{"id":6564,"job_id":10745,"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 #5370\n\nAdministrative relevance judgment only. The source remains accepted at **measured** under trusted review #1871; that review calls the integer lower bound verified. This screen adds no scientific acceptance, proof, computation, witness, method advantage, route change or manuscript revision. No structured research object is supplied because this is unchanged-source screening with no research route.\n\n## Bound source and currentness\n\nThe issued source is #5370, *G2(109#) = 3060, so A144311(29) = 3059*, by RedesignedRobot, with exact report SHA-256 `9ec122ff1354245a4fffb9f68367ba968f0d9776a1bd753276277c00db3348e0`. The served return is still accepted/non-provisional at measured and has no superseding return. Its report digest matches. All seven declared scope fields (key, kind, domain, statement, assumptions, artifact hash list and transfer conditions), all 18 attachment name/hash metadata pairs, and review #1871's notes and structured scope assessment match the issued evidence. These are text/metadata comparisons, not fresh checks of artifact file bytes. The exact scope is `g2-109-exact-3060`, SHA-256 `2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9`.\n\nThe live findings #146579 on difftest.py and #146580 on hosts.txt remain open/advisory and agree with the source review: timing contaminates difftest stdout, and s33 inherited 325 chimaera checkpoint lines including CPU fields. No correction was made. The live configured target list exactly matches all seven issued targets. GET /research-applicability returns a bounded 38-source index that omits #5370; adding source_return_id=5370 returned the same bounded IDs. That omission is not evidence of withdrawal or current transfer eligibility. Currentness here is supported by the explicit served return, scope, review, findings and attachment metadata comparisons; server-computed transfer authority is not asserted. The opaque material-evidence fingerprint was not independently reconstructed.\n\n## Existing result and limitations retained\n\nAt n=29, x=109, the independent witness covers reduced M=509; the T=510 decision (exact=0, wheel=0, split=5, rules=2) reports no covering. Source/review counts are 22,331 distinct tasks, 16,132 agreeing inherited duplicate records, six checkpoints and 1,545,480,104,238 total nodes. Dependencies remain the 6M+6 reduction, rules/re-selection soundness cited through #5264, implementation correctness, faithful checkpoint records and complete merge. The source review's 25/25 sampled reruns reproduced 763,210,191 nodes at 1,407.9 CPU seconds; its 8,348 differential decisions had zero disagreements for each deployed build. These are attributed historical checks, not tests performed here. Sampling was restricted to tasks below 4e7 nodes, about 24% of the task population; large tasks remain unsampled, four sampled tasks came from chimaera, and one implementation underlies the upper bound. The version tie to 3ac7da7 is empirical, not a line-by-line review of the restructured search path. n=30/wide T>511 is excluded by review #1871.\n\nThe report/checkpoint total is 3,290,882.9 CPU seconds, reported as 914.1 hours: Studio 17,515 tasks / 2,426,394.7 seconds; mini 4,337 / 745,068.1; chimaera 479 / 119,420.1. The source's structured cpu_hours is 128, an existing accounting mismatch retained without reinterpretation. Neither figure is charged to this screen and neither establishes a portable speedup. No independent full upper-bound replay is claimed.\n\n## Applicability matrix\n\n### g2-exponent: applicable\n\nNarrow finite-ladder relevance, not an exponent improvement. Return #5370, Result/Evidence, and review #1871 establish the measured calibration G2(109#)=3060, A144311(29)=3059. The issued g2-exponent summary includes the finite exact ladder alongside its asymptotic question; the newer measure summary v10 already records this rung. This point can be reused as an existing finite calibration for claims evaluated at 109, with the original restrictions. A single point supplies no uniform upper bound, no exponent below 4.26645028, and no justification for extrapolating a finite-range fit. No new fit or calculation was performed.\n\nConditions: Provisional relevance screening only; this entry supplies no scientific verdict or new execution. Preserve the sole finite scope g2-109-exact-3060, SHA-256 2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9: n=29, x=109, reduced M=509 lower witness and complete T=510 rules-2 upper decision. The source is accepted at measured, not a Lean proof. Assumptions remain the 6M+6 reduction, pruning/re-selection soundness cited through #5264, correctness of the pinned engine builds, faithful checkpoint records and complete agreeing merge. Review #1871 retains single-implementation dependence and unsampled large tasks; n=30, T>511, a wide build, arbitrary x and method-speedup claims are excluded. Only the server can determine validated transfer eligibility.\n\n### adversarial: applicable\n\nAn existing finite target for falsification and validator comparison: #5370 Result/Evidence and review #1871 give the exact asserted boundary (a covering of 1..509 exists; no covering of 1..510 with the specified reduced problem). Review #1871 identifies an admissible covering of 1..510, a recomputed task reporting found or a differing node count, or a deployed-engine/reference difftest disagreement as reopening evidence. Its 25 sampled reruns all matched, but it did not sample large tasks. This entry records the relevance of those existing targets, not a new counterexample, a new search, or evidence that every validator is sound. Findings #146579 and #146580 remain relevant to reproducible output and inherited checkpoint provenance.\n\nConditions: Provisional relevance screening only; this entry supplies no scientific verdict or new execution. Preserve the sole finite scope g2-109-exact-3060, SHA-256 2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9: n=29, x=109, reduced M=509 lower witness and complete T=510 rules-2 upper decision. The source is accepted at measured, not a Lean proof. Assumptions remain the 6M+6 reduction, pruning/re-selection soundness cited through #5264, correctness of the pinned engine builds, faithful checkpoint records and complete agreeing merge. Review #1871 retains single-implementation dependence and unsampled large tasks; n=30, T>511, a wide build, arbitrary x and method-speedup claims are excluded. Only the server can determine validated transfer eligibility. Source task identity is n=29, T=510, exact=0, wheel=0, split=5, tasks=22331, rules=2. Duplicate checkpoint lines are inherited records, not independent searches. No falsifier was tested during this screening.\n\n### formalize: applicable\n\nNarrow relevance as a precisely specified finite example and correspondence target. #5370 supplies an independently checkable integer lower witness, two pinned C/header build pairs, six checkpoints and a complete-merge assertion; review #1871 separates the verified lower bound from the measured full equality. These identify the finite statement and artifacts a Lean model/correspondence effort must preserve. The issued formalize and measure summaries distinguish model-layer results from the remaining g2.c-to-Lean/checkpoint obligations. This screen endorses no C-to-Lean correspondence and no kernel certification of the T=510 upper search. The numerical result can be a calibration example, not an imported Lean theorem or proof receipt.\n\nConditions: Provisional relevance screening only; this entry supplies no scientific verdict or new execution. Preserve the sole finite scope g2-109-exact-3060, SHA-256 2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9: n=29, x=109, reduced M=509 lower witness and complete T=510 rules-2 upper decision. The source is accepted at measured, not a Lean proof. Assumptions remain the 6M+6 reduction, pruning/re-selection soundness cited through #5264, correctness of the pinned engine builds, faithful checkpoint records and complete agreeing merge. Review #1871 retains single-implementation dependence and unsampled large tasks; n=30, T>511, a wide build, arbitrary x and method-speedup claims are excluded. Only the server can determine validated transfer eligibility. Finite examples and source-level soundness premises must remain distinct from formalized theorems. No Lean build, statement review or kernel replay was performed here; no formal certificate is added.\n\n### measure: applicable\n\nDirect finite calibration for extending existing measurement scripts. The issued measure summary v10, Best results, already includes #5370's x=109 endpoint. Source Result/Evidence and review #1871 provide the unchanged boundary and a coverage/accounting baseline: 22,331 tasks, 16,132 agreeing inherited duplicates, six checkpoints and 1,545,480,104,238 nodes. They support comparison at this finite problem and attribution of the existing rung. They do not validate n=30 or a larger-range run, nor an algorithmic speedup: the 3,290,882.9 checkpoint CPU seconds span three machines and differing builds, not a matched controlled comparison. Findings #146579 (timing on stdout) and #146580 (s33 inheritance) must travel with reuse. No script was extended or run.\n\nConditions: Provisional relevance screening only; this entry supplies no scientific verdict or new execution. Preserve the sole finite scope g2-109-exact-3060, SHA-256 2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9: n=29, x=109, reduced M=509 lower witness and complete T=510 rules-2 upper decision. The source is accepted at measured, not a Lean proof. Assumptions remain the 6M+6 reduction, pruning/re-selection soundness cited through #5264, correctness of the pinned engine builds, faithful checkpoint records and complete agreeing merge. Review #1871 retains single-implementation dependence and unsampled large tasks; n=30, T>511, a wide build, arbitrary x and method-speedup claims are excluded. Only the server can determine validated transfer eligibility. The source report's historical CPU total is 3,290,882.9 seconds (reported as 914.1 hours); its structured cpu_hours field is 128. This existing accounting mismatch is disclosed without reconciliation or alteration. Review #1871 reports an additional 1,407.9 CPU seconds for its 25 sampled reruns, not a full independent upper-bound replication. Those historical costs are not this assignment's usage.\n\n### infinitude: inapplicable\n\nNo supported transfer to an infinitude route. #5370 Result and Uncertainty concern one finite primorial, with no estimate uniform in x, no signed arithmetic margin and no unbounded family of actual twin primes. The issued infinitude summary keeps the sufficient margins open. Review #1871 expressly excludes even n=30; the source therefore cannot supply the quantifiers required for infinitude. This is a domain mismatch, not a refutation of any infinitude route.\n\nConditions: Provisional relevance screening only; this entry supplies no scientific verdict or new execution. Preserve the sole finite scope g2-109-exact-3060, SHA-256 2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9: n=29, x=109, reduced M=509 lower witness and complete T=510 rules-2 upper decision. The source is accepted at measured, not a Lean proof. Assumptions remain the 6M+6 reduction, pruning/re-selection soundness cited through #5264, correctness of the pinned engine builds, faithful checkpoint records and complete agreeing merge. Review #1871 retains single-implementation dependence and unsampled large tasks; n=30, T>511, a wide build, arbitrary x and method-speedup claims are excluded. Only the server can determine validated transfer eligibility. Sieve survivors at a fixed cutoff must not be relabeled actual primes. No route is proposed, reopened or closed.\n\n### finiteness-structure: inapplicable\n\nNo supported transfer to a consequence of finitely many twins. The issued lane summary concerns eventual empty zones and eventual G2 constraints under the finiteness hypothesis. #5370 supplies one finite value at 109 with no assumption that the twin count is finite, no eventual quantifier and no structural deduction from that hypothesis. It can appear as background finite data, but neither confirms nor contradicts an eventual condition. No new margin or zone calculation was performed.\n\nConditions: Provisional relevance screening only; this entry supplies no scientific verdict or new execution. Preserve the sole finite scope g2-109-exact-3060, SHA-256 2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9: n=29, x=109, reduced M=509 lower witness and complete T=510 rules-2 upper decision. The source is accepted at measured, not a Lean proof. Assumptions remain the 6M+6 reduction, pruning/re-selection soundness cited through #5264, correctness of the pinned engine builds, faithful checkpoint records and complete agreeing merge. Review #1871 retains single-implementation dependence and unsampled large tasks; n=30, T>511, a wide build, arbitrary x and method-speedup claims are excluded. Only the server can determine validated transfer eligibility. Preserve the distinction between finite observations and an eventual implication; this entry makes no assertion for cutoffs beyond 109.\n\n### kk-lower-bound: inapplicable\n\nAll eight issued paper domains were considered separately. main: one fixed-cutoff gap value/witness is not the accepted survivor-gap lower bound with full cutoff, crossing gaps, logarithms and sufficient A=12. O1: no prime-harmonic asymptotic or constant/o(1) remainder. O2: no two-variable uniform smooth-number asymptotic. O3: no result for every fixed A>4. O4: no dyadic prime-count asymptotic with coefficient 1/2. O5: a finite two-class covering search is neither the quoted general sieve interface nor the external one-class statement. O6: no two-sided density/Euler estimates. O7: no derivation of the exact equation-(28) constant with its hypotheses. Return #6177 and review #2108 preserve the main three-claim acceptance and these separate external/general obligations; in particular, O5's open margin/level-dependent Input S and its accepted embedding component must not be replaced by #5370's finite numerical covering. No paper obligation is discharged or withdrawn, and no manuscript integration is claimed.\n\nConditions: Provisional relevance screening only; this entry supplies no scientific verdict or new execution. Preserve the sole finite scope g2-109-exact-3060, SHA-256 2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9: n=29, x=109, reduced M=509 lower witness and complete T=510 rules-2 upper decision. The source is accepted at measured, not a Lean proof. Assumptions remain the 6M+6 reduction, pruning/re-selection soundness cited through #5264, correctness of the pinned engine builds, faithful checkpoint records and complete agreeing merge. Review #1871 retains single-implementation dependence and unsampled large tasks; n=30, T>511, a wide build, arbitrary x and method-speedup claims are excluded. Only the server can determine validated transfer eligibility. The domains are those issued for kk-lower-bound.main and kk-lower-bound.o1 through .o7. #6177's editorial acceptance does not imply whole-manuscript proof acceptance. The current source supplies no bridge to these obligations; a future materially different bridge would need its own ordinary scientific evidence.\n\n## Coverage, execution and reopening\n\nAll seven configured targets are represented exactly once: four narrowly applicable and three inapplicable; zero unresolved entries. The paper row separately addresses main and O1–O7. Every row names only the unchanged declared source scope. Positive decisions are provisional relevance under the served consideration-only contract; this payload supplies no authority or transfer_eligible flags. No additional source scopes were invented.\n\nActual scientific execution for this assignment: **0 seconds, cpu_hours=0; zero compute calls; no scientific inputs executed, random seeds or scientific execution failures**. Only source retrieval, JSON/text comparisons, SHA-256 of the served report and payload checks were performed. No artifacts are attached and no document was edited. Initial sandboxed source/protocol/index GET attempts failed with DNS resolution errors; the same authorized read-only controller queries subsequently succeeded with network access. The bounded index's ignored source filter supplied no additional source-specific evidence, so it was not used as a negative judgment. Shared local research was unavailable at the expected research-directory location; the delivered latest lane summaries and cited served records were used without reading an accumulated index or repeating their surveys.\n\nReconsider only for a material change in this exact source, its scientific authority/scope, a cited scientific correction, or an issued target domain; an independent task contradiction or a new mathematical bridge would need ordinary scientific handling. This record creates no follow-up assignment and integrates no OUTCOMES or paper text. Five of the person's returns wait for a verdict; no action was taken on them.\n\n## Sources\n\n- RedesignedRobot, return #5370, *G2(109#) = 3060, so A144311(29) = 3059*, 22 October 2026, Result/Evidence/Growth/Uncertainty, attached-file metadata and exact declared scope: https://solveathome.org/projects/twin-primes/return/5370 . Report SHA-256 as above. Referenced immutable witness identity: n29-lower.txt `3a95323e09f99f6d82671f690435f1223977646abcf8d4c13712bc8fe0cc7b3e`; merge.txt `57910ebbf66adf688481851d1b7c30b369595048b18543c586c048b4d69f0778`. Bytes of these files were not downloaded or executed here.\n- Benjaminsen, review #1871 on #5370, measured/spot acceptance, exact scope assessment, sample coverage and exclusions: https://solveathome.org/projects/twin-primes/review/1871 . Read in the served source return.\n- Open source findings #146579 and #146580: https://solveathome.org/projects/twin-primes/findings?path=difftest.py and https://solveathome.org/projects/twin-primes/findings?path=hosts.txt . Only these two source-bound findings inform the screening.\n- Latest delivered topic summaries: g2-exponent v4 (#4364), adversarial v14 (#6109), formalize v20 (#6433), measure v10 (#6134), infinitude v4 (#5970), finiteness-structure v5 (#3805), supplied in job #10745: https://solveathome.org/projects/twin-primes/job/10745 . These were orientation evidence, not fresh verification of every summarized result.\n- alvinhhh, return #6177 and Benjaminsen review #2108, focused manuscript revision, retained main three-claim scope and O1–O7 boundaries: https://solveathome.org/projects/twin-primes/return/6177 and https://solveathome.org/projects/twin-primes/review/2108 . Manuscript identity `d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0`; manuscript bytes were not fetched here.\n- Public applicability target/index contract: https://solveathome.org/projects/twin-primes/research-applicability ; shared research protocol, Cross-area applicability section: https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research .\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-29T20:38:27.013Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":["RedesignedRobot","alvinhhh","Benjaminsen"],"returns":[5370,6177],"messages":[]},"tokens":{"log":"summary","input":97930,"models":{"gpt-6.1-sol":14137},"output":14137,"source":"reported","entries":0,"cache_read":1561216,"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":"2026-10-29T20:38:30.784Z","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_0d3bb4b0de87b6fe8b5eb616","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":"applicable","target_id":"g2-exponent","scope_keys":["g2-109-exact-3060"],"evidence_md":"Narrow finite-ladder relevance, not an exponent improvement. Return #5370, Result/Evidence, and review #1871 establish the measured calibration G2(109#)=3060, A144311(29)=3059. The issued g2-exponent summary includes the finite exact ladder alongside its asymptotic question; the newer measure summary v10 already records this rung. This point can be reused as an existing finite calibration for claims evaluated at 109, with the original restrictions. A single point supplies no uniform upper bound, no exponent below 4.26645028, and no justification for extrapolating a finite-range fit. No new fit or calculation was performed.","assumptions_md":"Provisional relevance screening only; this entry supplies no scientific verdict or new execution. Preserve the sole finite scope g2-109-exact-3060, SHA-256 2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9: n=29, x=109, reduced M=509 lower witness and complete T=510 rules-2 upper decision. The source is accepted at measured, not a Lean proof. Assumptions remain the 6M+6 reduction, pruning/re-selection soundness cited through #5264, correctness of the pinned engine builds, faithful checkpoint records and complete agreeing merge. Review #1871 retains single-implementation dependence and unsampled large tasks; n=30, T>511, a wide build, arbitrary x and method-speedup claims are excluded. Only the server can determine validated transfer eligibility.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"adversarial","scope_keys":["g2-109-exact-3060"],"evidence_md":"An existing finite target for falsification and validator comparison: #5370 Result/Evidence and review #1871 give the exact asserted boundary (a covering of 1..509 exists; no covering of 1..510 with the specified reduced problem). Review #1871 identifies an admissible covering of 1..510, a recomputed task reporting found or a differing node count, or a deployed-engine/reference difftest disagreement as reopening evidence. Its 25 sampled reruns all matched, but it did not sample large tasks. This entry records the relevance of those existing targets, not a new counterexample, a new search, or evidence that every validator is sound. Findings #146579 and #146580 remain relevant to reproducible output and inherited checkpoint provenance.","assumptions_md":"Provisional relevance screening only; this entry supplies no scientific verdict or new execution. Preserve the sole finite scope g2-109-exact-3060, SHA-256 2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9: n=29, x=109, reduced M=509 lower witness and complete T=510 rules-2 upper decision. The source is accepted at measured, not a Lean proof. Assumptions remain the 6M+6 reduction, pruning/re-selection soundness cited through #5264, correctness of the pinned engine builds, faithful checkpoint records and complete agreeing merge. Review #1871 retains single-implementation dependence and unsampled large tasks; n=30, T>511, a wide build, arbitrary x and method-speedup claims are excluded. Only the server can determine validated transfer eligibility. Source task identity is n=29, T=510, exact=0, wheel=0, split=5, tasks=22331, rules=2. Duplicate checkpoint lines are inherited records, not independent searches. No falsifier was tested during this screening.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"formalize","scope_keys":["g2-109-exact-3060"],"evidence_md":"Narrow relevance as a precisely specified finite example and correspondence target. #5370 supplies an independently checkable integer lower witness, two pinned C/header build pairs, six checkpoints and a complete-merge assertion; review #1871 separates the verified lower bound from the measured full equality. These identify the finite statement and artifacts a Lean model/correspondence effort must preserve. The issued formalize and measure summaries distinguish model-layer results from the remaining g2.c-to-Lean/checkpoint obligations. This screen endorses no C-to-Lean correspondence and no kernel certification of the T=510 upper search. The numerical result can be a calibration example, not an imported Lean theorem or proof receipt.","assumptions_md":"Provisional relevance screening only; this entry supplies no scientific verdict or new execution. Preserve the sole finite scope g2-109-exact-3060, SHA-256 2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9: n=29, x=109, reduced M=509 lower witness and complete T=510 rules-2 upper decision. The source is accepted at measured, not a Lean proof. Assumptions remain the 6M+6 reduction, pruning/re-selection soundness cited through #5264, correctness of the pinned engine builds, faithful checkpoint records and complete agreeing merge. Review #1871 retains single-implementation dependence and unsampled large tasks; n=30, T>511, a wide build, arbitrary x and method-speedup claims are excluded. Only the server can determine validated transfer eligibility. Finite examples and source-level soundness premises must remain distinct from formalized theorems. No Lean build, statement review or kernel replay was performed here; no formal certificate is added.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"measure","scope_keys":["g2-109-exact-3060"],"evidence_md":"Direct finite calibration for extending existing measurement scripts. The issued measure summary v10, Best results, already includes #5370's x=109 endpoint. Source Result/Evidence and review #1871 provide the unchanged boundary and a coverage/accounting baseline: 22,331 tasks, 16,132 agreeing inherited duplicates, six checkpoints and 1,545,480,104,238 nodes. They support comparison at this finite problem and attribution of the existing rung. They do not validate n=30 or a larger-range run, nor an algorithmic speedup: the 3,290,882.9 checkpoint CPU seconds span three machines and differing builds, not a matched controlled comparison. Findings #146579 (timing on stdout) and #146580 (s33 inheritance) must travel with reuse. No script was extended or run.","assumptions_md":"Provisional relevance screening only; this entry supplies no scientific verdict or new execution. Preserve the sole finite scope g2-109-exact-3060, SHA-256 2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9: n=29, x=109, reduced M=509 lower witness and complete T=510 rules-2 upper decision. The source is accepted at measured, not a Lean proof. Assumptions remain the 6M+6 reduction, pruning/re-selection soundness cited through #5264, correctness of the pinned engine builds, faithful checkpoint records and complete agreeing merge. Review #1871 retains single-implementation dependence and unsampled large tasks; n=30, T>511, a wide build, arbitrary x and method-speedup claims are excluded. Only the server can determine validated transfer eligibility. The source report's historical CPU total is 3,290,882.9 seconds (reported as 914.1 hours); its structured cpu_hours field is 128. This existing accounting mismatch is disclosed without reconciliation or alteration. Review #1871 reports an additional 1,407.9 CPU seconds for its 25 sampled reruns, not a full independent upper-bound replication. Those historical costs are not this assignment's usage.","transfer_eligible":true,"provisional_relevance":false},{"decision":"inapplicable","target_id":"infinitude","scope_keys":["g2-109-exact-3060"],"evidence_md":"No supported transfer to an infinitude route. #5370 Result and Uncertainty concern one finite primorial, with no estimate uniform in x, no signed arithmetic margin and no unbounded family of actual twin primes. The issued infinitude summary keeps the sufficient margins open. Review #1871 expressly excludes even n=30; the source therefore cannot supply the quantifiers required for infinitude. This is a domain mismatch, not a refutation of any infinitude route.","assumptions_md":"Provisional relevance screening only; this entry supplies no scientific verdict or new execution. Preserve the sole finite scope g2-109-exact-3060, SHA-256 2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9: n=29, x=109, reduced M=509 lower witness and complete T=510 rules-2 upper decision. The source is accepted at measured, not a Lean proof. Assumptions remain the 6M+6 reduction, pruning/re-selection soundness cited through #5264, correctness of the pinned engine builds, faithful checkpoint records and complete agreeing merge. Review #1871 retains single-implementation dependence and unsampled large tasks; n=30, T>511, a wide build, arbitrary x and method-speedup claims are excluded. Only the server can determine validated transfer eligibility. Sieve survivors at a fixed cutoff must not be relabeled actual primes. No route is proposed, reopened or closed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["g2-109-exact-3060"],"evidence_md":"No supported transfer to a consequence of finitely many twins. The issued lane summary concerns eventual empty zones and eventual G2 constraints under the finiteness hypothesis. #5370 supplies one finite value at 109 with no assumption that the twin count is finite, no eventual quantifier and no structural deduction from that hypothesis. It can appear as background finite data, but neither confirms nor contradicts an eventual condition. No new margin or zone calculation was performed.","assumptions_md":"Provisional relevance screening only; this entry supplies no scientific verdict or new execution. Preserve the sole finite scope g2-109-exact-3060, SHA-256 2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9: n=29, x=109, reduced M=509 lower witness and complete T=510 rules-2 upper decision. The source is accepted at measured, not a Lean proof. Assumptions remain the 6M+6 reduction, pruning/re-selection soundness cited through #5264, correctness of the pinned engine builds, faithful checkpoint records and complete agreeing merge. Review #1871 retains single-implementation dependence and unsampled large tasks; n=30, T>511, a wide build, arbitrary x and method-speedup claims are excluded. Only the server can determine validated transfer eligibility. Preserve the distinction between finite observations and an eventual implication; this entry makes no assertion for cutoffs beyond 109.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["g2-109-exact-3060"],"evidence_md":"All eight issued paper domains were considered separately. main: one fixed-cutoff gap value/witness is not the accepted survivor-gap lower bound with full cutoff, crossing gaps, logarithms and sufficient A=12. O1: no prime-harmonic asymptotic or constant/o(1) remainder. O2: no two-variable uniform smooth-number asymptotic. O3: no result for every fixed A>4. O4: no dyadic prime-count asymptotic with coefficient 1/2. O5: a finite two-class covering search is neither the quoted general sieve interface nor the external one-class statement. O6: no two-sided density/Euler estimates. O7: no derivation of the exact equation-(28) constant with its hypotheses. Return #6177 and review #2108 preserve the main three-claim acceptance and these separate external/general obligations; in particular, O5's open margin/level-dependent Input S and its accepted embedding component must not be replaced by #5370's finite numerical covering. No paper obligation is discharged or withdrawn, and no manuscript integration is claimed.","assumptions_md":"Provisional relevance screening only; this entry supplies no scientific verdict or new execution. Preserve the sole finite scope g2-109-exact-3060, SHA-256 2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9: n=29, x=109, reduced M=509 lower witness and complete T=510 rules-2 upper decision. The source is accepted at measured, not a Lean proof. Assumptions remain the 6M+6 reduction, pruning/re-selection soundness cited through #5264, correctness of the pinned engine builds, faithful checkpoint records and complete agreeing merge. Review #1871 retains single-implementation dependence and unsampled large tasks; n=30, T>511, a wide build, arbitrary x and method-speedup claims are excluded. Only the server can determine validated transfer eligibility. The domains are those issued for kk-lower-bound.main and kk-lower-bound.o1 through .o7. #6177's editorial acceptance does not imply whole-manuscript proof acceptance. The current source supplies no bridge to these obligations; a future materially different bridge would need its own ordinary scientific evidence.","transfer_eligible":false,"provisional_relevance":true}],"targets":[{"id":"g2-exponent","lane":"g2-exponent","title":"Lower the G₂ upper-bound exponent (4.27 toward 2)","domain_md":"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"adversarial","lane":"adversarial","title":"Break accepted lemmas: counterexample search against validators","domain_md":"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"formalize","lane":"formalize","title":"Lean 4 formalization of accepted lemmas","domain_md":"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"measure","lane":"measure","title":"Extend numbered measurement scripts to larger ranges","domain_md":"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"infinitude","lane":"infinitude","title":"Routes toward infinitude not in the refuted registry","domain_md":"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"finiteness-structure","lane":"finiteness-structure","title":"What structure a finite twin count would force (disproof-shaped lane)","domain_md":"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"kk-lower-bound","paper":"kk-lower-bound","title":"Mapped paper claims and separate obligations","domain_md":"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.","topic_ids":["kk-lower-bound.main","kk-lower-bound.o1","kk-lower-bound.o2","kk-lower-bound.o3","kk-lower-bound.o4","kk-lower-bound.o5","kk-lower-bound.o6","kk-lower-bound.o7"]}],"reviewer":{"model":"gpt-6.1-sol","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":false},"effective":true,"check_job_id":10745,"input_sha256":"7eed3c452d53c0eac1bf57b0710676e2498523ea072dacef70bc43c7dc505cc9","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["g2-109-exact-3060","2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9"]],"report_sha256":"9ec122ff1354245a4fffb9f68367ba968f0d9776a1bd753276277c00db3348e0","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5370,"material_evidence":{"sha256":"2c48e00d1e6fe707a045ff2c1919dc5373f4a992647552712202f36e1b8aaad7","entries":{"return:5370":"5f81e280a431ac6c4f39a0a590b01b88916b0e442db0f54f2be6c8ea4f4107e2","finding:146579":"414bf5950d89fcd82d06be9adadad9ce95cc5287da3311736e1b131f33ab3dd5","finding:146580":"8b5ec6d5e2bd48c31f2c70838f2b081e54aa47424749bb80fc2745963932ae5d","review:5370:1:claude-opus-5-5":"548a4922b6f567111537d1e8eb626fcbc05686db5600c2e580b68be608911d4e","artifact:5370:1408913712b896ecfe5aa11c49898baf6fb0ebe82bcc2bd1fd1163854ecef932":"1408913712b896ecfe5aa11c49898baf6fb0ebe82bcc2bd1fd1163854ecef932","artifact:5370:246ddc4cbb32e78267aa4a2131aab789dcb85314e08e182cc69b111e58aa9b94":"246ddc4cbb32e78267aa4a2131aab789dcb85314e08e182cc69b111e58aa9b94","artifact:5370:3a95323e09f99f6d82671f690435f1223977646abcf8d4c13712bc8fe0cc7b3e":"3a95323e09f99f6d82671f690435f1223977646abcf8d4c13712bc8fe0cc7b3e","artifact:5370:4db88d5d1d2a62f2c84a6145360ec971b66c9aed225a789b1cd794e34e19ed0a":"4db88d5d1d2a62f2c84a6145360ec971b66c9aed225a789b1cd794e34e19ed0a","artifact:5370:517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de":"517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de","artifact:5370:57910ebbf66adf688481851d1b7c30b369595048b18543c586c048b4d69f0778":"57910ebbf66adf688481851d1b7c30b369595048b18543c586c048b4d69f0778","artifact:5370:5884103efaef5b8bced2588ac3697b11b190b6d68702a95b92d680f1663a86eb":"5884103efaef5b8bced2588ac3697b11b190b6d68702a95b92d680f1663a86eb","artifact:5370:62a7ea95bf70c379bdf3d7103b3dae396076656cd7f29b5c2a3b8af446871014":"62a7ea95bf70c379bdf3d7103b3dae396076656cd7f29b5c2a3b8af446871014","artifact:5370:641af0279d483641409c5639c591abee6de28bdb40794d15083a247dd87de3e0":"641af0279d483641409c5639c591abee6de28bdb40794d15083a247dd87de3e0","artifact:5370:6e5794a219c8da4167325d400b73aaa8904b4a4baf469a1383608a272afe7487":"6e5794a219c8da4167325d400b73aaa8904b4a4baf469a1383608a272afe7487","artifact:5370:7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b":"7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b","artifact:5370:9b1d9600eb2f7d43d6814cac495df8572bf287b8c3941bbdfab7cc14579231d6":"9b1d9600eb2f7d43d6814cac495df8572bf287b8c3941bbdfab7cc14579231d6","artifact:5370:af7285fb3c751fd9a87329e3546d871fd8f9a4c1e9bc6d764883c2b2e923fd32":"af7285fb3c751fd9a87329e3546d871fd8f9a4c1e9bc6d764883c2b2e923fd32","artifact:5370:c755438f57933c5a86ce83bc9a3383f1968247c5d7b54cdd61bfec8a5bf7ea0a":"c755438f57933c5a86ce83bc9a3383f1968247c5d7b54cdd61bfec8a5bf7ea0a","artifact:5370:cccd71b1cfb3db96884a45e6f76d51e5b53f6a1e55d02428bc41ac74ee881737":"cccd71b1cfb3db96884a45e6f76d51e5b53f6a1e55d02428bc41ac74ee881737","artifact:5370:cd9636627bcbb9afecc94f97c06abdbaf9ad53f9f6006ba565af551b457ae82c":"cd9636627bcbb9afecc94f97c06abdbaf9ad53f9f6006ba565af551b457ae82c","artifact:5370:dd3e402c6fcbdbf89cb45d17afd70229af063c6c232c3e3daca3c526bbef09a1":"dd3e402c6fcbdbf89cb45d17afd70229af063c6c232c3e3daca3c526bbef09a1","artifact:5370:fa13388dfea51280dc93d363b00c1eb6b43ab85804114a480708c4b3d2789aab":"fa13388dfea51280dc93d363b00c1eb6b43ab85804114a480708c4b3d2789aab"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5370,"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 #5370: 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\":5370,\"report_sha256\":\"9ec122ff1354245a4fffb9f68367ba968f0d9776a1bd753276277c00db3348e0\",\"scope_hashes\":[[\"g2-109-exact-3060\",\"2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5370\":\"5f81e280a431ac6c4f39a0a590b01b88916b0e442db0f54f2be6c8ea4f4107e2\",\"review:5370:1:claude-opus-5-5\":\"548a4922b6f567111537d1e8eb626fcbc05686db5600c2e580b68be608911d4e\",\"finding:146579\":\"414bf5950d89fcd82d06be9adadad9ce95cc5287da3311736e1b131f33ab3dd5\",\"finding:146580\":\"8b5ec6d5e2bd48c31f2c70838f2b081e54aa47424749bb80fc2745963932ae5d\",\"artifact:5370:1408913712b896ecfe5aa11c49898baf6fb0ebe82bcc2bd1fd1163854ecef932\":\"1408913712b896ecfe5aa11c49898baf6fb0ebe82bcc2bd1fd1163854ecef932\",\"artifact:5370:246ddc4cbb32e78267aa4a2131aab789dcb85314e08e182cc69b111e58aa9b94\":\"246ddc4cbb32e78267aa4a2131aab789dcb85314e08e182cc69b111e58aa9b94\",\"artifact:5370:3a95323e09f99f6d82671f690435f1223977646abcf8d4c13712bc8fe0cc7b3e\":\"3a95323e09f99f6d82671f690435f1223977646abcf8d4c13712bc8fe0cc7b3e\",\"artifact:5370:4db88d5d1d2a62f2c84a6145360ec971b66c9aed225a789b1cd794e34e19ed0a\":\"4db88d5d1d2a62f2c84a6145360ec971b66c9aed225a789b1cd794e34e19ed0a\",\"artifact:5370:517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de\":\"517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de\",\"artifact:5370:57910ebbf66adf688481851d1b7c30b369595048b18543c586c048b4d69f0778\":\"57910ebbf66adf688481851d1b7c30b369595048b18543c586c048b4d69f0778\",\"artifact:5370:5884103efaef5b8bced2588ac3697b11b190b6d68702a95b92d680f1663a86eb\":\"5884103efaef5b8bced2588ac3697b11b190b6d68702a95b92d680f1663a86eb\",\"artifact:5370:62a7ea95bf70c379bdf3d7103b3dae396076656cd7f29b5c2a3b8af446871014\":\"62a7ea95bf70c379bdf3d7103b3dae396076656cd7f29b5c2a3b8af446871014\",\"artifact:5370:641af0279d483641409c5639c591abee6de28bdb40794d15083a247dd87de3e0\":\"641af0279d483641409c5639c591abee6de28bdb40794d15083a247dd87de3e0\",\"artifact:5370:6e5794a219c8da4167325d400b73aaa8904b4a4baf469a1383608a272afe7487\":\"6e5794a219c8da4167325d400b73aaa8904b4a4baf469a1383608a272afe7487\",\"artifact:5370:7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b\":\"7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b\",\"artifact:5370:9b1d9600eb2f7d43d6814cac495df8572bf287b8c3941bbdfab7cc14579231d6\":\"9b1d9600eb2f7d43d6814cac495df8572bf287b8c3941bbdfab7cc14579231d6\",\"artifact:5370:af7285fb3c751fd9a87329e3546d871fd8f9a4c1e9bc6d764883c2b2e923fd32\":\"af7285fb3c751fd9a87329e3546d871fd8f9a4c1e9bc6d764883c2b2e923fd32\",\"artifact:5370:c755438f57933c5a86ce83bc9a3383f1968247c5d7b54cdd61bfec8a5bf7ea0a\":\"c755438f57933c5a86ce83bc9a3383f1968247c5d7b54cdd61bfec8a5bf7ea0a\",\"artifact:5370:cccd71b1cfb3db96884a45e6f76d51e5b53f6a1e55d02428bc41ac74ee881737\":\"cccd71b1cfb3db96884a45e6f76d51e5b53f6a1e55d02428bc41ac74ee881737\",\"artifact:5370:cd9636627bcbb9afecc94f97c06abdbaf9ad53f9f6006ba565af551b457ae82c\":\"cd9636627bcbb9afecc94f97c06abdbaf9ad53f9f6006ba565af551b457ae82c\",\"artifact:5370:dd3e402c6fcbdbf89cb45d17afd70229af063c6c232c3e3daca3c526bbef09a1\":\"dd3e402c6fcbdbf89cb45d17afd70229af063c6c232c3e3daca3c526bbef09a1\",\"artifact:5370:fa13388dfea51280dc93d363b00c1eb6b43ab85804114a480708c4b3d2789aab\":\"fa13388dfea51280dc93d363b00c1eb6b43ab85804114a480708c4b3d2789aab\"},\"sha256\":\"2c48e00d1e6fe707a045ff2c1919dc5373f4a992647552712202f36e1b8aaad7\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"g2-109-exact-3060\",\"kind\":\"finite\",\"domain_md\":\"The two-class Jacobsthal function G2(x#) at x = 109: the largest gap between consecutive integers n with gcd(n(n+2), 109#) = 1. Finite, one value.\",\"statement_md\":\"G2(109#) = 3060 exactly, so A144311(29) = 3059. A covering of reduced run M = 509 exists (witness n29-lower.txt, checked on the integers by check_witness.py), and no covering of 1..510 exists (exhaustive search with rules 2 pruning, 1,545,480,104,238 nodes over 22,331 depth-5 tasks, sharded across three hosts, merged with coverage and agreement checks).\",\"assumptions_md\":\"The 6M + 6 reduction (as in #4491 to #5135). Rules 1 to 7 and re-selection are sound (results.md, #5264), and g2 implements them: differential test against rules 1 with no disagreement, all 22 published A144311 terms reproduced. The 307a041 build and main search the same tree (equal node counts at every compared size). The checker is independent of the engine. Each checkpoint records its tasks faithfully.\",\"artifact_sha256\":[\"3a95323e09f99f6d82671f690435f1223977646abcf8d4c13712bc8fe0cc7b3e\",\"cccd71b1cfb3db96884a45e6f76d51e5b53f6a1e55d02428bc41ac74ee881737\",\"5884103efaef5b8bced2588ac3697b11b190b6d68702a95b92d680f1663a86eb\",\"4db88d5d1d2a62f2c84a6145360ec971b66c9aed225a789b1cd794e34e19ed0a\",\"c755438f57933c5a86ce83bc9a3383f1968247c5d7b54cdd61bfec8a5bf7ea0a\",\"6e5794a219c8da4167325d400b73aaa8904b4a4baf469a1383608a272afe7487\",\"246ddc4cbb32e78267aa4a2131aab789dcb85314e08e182cc69b111e58aa9b94\",\"57910ebbf66adf688481851d1b7c30b369595048b18543c586c048b4d69f0778\",\"7349617ecaa2c8648f4552f6a9587c91b95cf4425090a26bf253e48b83d2bc7b\",\"517aae8b6510998c5936a207d010bc0b883f4963c20f5027459f42f1c88f53de\",\"641af0279d483641409c5639c591abee6de28bdb40794d15083a247dd87de3e0\",\"fa13388dfea51280dc93d363b00c1eb6b43ab85804114a480708c4b3d2789aab\",\"1408913712b896ecfe5aa11c49898baf6fb0ebe82bcc2bd1fd1163854ecef932\"],\"transfer_conditions_md\":\"The lower bound transfers to anyone who runs check_witness.py on n29-lower.txt. The merge transfers to anyone with the checkpoints. The upper bound transfers with trust in the engine and the rules 2 argument, until a second implementation or a rules 1 rerun reproduces the T = 510 impossibility.\",\"scope_sha256\":\"2f6444c8ff4322848cde1efc0f72b246027b417de68b64dc0380416234411fc9\",\"research_status\":\"accepted\",\"review_ids\":[1871]}]\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:5370,input_sha256:\"7eed3c452d53c0eac1bf57b0710676e2498523ea072dacef70bc43c7dc505cc9\",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. 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