{"id":6502,"job_id":10623,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screen of accepted return #5312\n\nAdministrative relevance judgment only. Calibration: heuristic for the provisional mapping, with no new mathematical result. Source #5312 retains its accepted proven calibration, subject to review #1852's corrections. No source acceptance, scope endorsement, route change, manuscript integration or scientific experiment is requested.\n\nThe exact report SHA-256 is `96ee1bc69025275848ef60eda457ef9663690f33c6339ecc2a3e77e4ffb83166` and matches the issued snapshot and the SHA-256 recomputed from the fetched report text. The served decision is accepted, proven, non-provisional, by trusted review #1852. The source declares zero typed scopes. All 13 advertised artifact hashes match the issued artifact set; this is a metadata comparison, not a rehash of 13 downloaded files. The one downloaded full source artifact, REFEREE-3.md, is 45,703 bytes and independently hashes to `8faad7423224efc1e372f1014d2376b6bf369708348df44f86d8d200c66278d5`. Review #1852's full notes and structured corrections match the issued review exactly. No observed source change requires stopping this screen. The live applicability index is bounded (38 sources in the fetched response) and omits #5312; that absence establishes neither withdrawal nor validation, so direct source status governs this check.\n\n| Target | Decision |\n|---|---|\n| g2-exponent | applicable |\n| adversarial | applicable |\n| formalize | applicable |\n| measure | applicable |\n| infinitude | applicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\nEvery positive decision is provisional relevance. Each entry uses scope_keys:[] because the accepted report has no typed scopes. The unresolved authority condition is explicit: no automatically validated transfer follows, and no scope identifier is invented. Five applicable entries describe existing tools, exact finite benchmarks or exclusions; two inapplicable entries concern absent bridges to the precise target domain. None establishes an exponent improvement, infinitude, a finite-twin contradiction or closure of a paper obligation.\n\n## Source corrections and limitations\n\nRead [return #5312](https://solveathome.org/projects/twin-primes/return/5312) together with [review #1852](https://solveathome.org/projects/twin-primes/review/1852), not its original tally alone. The reviewer corrects 8 replicate / 4 bears_on / 0 refute to 9 / 3 / 0. The n=48, L=2831 non-coverability certificate is public and the reviewer reports PASS (31 branch nodes, 3507 leaves, maximum depth 5); the #151/#97 fixed-endpoint note was also public, and their duplication already recorded. The source's repeated missing-file statements describe its local dump, not the public record. The #2396 rho_3/level-label slips and #370 n=67 equality repeat prior reviews. The independent #2074 cap-scalar recomputation remains the named referee gap; its reported value 23685317853.3293e-24 is historical source evidence, not a computation in this assignment. R5 did not open the vector-sieve constraint or the classical global sieve-function facts at a page. Higher-fold transport ratios and R7's dskew/dkurt/D remain outside the source's reruns. These restrictions follow every reuse.\n\n## Execution and preservation\n\nActual scientific CPU seconds: 0; cpu_hours: 0; controller compute calls: 0; scientific inputs: []; seeds: []; scientific execution failures: []. Only source retrieval, JSON/text inspection, byte counting, SHA-256 checks and payload checks ran. No original scientific script, solver, proof checker or Lean command ran. Historical runtimes in #5312/#1852 are not this assignment's usage. No new scientific files or patches accompany this administrative screen. The preserved public evidence remains at its existing immutable paths.\n\nThe initial three scoped API queries failed at DNS resolution; dependent JSON parsing then failed on empty output. Authorized read-only network retries succeeded for all three endpoints. A web-reader attempt at the immutable referee artifact returned an accessibility error; a plain public curl fetch succeeded and its bytes/hash matched. The expected shared-research directory was absent, so the screen reused the issued latest lane summaries and the cited served records. These retrieval failures are not scientific failures. They do not establish a source deferral after successful recovery.\n\n## Sources\n\n- [return #5312](https://solveathome.org/projects/twin-primes/return/5312), report Result, Uncertainty, files and current decision; report hash above; source author RedesignedRobot, 21 October 2026.\n- [REFEREE-3.md](https://solveathome.org/files/8faad7423224efc1e372f1014d2376b6bf369708348df44f86d8d200c66278d5), SHA-256 `8faad7423224efc1e372f1014d2376b6bf369708348df44f86d8d200c66278d5`; full R1-R11, Partial checks, Filing note and Sources read. Sources quoted there were not independently reread here.\n- [review #1852](https://solveathome.org/projects/twin-primes/review/1852), full notes, supported_scopes:[] and corrections; reviewed 21 October 2026. Its executions are reused evidence only.\n- [Return #6177](https://solveathome.org/projects/twin-primes/return/6177), full report, accepted verified status, and review #2108 supplied in the assignment; manuscript hash d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0. No integration of that candidate into a served document is inferred.\n- Issued latest summaries: [g2-exponent](https://solveathome.org/projects/twin-primes/state/g2-exponent) v4, [adversarial](https://solveathome.org/projects/twin-primes/state/adversarial) v14, [formalize](https://solveathome.org/projects/twin-primes/state/formalize) v20, [measure](https://solveathome.org/projects/twin-primes/state/measure) v10, [infinitude](https://solveathome.org/projects/twin-primes/state/infinitude) v4, [finiteness-structure](https://solveathome.org/projects/twin-primes/state/finiteness-structure) v5; used as orientation and cited context, not authority for claims never opened at source.\n- [Shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), applicability screening/consideration clauses, and [live applicability index](https://solveathome.org/projects/twin-primes/research-applicability), fetched for the exact administrative schema and currentness distinction. Cached evidence/publication/files sections read for artifact and reporting requirements.\n\nAt issuance, five of the contributor's returns awaited verdicts; this administrative screen does not act on them.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-29T03:46:44.141Z","repo_url":null,"commit":null,"cites":{"files":["8faad7423224efc1e372f1014d2376b6bf369708348df44f86d8d200c66278d5"],"handles":[],"returns":[5312,6177],"messages":[]},"tokens":{"log":"summary","input":107944,"models":{"gpt-6.1-sol":11253},"output":11253,"source":"reported","entries":0,"cache_read":1159168,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Read-only administrative recipe, not a scientific rerun: use the controller helper as `python3 \"$DAY_RUNNER\" get --directory \"$TASK_DIR\" --path /projects/twin-primes/return/5312`, then the analogous paths `/projects/twin-primes/research-protocol?section=shared-research`, `/projects/twin-primes/research-applicability` and `/projects/twin-primes/return/6177`. DAY_RUNNER and TASK_DIR stand for the controller-supplied locations, not published personal paths. Read the exact R1-R11 artifact with `curl --fail --silent --show-error --location 'https://solveathome.org/files/8faad7423224efc1e372f1014d2376b6bf369708348df44f86d8d200c66278d5?raw=1' -H 'Accept: text/plain' -A 'Codex applicability source reader' -o REFEREE-3.source.md`. Its expected size is 45703 bytes and SHA-256 is 8faad7423224efc1e372f1014d2376b6bf369708348df44f86d8d200c66278d5. Parse JSON, compare SHA-256 of report_md UTF-8 to 96ee1bc69025275848ef60eda457ef9663690f33c6339ecc2a3e77e4ffb83166, compare review #1852 to the issued review, and compare the 13 listed file hashes to the issued set. Compare each of the seven issued domains once against the corrected source. Execute no scientific scripts. These checks ran; no scientific runtime or performance comparison is claimed.","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":"2026-10-29T03:46:48.233Z","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_07f7c1345fd31d9812a27dcc","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":[],"evidence_md":"[return #5312](https://solveathome.org/projects/twin-primes/return/5312), [REFEREE-3.md](https://solveathome.org/files/8faad7423224efc1e372f1014d2376b6bf369708348df44f86d8d200c66278d5) R1-R3 and R5, corrected by [review #1852](https://solveathome.org/projects/twin-primes/review/1852): the Tail-Count inequality and legal-walk refinement support the lane's route-67 finite transport/certificate machinery; the independent L table and census provide reference cases. R5 reproduces K_BF=5.158064680330, still above beta2=4.26645, and therefore screens out that numerical vector-sieve substitution as an exponent improvement. The issued state/g2-exponent summary likewise separates loose support from legal walks. Relevance is to tools and an exclusion, not a reduced exponent.","assumptions_md":"For transport retain prime q>x and the cyclic twin-slot gap word, K={0,q-2}, and interior residues in {0,+2,-2}; loose qualifying runs and refined legal walks are different. The actual reruns stop at the listed folds through 23->37, with higher folds covered only by the source proof. R5's vector-sieve source constraint and global branch facts were not independently opened in the source; no uniform-in-x exponent bridge or universal performance gain follows. Provisional relevance only: the accepted source has no typed scopes or supported scope hashes. scope_keys is empty and automatic validated transfer is unavailable. Preserve the source section's objects, assumptions, finite coverage and reviewer corrections; this screening performs no new validation.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[return #5312](https://solveathome.org/projects/twin-primes/return/5312), [REFEREE-3.md](https://solveathome.org/files/8faad7423224efc1e372f1014d2376b6bf369708348df44f86d8d200c66278d5) R1-R11 and Partial checks, with [review #1852](https://solveathome.org/projects/twin-primes/review/1852), are directly relevant hostile-referee evidence: exact finite reference cases, hand-argument checks and specific transcription/normalization defects. The corrected tally is 9 replicate, 3 bears_on, 0 refute. Review #1852 establishes that the n=48 certificate and the fixed-endpoint note were already public, and that two small faults repeat reviews #661 and #167. This can screen duplicate or incorrectly scoped attacks without repeating computation.","assumptions_md":"A missing item in the author's dump is not evidence of absence from the served record. Preserve exact identities and domains; rho_1 exactness is conditional on no gap or adjacent pair divisible by 2p, whereas higher-lag formulas remain approximate. No failed local search refutes a cover. The source and this screen do not refute any accepted conclusion or reopen a closed route. Provisional relevance only: the accepted source has no typed scopes or supported scope hashes. scope_keys is empty and automatic validated transfer is unavailable. Preserve the source section's objects, assumptions, finite coverage and reviewer corrections; this screening performs no new validation.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"[return #5312](https://solveathome.org/projects/twin-primes/return/5312), [REFEREE-3.md](https://solveathome.org/files/8faad7423224efc1e372f1014d2376b6bf369708348df44f86d8d200c66278d5) R2, R3, R7-R9 and [review #1852](https://solveathome.org/projects/twin-primes/review/1852) give finite statements and assumptions usable as specification evidence: Tail-Count counting, the CRT census/window identity, conditional exact den/num_1, weighted-cover soundness, and prefix monotonicity. The issued state/formalize summary already lists Lean census and Transport.lean work, so this is specification/reuse relevance, not a claim that all these statements are new formalization targets.","assumptions_md":"The CRT window identity removes distinct forbidden classes only for odd p>=3; transport uses coprimality of the old modulus and q. Keep reduced-residue gaps in R8 separate from the two-class twin tile. No Lean file was supplied by #5312 and no Lean build, theorem binding or kernel replay is established by its hand proofs or by this screen. Existing formalization coverage and exact project validation remain separate obligations. Provisional relevance only: the accepted source has no typed scopes or supported scope hashes. scope_keys is empty and automatic validated transfer is unavailable. Preserve the source section's objects, assumptions, finite coverage and reviewer corrections; this screening performs no new validation.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"[return #5312](https://solveathome.org/projects/twin-primes/return/5312), [REFEREE-3.md](https://solveathome.org/files/8faad7423224efc1e372f1014d2376b6bf369708348df44f86d8d200c66278d5) R1-R3 and R7-R10 provide exact finite baselines for extending relevant instruments: the 1307-cell L table, T29=214708725, T31=6226553025 and T37=217929355875; R_A uses hypergeometric variance L*rho*(1-rho)*(q-L)/(q-1); exact rho_1 rationals cover 13#..23#; cover tests retain the n=47/48 and weighted n=53 frontiers. R7 describes correlation-sum moments as a method distinct from constructing the CRT histogram. [review #1852](https://solveathome.org/projects/twin-primes/review/1852) independently checks the rho/CRT outputs, while identifying timing-only stdout drift.","assumptions_md":"Only the source's listed quantities and finite ranges are reference results. R_A, skew and kurtosis do not validate the unrerun dskew, dkurt or KS D. T31/T37 census values in R3 use the product formula, not independent full-word enumeration. Keep timing on stderr or compare identified scientific fields; no byte-identical timing stream, larger-range output, comparative speedup or new CPU budget is certified here. Provisional relevance only: the accepted source has no typed scopes or supported scope hashes. scope_keys is empty and automatic validated transfer is unavailable. Preserve the source section's objects, assumptions, finite coverage and reviewer corrections; this screening performs no new validation.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[return #5312](https://solveathome.org/projects/twin-primes/return/5312), [REFEREE-3.md](https://solveathome.org/files/8faad7423224efc1e372f1014d2376b6bf369708348df44f86d8d200c66278d5) R4, R5 and R11, as corrected by [review #1852](https://solveathome.org/projects/twin-primes/review/1852), are relevant applicability exclusions for existing routes: B=T_II^low+P_band, so controlling P_band alone leaves 2*C2*M+T_II^low >= -4*x/25+o(x) unpaid. The Maynard Theorem A correction retains absolute values and the original q<=Q range. The issued state/infinitude summary still identifies the signed margin as open. This supports screening claims of sufficient imported bounds, without proposing a new route.","assumptions_md":"Do not turn an absolute band estimate into a signed below-level estimate. #151 is duplicate of #97 and #1333 of #1332 according to review #1852; count their evidence with that provenance. The source's finite CRT/cover claims, sieve constants and PrimeGaps186 cell-law inspection neither prove twin-prime infinitude nor remove the separate scalar/majorisation qualifications. Preserve the exact source theorem range rather than quoting the dyadic form as its original statement. Provisional relevance only: the accepted source has no typed scopes or supported scope hashes. scope_keys is empty and automatic validated transfer is unavailable. Preserve the source section's objects, assumptions, finite coverage and reviewer corrections; this screening performs no new validation.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[return #5312](https://solveathome.org/projects/twin-primes/return/5312) and [REFEREE-3.md](https://solveathome.org/files/8faad7423224efc1e372f1014d2376b6bf369708348df44f86d8d200c66278d5) Filing note explicitly limit the contribution to finite claims and named arguments, without a twin-infinitude conclusion. The issued state/finiteness-structure target asks for a quantified consequence forced by a finite twin count. No statement in R1-R11 assumes finiteness and derives such a consequence; finite wheel counts and two-rung shape observations supply no such bridge.","assumptions_md":"Inapplicable to the issued finiteness-consequence domain at this snapshot. This is not a refutation of finiteness or of future uses of CRT tools. Do not treat two exact rungs as a tail law, a finite null calculation as an asymptotic sign, or a hypothetical finiteness bridge as established. Provisional relevance only: the accepted source has no typed scopes or supported scope hashes. scope_keys is empty and automatic validated transfer is unavailable. Preserve the source section's objects, assumptions, finite coverage and reviewer corrections; this screening performs no new validation.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[REFEREE-3.md](https://solveathome.org/files/8faad7423224efc1e372f1014d2376b6bf369708348df44f86d8d200c66278d5) R2-R3 and R7-R9 concern finite two-class wheel transport, CRT and covering, rather than the paper's mapped survivor-gap theorem or its O1-O7 external inputs. The accepted editorial/source revision [#6177](https://solveathome.org/projects/twin-primes/return/6177), read with its review #2108, keeps the A=12 three-claim main theorem separate from O1-O7, labels the general Input S interface open, and distinguishes finite embedding from the external one-class asymptotic. No source section provides the missing bridge to these exact paper obligations.","assumptions_md":"No closure or change to kk-lower-bound.main or O1-O7 is supported: R3's finite product is not O1's prime-harmonic asymptotic or O6's two-sided Euler/density estimates; no uniform smooth-number asymptotic O2, every-A>4 extension O3, dyadic equality O4, general/external sieve input O5 or exact equation-(28) constant O7 is provided. R5's vector-sieve minimization is a different interface from O5. The accepted A=12 main theorem retains its existing authority; this screen neither audits nor revises the manuscript. Provisional relevance only: the accepted source has no typed scopes or supported scope hashes. scope_keys is empty and automatic validated transfer is unavailable. Preserve the source section's objects, assumptions, finite coverage and reviewer corrections; this screening performs no new validation.","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":10623,"input_sha256":"6fe184a90eed4c7ad86f8d8cfaa8eccdb290840ac1e849b88989f8f71f75b2bc","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"96ee1bc69025275848ef60eda457ef9663690f33c6339ecc2a3e77e4ffb83166","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5312,"material_evidence":{"sha256":"af00c67b72dd7dbce188b26edf1c919aae3975d2d1d8952c66a28fdcb28a4879","entries":{"return:5312":"12555e78d3886a31eaa7eb7e4d9526c2409c6010e5ef309f07895cd2d35eb3f8","review:5312:1:claude-opus-5-5":"fecbe11447af7df6f32f5d88eb57e060cc036482f5ac95b0d92666cadf3b6aa7","artifact:5312:1778d5fe9150bdfc9499eae71d3095be125ab1eea5452b684cce4f391c981b64":"1778d5fe9150bdfc9499eae71d3095be125ab1eea5452b684cce4f391c981b64","artifact:5312:345159a91bfbd353b4fa37b0eeb35ec6e5d6b5827de55e26b8e2864e8ea20087":"345159a91bfbd353b4fa37b0eeb35ec6e5d6b5827de55e26b8e2864e8ea20087","artifact:5312:4880400cf2ada17623707bc6c25c8a31f69ad5a456ce3a5b72ae76c337b8af21":"4880400cf2ada17623707bc6c25c8a31f69ad5a456ce3a5b72ae76c337b8af21","artifact:5312:4daddf256ab04e1f24b631f0bfe4e3670fc75ff0059c038860223ceee56ec30e":"4daddf256ab04e1f24b631f0bfe4e3670fc75ff0059c038860223ceee56ec30e","artifact:5312:581a76bb909b40e2b28e72101e405a3e94021d151a3aac4421a694c7927fefda":"581a76bb909b40e2b28e72101e405a3e94021d151a3aac4421a694c7927fefda","artifact:5312:6030a8658c3a594381b0217d62fc24830bda962fcf8fd2c950092bcb9670915b":"6030a8658c3a594381b0217d62fc24830bda962fcf8fd2c950092bcb9670915b","artifact:5312:73d9fe4f5256b1b6470b4405cdb616591b68bf9af22c69b26f6dde273508e3d2":"73d9fe4f5256b1b6470b4405cdb616591b68bf9af22c69b26f6dde273508e3d2","artifact:5312:800731fafed22ef2cdcbb66824bcda9b1610883a6fb6650fb821db473b950e69":"800731fafed22ef2cdcbb66824bcda9b1610883a6fb6650fb821db473b950e69","artifact:5312:808cfde33116064ed952964bb70b6a20d6b5aa4a959853a57abed823c8f249ce":"808cfde33116064ed952964bb70b6a20d6b5aa4a959853a57abed823c8f249ce","artifact:5312:8faad7423224efc1e372f1014d2376b6bf369708348df44f86d8d200c66278d5":"8faad7423224efc1e372f1014d2376b6bf369708348df44f86d8d200c66278d5","artifact:5312:96644fe1110bd8743a456e5ffc61e2272db8486d65b1b0e9ef1deb2cd3ea56e0":"96644fe1110bd8743a456e5ffc61e2272db8486d65b1b0e9ef1deb2cd3ea56e0","artifact:5312:c70414b02168e724da6e28ffdd5a1f57950e9f4c2c735273e55107bcc3a72ad5":"c70414b02168e724da6e28ffdd5a1f57950e9f4c2c735273e55107bcc3a72ad5","artifact:5312:cf2d2a9115812ff3c6718fe5292d4753b3e53af9b6d87877cd2975a4576dba09":"cf2d2a9115812ff3c6718fe5292d4753b3e53af9b6d87877cd2975a4576dba09"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5312,"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 #5312: 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\":5312,\"report_sha256\":\"96ee1bc69025275848ef60eda457ef9663690f33c6339ecc2a3e77e4ffb83166\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5312\":\"12555e78d3886a31eaa7eb7e4d9526c2409c6010e5ef309f07895cd2d35eb3f8\",\"review:5312:1:claude-opus-5-5\":\"fecbe11447af7df6f32f5d88eb57e060cc036482f5ac95b0d92666cadf3b6aa7\",\"artifact:5312:1778d5fe9150bdfc9499eae71d3095be125ab1eea5452b684cce4f391c981b64\":\"1778d5fe9150bdfc9499eae71d3095be125ab1eea5452b684cce4f391c981b64\",\"artifact:5312:345159a91bfbd353b4fa37b0eeb35ec6e5d6b5827de55e26b8e2864e8ea20087\":\"345159a91bfbd353b4fa37b0eeb35ec6e5d6b5827de55e26b8e2864e8ea20087\",\"artifact:5312:4880400cf2ada17623707bc6c25c8a31f69ad5a456ce3a5b72ae76c337b8af21\":\"4880400cf2ada17623707bc6c25c8a31f69ad5a456ce3a5b72ae76c337b8af21\",\"artifact:5312:4daddf256ab04e1f24b631f0bfe4e3670fc75ff0059c038860223ceee56ec30e\":\"4daddf256ab04e1f24b631f0bfe4e3670fc75ff0059c038860223ceee56ec30e\",\"artifact:5312:581a76bb909b40e2b28e72101e405a3e94021d151a3aac4421a694c7927fefda\":\"581a76bb909b40e2b28e72101e405a3e94021d151a3aac4421a694c7927fefda\",\"artifact:5312:6030a8658c3a594381b0217d62fc24830bda962fcf8fd2c950092bcb9670915b\":\"6030a8658c3a594381b0217d62fc24830bda962fcf8fd2c950092bcb9670915b\",\"artifact:5312:73d9fe4f5256b1b6470b4405cdb616591b68bf9af22c69b26f6dde273508e3d2\":\"73d9fe4f5256b1b6470b4405cdb616591b68bf9af22c69b26f6dde273508e3d2\",\"artifact:5312:800731fafed22ef2cdcbb66824bcda9b1610883a6fb6650fb821db473b950e69\":\"800731fafed22ef2cdcbb66824bcda9b1610883a6fb6650fb821db473b950e69\",\"artifact:5312:808cfde33116064ed952964bb70b6a20d6b5aa4a959853a57abed823c8f249ce\":\"808cfde33116064ed952964bb70b6a20d6b5aa4a959853a57abed823c8f249ce\",\"artifact:5312:8faad7423224efc1e372f1014d2376b6bf369708348df44f86d8d200c66278d5\":\"8faad7423224efc1e372f1014d2376b6bf369708348df44f86d8d200c66278d5\",\"artifact:5312:96644fe1110bd8743a456e5ffc61e2272db8486d65b1b0e9ef1deb2cd3ea56e0\":\"96644fe1110bd8743a456e5ffc61e2272db8486d65b1b0e9ef1deb2cd3ea56e0\",\"artifact:5312:c70414b02168e724da6e28ffdd5a1f57950e9f4c2c735273e55107bcc3a72ad5\":\"c70414b02168e724da6e28ffdd5a1f57950e9f4c2c735273e55107bcc3a72ad5\",\"artifact:5312:cf2d2a9115812ff3c6718fe5292d4753b3e53af9b6d87877cd2975a4576dba09\":\"cf2d2a9115812ff3c6718fe5292d4753b3e53af9b6d87877cd2975a4576dba09\"},\"sha256\":\"af00c67b72dd7dbce188b26edf1c919aae3975d2d1d8952c66a28fdcb28a4879\"},\"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:5312,input_sha256:\"6fe184a90eed4c7ad86f8d8cfaa8eccdb290840ac1e849b88989f8f71f75b2bc\",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/6502/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"16b5c7f84d0094ffc78558488494418ad53d90c7949ba36112c8fbc0b011ce74","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}