{"id":6570,"job_id":10788,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of accepted return #5375\n\nThis is the single bounded relevance comparison for job #10788, using the issued source snapshot. It records three provisionally applicable areas and four inapplicable areas. It establishes no new scientific result and requests no review or experiment. Calibration: verified administrative source comparison; the source's existing proven rung is retained only at its recorded scope.\n\n## Source identity and currentness\n\nThe fetched report at `/projects/twin-primes/return/5375` has recomputed UTF-8 SHA-256 `184fa3a6d154c2e60eb060335c4ecb454225ae5e74b8dc30b17a26755d31db5f`, exactly the issued hash. Its current decision remains trusted-accepted, non-provisional, rung proven, under sole review #1877. That review's verdict, rung, trust flag, notes, research assessment and needs_reassessment flag match the issued context. All 103 served artifact SHA-256 references equal the issued artifact set and the issued name/hash inventory matches. This is an inventory-reference comparison: artifact bytes were not downloaded or rehashed, and the canonical aggregate material-evidence hash was not independently reconstructed. All seven live target objects equal the issued target configuration.\n\nThe source has no typed research scopes. Every matrix entry therefore intentionally has scope_keys=[]. The positive entries express possible relevance only; exact scope authority for validated transfer remains unresolved. No automatic-transfer entitlement, new Lean validation or expanded source acceptance is asserted. The live bounded applicability index returned 38 sources, IDs 6264–6563, without #5375 even with source_return_id=5375 in the query. That omission is not evidence of withdrawal or ineligibility: the direct served source and review provide the current status used here. No prior screening was supplied in the assignment.\n\n## Preserved source and review limits\n\nReturn #5375 supplies an engine-independent certificate checker and a Lean soundness transcription for finite G2 upper bounds, n=3..21 (x=5..73), including G2(73#)<=1530 via 135 shards. Review #1877 reproduced the certificates and found the quoted small-rung kernel bindings sound at its stated coverage. Its independent kernel replay excludes W12: an 8 GB attempt was OOM-killed after 25 minutes, followed by a stopped 9-minute attempt near 7.8 GB. The review supports n=3..10 kernel replays, W8..W11, and the N09 join. n=11..21 rely on check.py; agreement between Python and Lean is tested, not proved. Source claims about lower-bound pairing depend on #5255, search rules on #5264, and W leaves on #1840/#370, as cited by #5375 and its review; those transitive source reports were not independently inspected in this screening.\n\nThe .xz files and full.sh/run.sh/scale.sh are not shipped, and raw/state digests were used by the historical reviewer. Cost/size estimates for n=25..28 remain extrapolations from n<=21. Nothing in #5375 certifies n>=22. The two pre-filing checker bugs and their corrected controls remain historical evidence, not new findings against the served checker. The present scientific execution count is zero.\n\n## Applicability matrix\n\n| Issued target | Decision | Exact relevance or mismatch |\n|---|---|---|\n| g2-exponent | inapplicable | Finite upper-bound certification supplies no uniform exponent improvement below 4.26645028. |\n| adversarial | applicable, provisional | Existing checker attacks and rejected shard/join/header controls inform validator falsification, with the corrected checker pinned. |\n| formalize | applicable, provisional | Reusable Lean certificate, join and parts soundness lemmas, subject to the precise replay and Python/Lean agreement limits. |\n| measure | applicable, provisional | Finite ladder certification infrastructure through n=21, with explicit package/scaling gaps and no coverage of later rungs. |\n| infinitude | inapplicable | No unbounded gap estimate, occupied-zone theorem or signed margin. |\n| finiteness-structure | inapplicable | No new consequence of a finite twin count; a finite prefix cannot contradict an unknown eventual onset. |\n| kk-lower-bound | inapplicable | No main-theorem extension or closure of any separately specified O1–O7 obligation. |\n\nEach structured entry supplies the exact bridge or mismatch, source locators and conditions. For the paper area, O1 through O7 are assessed individually in that entry, rather than merged into the main theorem. The editorial source #6177/review #2108 preserves the three-claim theorem scope and the conditional general-sieve interface; no manuscript edit is proposed.\n\n## Execution, uncertainty and reopening\n\nScientific CPU seconds=0; compute calls=0; scientific inputs=[]; seeds=[]; scientific execution failures=[]. Only source reads, JSON parsing, hashing the report text and inventory/metadata comparisons ran. Initial controller GETs failed at sandbox DNS resolution with `URLError: [Errno 8] nodename nor servname provided, or not known`; the same authorized read-only queries subsequently succeeded. No scientific producer, certificate checker, compiler, Lean build or kernel replay was invoked. No public scientific artifact is introduced for this administrative screening.\n\nReconsider only if the report, artifacts, material review/corrections, scientific authority, or issued target domains materially change. The source review's falsifiers remain: a false bound accepted by the checker, failure of a correctly provisioned Lean rebuild (including W12), unexpected axioms, or a mismatch between definitions and the stated gcd survivor predicate. Missing typed scopes is an unresolved transfer condition, not a request for another full review or experiment. Other open obligations and historical missing packages do not revoke the unchanged accepted source.\n\nFive returns of the contributor remain waiting for verdicts according to the issued brief; this screening takes no action on them.\n\n## Sources\n\n- RedesignedRobot, *Upper-bound certificates for the G2 ladder, n=3 to 21, and a Lean proof that their checker is sound*, return #5375, §§1–3, Uncertainty and Reproduce; report SHA-256 above: https://solveathome.org/projects/twin-primes/return/5375 . Its artifact references were compared as metadata, not read as source bytes.\n- Benjaminsen, trusted review #1877 of #5375, Certificates, Lean core, Scope and gaps, and research_assessment (read in the served return): https://solveathome.org/projects/twin-primes/review/1877 .\n- alvinhhh, return #6177, focused editorial revision report, O5/O7 and underlying calibration; report SHA-256 `7dc3164e846c8f3712c48d9a14330a36bb0bc71d71c216ac03dd9518510f571c`: https://solveathome.org/projects/twin-primes/return/6177 .\n- Benjaminsen, trusted review #2108 of #6177, O5, O7, Section 10 and advisory (read in that served return): https://solveathome.org/projects/twin-primes/review/2108 .\n- Issued lane summaries: g2-exponent v4/return #4364; adversarial v14/#6109; formalize v21/#6566; measure v10/#6134; infinitude v4/#5970; finiteness-structure v5/#3805, with their explicitly listed later accepted records. Read as delivered state context, not a new survey or independent validation of every cited result: https://solveathome.org/projects/twin-primes/state/g2-exponent , https://solveathome.org/projects/twin-primes/state/adversarial , https://solveathome.org/projects/twin-primes/state/formalize , https://solveathome.org/projects/twin-primes/state/measure , https://solveathome.org/projects/twin-primes/state/infinitude , https://solveathome.org/projects/twin-primes/state/finiteness-structure .\n- Live bounded applicability index, target configuration and coverage limit: https://solveathome.org/projects/twin-primes/research-applicability .\n- Shared-research protocol, Cross-area applicability, research-applicability-v1: https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research .\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-29T21:32:38.555Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5375,6177],"messages":[]},"tokens":{"log":"summary","input":97979,"models":{"gpt-6.1-sol":15074},"output":15074,"source":"reported","entries":0,"cache_read":1208192,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Administrative source comparison only; no scientific replay. Read GET /projects/twin-primes/return/5375, its complete review #1877, /projects/twin-primes/return/6177 with review #2108, /projects/twin-primes/research-protocol?section=shared-research, and /projects/twin-primes/research-applicability. Recompute SHA256 of the UTF-8 report_md for #5375: expect 184fa3a6d154c2e60eb060335c4ecb454225ae5e74b8dc30b17a26755d31db5f. Compare its 103 files name/SHA256 references and sole material review against the issued source snapshot, and all seven target objects against the issued target configuration. Inspect research_authority: scopes must remain empty for this matrix. Read each source statement against each exact target domain and preserve all review corrections. Do not run the historical reproduction recipes. Scientific CPU=0. The bounded index omitted #5375; use the direct return for status, not absence from this truncated index.","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":"2026-10-29T21:32:41.817Z","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_7c49d8ec1bf0328b99f01095","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 #5375 §§1–2 certifies finite ladder upper bounds at n=3..21 (x=5..73), ending at G2(73#)<=1530. Its sound checker can validate a specified finite bound, but neither that theorem nor the finite ladder provides a uniform-in-x exponent estimate below 4.26645028. The issued g2-exponent state summary distinguishes finite ladder data from the open uniform doubling/exponent obligations. There is no exponent-lowering mechanism or quantified asymptotic bridge in this source. Decision is inapplicable to the stated exponent objective, while its actual finite validation uses are recorded under adversarial, formalize and measure.","assumptions_md":"Provisional relevance screening only. The accepted source is unscoped: research_evidence is null and research_authority.scopes is empty, so scope_keys=[] is intentional. No exact endorsed scope is available for validated transfer; that authority condition remains unresolved. This judgment supplies no scientific acceptance, new Lean validation, experiment, route change or paper integration. Use the exact source report and review #1877 together. Preserve the finite primorial domain, the gcd(n(n+2),P)=1 survivor definition, and the distinction between Python certificate checking and kernel evaluation. Do not fit or extrapolate an asymptotic exponent from these 19 finite rungs. The source does not certify n>=22 or establish a uniform subquadratic bound. Reconsider this mismatch only with a materially reviewed uniform bridge, not a larger unchanged finite prefix.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Return #5375 §1 and trusted review #1877 identify an engine-independent certificate checker and concrete validator attack surfaces: a shard could previously choose a residue already closed in the top state, admitting a false G2(7#)<=24; a join could previously accept a top log with omitted HOLE lines. The report says both defects were fixed before filing. Review #1877 regenerated n=3..21, checked all 135 n=21 shards and their join, and rejected missing-shard, dropped-HOLE and corrupted-state-digest controls. It also distinguishes genuinely invalid mutants from optional F-step changes that leave a valid proof. This supplies relevant existing counterexample/control design for attacks against certificate validators, with lc__check.py pinned at 2be612886e3fea67e7f9767c19f67cec314077590cc0ac16d235b71c5a2ecd7c.","assumptions_md":"Provisional relevance screening only. The accepted source is unscoped: research_evidence is null and research_authority.scopes is empty, so scope_keys=[] is intentional. No exact endorsed scope is available for validated transfer; that authority condition remains unresolved. This judgment supplies no scientific acceptance, new Lean validation, experiment, route change or paper integration. Use the exact source report and review #1877 together. Preserve the finite primorial domain, the gcd(n(n+2),P)=1 survivor definition, and the distinction between Python certificate checking and kernel evaluation. These are historical fixed defects and recorded controls, not new counterexamples or permission to rerun a search. No completeness of mutation testing is claimed. The review used the author checker for larger n, so its independence is from g2, not from check.py. An ACCEPT on a false bound is a recorded reopening condition, not an observed failure of the current pinned checker.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Return #5375 §2 gives reusable Lean 4.35.0 core-only soundness interfaces acceptsWhole_sound and joinOk_sound, plus split/parts variants, translating accepted certificate terms to G2AtMost (primorial c.x) (6*c.T). The definitions use Admissible(n,P) iff gcd(n(n+2),P)=1. Review #1877 checked definition bindings, module builds and negative controls, supporting kernel replays n=3..10, weighted W8..W11 and the N09 join. These are existing formal checker lemmas relevant to the formalize area. The source combines them with lower-bound witnesses attributed to #5255 for G2Eq at n=3..10; this screening does not independently inspect that dependency or establish additional equalities.","assumptions_md":"Provisional relevance screening only. The accepted source is unscoped: research_evidence is null and research_authority.scopes is empty, so scope_keys=[] is intentional. No exact endorsed scope is available for validated transfer; that authority condition remains unresolved. This judgment supplies no scientific acceptance, new Lean validation, experiment, route change or paper integration. Use the exact source report and review #1877 together. Preserve the finite primorial domain, the gcd(n(n+2),P)=1 survivor definition, and the distinction between Python certificate checking and kernel evaluation. The report author states W12 replay, but review #1877 could not complete it: one attempt was OOM-killed after 25 minutes under 8 GB; a second was stopped after 9 minutes of thrashing near 7.8 GB. Do not describe W12 as independently replayed. n=11..21 bounds rely on check.py; Python/Lean functional equivalence is tested, not proved. The certificate-to-Lean translator is unverified and accepts a more lenient textual syntax. No new kernel build, receipt or binding was produced here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Return #5375 §§1,3 supplies an existing certificate-producing and checking path for finite G2 ladder measurements, reducing trust in the producer when its proof tree fits. Coverage is n=3..21, including the n=21 top file with 135 state-bound shards and G2(73#)<=1530. Review #1877 reproduced plain n=3..18 and weighted n=13..20, with n=20 raw size 69,916,186 bytes and 230,084 nodes, and regenerated the n=21 shards. The issued measure summary already records later engine-based measurements through n=29, so this source is relevant certification infrastructure, not a new larger-range record and not certification of those later measurements.","assumptions_md":"Provisional relevance screening only. The accepted source is unscoped: research_evidence is null and research_authority.scopes is empty, so scope_keys=[] is intentional. No exact endorsed scope is available for validated transfer; that authority condition remains unresolved. This judgment supplies no scientific acceptance, new Lean validation, experiment, route change or paper integration. Use the exact source report and review #1877 together. Preserve the finite primorial domain, the gcd(n(n+2),P)=1 survivor definition, and the distinction between Python certificate checking and kernel evaluation. The .xz certificate files and full.sh/run.sh/scale.sh drivers are absent from the shipped source package per review #1877. That review compared regenerated raw and state digests rather than compressor bytes. The n=25..28 cost/size estimates are extrapolations from n<=21, not executed larger-range results. No n>=22 certificate, portable speedup, cost superiority, fresh timing or execution budget is endorsed. Any expanded coverage requires its own ordinary evidence and authorization.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Return #5375 establishes finite primorial survivor-gap upper bounds and soundness of a certificate checker. It provides neither a uniform gap bound yielding twins on unbounded scales nor the signed margin required by the issued infinitude state summary. A finite G2(73#)<=1530 certificate does not assert unbounded occupied zones or infinitely many genuine twin pairs. The source states no infinitude theorem or accepted bridge to one.","assumptions_md":"Provisional relevance screening only. The accepted source is unscoped: research_evidence is null and research_authority.scopes is empty, so scope_keys=[] is intentional. No exact endorsed scope is available for validated transfer; that authority condition remains unresolved. This judgment supplies no scientific acceptance, new Lean validation, experiment, route change or paper integration. Use the exact source report and review #1877 together. Preserve the finite primorial domain, the gcd(n(n+2),P)=1 survivor definition, and the distinction between Python certificate checking and kernel evaluation. Do not replace finite n=3..21 quantifiers by all sufficiently large x or infinitely many x. Survivor admissibility at one cutoff is not an unbounded prime-pair detector. No route is reopened or refuted by this mismatch.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The issued finiteness-structure summary records the eventual consequence G2(x#)>=x_next^2-2 under finitely many twins. Return #5375 provides only finite prefix upper bounds, with no bound on where such an eventual consequence must begin and no structural theorem assuming a finite twin count. Thus it supplies no new quantified consequence of finiteness and no contradiction of an eventual tail. Its finite certification mechanism alone does not meet this area’s stated conditional-structure objective.","assumptions_md":"Provisional relevance screening only. The accepted source is unscoped: research_evidence is null and research_authority.scopes is empty, so scope_keys=[] is intentional. No exact endorsed scope is available for validated transfer; that authority condition remains unresolved. This judgment supplies no scientific acceptance, new Lean validation, experiment, route change or paper integration. Use the exact source report and review #1877 together. Preserve the finite primorial domain, the gcd(n(n+2),P)=1 survivor definition, and the distinction between Python certificate checking and kernel evaluation. Keep eventual quantifiers explicit. No finite-prefix numerical margin determines an unknown onset, tail exponent, or whether the twin count is finite. The lane’s existing conditional reductions are context from the issued summary, not newly proved or independently validated here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Return #5375 §§1–2 concerns finite upper-bound certificates for G2 at primorials, not the mapped survivor-gap lower-bound theorem with sufficient A=12. Each separate obligation mismatches: O1 has no prime-harmonic constant/o(1) proof here; O2 has no two-variable uniform smooth-number asymptotic; O3 has no extension to every fixed A>4; O4 has no dyadic prime-count asymptotic with coefficient 1/2; O5 receives neither the general sieve interface nor the external one-class asymptotic from a finite covering checker; O6 receives no two-sided density/Euler estimate; O7 receives no derivation of the stated equation-(28) constant and parameter range. Return #6177 and trusted review #2108 preserve the accepted main theorem’s three-claim scope, keep the general Input S explicitly open/conditional, and separate the embedding evidence attributed to #5265. None identifies #5375 as closing these obligations.","assumptions_md":"Provisional relevance screening only. The accepted source is unscoped: research_evidence is null and research_authority.scopes is empty, so scope_keys=[] is intentional. No exact endorsed scope is available for validated transfer; that authority condition remains unresolved. This judgment supplies no scientific acceptance, new Lean validation, experiment, route change or paper integration. Use the exact source report and review #1877 together. Preserve the finite primorial domain, the gcd(n(n+2),P)=1 survivor definition, and the distinction between Python certificate checking and kernel evaluation. Main and O1–O7 remain separate. The source’s use of covering certificates or weighted leaves is not identification with a uniform sieve theorem, external asymptotic, or historical constant pricing. #6177 is an accepted verified editorial revision; it does not enlarge the earlier proof scope. Its review’s advisory concerning the Omega_2 constant A2 supplied via kappa and O5 attribution is preserved; this screening does not repair or integrate the manuscript.","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 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applicability screening of accepted scientific return #5375: 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: 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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:5375,input_sha256:\"e88c734ff19875089d49ba0d86979cf0134f637bc41b75736314af59806a8a38\",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/6570/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"8d0347147bde8ce4ce49eb20323e3d7474ec7d07b8750f8599a21a7dc6ca5f74","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}