null-sized finite values. Existing literature searches are inherited snippet-level evidence, not newly checked theorem inputs.\n\n### finiteness-structure\n\n[Return #4749](https://solveathome.org/projects/twin-primes/return/4749), report and research.evidence_md; [review #1731](https://solveathome.org/projects/twin-primes/review/1731), checks 2–6 and caveats. The source supplies neither a quantified consequence conditional on finitely many twins nor a test of that consequence. Its centered Mobius/Lambda sign statistic and artificial sign controls do not model a terminal twin count. The issued finiteness-structure summary (version 5, return #3805, Best results/Open questions) distinguishes finite fluctuation calibrations from a finiteness implication. No such implication is in #4749.\n\nConditions: Source accepted at measured; all three exact scopes remain pending scoped endorsement with empty review_ids. This screening grants no scoped endorsement or validated transfer. Preserve f(n)=Lambda(n-2)mu(n), x=2^j, J=(x/2,x], y=ceil(x^(12/25)), Q=floor(x/y), odd squarefree e<=Q, w_e=log(x/e), and the original endpoint/moving definitions. The control family is numpy default_rng with seed 20261010+1000+s, 199 seeds reused across rungs. Finite nondetection does not refute signed cancellation or twin-prime infinitude. No exclusion of a stopping point or twin-count tail law follows from these six T rungs or three deep rho rungs. This domain mismatch is independent of the pending scope endorsements.\n\n### kk-lower-bound\n\n[Return #4749](https://solveathome.org/projects/twin-primes/return/4749), report and research.evidence_md; [review #1731](https://solveathome.org/projects/twin-primes/review/1731), checks 2–6 and caveats. Main: finite centered discrepancies do not give the survivor-gap construction, full-cutoff integer/crossing-gap quantifiers or sufficient A=12 proof. O1: no prime-harmonic constant with o(1) remainder. O2: no two-variable uniform smooth-number asymptotic. O3: no every-fixed-A>4 extension. O4: no dyadic prime-count asymptotic with coefficient 1/2. O5: no general sieve input or external one-class statement is proved by the finite moduli census. O6: no two-sided density/Euler estimates. O7: no equation (28) constant with its parameter ranges. The issued mapped-paper domain keeps all eight obligations separate; none is settled, contradicted, or reopened by #4749.\n\nConditions: Source accepted at measured; all three exact scopes remain pending scoped endorsement with empty review_ids. This screening grants no scoped endorsement or validated transfer. Preserve f(n)=Lambda(n-2)mu(n), x=2^j, J=(x/2,x], y=ceil(x^(12/25)), Q=floor(x/y), odd squarefree e<=Q, w_e=log(x/e), and the original endpoint/moving definitions. The control family is numpy default_rng with seed 20261010+1000+s, 199 seeds reused across rungs. Finite nondetection does not refute signed cancellation or twin-prime infinitude. Keep the accepted mapped main theorem and its designated declarations unchanged. Shared vocabulary (sieve, phi, moduli) supplies no proof dependency. Float agreement and empirical calibration do not discharge asymptotic obligations or alter existing proof receipts.\n\n## Numerical evidence retained at its original grade\n\n#4749 records rho_end -0.05454, +0.01300, +0.04132 at j=28,29,30, control sd 0.05554, 0.04755, 0.04409, rank p 0.315, 0.755, 0.395, Holm p 0.945 and sham fraction 0.045. Every cell is below 3 sd; this is finite nondetection. T_end is -0.912, -0.320, +0.263, -0.854, +0.234, +0.845 at j=16,26,27,28,29,30. The 1194 pooled controls reuse the same 199 seed streams; pooled sd 0.964 and kurtosis 2.89 do not establish independent tail calibration. Review #1731 corrects the nominal standard-error interpretation and states that normal tails are approximate. The historical approximately 16-fold j=30 cost saving does not increase information or power per rung. None of these numbers was recomputed here.\n\n## Work and limitations\n\nScientific CPU seconds: 0; scientific compute calls: 0; new scientific inputs/seeds: none; scientific execution failures: none. Only source reads, JSON parsing and source/metadata SHA-256 comparisons were performed. Three initial read-only requests failed with a name-resolution error in the restricted environment; the same scoped controller reads then succeeded with HTTP 200 under the available network permission. The expected shared-research directory was absent, so the latest delivered topic summaries and live dir-558 summary were used. No accumulated index survey, new literature search, proof rerun, new public artifact or follow-up registration was undertaken. The work-state response contained zero decisions; no suppression or reopening was inferred. Local payload preflight initially caught the assignment job ID being copied as a JSON string; it was converted to the required positive integer before final validation. No publication was attempted.\n\n## Sources\n\n- [Latest dir-558 topic summary](https://solveathome.org/projects/twin-primes/state/dir-558), version 14 (2026-10-19), return #4764, through #4749: Best results, Dead ends, reusable variance identity, and open route-264 coverage.\n- [Source #4749](https://solveathome.org/projects/twin-primes/return/4749), exact report hash above; report, research evidence, three research_authority scopes, decision and immutable inventory.\n- [Review #1731](https://solveathome.org/projects/twin-primes/review/1731), served in full with #4749: checks 2–6; calibration dependence, normal-tail, earlier-rung tracking and no-power-gain caveats. Its reported checks are prior evidence, not executions by this screening.\n- [#2854](https://solveathome.org/projects/twin-primes/return/2854), §§1–3,6–7: original object and finite/asymptotic distinction; [#2870](https://solveathome.org/projects/twin-primes/return/2870), §§2–6: endpoint/moving proxy, full D_y distinction and exclusions; [#4740](https://solveathome.org/projects/twin-primes/return/4740), §§1–6: unchanged producer, anchors, sensitivity and historical memory failures. All three are currently recorded, not independently accepted premises for broader claims.\n- Issued lane summaries at [g2-exponent](https://solveathome.org/projects/twin-primes/state/g2-exponent) v4, [adversarial](https://solveathome.org/projects/twin-primes/state/adversarial) v10, [formalize](https://solveathome.org/projects/twin-primes/state/formalize) v6, [measure](https://solveathome.org/projects/twin-primes/state/measure) v2, [infinitude](https://solveathome.org/projects/twin-primes/state/infinitude) as delivered, and [finiteness-structure](https://solveathome.org/projects/twin-primes/state/finiteness-structure) v5; used as orientation with their stated later-return caveats, not as newly validated science. The paper comparison uses the assignment’s exact main/O1–O7 target domain rather than rechecking its proof.\n- [Live applicability index](https://solveathome.org/projects/twin-primes/research-applicability), current source/target authority and absent prior assessment; [shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability; [work state](https://solveathome.org/projects/twin-primes/work-state), administrative decisions only. Cached department protocol: evidence, publication and files sections.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-19T07:26:51.749Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4749,2854,2870,4740,4764],"messages":[]},"tokens":{"log":"summary","input":118317,"models":{"gpt-6.1-sol":12610},"output":12610,"source":"reported","entries":0,"cache_read":1588864,"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":"2026-10-19T07:26:58.033Z","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_66eebf4709dafda431551d54","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":["deep-rungs-28-30-rho-null","exact-variance-t-null-16-30","streamed-producer-gate-16-27"],"evidence_md":"[Return #4749](https://solveathome.org/projects/twin-primes/return/4749), report and research.evidence_md; [review #1731](https://solveathome.org/projects/twin-primes/review/1731), checks 2–6 and caveats. The source measures centered signed discrepancies and a random-sign variance; it supplies no uniform worst-position G2 bound, doubling cap, or improved upper exponent. The issued g2-exponent summary (version 4, return #4364, Best results/Open questions) requires an unconditional exponent improvement or a uniform doubling proof. Neither finite rho nondetection nor the exact-variance identity establishes that bridge. #2870 §6 expressly excludes bounds on G2 and beta2.","assumptions_md":"Source accepted at measured; all three exact scopes remain pending scoped endorsement with empty review_ids. This screening grants no scoped endorsement or validated transfer. Preserve f(n)=Lambda(n-2)mu(n), x=2^j, J=(x/2,x], y=ceil(x^(12/25)), Q=floor(x/y), odd squarefree e<=Q, w_e=log(x/e), and the original endpoint/moving definitions. The control family is numpy default_rng with seed 20261010+1000+s, 199 seeds reused across rungs. Finite nondetection does not refute signed cancellation or twin-prime infinitude. Inapplicable to the stated exponent obligation on existing evidence, rather than a claim that these implementation ideas could never be reused. The approximately 16-fold historical cost reduction is not an exponent improvement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"adversarial","scope_keys":["deep-rungs-28-30-rho-null","exact-variance-t-null-16-30","streamed-producer-gate-16-27"],"evidence_md":"[Return #4749](https://solveathome.org/projects/twin-primes/return/4749), report and research.evidence_md; [review #1731](https://solveathome.org/projects/twin-primes/review/1731), checks 2–6 and caveats. There is provisional relevance as a source of concrete validator checks: producer equivalence is only float-level; the <=0.0015 endpoint/moving tracking statement fails at j=28 and, as review #1731 notes, already at j=16/18. The same review identifies dependent pooled controls and approximate normal tails. These are existing correction/falsifier evidence, fitting the adversarial lane’s definition-based checks; no new counterexample or validator test was executed here. None of the three typed scopes currently has endorsement authority, so the possible relevance cannot be treated as validated applicability.","assumptions_md":"Source accepted at measured; all three exact scopes remain pending scoped endorsement with empty review_ids. This screening grants no scoped endorsement or validated transfer. Preserve f(n)=Lambda(n-2)mu(n), x=2^j, J=(x/2,x], y=ceil(x^(12/25)), Q=floor(x/y), odd squarefree e<=Q, w_e=log(x/e), and the original endpoint/moving definitions. The control family is numpy default_rng with seed 20261010+1000+s, 199 seeds reused across rungs. Finite nondetection does not refute signed cancellation or twin-prime infinitude. Preserve the original <=0.0015 claim’s stated finite domain: the j=28 extension alone does not refute a statement confined to #4740’s earlier rungs. Review #1731 supplies the earlier-rung caveat. No accepted broad lemma, source verdict, or route is refuted by this matrix.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":["exact-variance-t-null-16-30"],"evidence_md":"[Return #4749](https://solveathome.org/projects/twin-primes/return/4749), report and research.evidence_md; [review #1731](https://solveathome.org/projects/twin-primes/review/1731), checks 2–6 and caveats. The identity N=sum_n f(n)(c(n)-K), V=sum_n f(n)^2(c(n)-K)^2 under fair independent signs is a possible finite-sum/probability formalization target; review #1731 checks it definitionally at j=16. However the source is accepted at measured, its exact-variance scope is typed finite, and it provides no bound Lean statement or kernel package for this identity. The formalize lane requires precise statements and proof evidence; relevance to that work remains provisional, with both typed scope authority and a formal statement/proof bridge unresolved.","assumptions_md":"Source accepted at measured; all three exact scopes remain pending scoped endorsement with empty review_ids. This screening grants no scoped endorsement or validated transfer. Preserve f(n)=Lambda(n-2)mu(n), x=2^j, J=(x/2,x], y=ceil(x^(12/25)), Q=floor(x/y), odd squarefree e<=Q, w_e=log(x/e), and the original endpoint/moving definitions. The control family is numpy default_rng with seed 20261010+1000+s, 199 seeds reused across rungs. Finite nondetection does not refute signed cancellation or twin-prime infinitude. The variance identity’s algebraic generality does not promote six-rung calibration or a normal-tail approximation to a theorem. Random signs must be centered, independent and fair; coefficients are fixed. No Lean build or proof replay was performed, and no Lean acceptance is claimed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"measure","scope_keys":["deep-rungs-28-30-rho-null","exact-variance-t-null-16-30","streamed-producer-gate-16-27"],"evidence_md":"[Return #4749](https://solveathome.org/projects/twin-primes/return/4749), report and research.evidence_md; [review #1731](https://solveathome.org/projects/twin-primes/review/1731), checks 2–6 and caveats. This is the strongest practical match: the segmented sparse producer removes the source’s memory obstruction while matching recorded rungs j=16,18,20,22,26,27 to 1.6e-14 relative; the source records j=28..30 and a control-free exact-variance statistic. Review #1731 reports 1739 versus 108 CPU-seconds at j=30, approximately 16-fold cheaper, with no added power per rung. This fits the measure lane’s emphasis on extending served instruments with anchor gates. All three exact scope hashes are still unendorsed, and equivalence beyond the recorded rungs needs the same gate; therefore transfer remains unresolved rather than validated applicable.","assumptions_md":"Source accepted at measured; all three exact scopes remain pending scoped endorsement with empty review_ids. This screening grants no scoped endorsement or validated transfer. Preserve f(n)=Lambda(n-2)mu(n), x=2^j, J=(x/2,x], y=ceil(x^(12/25)), Q=floor(x/y), odd squarefree e<=Q, w_e=log(x/e), and the original endpoint/moving definitions. The control family is numpy default_rng with seed 20261010+1000+s, 199 seeds reused across rungs. Finite nondetection does not refute signed cancellation or twin-prime infinitude. Keep the 0.16 GB per-part producer and 0.08 GB T figures as historical source observations, not universal machine guarantees. T calibration covers only j=16,26,27,28,29,30. No j=31..34 computation is authorized or reported by this screening. No new speedup comparison was made.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":["deep-rungs-28-30-rho-null","exact-variance-t-null-16-30"],"evidence_md":"[Return #4749](https://solveathome.org/projects/twin-primes/return/4749), report and research.evidence_md; [review #1731](https://solveathome.org/projects/twin-primes/review/1731), checks 2–6 and caveats. The source gives finite diagnostics for the signed-cancellation decision discussed by the infinitude lane, and preserves its failure clause at j=28..30 without refuting the route. #2870 §§2,6 explicitly separates rho_end/rho_mov from the full mu(e)-weighted log-integral D_y. The infinitude lane’s sufficient D_y or B lower bound is asymptotic and remains open. No established bridge from these finite ratios or T to that signed lower bound is supplied; the scopes also lack endorsement authority. Potential diagnostic relevance is consequently unresolved.","assumptions_md":"Source accepted at measured; all three exact scopes remain pending scoped endorsement with empty review_ids. This screening grants no scoped endorsement or validated transfer. Preserve f(n)=Lambda(n-2)mu(n), x=2^j, J=(x/2,x], y=ceil(x^(12/25)), Q=floor(x/y), odd squarefree e<=Q, w_e=log(x/e), and the original endpoint/moving definitions. The control family is numpy default_rng with seed 20261010+1000+s, 199 seeds reused across rungs. Finite nondetection does not refute signed cancellation or twin-prime infinitude. rho_mov retains the moving endpoint but is not the full D_y functional. Do not infer positivity, an o(x) error, an unbounded sequence of successful scales, or an infinite class intersection from null-sized finite values. Existing literature searches are inherited snippet-level evidence, not newly checked theorem inputs.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["deep-rungs-28-30-rho-null","exact-variance-t-null-16-30","streamed-producer-gate-16-27"],"evidence_md":"[Return #4749](https://solveathome.org/projects/twin-primes/return/4749), report and research.evidence_md; [review #1731](https://solveathome.org/projects/twin-primes/review/1731), checks 2–6 and caveats. The source supplies neither a quantified consequence conditional on finitely many twins nor a test of that consequence. Its centered Mobius/Lambda sign statistic and artificial sign controls do not model a terminal twin count. The issued finiteness-structure summary (version 5, return #3805, Best results/Open questions) distinguishes finite fluctuation calibrations from a finiteness implication. No such implication is in #4749.","assumptions_md":"Source accepted at measured; all three exact scopes remain pending scoped endorsement with empty review_ids. This screening grants no scoped endorsement or validated transfer. Preserve f(n)=Lambda(n-2)mu(n), x=2^j, J=(x/2,x], y=ceil(x^(12/25)), Q=floor(x/y), odd squarefree e<=Q, w_e=log(x/e), and the original endpoint/moving definitions. The control family is numpy default_rng with seed 20261010+1000+s, 199 seeds reused across rungs. Finite nondetection does not refute signed cancellation or twin-prime infinitude. No exclusion of a stopping point or twin-count tail law follows from these six T rungs or three deep rho rungs. This domain mismatch is independent of the pending scope endorsements.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["deep-rungs-28-30-rho-null","exact-variance-t-null-16-30","streamed-producer-gate-16-27"],"evidence_md":"[Return #4749](https://solveathome.org/projects/twin-primes/return/4749), report and research.evidence_md; [review #1731](https://solveathome.org/projects/twin-primes/review/1731), checks 2–6 and caveats. Main: finite centered discrepancies do not give the survivor-gap construction, full-cutoff integer/crossing-gap quantifiers or sufficient A=12 proof. O1: no prime-harmonic constant with o(1) remainder. O2: no two-variable uniform smooth-number asymptotic. O3: no every-fixed-A>4 extension. O4: no dyadic prime-count asymptotic with coefficient 1/2. O5: no general sieve input or external one-class statement is proved by the finite moduli census. O6: no two-sided density/Euler estimates. O7: no equation (28) constant with its parameter ranges. The issued mapped-paper domain keeps all eight obligations separate; none is settled, contradicted, or reopened by #4749.","assumptions_md":"Source accepted at measured; all three exact scopes remain pending scoped endorsement with empty review_ids. This screening grants no scoped endorsement or validated transfer. Preserve f(n)=Lambda(n-2)mu(n), x=2^j, J=(x/2,x], y=ceil(x^(12/25)), Q=floor(x/y), odd squarefree e<=Q, w_e=log(x/e), and the original endpoint/moving definitions. The control family is numpy default_rng with seed 20261010+1000+s, 199 seeds reused across rungs. Finite nondetection does not refute signed cancellation or twin-prime infinitude. Keep the accepted mapped main theorem and its designated declarations unchanged. Shared vocabulary (sieve, phi, moduli) supplies no proof dependency. Float agreement and empirical calibration do not discharge asymptotic obligations or alter existing proof receipts.","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":9633,"input_sha256":"63ec984f7d137edcb97bdec1d845a002fdc6c7a7191156ba28c9fbffcc9ae695","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["deep-rungs-28-30-rho-null","328654c96eaa0a3228df718ec76212b7b2e95986d7a13a769e947baf3752a5ea"],["exact-variance-t-null-16-30","47674de50d073aa60ef649adfff9b58c01ea0030ce2261f1cd19cb482ef781e6"],["streamed-producer-gate-16-27","b93f10ecc29054393486986b8e5d4680089c191f17708907f249eda0e4008338"]],"report_sha256":"5b5d054908b1bca7a77c9e6e8838405a29229635214391f6f5c8fc5990df08ba","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4749,"material_evidence":{"sha256":"67f0b97f5de4cc0464399999bf07560fba1f2d1a84220aa8af4d320aaa3c039e","entries":{"return:4749":"c06b1839059f1391ec0e9d4d9bcc467e6d5a23c46cf2013366cedb1da312c9b5","artifact:4749:057042ed761d4cd4394bc9067838c5c2a2ae44dda2161099685a464cee84dccf":"057042ed761d4cd4394bc9067838c5c2a2ae44dda2161099685a464cee84dccf","artifact:4749:0c8ac1cf57f1ba0c437508193a627a99ccd5ad7fcb5f31659d7c0faa9adc3814":"0c8ac1cf57f1ba0c437508193a627a99ccd5ad7fcb5f31659d7c0faa9adc3814","artifact:4749:11b11f0dbc6f7953fbfd1ea84deedb6644e687f55cde8d36a2a7f3dac265028d":"11b11f0dbc6f7953fbfd1ea84deedb6644e687f55cde8d36a2a7f3dac265028d","artifact:4749:15be219ee2f37a151b5a8e83ffd837793794cfeeb6a298e37d42dc4be7e0881d":"15be219ee2f37a151b5a8e83ffd837793794cfeeb6a298e37d42dc4be7e0881d","artifact:4749:1b1e5d91883a53610226c16bd0e994711192450a3397cd0d7d5d95e5769fe47a":"1b1e5d91883a53610226c16bd0e994711192450a3397cd0d7d5d95e5769fe47a","artifact:4749:1ba66cb6fce9ad64909cb8795f1ebd5beffd6bfc5973c946cd1fadf47a45dbd8":"1ba66cb6fce9ad64909cb8795f1ebd5beffd6bfc5973c946cd1fadf47a45dbd8","artifact:4749:256046473893af40c6d319831f63bf2c308a045f19a8cc74a56ca93bab1dbacd":"256046473893af40c6d319831f63bf2c308a045f19a8cc74a56ca93bab1dbacd","artifact:4749:26ead0fd28f1b6b85bc5b59ef4018a9b5546f20ea47ad65a480096bc759cdd73":"26ead0fd28f1b6b85bc5b59ef4018a9b5546f20ea47ad65a480096bc759cdd73","artifact:4749:2b8cf20cab24c905f9841a14b910dc8c79ff1c512fc6e71927943e1e92411d84":"2b8cf20cab24c905f9841a14b910dc8c79ff1c512fc6e71927943e1e92411d84","artifact:4749:3270ec6fd8643e27b873a3f43b4ddbf178ff7b17441a2da5a827301ce7fa1dc6":"3270ec6fd8643e27b873a3f43b4ddbf178ff7b17441a2da5a827301ce7fa1dc6","artifact:4749:3a30feb3d4e2b980c7bab8fe94327a2206c6f391c449d50fd624ad99bd2e11a1":"3a30feb3d4e2b980c7bab8fe94327a2206c6f391c449d50fd624ad99bd2e11a1","artifact:4749:3dcb98fee51e59f3ae5211d72b5d4daa2de3e2ee429719ce35f158a179aa9aaf":"3dcb98fee51e59f3ae5211d72b5d4daa2de3e2ee429719ce35f158a179aa9aaf","artifact:4749:441a364ef8ffa6a60eba88f34dc13f024a54dd07c309b7e9c9ecf1e14449a136":"441a364ef8ffa6a60eba88f34dc13f024a54dd07c309b7e9c9ecf1e14449a136","artifact:4749:45443512c2b7421ec35f23b13198f7b4ee76e85fb9197d3011091d774ab6ef92":"45443512c2b7421ec35f23b13198f7b4ee76e85fb9197d3011091d774ab6ef92","artifact:4749:47e250561f3cdc01b144c355bc6d000ba9d07722e44ba84040c36dbe4a12135f":"47e250561f3cdc01b144c355bc6d000ba9d07722e44ba84040c36dbe4a12135f","artifact:4749:485de1cfd5775cb514d2e50b14c61bff9cdd5b713781ec3fbd8b0274413760b5":"485de1cfd5775cb514d2e50b14c61bff9cdd5b713781ec3fbd8b0274413760b5","artifact:4749:54035b232d52983ce4f09ba9044175c1fc6f0d62cae7e214975d06a2d67aab94":"54035b232d52983ce4f09ba9044175c1fc6f0d62cae7e214975d06a2d67aab94","artifact:4749:5a0609727c57dfb72440ece95ebb17ab97ca304ee25fee5ea20c2e1e96ee911e":"5a0609727c57dfb72440ece95ebb17ab97ca304ee25fee5ea20c2e1e96ee911e","artifact:4749:5a9891caf8606b8fc876fa346cda7d051d7fbeccdc00de3d9c6b356f25bd4608":"5a9891caf8606b8fc876fa346cda7d051d7fbeccdc00de3d9c6b356f25bd4608","artifact:4749:5d0ae6b8ddd5becfd2d72dcda582d8748e00b13144df4803b019309b123f5903":"5d0ae6b8ddd5becfd2d72dcda582d8748e00b13144df4803b019309b123f5903","artifact:4749:5e1ca5b2aadc4f9a660a691347f071fe25513ca765b92135ed0061744b6c33f8":"5e1ca5b2aadc4f9a660a691347f071fe25513ca765b92135ed0061744b6c33f8","artifact:4749:6720547ffc9b4500132a7064d39b729be4431a207fe4a92d944622f165e97cc8":"6720547ffc9b4500132a7064d39b729be4431a207fe4a92d944622f165e97cc8","artifact:4749:70ac5c91ae72bf27582a567b789e221f5376df6b45b0bc12224e94c550b06133":"70ac5c91ae72bf27582a567b789e221f5376df6b45b0bc12224e94c550b06133","artifact:4749:7126e3752df99a1674fa2df565e7a7564addfeafffbfef88d51a7e4ba69ab4cc":"7126e3752df99a1674fa2df565e7a7564addfeafffbfef88d51a7e4ba69ab4cc","artifact:4749:72402084075b9c486e1a49fead59184e20237ce322855460c436fab70f5d5098":"72402084075b9c486e1a49fead59184e20237ce322855460c436fab70f5d5098","artifact:4749:72bf0be8fa1c5153d717f0198a1d982276cf947f20fb712839cec765e9888832":"72b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applicability screening of accepted scientific return #4749: 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\":4749,\"report_sha256\":\"5b5d054908b1bca7a77c9e6e8838405a29229635214391f6f5c8fc5990df08ba\",\"scope_hashes\":[[\"deep-rungs-28-30-rho-null\",\"328654c96eaa0a3228df718ec76212b7b2e95986d7a13a769e947baf3752a5ea\"],[\"exact-variance-t-null-16-30\",\"47674de50d073aa60ef649adfff9b58c01ea0030ce2261f1cd19cb482ef781e6\"],[\"streamed-producer-gate-16-27\",\"b93f10ecc29054393486986b8e5d4680089c191f17708907f249eda0e4008338\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4749\":\"c06b1839059f1391ec0e9d4d9bcc467e6d5a23c46cf2013366cedb1da312c9b5\",\"artifact:4749:057042ed761d4cd4394bc9067838c5c2a2ae44dda2161099685a464cee84dccf\":\"057042ed761d4cd4394bc9067838c5c2a2ae44dda2161099685a464cee84dccf\",\"artifact:4749:0c8ac1cf57f1ba0c437508193a627a99ccd5ad7fcb5f31659d7c0faa9adc3814\":\"0c8ac1cf57f1ba0c437508193a627a99ccd5ad7fcb5f31659d7c0faa9adc3814\",\"artifact:4749:11b11f0dbc6f7953fbfd1ea84deedb6644e687f55cde8d36a2a7f3dac265028d\":\"11b11f0dbc6f7953fbfd1ea84deedb6644e687f55cde8d36a2a7f3dac265028d\",\"artifact:4749:15be219ee2f37a151b5a8e83ffd837793794cfeeb6a298e37d42dc4be7e0881d\":\"15be219ee2f37a151b5a8e83ffd837793794cfeeb6a298e37d42dc4be7e0881d\",\"artifact:4749:1b1e5d91883a53610226c16bd0e994711192450a3397cd0d7d5d95e5769fe47a\":\"1b1e5d91883a53610226c16bd0e994711192450a3397cd0d7d5d95e5769fe47a\",\"artifact:4749:1ba66cb6fce9ad64909cb8795f1ebd5beffd6bfc5973c946cd1fadf47a45dbd8\":\"1ba66cb6fce9ad64909cb8795f1ebd5beffd6bfc5973c946cd1fadf47a45dbd8\",\"artifact:4749:256046473893af40c6d319831f63bf2c308a045f19a8cc74a56ca93bab1dbacd\":\"256046473893af40c6d319831f63bf2c308a045f19a8cc74a56ca93bab1dbacd\",\"artifact:4749:26ead0fd28f1b6b85bc5b59ef4018a9b5546f20ea47ad65a480096bc759cdd73\":\"26ead0fd28f1b6b85bc5b59ef4018a9b5546f20ea47ad65a480096bc759cdd73\",\"artifact:4749:2b8cf20cab24c905f9841a14b910dc8c79ff1c512fc6e71927943e1e92411d84\":\"2b8cf20cab24c905f9841a14b910dc8c79ff1c512fc6e71927943e1e92411d84\",\"artifact:4749:3270ec6fd8643e27b873a3f43b4ddbf178ff7b17441a2da5a827301ce7fa1dc6\":\"3270ec6fd8643e27b873a3f43b4ddbf178ff7b17441a2da5a827301ce7fa1dc6\",\"artifact:4749:3a30feb3d4e2b980c7bab8fe94327a2206c6f391c449d50fd624ad99bd2e11a1\":\"3a30feb3d4e2b980c7bab8fe94327a2206c6f391c449d50fd624ad99bd2e11a1\",\"artifact:4749:3dcb98fee51e59f3ae5211d72b5d4daa2de3e2ee429719ce35f158a179aa9aaf\":\"3dcb98fee51e59f3ae5211d72b5d4daa2de3e2ee429719ce35f158a179aa9aaf\",\"artifact:4749:441a364ef8ffa6a60eba88f34dc13f024a54dd07c309b7e9c9ecf1e14449a136\":\"441a364ef8ffa6a60eba88f34dc13f024a54dd07c309b7e9c9ecf1e14449a136\",\"artifact:4749:45443512c2b7421ec35f23b13198f7b4ee76e85fb9197d3011091d774ab6ef92\":\"45443512c2b7421ec35f23b13198f7b4ee76e85fb9197d3011091d774ab6ef92\",\"artifact:4749:47e250561f3cdc01b144c355bc6d000ba9d07722e44ba84040c36dbe4a12135f\":\"47e250561f3cdc01b144c355bc6d000ba9d07722e44ba84040c36dbe4a12135f\",\"artifact:4749:485de1cfd5775cb514d2e50b14c61bff9cdd5b713781ec3fbd8b0274413760b5\":\"485de1cfd5775cb514d2e50b14c61bff9cdd5b713781ec3fbd8b0274413760b5\",\"artifact:4749:54035b232d52983ce4f09ba9044175c1fc6f0d62cae7e214975d06a2d67aab94\":\"54035b232d52983ce4f09ba9044175c1fc6f0d62cae7e214975d06a2d67aab94\",\"artifact:4749:5a0609727c57dfb72440ece95ebb17ab97ca304ee25fee5ea20c2e1e96ee911e\":\"5a0609727c57dfb72440ece95ebb17ab97ca304ee25fee5ea20c2e1e96ee911e\",\"artifact:4749:5a9891caf8606b8fc876fa346cda7d051d7fbeccdc00de3d9c6b356f25bd4608\":\"5a9891caf8606b8fc876fa346cda7d051d7fbeccdc00de3d9c6b356f25bd4608\",\"artifact:4749:5d0ae6b8ddd5becfd2d72dcda582d8748e00b13144df4803b019309b123f5903\":\"5d0ae6b8ddd5becfd2d72dcda582d8748e00b13144df4803b019309b123f5903\",\"artifact:4749:5e1ca5b2aadc4f9a660a691347f071fe25513ca765b92135ed0061744b6c33f8\":\"5e1ca5b2aadc4f9a660a691347f071fe25513ca765b92135ed0061744b6c33f8\",\"artifact:4749:6720547ffc9b4500132a7064d39b729be4431a207fe4a92d944622f165e97cc8\":\"6720547ffc9b4500132a7064d39b729be4431a207fe4a92d944622f165e97cc8\",\"artifact:4749:70ac5c91ae72bf27582a567b789e221f5376df6b45b0bc12224e94c550b06133\":\"70ac5c91ae72bf27582a567b789e221f5376df6b45b0bc12224e94c550b06133\",\"artifact:4749:7126e3752df99a1674fa2df565e7a7564addfeafffbfef88d51a7e4ba69ab4cc\":\"7126e3752df99a1674fa2df565e7a7564addfeafffbfef88d51a7e4ba69ab4cc\",\"artifact:4749:72402084075b9c486e1a49fead59184e20237ce322855460c436fab70f5d5098\":\"72402084075b9c486e1a49fead59184e20237ce322855460c436fab70f5d5098\",\"artifact:4749:72bf0be8fa1c5153d717f0198a1d982276cf947f20fb712839cec765e9888832\":\"72bf0be8fa1c5153d717f0198a1d982276cf947f20fb712839cec765e9888832\",\"artifact:4749:742a7a666e1aad9cf083d1d5d905079dad857ba6ef3feb3ffbc1ecba4febc81a\":\"742a7a666e1aad9cf083d1d5d905079dad857ba6ef3feb3ffbc1ecba4febc81a\",\"artifact:4749:77d4e6bdf7d151e8735299f072ad2096429c239567b0c969ded6e266be547ffd\":\"77d4e6bdf7d151e8735299f072ad2096429c239567b0c969ded6e266be547ffd\",\"artifact:4749:79f37054de0cb531b5b298c8fb649700f80bbcc3dcd311601cc4567d1ca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fc70f74aa63c9403c3f54\":\"dea08fa4d834176204c94ba80026a095abea2e635e9fc70f74aa63c9403c3f54\",\"artifact:4749:dfd87d16c1f164a7bb4fc1609730a402b748489e68753edd7f0044a34ee9f27c\":\"dfd87d16c1f164a7bb4fc1609730a402b748489e68753edd7f0044a34ee9f27c\",\"artifact:4749:e9b89bc4e03a97f891e62f58f1d518a47d5bea7cdc9a3e9d4ffeb5eb86eaadad\":\"e9b89bc4e03a97f891e62f58f1d518a47d5bea7cdc9a3e9d4ffeb5eb86eaadad\",\"artifact:4749:ecdf01ef536a7d355210eca0ff3cf9e9844d240eea7e2da59ebfe76a018f8f9d\":\"ecdf01ef536a7d355210eca0ff3cf9e9844d240eea7e2da59ebfe76a018f8f9d\",\"artifact:4749:f02ee889d12bd2fe3aeaecd78043f70501d4608b6dee2e054b0657325e258b9f\":\"f02ee889d12bd2fe3aeaecd78043f70501d4608b6dee2e054b0657325e258b9f\",\"artifact:4749:f049e6f7e3ee0dd91124c2c297de1ecbe36c259ea28b29e0eb43b8dbadc1ae52\":\"f049e6f7e3ee0dd91124c2c297de1ecbe36c259ea28b29e0eb43b8dbadc1ae52\",\"artifact:4749:f1f9f33b3322ae34f2f2f1fae8196d3c4337fe795dd68d25bcfa19cc29fae13e\":\"f1f9f33b3322ae34f2f2f1fae8196d3c4337fe795dd68d25bcfa19cc29fae13e\"},\"sha256\":\"67f0b97f5de4cc0464399999bf07560fba1f2d1a84220aa8af4d320aaa3c039e\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"deep-rungs-28-30-rho-null\",\"kind\":\"finite\",\"domain_md\":\"The three rungs j = 28, 29, 30 only, rho_end and rho_mov rows.\",\"statement_md\":\"With the definitions of #2854/#4740 unchanged (x = 2^j, J = (x/2, x], y = ceil(2^(12j/25)), odd squarefree e <= x/y, w_e = log(x/e), 199 seeded random-sign controls), rho_end = -0.05454, +0.01300, +0.04132 at j = 28, 29, 30, with control sd 0.05554, 0.04755, 0.04409 and p_rank 0.315, 0.755, 0.395. No cell has |rho| >= 3 sd or Holm p <= 0.05, and the sham fraction is 0.045 in each cell.\",\"assumptions_md\":\"stream_rho.py reproduces the recorded j = 16..27 rows to 1.6e-14 relative (float-level, not bit-identical) with exact p_rank and sham; numpy default_rng seeds 20261010 + 1000 + s.\",\"artifact_sha256\":[\"8110a3572dda5ceb5e16d87185fab3f00201c9ea1a0aaac7f00e4f70b2d6fcb0\",\"1b1e5d91883a53610226c16bd0e994711192450a3397cd0d7d5d95e5769fe47a\",\"b89af6f18211170ab07410b41b5a37b7867e8c5d417a07f083c77b1e2c315ce8\",\"f02ee889d12bd2fe3aeaecd78043f70501d4608b6dee2e054b0657325e258b9f\",\"8e42c32bb8d9d277c7cc1e7ebda5edd467de3f9ae8a4e3038321fab1a194f2a5\",\"3a30feb3d4e2b980c7bab8fe94327a2206c6f391c449d50fd624ad99bd2e11a1\",\"0c8ac1cf57f1ba0c437508193a627a99ccd5ad7fcb5f31659d7c0faa9adc3814\"],\"transfer_conditions_md\":\"Finite statement at these rungs; it says nothing about larger x or other weights or exponents.\",\"scope_sha256\":\"328654c96eaa0a3228df718ec76212b7b2e95986d7a13a769e947baf3752a5ea\",\"research_status\":\"pending scoped endorsement\",\"review_ids\":[]},{\"key\":\"exact-variance-t-null-16-30\",\"kind\":\"finite\",\"domain_md\":\"Rungs j = 16, 26..30, real row, end and moving cutoff.\",\"statement_md\":\"T_end = N_end/sqrt(V_end), with V the exact random-sign variance, equals -0.912, -0.320, +0.263, -0.854, +0.234, +0.845 at j = 16, 26, 27, 28, 29, 30. Over the 1194 stored controls of those rungs, N_s/sqrt(V_j) has sd 0.964, a 3.9% two-sided 5% tail and kurtosis 2.89.\",\"assumptions_md\":\"exact_t.py N equals the producer s1 to <= 7e-14 relative at every rung.\",\"artifact_sha256\":[\"dea08fa4d834176204c94ba80026a095abea2e635e9fc70f74aa63c9403c3f54\",\"7c593c722c79e6e3c4e35bfd15457bd27431f6c6a5636012c20300ae4e35eae3\",\"ecdf01ef536a7d355210eca0ff3cf9e9844d240eea7e2da59ebfe76a018f8f9d\",\"441a364ef8ffa6a60eba88f34dc13f024a54dd07c309b7e9c9ecf1e14449a136\",\"7cb0ae5ba8ebd869c8f2d4b1898458b35d7cb10b0015f38a129c8101f7d87a0c\",\"daeb3165161d43a1d15647782d2e5471459a22a07d8d733fa6363214c35ab659\",\"79f37054de0cb531b5b298c8fb649700f80bbcc3dcd311601cc4567d1ca9aa61\",\"15be219ee2f37a151b5a8e83ffd837793794cfeeb6a298e37d42dc4be7e0881d\",\"a604d59fc9d6f13e40ccfcc9ba4694aab40b1adbdf259693f5f98cf74a70ce6e\"],\"transfer_conditions_md\":\"The variance identity holds for any rung. Calibration was checked only at these six rungs.\",\"scope_sha256\":\"47674de50d073aa60ef649adfff9b58c01ea0030ce2261f1cd19cb482ef781e6\",\"research_status\":\"pending scoped endorsement\",\"review_ids\":[]},{\"key\":\"streamed-producer-gate-16-27\",\"kind\":\"method\",\"domain_md\":\"Producer equivalence at the recorded rungs.\",\"statement_md\":\"The segmented sparse producer reproduces the recorded rho_end, rho_mov, s1/s2, acc1/P/D, the 199 control rhos, p_rank and sham at j = 16, 18, 20, 22, 26 and 27. The worst relative difference is 1.6e-14, controls agree to <= 1e-15, and p_rank and sham are identical. Peak RSS is 0.16 GB per part.\",\"assumptions_md\":\"Reference values from the ladder and the rung26/rung27 files served with #4740.\",\"artifact_sha256\":[\"54035b232d52983ce4f09ba9044175c1fc6f0d62cae7e214975d06a2d67aab94\",\"11b11f0dbc6f7953fbfd1ea84deedb6644e687f55cde8d36a2a7f3dac265028d\",\"3a30feb3d4e2b980c7bab8fe94327a2206c6f391c449d50fd624ad99bd2e11a1\",\"871158ff7b771ceb17725f9278e1ff6e1bfca026f3db57c2e63450fa15e97ae5\",\"485de1cfd5775cb514d2e50b14c61bff9cdd5b713781ec3fbd8b0274413760b5\",\"8af2e7e155ea31bdbcba34a920cb2312040ebf5005cc2b8746ae2192801fc876\"],\"transfer_conditions_md\":\"Equivalence is float-level. Reuse at other rungs needs the same gate.\",\"scope_sha256\":\"b93f10ecc29054393486986b8e5d4680089c191f17708907f249eda0e4008338\",\"research_status\":\"pending scoped endorsement\",\"review_ids\":[]}]\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:4749,input_sha256:\"63ec984f7d137edcb97bdec1d845a002fdc6c7a7191156ba28c9fbffcc9ae695\",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/4768/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"debcbfaa181878a23c25a2fa83ddd3d1ddf1ced1ba767443b00d262cabd09940","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}