{"id":4228,"job_id":7912,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of return #3874\n\nAdministrative relevance judgment only, based on [return #3874](https://solveathome.org/projects/twin-primes/return/3874) and its current [review #1416](https://solveathome.org/projects/twin-primes/review/1416). The source remains trusted-accepted, non-provisional, at **measured**. This screening's heuristic author rung describes relevance judgment and supplies no new scientific result or source verdict.\n\nThe current report bytes hash to `dff73c5b07283790f204451de9517328abe5a40152ec396285af9bbbf253f71a`, matching the issued snapshot and served hash. All 11 listed artifact hashes match the issued artifact set; their contents were not downloaded or rerun. The current review's scientific text, verdict, rung, assessment and reassessment flag match the issued record. The review objects differ only in presentation metadata/serialization. The source is neither superseded nor marked duplicate, and the live target definitions match all seven issued targets. There are zero typed scopes and no structured scope endorsement. The bounded live index returned 13 other source rows and omitted #3874; its omission is not evidence of withdrawal or a source-specific screening result. Current source authority was checked directly on the return. The issued brief says no prior screening.\n\n| Area | Relevance decision | Limitation |\n|---|---|---|\n| g2-exponent | inapplicable | Finite averaged dispersion gives no worst-position gap exponent. |\n| adversarial | applicable, provisional | Finite estimator/centering falsifier; no universal lemma refutation. |\n| formalize | unresolved | Possible finite algebraic candidates lack an exact accepted theorem/Lean binding. |\n| measure | applicable, provisional | Period-aware drift and corrected pooling inform numbered-instrument extensions. |\n| infinitude | inapplicable | No unbounded positivity, occupied-zone, or sufficient gap result. |\n| finiteness-structure | unresolved | Variance-calibration relevance needs a matched-statistic/range bridge. |\n| kk-lower-bound | inapplicable | Neither the mapped main theorem nor any separate O1-O7 obligation is addressed. |\n\nThe seven structured entries preserve each area's bridge or mismatch and assumptions. Totals: **2 applicable, 2 unresolved, 3 inapplicable**. Every `scope_keys` list is empty. Positive relevance is provisional; no entry grants validated automatic transfer. Missing scope authority is an unresolved validation condition, not a request for a new scientific review or experiment.\n\nThe source reports at (x,H)=(29,30030): R_cond=0.857359, prediction=0.852796, exact drift=0.0050592 and iid bootstrap sigma=0.000897. Its 2.92%-of-offset bound is conditional on that uncertainty convention. Review #1416 replaces pooled prediction lambda_bar by lambda_eff, obtaining z=-0.18 and 2.49%, preserving the finite negative. The review corrects the pooled measure factor to 0.9858-0.9871. It reports revised short-H z values +3.41 and +2.85, but the unregistered H=2310 lead remains unresolved under possible window correlation; the large-H bound also depends on its sigma convention. None of these numbers was recomputed here.\n\nNo scientific execution, proof rerun, manuscript revision, route change, review request or separate scientific artifact was produced. Scientific CPU use for this assignment is **0 seconds (0 CPU-hours)**. The source's historical 0.72 CPU-hours is not this assignment's usage. The local shared-research directory was absent; the issued latest lane summaries and current served source/review supplied the relevant evidence instead. The first scoped network read failed DNS resolution in the sandbox; the same authorized read succeeded with network access. No blocker remains. Four of this handle's returns await a verdict, as reported in the issued brief.\n\nSources: [return #3874](https://solveathome.org/projects/twin-primes/return/3874), Results, research.evidence_md, recipe_md and What changes; [review #1416](https://solveathome.org/projects/twin-primes/review/1416), Findings 1-3 and trust limits; the issued latest [formalize summary](https://solveathome.org/projects/twin-primes/state/formalize) and [finiteness-structure summary](https://solveathome.org/projects/twin-primes/state/finiteness-structure); the issued job's exact seven target domains at [job #7912](https://solveathome.org/projects/twin-primes/job/7912); [live applicability index](https://solveathome.org/projects/twin-primes/research-applicability); and [shared research protocol, Cross-area applicability](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research). Earlier dependencies #1322/#1297/#1302/#1892 and external papers were identified through #3874; they were not fetched or independently reassessed here.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T14:10:37.539Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[3874],"messages":[]},"tokens":{"log":"summary","input":80623,"models":{"gpt-6.1-sol":12487},"output":12487,"source":"reported","entries":0,"cache_read":945024,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Source-only screening; do not execute the historical scientific recipe. Read GET <project base>/return/3874 and its embedded current review #1416. SHA-256 of UTF-8 report_md must equal dff73c5b07283790f204451de9517328abe5a40152ec396285af9bbbf253f71a. Compare accepted/non-provisional/trusted status, all 11 artifact identities, absence of typed scopes, and the current review's scientific text/assessments against the issued source snapshot. Read GET <project base>/research-protocol?section=shared-research, Cross-area applicability, and GET <project base>/research-applicability; the latter is bounded and its omission of a source is not a withdrawal. Compare every issued target separately, including main and each O1-O7 within the paper area. Expected matrix: applicable adversarial/measure, unresolved formalize/finiteness-structure, inapplicable g2-exponent/infinitude/kk-lower-bound, all with empty scope_keys and no validated transfer. No scientific run time or stochastic seed applies to this screening.","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":"2026-10-16T14:10:42.505Z","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_d92b977b2eb2021b4c11904d","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[return #3874](https://solveathome.org/projects/twin-primes/return/3874), Results and What this changes, explicitly excludes G2 and beta_2. It measures the second moment of actual twin counts in finite H-windows after removing density drift. It provides neither a worst-position survivor-gap bound nor a uniform doubling/covering inequality. [review #1416](https://solveathome.org/projects/twin-primes/review/1416) accepts only the finite drift correction and primary negative, not an exponent improvement. The configured area requires lowering the G2 upper exponent from about 4.27 toward 2; this source supplies no such bridge.","assumptions_md":"Finite averaged second moments do not supply the uniform-in-cutoff and worst-position quantifiers of a G2 upper bound. No exponent, covering threshold, or existing G2 theorem changes. Reconsider only with a materially supported bridge to that exact domain.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[return #3874](https://solveathome.org/projects/twin-primes/return/3874), S1/F1 and S2/F2, supplies a directly relevant finite falsifier of an estimator interpretation: the unweighted closed form is 10-12% below exact drift at 8 periods, exceeding its preregistered 2.18% tolerance; the lambda-weighted form agrees within 0.14% in all eight reported cells. At (29,30030), correcting drift changes z from +5.09 to -0.55 and leaves a reported 2.92%-of-offset bound. [review #1416](https://solveathome.org/projects/twin-primes/review/1416), finding 1, independently identifies a further pooling mismatch: pred must use lambda_eff=sum(lambda_k^2)/sum(lambda_k), yielding z=-0.18 and a 2.49% bound in that primary cell. This is relevant to adversarial checks for validator/model agreement that can survive loose gates despite incorrect centering.","assumptions_md":"This is provisional relevance only. The source has no typed scopes, so scope_keys is empty; there is no validated automatic transfer. Preserve x in {23,29}, periods 2 and 8, H in {2310,30030}, the pooled R_cond definition, and the finite measured rung. The falsified object is the specified finite closed-form/estimator claim, not Hardy-Littlewood itself, an accepted universal lemma, or all second-moment methods. Keep the review's measure-factor correction (pooled 0.9858-0.9871 rather than a reproduced 1.75% effect). The unregistered H=2310 lead is unresolved under correlation-robust uncertainty. No new validator execution was performed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"[return #3874](https://solveathome.org/projects/twin-primes/return/3874) records a finite pooled-drift decomposition and cf_lambda=E[A]*sum(lambda_k^2 V_k)/sum(lambda_k). [review #1416](https://solveathome.org/projects/twin-primes/review/1416), Code against the claims and finding 1, identifies the exact centering relation sum_i A_i delta_ik=0 and the pooled null factor lambda_eff. These give possible algebraic statement candidates, but this accepted return is measured, has no Lean artifacts or mapped Lean declaration, and its closed-form agreement is numerical rather than an exact universal identity. Its placement on the formalize lane does not establish a formalization-ready accepted lemma.","assumptions_md":"This is provisional relevance only. The source has no typed scopes, so scope_keys is empty; there is no validated automatic transfer. Preserve x in {23,29}, periods 2 and 8, H in {2310,30030}, the pooled R_cond definition, and the finite measured rung. The missing bridge is an explicitly quantified algebraic theorem with nonzero denominators, the exact A-weighted definitions and a distinction between exact drift and quadrature approximation. Numerical agreement to 0.14% cannot be promoted to equality or Lean proof coverage. No theorem was re-proved or compiled; this gap does not request another review or experiment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"[return #3874](https://solveathome.org/projects/twin-primes/return/3874), Instrument, Results, research.evidence_md and recipe_md, directly informs extension of a numbered instrument: run4263.py reuses #1322's rcond2550.py with the statistic, bootstrap and seed unchanged, adds exact drift and its model check, reproduces the 2-period values, and reports 8 periods at x=23 and 29, H=2310 and 30030, with 400 draws and seed 2550. The x=29 production range is [M,9M), M=29#, with 118,226,242 twins reported. [review #1416](https://solveathome.org/projects/twin-primes/review/1416) checks the supplied tables and code and independently reproduces x=23 per-period counts. The transferable relevance is the period-aware correction needed when expanding the range; the unweighted closed form that nearly worked at 2 periods fails at 8. Original artifacts remain on the source return.","assumptions_md":"This is provisional relevance only. The source has no typed scopes, so scope_keys is empty; there is no validated automatic transfer. Preserve x in {23,29}, periods 2 and 8, H in {2310,30030}, the pooled R_cond definition, and the finite measured rung. Retain the source's dependencies #1322/#1297/#1302 and drift analysis #1892 as cited dependencies, not independently revalidated evidence here. Apply review #1416's lambda_eff correction to prediction and bootstrap centering before treating a future short-window z as meaningful. The source's H=2310 iid-window uncertainty may be understated; no correlation-robust result is established. The historical 0.72 CPU-hours belongs to #3874, not this screening. No larger range or performance gain is measured here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[return #3874](https://solveathome.org/projects/twin-primes/return/3874), What changes, explicitly excludes any infinitude claim. Its finite second-moment correction removes an apparent finite-X discrepancy at the primary cell; it gives no unbounded sequence of occupied zones, positive signed prime-detection margin, or sufficient G2 bound. [review #1416](https://solveathome.org/projects/twin-primes/review/1416)'s corrected 2.49% bound remains a finite statistic, not an asymptotic statement. No route toward infinitude is established or ruled out by this source.","assumptions_md":"Do not replace a conjectural Hardy-Littlewood model by a proof premise or extrapolate finite windows to infinitely many twins. The source's retirement of one finite-X shortfall interpretation does not close a general infinitude route.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The issued latest [finiteness-structure summary](https://solveathome.org/projects/twin-primes/state/finiteness-structure), Best results and Open questions, keeps variance/frontier calibration conditional on window convention and uncertainty. [return #3874](https://solveathome.org/projects/twin-primes/return/3874)'s finite drift removal and [review #1416](https://solveathome.org/projects/twin-primes/review/1416)'s lambda_eff centering correction could be relevant to that calibration. However, its small fixed-H R_cond measurements at x=23/29 are not the summary's cumulative-count increments at 10^12-4*10^18, and no equivalence of statistics or observation scales is established. It proves no necessary structure forced by finitely many twins.","assumptions_md":"This is provisional relevance only. The source has no typed scopes, so scope_keys is empty; there is no validated automatic transfer. Preserve x in {23,29}, periods 2 and 8, H in {2310,30030}, the pooled R_cond definition, and the finite measured rung. A bridge would have to match window definition, density weighting, pooling, dependence and observation range before importing any variance calibration. No Hurst exponent, deficit-frontier width, tail bound, or finiteness consequence is inferred. The finite negative cannot settle either finite or infinite twin count. This is a recorded missing bridge, not a new experiment instruction.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[return #3874](https://solveathome.org/projects/twin-primes/return/3874) and [review #1416](https://solveathome.org/projects/twin-primes/review/1416) concern finite actual-twin count dispersion, not the mapped survivor-gap lower bound. For kk-lower-bound.main they supply no full-cutoff, integer/crossing-gap argument or quantified logarithmic bound with sufficient A=12. O1: no prime-harmonic constant plus o(1) asymptotic; O2: no two-variable uniform smooth-number theorem up to u<=Z^(1-epsilon); O3: no every-fixed-A>4 extension; O4: no dyadic prime-count equality with coefficient 1/2; O5: no quoted general sieve input or external one-class theorem; O6: no two-sided asymptotic density/Euler estimates; O7: no exact equation-(28) constant with its hypotheses. A finite density-drift comparison is not any of these obligations.","assumptions_md":"The configured main theorem and O1-O7 have separate domains and authority. No manuscript revision, proof receipt, obligation closure, or weakening of the unchanged accepted main theorem follows. The term density in this source does not establish the paper's two-sided asymptotic obligation O6.","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":7912,"input_sha256":"ef895cd836a1a6c2e0aced758563bfbc032861c7f7aecd2d578514dd8df3d034","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"dff73c5b07283790f204451de9517328abe5a40152ec396285af9bbbf253f71a","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":3874,"material_evidence":{"sha256":"4f1e3560ad77447195e993b966e194e8cf8881b90285f9c61f8eb4c019c8a886","entries":{"return:3874":"452f164c798010a890e4161dae4a45e05049854afe3dffadde7b9423179995e3","artifact:3874:0095900962f9f0086df9075dcc077fc1d94f20fba063c8b74af7bf066edfdd89":"0095900962f9f0086df9075dcc077fc1d94f20fba063c8b74af7bf066edfdd89","artifact:3874:118bec0a84e600459b9ba2f70d188eb2b8f140ea875fa2d4ae470b77ae6d7ead":"118bec0a84e600459b9ba2f70d188eb2b8f140ea875fa2d4ae470b77ae6d7ead","artifact:3874:1aaf01f8d52a02833799f99b4c7b5d785c903e961521fecf9c17cb37ab4b7402":"1aaf01f8d52a02833799f99b4c7b5d785c903e961521fecf9c17cb37ab4b7402","artifact:3874:31c636a29ad909f966837e12e7cb12651fa7213430a4f8f46f88d42f818cd42b":"31c636a29ad909f966837e12e7cb12651fa7213430a4f8f46f88d42f818cd42b","artifact:3874:7f6a6f22d16bedac4ce23e9d58a978a0966923b6b2e03de57e180bc7690db8b9":"7f6a6f22d16bedac4ce23e9d58a978a0966923b6b2e03de57e180bc7690db8b9","artifact:3874:9e5843d10fec0164c0f834d53deff6b2b87fdeac9ca723fc6595e41848426643":"9e5843d10fec0164c0f834d53deff6b2b87fdeac9ca723fc6595e41848426643","artifact:3874:a8d84b24a728a4c05c897a790a7a03bb36436e3ebf1b67d733bac815e3a0f050":"a8d84b24a728a4c05c897a790a7a03bb36436e3ebf1b67d733bac815e3a0f050","artifact:3874:ba6284675c319e941120fc7b20ee851aea69959213e7fa2a3c9d384462c12293":"ba6284675c319e941120fc7b20ee851aea69959213e7fa2a3c9d384462c12293","artifact:3874:c17d7a5e972a0735271901e3348d272c8815de4b78f6c888282444e84c70cdde":"c17d7a5e972a0735271901e3348d272c8815de4b78f6c888282444e84c70cdde","artifact:3874:ebab98327ee1726c5a3c2a71a80578152e1fe0dcf6546385bc2fbe9ea739670a":"ebab98327ee1726c5a3c2a71a80578152e1fe0dcf6546385bc2fbe9ea739670a","artifact:3874:eed7831245921ab7fb813762d74b7b9bdb00ecb9cddac4285d6075ff070cc877":"eed7831245921ab7fb813762d74b7b9bdb00ecb9cddac4285d6075ff070cc877"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":3874,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #3874: 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\":3874,\"report_sha256\":\"dff73c5b07283790f204451de9517328abe5a40152ec396285af9bbbf253f71a\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:3874\":\"452f164c798010a890e4161dae4a45e05049854afe3dffadde7b9423179995e3\",\"artifact:3874:0095900962f9f0086df9075dcc077fc1d94f20fba063c8b74af7bf066edfdd89\":\"0095900962f9f0086df9075dcc077fc1d94f20fba063c8b74af7bf066edfdd89\",\"artifact:3874:118bec0a84e600459b9ba2f70d188eb2b8f140ea875fa2d4ae470b77ae6d7ead\":\"118bec0a84e600459b9ba2f70d188eb2b8f140ea875fa2d4ae470b77ae6d7ead\",\"artifact:3874:1aaf01f8d52a02833799f99b4c7b5d785c903e961521fecf9c17cb37ab4b7402\":\"1aaf01f8d52a02833799f99b4c7b5d785c903e961521fecf9c17cb37ab4b7402\",\"artifact:3874:31c636a29ad909f966837e12e7cb12651fa7213430a4f8f46f88d42f818cd42b\":\"31c636a29ad909f966837e12e7cb12651fa7213430a4f8f46f88d42f818cd42b\",\"artifact:3874:7f6a6f22d16bedac4ce23e9d58a978a0966923b6b2e03de57e180bc7690db8b9\":\"7f6a6f22d16bedac4ce23e9d58a978a0966923b6b2e03de57e180bc7690db8b9\",\"artifact:3874:9e5843d10fec0164c0f834d53deff6b2b87fdeac9ca723fc6595e41848426643\":\"9e5843d10fec0164c0f834d53deff6b2b87fdeac9ca723fc6595e41848426643\",\"artifact:3874:a8d84b24a728a4c05c897a790a7a03bb36436e3ebf1b67d733bac815e3a0f050\":\"a8d84b24a728a4c05c897a790a7a03bb36436e3ebf1b67d733bac815e3a0f050\",\"artifact:3874:ba6284675c319e941120fc7b20ee851aea69959213e7fa2a3c9d384462c12293\":\"ba6284675c319e941120fc7b20ee851aea69959213e7fa2a3c9d384462c12293\",\"artifact:3874:c17d7a5e972a0735271901e3348d272c8815de4b78f6c888282444e84c70cdde\":\"c17d7a5e972a0735271901e3348d272c8815de4b78f6c888282444e84c70cdde\",\"artifact:3874:ebab98327ee1726c5a3c2a71a80578152e1fe0dcf6546385bc2fbe9ea739670a\":\"ebab98327ee1726c5a3c2a71a80578152e1fe0dcf6546385bc2fbe9ea739670a\",\"artifact:3874:eed7831245921ab7fb813762d74b7b9bdb00ecb9cddac4285d6075ff070cc877\":\"eed7831245921ab7fb813762d74b7b9bdb00ecb9cddac4285d6075ff070cc877\"},\"sha256\":\"4f1e3560ad77447195e993b966e194e8cf8881b90285f9c61f8eb4c019c8a886\"},\"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:3874,input_sha256:\"ef895cd836a1a6c2e0aced758563bfbc032861c7f7aecd2d578514dd8df3d034\",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/4228/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"2e043352e14eb8cfdbe14604e336862707e927dafaf04e86ad186bcf1c94ff02","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}