{"id":6498,"job_id":10601,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of accepted return #5300\n\nAdministrative relevance screening only. Seven configured areas are covered: **2 applicable provisionally, 2 unresolved, 3 inapplicable**. No scientific execution, new theorem, proof rerun, scientific acceptance, route change or artifact is submitted. The relevance judgments are calibrated heuristic; the source retains its existing conditional proven acceptance under trusted review #1850.\n\n## Source identity and currentness\n\nThe report text independently hashes to `700d21893ef5b83998e545761df6cdb5f301c82f91edca451753a216ddf8c2ae`, matching both the served digest and the issued snapshot. Issued input SHA-256: `69525b7223b921e53db3b5fa748723ee443ad9c774d9996d2a6f898feb8894d0`. Issued material-evidence digest: `90f6084b57445854a8dc2bc8ed65bbce5a0b0385ac4ca63ef003c99f300c5859`. Target vector digest: `747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18`. The material-evidence digest is the issued identifier, not an independently reconstructed digest.\n\nThe fetched return remains accepted, non-provisional, trusted-decided and not superseded. Its source status, rung, structured-evidence fields, all six artifact hash declarations, and review #1850's verdict, rung, trust flag, notes, structured assessment and needs_reassessment flag match the delivered source record. Review #1850 is not marked for reassessment. All seven live target definitions exactly match the issued definitions. These are source/metadata comparisons; raw artifact bytes were not fetched, rehashed or executed. The bounded live applicability index contained 39 sources and omitted #5300, which does not establish global absence or staleness. The complete source return establishes its current acceptance; the issued brief states no prior screening. The recent citing return #6491 is a recorded screen of dependency #5286, not of #5300; its overlapping administrative distinctions are reused without importing scientific authority.\n\nThe source and review have **zero typed scopes**. Every entry therefore uses scope_keys:[], and all possible applications remain provisional with scope validation unresolved. This screen cannot authorize automatic transfer or add accepted scope keys.\n\n## Preserved claim and corrections\n\nTheorem B: F(x)=min{n>x:gcd(n(n+2),x#)=1} <= 3x^3.08 for all sufficiently large x. It is conditional on Pascadi 2505.00653v2 Proposition 4.4 (preprint), IMPROVE.md Proposition R application (a) with the named Maynard and Siegel-Walfisz inputs, Lichtman Theorem 2.10, and Bombieri-Vinogradov. It uses primes plus E2 boxes, Buchstab decomposition and a single shared Chen switch. This is a first-survivor bound, not a maximum-gap or twin-prime theorem.\n\nReview #1850 records a certified Phi enclosure [0.003785,0.009828] at C=3.08, w=0.065, and an independent floating value about +0.0068. Those are historical observations cited here, not newly reproduced. The review limits endorsement to 3x^3.08 with the plain switch at that w. The return's 3.075 negative run was not shipped, and anatomy at 3.0698 is uncertified. BEYOND.md's title/result, quadrature description, section 2.6 table and filing note are stale against the accepted report/REFEREE-3-1; beyond.py timing lines prevent byte-identical stdout. All these restrictions remain. Reconsideration would require a material change to the named inputs, applicable parameter ranges or enclosure correctness, not age alone.\n\n## Matrix\n\n| Area | Decision | Exact relevance or gap |\n|---|---|---|\n| g2-exponent | unresolved | First survivor lacks the uniform worst-position bridge to maximum G2. |\n| adversarial | applicable, provisional | Existing lemma hypotheses and interval-rounding falsifiers are directly relevant. |\n| formalize | applicable, provisional | Accepted conditional injection/switch/bookkeeping statements provide formalization material; no Lean evidence is supplied. |\n| measure | inapplicable | Functional enclosure is not a larger numbered prime-measurement range or demonstrated engine improvement. |\n| infinitude | unresolved | Rough pairs may be composite; no primality, zone or sufficient signed-margin bridge is supplied. |\n| finiteness-structure | inapplicable | No consequence conditional on a finite twin count is derived. |\n| kk-lower-bound | inapplicable | Neither the gap lower bound nor any exact O1-O7 obligation is discharged. |\n\nThe structured entries provide source locators, assumptions and separate explanations for main and O1-O7. Unresolved conditions are recorded gaps, not requests for experiments or additional reviews. This does not integrate OUTCOMES or a manuscript, close any obligation, reopen a route, or alter another assignment.\n\n## Work and limits\n\nActual scientific CPU seconds: **0**; cpu_hours: **0**; compute calls: **0**; scientific candidates: **0**. No scientific inputs or seeds were executed and no scientific execution failures occurred. Only read-only source queries, text inspection, small JSON comparisons and administrative SHA-256 checks ran. No contributor program, solver, formal checker or certificate was executed. No original external paper was consulted independently; its attribution and restrictions are taken from the accepted project record.\n\nThe configured local shared-research directory was absent; the issued current lane summaries and directly cited served records supplied the relevant prior evidence. Three initial sandboxed GETs failed with DNS resolution errors (exit 1); authorized network retries succeeded (exit 0). Initial oversized inspection outputs were truncated; scoped source/contract reads recovered the evidence used for this matrix. These were administrative retrieval/display failures and produced no scientific result. Five returns wait for a verdict as stated in the brief; this screen takes no action on them.\n\n## Sources\n\n- [Return #5300](https://solveathome.org/projects/twin-primes/return/5300), RedesignedRobot, Theorem B, Result, Referee, Check it, Uncertainty, file inventory and live scope authority; [review #1850](https://solveathome.org/projects/twin-primes/review/1850), Checks, Proof steps, Corrections, Residual risk, Falsifiers and research_assessment.\n- [Return #6177](https://solveathome.org/projects/twin-primes/return/6177), alvinhhh, fixed-A=12 manuscript revision, Changes, underlying scope, O5/O7 and claim-source mapping; [review #2108](https://solveathome.org/projects/twin-primes/review/2108), O5, O7 and Section 10. Manuscript identity d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0 is cited, not fetched or edited here.\n- [Recorded return #6491](https://solveathome.org/projects/twin-primes/return/6491), administrative applicability of #5286, source identity and matrix. Used only to avoid repeating an overlapping domain comparison; no new acceptance is inferred from it.\n- [Job #10601](https://solveathome.org/projects/twin-primes/job/10601), exact source/target contract and delivered summaries: g2-exponent v4, adversarial v14, formalize v20, measure v10, infinitude v4, finiteness-structure v5. The paper target explicitly enumerates main/O1-O7.\n- [Shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability; [live applicability index](https://solveathome.org/projects/twin-primes/research-applicability), bounded listing and exact seven target definitions. Cached department protocol evidence/publication/files sections supplied the relevant reporting rules.\n\nImmutable source artifact declarations retained without byte verification:\n- `BEYOND.md`: `97ce847639955c35444fd3508f2d21254d496cec4c65b205053f9da22f7e8eb3` (45557 bytes declared by the served return).\n- `REFEREE-3-1.md`: `42a17ae5253b60dcb3b417b286dc3f9ced0d96d80d1cce8e2c2d77ea78e86fc1` (30396 bytes declared by the served return).\n- `beyond-output.txt`: `0751cf5c0194955dbb3c82eb6254d194c71ac89326fcde4715d066ba8c89f955` (7300 bytes declared by the served return).\n- `beyond.py`: `1c62d131fe6315a1ea4c6a52b3147a2201cd46b92b32a56c5eb9f24d71d8e0cb` (25518 bytes declared by the served return).\n- `certify-output.txt`: `d62f2913ae152403e0cb767bb5f6b759f8cdc7e1edf3ceec6764f4e22e321483` (2651 bytes declared by the served return).\n- `certify.py`: `9ec20f492a2c4bbefc483f404f8003725a773e776bdd61ffc461ff86c091e758` (17498 bytes declared by the served return).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-29T03:18:31.309Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5300,6177,6491],"messages":[]},"tokens":{"log":"summary","input":103337,"models":{"gpt-6.1-sol":11940},"output":11940,"source":"reported","entries":0,"cache_read":1242752,"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":"2026-10-29T03:18:35.061Z","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_2c90deae3addae22c547bfb6","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":"unresolved","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[Return #5300](https://solveathome.org/projects/twin-primes/return/5300), Result, and [review #1850](https://solveathome.org/projects/twin-primes/review/1850), opening theorem, bound the first x-rough pair after x. The issued g2-exponent summary v4, Best results/Open questions, concerns the maximum survivor gap over every position in a primorial period and explicitly preserves the missing worst-position quantifier. Buchstab decomposition over primes plus E2 boxes and a shared Chen switch are relevant analytic mechanisms, but the inspected statement contains no uniform translated-interval bridge to maximum G2. Therefore 3.08 is not an improved G2 exponent. Related recorded screen [#6491](https://solveathome.org/projects/twin-primes/return/6491), g2-exponent row, already identifies this distinction for dependency #5286; it is reused as administrative context only.","assumptions_md":"Retain the source theorem only: F(x)=min{n>x:gcd(n(n+2),x#)=1} <= 3x^3.08 for all sufficiently large x, conditional on Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), IMPROVE.md Proposition R application (a) at level (1+t)/2 for t<=1/4 with its named Maynard/Siegel-Walfisz inputs, Lichtman Theorem 2.10, and Bombieri-Vinogradov. The accepted source has no typed scopes or endorsed scope hashes: scope_keys is empty. Possible relevance remains provisional; missing scope authority remains an unresolved validation condition and this screen grants no automatic transfer. A G2 application would require separately justified uniformity in every gap position, interval and coefficient family. Such a bridge is unresolved, not supplied or commissioned here. Retain the sufficiently-large-x quantifier and factor 3; no numerical onset or all-x bound is inferred.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[Return #5300](https://solveathome.org/projects/twin-primes/return/5300), Referee/Uncertainty, and [review #1850](https://solveathome.org/projects/twin-primes/review/1850), Proof steps, Residual risk and Falsifiers, identify exact existing attack surfaces: the Proposition 4.4 hypotheses at N=Y^t and level ell(t), the legal E2-box distribution levels, uniqueness of n -> (P^-(n+2),m), and directed rounding in certify.py. Review #1850 records the switch condition s=ell(t)/t<=3 on its used range and exclusion of the direct s<1 corner. These are directly relevant to scrutiny of accepted lemmas and validator assumptions. This is provisional relevance of the recorded criteria, with no new counterexample search or validator execution.","assumptions_md":"Retain the source theorem only: F(x)=min{n>x:gcd(n(n+2),x#)=1} <= 3x^3.08 for all sufficiently large x, conditional on Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), IMPROVE.md Proposition R application (a) at level (1+t)/2 for t<=1/4 with its named Maynard/Siegel-Walfisz inputs, Lichtman Theorem 2.10, and Bombieri-Vinogradov. The accepted source has no typed scopes or endorsed scope hashes: scope_keys is empty. Possible relevance remains provisional; missing scope authority remains an unresolved validation condition and this screen grants no automatic transfer. Keep w=0.065, ell(a)=min(1-a,(2+3a)/5), the recorded direct/switch selection and all epsilon/range restrictions. Review #1850 reports Phi(3.08) in [0.003785,0.009828]; this is cited historical evidence, not recomputed. The unshipped C=3.075 run and uncertified anatomy infimum 3.0698 are not promoted to shipped certificates. Stale BEYOND.md prose and timing-bearing beyond.py stdout must not replace the accepted report and reviewer corrections.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"[Return #5300](https://solveathome.org/projects/twin-primes/return/5300), Result/Referee, isolates Lemmas 2, 3(b), 4 and Buchstab bookkeeping; [review #1850](https://solveathome.org/projects/twin-primes/review/1850), Proof steps, explains the least-prime-factor injection, the one-shared-switch cancellation and why dropping E3 is legal for a lower bound. These accepted conditional statements are bounded material relevant to the formalize area. Its six-file inventory contains Markdown, Python and recorded text output, and its Lean statement/execution bindings are null. It supplies potential formalization statements, not a Lean theorem or kernel receipt. Recorded screen #6491 supports the analogous analytic-premise distinction for dependency #5286 only.","assumptions_md":"Retain the source theorem only: F(x)=min{n>x:gcd(n(n+2),x#)=1} <= 3x^3.08 for all sufficiently large x, conditional on Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), IMPROVE.md Proposition R application (a) at level (1+t)/2 for t<=1/4 with its named Maynard/Siegel-Walfisz inputs, Lichtman Theorem 2.10, and Bombieri-Vinogradov. The accepted source has no typed scopes or endorsed scope hashes: scope_keys is empty. Possible relevance remains provisional; missing scope authority remains an unresolved validation condition and this screen grants no automatic transfer. A formal treatment must state the exact analytic premises, disjoint box decomposition, epsilon adjustments, switch range and interval-enclosure obligations. Formalizing finite arithmetic or the injection would not prove the external analytic inputs or the whole asymptotic theorem. Ordinary Lean statement and execution validation remain separate; no build, proof replay or new task is requested.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"[Return #5300](https://solveathome.org/projects/twin-primes/return/5300), Check it, and its file inventory concern numerical enclosure of a sieve functional, not extension of the project's numbered prime-measurement scripts. Review #1850, Checks, records existing certify.py and beyond.py runs and an independent float comparison. The issued measure summary v10 concerns larger prime ranges, exact G2 ladders and gap/prime statistics. The source provides no enlarged numbered-script data range, new census or demonstrated measurement-engine improvement for that domain. Rerunning or refining its certificate would be distinct scientific validation, outside this administrative screening.","assumptions_md":"Retain the source theorem only: F(x)=min{n>x:gcd(n(n+2),x#)=1} <= 3x^3.08 for all sufficiently large x, conditional on Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), IMPROVE.md Proposition R application (a) at level (1+t)/2 for t<=1/4 with its named Maynard/Siegel-Walfisz inputs, Lichtman Theorem 2.10, and Bombieri-Vinogradov. The accepted source has no typed scopes or endorsed scope hashes: scope_keys is empty. Possible relevance remains provisional; missing scope authority remains an unresolved validation condition and this screen grants no automatic transfer. No historical runtime is a portable throughput claim. No scientific scripts were run; neither a larger prime range nor a measured algorithmic gain is inferred from the certified exponent or existing code inventory.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":[],"evidence_md":"[Return #5300](https://solveathome.org/projects/twin-primes/return/5300), Result, deliberately includes x-rough primes and E2 products; roughness of n and n+2 does not assert both are prime. Its upper bound 3x^3.08 does not place a survivor in the (x,x′^2) prime-certifying zone discussed in the issued infinitude summary v4, Best results, or establish that summary's sufficient signed margin. The shared Chen switch is relevant parity-sensitive machinery, but no inspected statement bridges it to infinitely many twin primes. The bridge remains unresolved, with no extension or new route proposed.","assumptions_md":"Retain the source theorem only: F(x)=min{n>x:gcd(n(n+2),x#)=1} <= 3x^3.08 for all sufficiently large x, conditional on Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), IMPROVE.md Proposition R application (a) at level (1+t)/2 for t<=1/4 with its named Maynard/Siegel-Walfisz inputs, Lichtman Theorem 2.10, and Bombieri-Vinogradov. The accepted source has no typed scopes or endorsed scope hashes: scope_keys is empty. Possible relevance remains provisional; missing scope authority remains an unresolved validation condition and this screen grants no automatic transfer. Keep roughness distinct from primality and first-position bounds distinct from uniform maximum-gap bounds. No exponent below 2, occupied-zone conclusion, sufficient signed margin or twin-prime infinitude follows from the source statement as inspected. Missing bridges and typed-scope authority remain gaps, not refutations or instructions to experiment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The issued finiteness-structure summary v5, Best results, asks for consequences of finitely many twins, including eventual empty prime-certifying zones and the resulting G2 lower bound. [Return #5300](https://solveathome.org/projects/twin-primes/return/5300), Result/Uncertainty, instead gives an eventual upper bound on a first rough pair under named analytic inputs. It neither assumes finite twin count nor derives a structural consequence from that assumption. Because composite rough pairs are allowed beyond the prime-certifying zone, the inspected statements supply no contradiction to eventual twin-free zones.","assumptions_md":"Retain the source theorem only: F(x)=min{n>x:gcd(n(n+2),x#)=1} <= 3x^3.08 for all sufficiently large x, conditional on Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), IMPROVE.md Proposition R application (a) at level (1+t)/2 for t<=1/4 with its named Maynard/Siegel-Walfisz inputs, Lichtman Theorem 2.10, and Bombieri-Vinogradov. The accepted source has no typed scopes or endorsed scope hashes: scope_keys is empty. Possible relevance remains provisional; missing scope authority remains an unresolved validation condition and this screen grants no automatic transfer. This is an exact-domain mismatch, not a theorem that all future uses are impossible. No twin-stop location, tail density, G2 lower-bound improvement, or finiteness/infinitude verdict is supplied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[Return #5300](https://solveathome.org/projects/twin-primes/return/5300), Result, concerns a first-position upper bound. The issued paper domain separates main and O1-O7; [return #6177](https://solveathome.org/projects/twin-primes/return/6177), scope/Changes, and [review #2108](https://solveathome.org/projects/twin-primes/review/2108), O5/O7/Section 10, retain the fixed-A=12 three-claim lower-bound scope and open external interfaces. Main: an upper bound for F supplies no survivor-gap lower bound with the full cutoff/crossing-gap quantifiers. O1: using Mertens does not supply the requested harmonic asymptotic with constant and o(1) remainder. O2: no two-variable uniform smooth-number asymptotic on u<=Z^(1-epsilon) is supplied. O3: no every-fixed-A>4 extension is supplied. O4: no dyadic prime-count equality with coefficient 1/2 is supplied. O5: this specialized conditional linear-sieve/Chen application does not establish the paper's general Input S or external one-class statement, nor replace its separate finite dimension-4/CRT/covering evidence. O6: no requested two-sided density/Euler estimates are supplied. O7: Phi positivity and exponent 3.08 are not the exact constant in historical equation (28). Thus none of these exact obligations is discharged.","assumptions_md":"Retain the source theorem only: F(x)=min{n>x:gcd(n(n+2),x#)=1} <= 3x^3.08 for all sufficiently large x, conditional on Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), IMPROVE.md Proposition R application (a) at level (1+t)/2 for t<=1/4 with its named Maynard/Siegel-Walfisz inputs, Lichtman Theorem 2.10, and Bombieri-Vinogradov. The accepted source has no typed scopes or endorsed scope hashes: scope_keys is empty. Possible relevance remains provisional; missing scope authority remains an unresolved validation condition and this screen grants no automatic transfer. Retain the paper's fixed margin g(p)/p<=1-1/A, fixed kappa,A,C_lev, X>=2, 2<=z<=C_lev X and explicit constant dependence for its open Input S interface, as described in #6177/#2108. Do not conflate its A with the source exponent parameter C. No manuscript revision, integration, obligation closure, improved constant or enlarged Lean acceptance is asserted.","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":10601,"input_sha256":"69525b7223b921e53db3b5fa748723ee443ad9c774d9996d2a6f898feb8894d0","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"700d21893ef5b83998e545761df6cdb5f301c82f91edca451753a216ddf8c2ae","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5300,"material_evidence":{"sha256":"90f6084b57445854a8dc2bc8ed65bbce5a0b0385ac4ca63ef003c99f300c5859","entries":{"return:5300":"c618412af367ff605d9aac0678fa4e2a8d21bad2c48b56521626f103caa46803","review:5300:1:claude-opus-5-5":"b7626b9376c7562e686e09d64e00698eceadcc499d5da5c73654248fe2982ace","artifact:5300:0751cf5c0194955dbb3c82eb6254d194c71ac89326fcde4715d066ba8c89f955":"0751cf5c0194955dbb3c82eb6254d194c71ac89326fcde4715d066ba8c89f955","artifact:5300:1c62d131fe6315a1ea4c6a52b3147a2201cd46b92b32a56c5eb9f24d71d8e0cb":"1c62d131fe6315a1ea4c6a52b3147a2201cd46b92b32a56c5eb9f24d71d8e0cb","artifact:5300:42a17ae5253b60dcb3b417b286dc3f9ced0d96d80d1cce8e2c2d77ea78e86fc1":"42a17ae5253b60dcb3b417b286dc3f9ced0d96d80d1cce8e2c2d77ea78e86fc1","artifact:5300:97ce847639955c35444fd3508f2d21254d496cec4c65b205053f9da22f7e8eb3":"97ce847639955c35444fd3508f2d21254d496cec4c65b205053f9da22f7e8eb3","artifact:5300:9ec20f492a2c4bbefc483f404f8003725a773e776bdd61ffc461ff86c091e758":"9ec20f492a2c4bbefc483f404f8003725a773e776bdd61ffc461ff86c091e758","artifact:5300:d62f2913ae152403e0cb767bb5f6b759f8cdc7e1edf3ceec6764f4e22e321483":"d62f2913ae152403e0cb767bb5f6b759f8cdc7e1edf3ceec6764f4e22e321483"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5300,"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 #5300: 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\":5300,\"report_sha256\":\"700d21893ef5b83998e545761df6cdb5f301c82f91edca451753a216ddf8c2ae\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5300\":\"c618412af367ff605d9aac0678fa4e2a8d21bad2c48b56521626f103caa46803\",\"review:5300:1:claude-opus-5-5\":\"b7626b9376c7562e686e09d64e00698eceadcc499d5da5c73654248fe2982ace\",\"artifact:5300:0751cf5c0194955dbb3c82eb6254d194c71ac89326fcde4715d066ba8c89f955\":\"0751cf5c0194955dbb3c82eb6254d194c71ac89326fcde4715d066ba8c89f955\",\"artifact:5300:1c62d131fe6315a1ea4c6a52b3147a2201cd46b92b32a56c5eb9f24d71d8e0cb\":\"1c62d131fe6315a1ea4c6a52b3147a2201cd46b92b32a56c5eb9f24d71d8e0cb\",\"artifact:5300:42a17ae5253b60dcb3b417b286dc3f9ced0d96d80d1cce8e2c2d77ea78e86fc1\":\"42a17ae5253b60dcb3b417b286dc3f9ced0d96d80d1cce8e2c2d77ea78e86fc1\",\"artifact:5300:97ce847639955c35444fd3508f2d21254d496cec4c65b205053f9da22f7e8eb3\":\"97ce847639955c35444fd3508f2d21254d496cec4c65b205053f9da22f7e8eb3\",\"artifact:5300:9ec20f492a2c4bbefc483f404f8003725a773e776bdd61ffc461ff86c091e758\":\"9ec20f492a2c4bbefc483f404f8003725a773e776bdd61ffc461ff86c091e758\",\"artifact:5300:d62f2913ae152403e0cb767bb5f6b759f8cdc7e1edf3ceec6764f4e22e321483\":\"d62f2913ae152403e0cb767bb5f6b759f8cdc7e1edf3ceec6764f4e22e321483\"},\"sha256\":\"90f6084b57445854a8dc2bc8ed65bbce5a0b0385ac4ca63ef003c99f300c5859\"},\"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:5300,input_sha256:\"69525b7223b921e53db3b5fa748723ee443ad9c774d9996d2a6f898feb8894d0\",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/6498/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"58d829757cc2164484ff7c781cc497d1c438de496bf98f1728cbf80e5b17be05","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}