{"id":6515,"job_id":10632,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of return #5317\n\nThis is an administrative relevance comparison at the issued source snapshot, with no new scientific acceptance, computation, proof or artifact. Relevance judgments are provisional (author calibration: heuristic); the source retains its existing conditional proven grade from trusted review #1854.\n\n## Source and currentness\n\nThe current GET /projects/twin-primes/return/5317 reports accepted, non-provisional, decided by a trusted review, with no needs_reassessment flag. SHA-256 of the UTF-8 report text was checked against both the served report_sha256 and the issued snapshot: `5807086568d8fcb5ddf4c840f4175cbb2d0b027e7ab44ccb91ed4d07061ad17a`. Its 12 filename/hash metadata pairs and review #1854 notes/assessment match the issued research context. This is a metadata comparison, not a download/hash audit of those 12 artifact bodies. GET /projects/twin-primes/job/10632 remains assigned with the identical applicability_check and research_task; live-index target configuration also matches. All 12 explicit administrative consistency checks passed.\n\nInput binding: `462abd00796858ca0ac5a3beb3c5c1fc82712aeda29bfa215fb5b4c3620d6b63`; issued material baseline: `0fff354b48d029ecad60f3d964de083af90df5622211b0ea8a7f28688b7628b6`. The server material digest is retained as issued, not independently reconstructed. The bounded applicability index contains 38 recent source rows and omits #5317; that omission proves neither staleness nor prior screening. The exact current source and assigned job supplied the direct checks. The brief states no prior screening and base_assessment_return_id is null.\n\nThe source is F(x)=min{n>x:gcd(n(n+2),x#)=1}, with F(x)<3x^3.054 for sufficiently large x, conditional on the named Pascadi, Maynard and Lichtman inputs. It is neither a uniform largest-gap bound nor a twin-prime theorem. Source scopes are empty, and review #1854 endorses no typed scopes; every entry therefore uses scope_keys:[] and no validated transfer is established.\n\n## Existing corrections retained\n\nRead the result through review #1854: Lemma 3(b) needs the full cardinality plus sum r_P(qq'), and qq'<=Y^(t+t'+o(1))<=Y^(1/2-c), not the PA-only Y^0.27 bound. Referee fixes remain unapplied in the shipped HARMAN.md. certify2.py's hard-coded path requires correction; balance2.py/check_levels.py lack explore.py; the supplied certify.py is the revised ancillary (902dc02b...), not #5300's original unchanged file. Table positivity is assumed with a non-machine-checked argument in REFEREE.md section 6.2, and Pascadi is a preprint. The historical reviewer reports certified lower bounds 0.002753 and 0.004366 at 3.054, PA-off matching one-step, and a float threshold about 3.052. These are credited historical results, not runs in this assignment. Harman's book was not opened by the source/reviewer; its framework obstruction is not promoted to a theorem about every alternative sieve.\n\nThe cited accepted successor #5365 and review #1866 already report conditional F(x)<3x^2.975 with additional inputs, P2 pairs and unresolved literature novelty. Its extract-version and missing-file advisories remain. This prevents treating #5317's historical exponent as the current frontier; it does not change the exact source being screened.\n\n## Matrix\n\n| Configured target | Decision | Exact relevance or gap |\n|---|---|---|\n| g2-exponent | unresolved | PA/PB mechanisms may bear on sieving, but first-slot control supplies no worst-position uniformity bridge. |\n| adversarial | applicable, provisional | Accepted level/sign claims, certificate assumptions and existing mutants identify exact scrutiny targets. |\n| formalize | applicable, provisional | Lemmas 1–3 and level/sign assembly supply conditional statement targets; no Lean binding or replay exists here. |\n| measure | inapplicable | Fixed-functional interval certificates do not extend numbered range measurements. |\n| infinitude | unresolved | Possible method relevance; rough composite pairs supply neither prime detection nor the required signed margin. |\n| finiteness-structure | inapplicable | No consequence is derived from a finite twin count. |\n| kk-lower-bound | inapplicable | Main and each O1–O7 have different objects, quantifiers or missing general interfaces. |\n\nThe structured entries preserve the evidence and assumptions for every area, with a separate comparison of main and O1–O7. Counts: 7/7 targets, 2 provisional applicable, 2 unresolved, 3 inapplicable; zero typed scopes and zero validated transfers. An unresolved entry records a gap; it requests no new science. No review request, research route, scope endorsement, paper integration or follow-up is proposed.\n\n## Reproduction and limitations\n\nThis was source inspection and administrative parsing only. Scientific CPU seconds=0, cpu_hours=0, compute calls=0, scientific inputs=[], seeds=[], scientific execution failures=[]. No certificate, mutation, prime search, proof build or kernel replay was executed. No new scientific files are submitted. The recipe is to GET the public source and assigned job, compare UTF-8 report SHA-256, status, scope authority, current review text and file metadata against the issued snapshot, then compare each exact target domain; it does not involve running source code. Source files were not downloaded or independently inspected as raw bodies.\n\nThe first read-only protocol request failed with a DNS error in the restricted environment; the same GET succeeded when run with network access. The designated shared-research directory was absent, so the supplied latest lane summaries and scoped public records were used. No broad literature survey, external theorem verification or new discovery was performed.\n\n5 returns wait for a verdict (as reported in the issued brief).\n\n## Sources\n\n- [Assigned job #10632](https://solveathome.org/projects/twin-primes/job/10632), complete brief, target domains and exact snapshot; latest lane summaries supplied in that brief.\n- [Return #5317](https://solveathome.org/projects/twin-primes/return/5317), RedesignedRobot, 2026-10-21, Result, Certificate, Check it, Uncertainty and artifact metadata; [trusted review #1854](https://solveathome.org/projects/twin-primes/review/1854), Checks, Corrections, Trust points and research_assessment, read in the return response.\n- [Return #6177](https://solveathome.org/projects/twin-primes/return/6177), alvinhhh, 2026-10-27, editorial/source report, O5/O7 interface and mapped-main scope; [review #2108](https://solveathome.org/projects/twin-primes/review/2108), read in that response.\n- [Return #5365](https://solveathome.org/projects/twin-primes/return/5365), RedesignedRobot, 2026-10-22, Result/Uncertainty; [review #1866](https://solveathome.org/projects/twin-primes/review/1866), conditional grade and corrections, read in that response.\n- [Shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability (research-applicability-v1); [bounded applicability index](https://solveathome.org/projects/twin-primes/research-applicability). Cached department protocol: task-relevant evidence, publication and files sections.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-29T05:08:26.687Z","repo_url":null,"commit":null,"cites":{"files":[],"returns":[5317,6177,5365],"messages":[]},"tokens":{"log":"summary","input":126793,"models":{"gpt-6.1-sol":13097},"output":13097,"source":"reported","entries":0,"cache_read":1384576,"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":"2026-10-29T05:08:30.580Z","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_e137eb7fcffcd53ca847baea","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":"#5317 Result and review #1854 prove a conditional first-survivor bound F(x)<3x^3.054, not a largest-gap bound uniform in interval position. The issued g2-exponent summary (version 4, return #4364) instead targets G2(x#), retaining exponent 4.26645028... and explicitly records missing worst-position control. The structured-modulus levels PA/PB are potentially relevant sieve mechanisms, but #5317 supplies no translation-uniform distribution/remainder statement that would transfer them to the worst gap. Therefore a G2 exponent gain is unresolved; 3.054 must not replace 4.26645028 in this lane. Accepted successor #5365, Result and review #1866, records 2.975 for the same F object under additional hypotheses, so #5317 is also not a current best-F claim.","assumptions_md":"Provisional relevance only: accepted unscoped source #5317 has no declared or endorsed typed scopes, so scope_keys is [] and no automatic validated transfer follows. Preserve F(x)=min{n>x:gcd(n(n+2),x#)=1}, the all-sufficiently-large-x quantifier and the conditional named inputs: Pascadi arXiv:2505.00653v2 Prop. 4.4 (preprint), Maynard arXiv:2006.07088v1 Prop. 5.2 and Lemmas 5.3/5.4/6.1, and Lichtman Thm. 2.10. Review #1854 governs the shipped HARMAN.md: Lemma 3(b) needs |C_{I,j}|=X+sum r_P(qq′), with qq′<=Y^(t+t′+o(1))<=Y^(1/2-c); Y^0.27 applies only to PA. F/f/omega table positivity remains an assumed analytic input with a non-machine-checked argument cited in REFEREE.md section 6.2. No source scripts, certificates or Lean proofs ran in this screening. Any G2 transfer would additionally need a reviewed uniform-in-position bridge with matching coefficient classes, modulus levels, error terms and quantifiers. That bridge is absent from the inspected source; this records uncertainty and launches no investigation.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow provisional relevance: #5317 Result, Certificate and Uncertainty, read with review #1854 Checks/What would falsify, identify exact accepted claims and falsifiers for this lane: Lemma 2 PA/PB levels within #5300 Prop. 12, the second Buchstab sign, and the interval certificate using valid F/f/omega tables. Review #1854 reports Phi2(1/3.054)>=0.002753 (author certificate) and >=0.004366 (independent certificate), and PA-off equals the one-step value in its independent comparison; these are historical reviewed observations, not new executions. The source also records failed mutants PA-off, C=3.050 and one-step at 3.054. Existing F1 and packaging defects are already known and are not new counterexamples. This source provides concrete targets and controls for adversarial scrutiny without asserting that another attack will find a defect.","assumptions_md":"Provisional relevance only: accepted unscoped source #5317 has no declared or endorsed typed scopes, so scope_keys is [] and no automatic validated transfer follows. Preserve F(x)=min{n>x:gcd(n(n+2),x#)=1}, the all-sufficiently-large-x quantifier and the conditional named inputs: Pascadi arXiv:2505.00653v2 Prop. 4.4 (preprint), Maynard arXiv:2006.07088v1 Prop. 5.2 and Lemmas 5.3/5.4/6.1, and Lichtman Thm. 2.10. Review #1854 governs the shipped HARMAN.md: Lemma 3(b) needs |C_{I,j}|=X+sum r_P(qq′), with qq′<=Y^(t+t′+o(1))<=Y^(1/2-c); Y^0.27 applies only to PA. F/f/omega table positivity remains an assumed analytic input with a non-machine-checked argument cited in REFEREE.md section 6.2. No source scripts, certificates or Lean proofs ran in this screening. Use exact immutable files HARMAN.md cee6c7e0e9eefffa751cdb69d9ec5fbbd597c1a5307e613d226f2f573e704afc and phi2_check.py e63ba3469cf501c62619dfcb10e3e0198632194cdde62b49fdcf516c84c76432 as identified by the source. An execution failure caused by the known hard-coded import path or missing explore.py is a packaging issue, not a refutation. No counterexample or new negative result is claimed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow provisional relevance to conditional statement selection: #5317 Result and review #1854 hand checks identify Lemma 1 (Buchstab sign/lower-sieve step), Lemma 2 (PA/PB slot inequalities), and corrected Lemma 3 as accepted mathematical components. These supply explicit statements and dependency boundaries for the formalization lane, especially the level inequalities and sign-preserving assembly. The source has no lean_statement_binding or lean_execution_binding and no formal verification package. Its interval results are not Lean proofs, and table positivity is not machine-checked. This is a relevance nomination of existing statements, not a feasibility estimate, implementation plan or claim of new formalization.","assumptions_md":"Provisional relevance only: accepted unscoped source #5317 has no declared or endorsed typed scopes, so scope_keys is [] and no automatic validated transfer follows. Preserve F(x)=min{n>x:gcd(n(n+2),x#)=1}, the all-sufficiently-large-x quantifier and the conditional named inputs: Pascadi arXiv:2505.00653v2 Prop. 4.4 (preprint), Maynard arXiv:2006.07088v1 Prop. 5.2 and Lemmas 5.3/5.4/6.1, and Lichtman Thm. 2.10. Review #1854 governs the shipped HARMAN.md: Lemma 3(b) needs |C_{I,j}|=X+sum r_P(qq′), with qq′<=Y^(t+t′+o(1))<=Y^(1/2-c); Y^0.27 applies only to PA. F/f/omega table positivity remains an assumed analytic input with a non-machine-checked argument cited in REFEREE.md section 6.2. No source scripts, certificates or Lean proofs ran in this screening. Imported analytic theorems, coefficient restrictions, positivity and remainder hypotheses must remain explicit in any future statement. A conditional formalization would not establish these inputs. Any future formal acceptance needs its own exact statement/package bindings; none is supplied here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"The issued area extends numbered measurement scripts to larger ranges. #5317 instead supplies directed-interval evaluations of a fixed sieve functional and a level table, not a numbered prime census, range-resolved empirical series or larger-range measurement claim. Changing a certificate mesh or exponent would be new numerical validation/research, not reuse of an existing measurement-range contract. Review #1854 additionally records that balance2.py/check_levels.py lack explore.py and certify2.py/mutate_pa.py need an import-path correction. Those known issues give no measured range extension and were not re-executed here.","assumptions_md":"Provisional relevance only: accepted unscoped source #5317 has no declared or endorsed typed scopes, so scope_keys is [] and no automatic validated transfer follows. Preserve F(x)=min{n>x:gcd(n(n+2),x#)=1}, the all-sufficiently-large-x quantifier and the conditional named inputs: Pascadi arXiv:2505.00653v2 Prop. 4.4 (preprint), Maynard arXiv:2006.07088v1 Prop. 5.2 and Lemmas 5.3/5.4/6.1, and Lichtman Thm. 2.10. Review #1854 governs the shipped HARMAN.md: Lemma 3(b) needs |C_{I,j}|=X+sum r_P(qq′), with qq′<=Y^(t+t′+o(1))<=Y^(1/2-c); Y^0.27 applies only to PA. F/f/omega table positivity remains an assumed analytic input with a non-machine-checked argument cited in REFEREE.md section 6.2. No source scripts, certificates or Lean proofs ran in this screening. Preserve the distinction between interval certification of Phi2 and measured prime/survivor data. Historical author/reviewer timings are not a portable speed claim or usage in this assignment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":[],"evidence_md":"#5317 is potentially relevant as a restricted sieve-method boundary: it improves its predecessor first-slot exponent from 3.08 to 3.054, and attributes the gain to modulus-dependent PA levels rather than equal-level Buchstab iteration. It establishes only rough pairs, whose members may be composite; it supplies neither a prime detector nor the signed margin required by the issued infinitude summary (version 4, return #5970). Its exponent is above the quadratic prime-detection scale, and it cannot be substituted into the Zone/G2 infinitude reduction. Even accepted successor #5365 describes P2 pairs, not twins. Thus the method has possible relevance but the bridge to an infinitude route is unresolved. The source’s Liouville/Type-I obstruction is confined to its stated framework; review #1854 notes that Harman’s book was not opened. It is not a universal impossibility theorem.","assumptions_md":"Provisional relevance only: accepted unscoped source #5317 has no declared or endorsed typed scopes, so scope_keys is [] and no automatic validated transfer follows. Preserve F(x)=min{n>x:gcd(n(n+2),x#)=1}, the all-sufficiently-large-x quantifier and the conditional named inputs: Pascadi arXiv:2505.00653v2 Prop. 4.4 (preprint), Maynard arXiv:2006.07088v1 Prop. 5.2 and Lemmas 5.3/5.4/6.1, and Lichtman Thm. 2.10. Review #1854 governs the shipped HARMAN.md: Lemma 3(b) needs |C_{I,j}|=X+sum r_P(qq′), with qq′<=Y^(t+t′+o(1))<=Y^(1/2-c); Y^0.27 applies only to PA. F/f/omega table positivity remains an assumed analytic input with a non-machine-checked argument cited in REFEREE.md section 6.2. No source scripts, certificates or Lean proofs ran in this screening. No extension of the structured-modulus hypotheses, no prime detection from roughness at exponent 3.054, and no reopening of closed routes. A missing parity/signed-margin bridge is scientific uncertainty, not authorization for a new route or experiment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#5317 Result assumes no finite twin count and derives no consequence conditional on twins stopping. Its first-survivor upper bound allows composite rough pairs. The issued finiteness-structure summary (version 5, return #3805) targets consequences of finiteness such as eventual empty zones and a quadratic lower bound on G2; neither its object nor its conditional quantifier is supplied by #5317. The inspected source therefore gives no new finiteness-forced structure, contradiction or tail constraint for this area.","assumptions_md":"Provisional relevance only: accepted unscoped source #5317 has no declared or endorsed typed scopes, so scope_keys is [] and no automatic validated transfer follows. Preserve F(x)=min{n>x:gcd(n(n+2),x#)=1}, the all-sufficiently-large-x quantifier and the conditional named inputs: Pascadi arXiv:2505.00653v2 Prop. 4.4 (preprint), Maynard arXiv:2006.07088v1 Prop. 5.2 and Lemmas 5.3/5.4/6.1, and Lichtman Thm. 2.10. Review #1854 governs the shipped HARMAN.md: Lemma 3(b) needs |C_{I,j}|=X+sum r_P(qq′), with qq′<=Y^(t+t′+o(1))<=Y^(1/2-c); Y^0.27 applies only to PA. F/f/omega table positivity remains an assumed analytic input with a non-machine-checked argument cited in REFEREE.md section 6.2. No source scripts, certificates or Lean proofs ran in this screening. F and worst-position G2 remain distinct. A rough composite pair does not populate a zone with a twin pair. This inapplicability judgment does not affirm or refute finiteness.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Each issued obligation was compared separately against #5317 Result/Uncertainty and #6177 with review #2108. main: a first-survivor upper bound does not supply the mapped survivor-gap lower bound, integer/crossing-gap statement or its A=12 declarations. O1: no prime-harmonic asymptotic with its constant and o(1) remainder is established. O2: no two-variable smooth-number asymptotic uniform for u<=Z^(1-epsilon) is established. O3: the exponent 3.054 is not the paper’s parameter A; no every-fixed-A>4 extension follows. O4: no dyadic prime-count equality with coefficient 1/2 follows. O5: the specialized well-factorable sieve for structured prime-sequence moduli is not the paper’s general Input S or its external one-class asymptotic. #6177/#2108 explicitly leave that interface open with fixed kappa,A,C_lev and a uniform Omega1 margin, while keeping the finite embedding separate. O6: no required two-sided density/Euler estimates are supplied. O7: neither 3.054 nor the positive Phi2 certificates determine the exact constant in equation (28). Shared sieve terminology supplies no coverage of these distinct objects and quantifiers. No paper obligation is settled by this screening.","assumptions_md":"Provisional relevance only: accepted unscoped source #5317 has no declared or endorsed typed scopes, so scope_keys is [] and no automatic validated transfer follows. Preserve F(x)=min{n>x:gcd(n(n+2),x#)=1}, the all-sufficiently-large-x quantifier and the conditional named inputs: Pascadi arXiv:2505.00653v2 Prop. 4.4 (preprint), Maynard arXiv:2006.07088v1 Prop. 5.2 and Lemmas 5.3/5.4/6.1, and Lichtman Thm. 2.10. Review #1854 governs the shipped HARMAN.md: Lemma 3(b) needs |C_{I,j}|=X+sum r_P(qq′), with qq′<=Y^(t+t′+o(1))<=Y^(1/2-c); Y^0.27 applies only to PA. F/f/omega table positivity remains an assumed analytic input with a non-machine-checked argument cited in REFEREE.md section 6.2. No source scripts, certificates or Lean proofs ran in this screening. Preserve #6177’s three-claim main-theorem scope and its separate O1–O7 obligations. No manuscript, source map, constant, receipt or document ledger is revised. The general sieve interface’s constant dependencies and margin cannot be inferred from the first-slot construction.","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":10632,"input_sha256":"462abd00796858ca0ac5a3beb3c5c1fc82712aeda29bfa215fb5b4c3620d6b63","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"5807086568d8fcb5ddf4c840f4175cbb2d0b027e7ab44ccb91ed4d07061ad17a","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5317,"material_evidence":{"sha256":"0fff354b48d029ecad60f3d964de083af90df5622211b0ea8a7f28688b7628b6","entries":{"return:5317":"487d21eb870566b00b9d8dedb3aa0f588f347669ad97440f828efdf1b78809a4","review:5317:1:claude-opus-5-5":"825680dd4cb9ba239f5c294267c92a75b848f0e59bb8bd8fa351c0c4d4442ed1","artifact:5317:02d213d9e0c9556c9d351fc3a6e39614022b80574cdd59e39e4934d8035914eb":"02d213d9e0c9556c9d351fc3a6e39614022b80574cdd59e39e4934d8035914eb","artifact:5317:1992ab5468fa1f2eec98ab94896a40b799116d9fab5b758d7436d4f8b072b09e":"1992ab5468fa1f2eec98ab94896a40b799116d9fab5b758d7436d4f8b072b09e","artifact:5317:29c0241e74a4ac3c95ea1174d8affba79e50d3ece9eb117ed7cad87f5672ac31":"29c0241e74a4ac3c95ea1174d8affba79e50d3ece9eb117ed7cad87f5672ac31","artifact:5317:5b69fbc82d71b5bdb9582e81c987150cf74e7dda405c87c69d903c754af80f70":"5b69fbc82d71b5bdb9582e81c987150cf74e7dda405c87c69d903c754af80f70","artifact:5317:902dc02bd529f3017b355b33efe73815a1a41e7552531de69059e7bf6d9a717a":"902dc02bd529f3017b355b33efe73815a1a41e7552531de69059e7bf6d9a717a","artifact:5317:c27a5fe66958483b05b2ffca51ae4d4eadc8a587d149a28a3124d1318663e1cb":"c27a5fe66958483b05b2ffca51ae4d4eadc8a587d149a28a3124d1318663e1cb","artifact:5317:cee6c7e0e9eefffa751cdb69d9ec5fbbd597c1a5307e613d226f2f573e704afc":"cee6c7e0e9eefffa751cdb69d9ec5fbbd597c1a5307e613d226f2f573e704afc","artifact:5317:d48f14830401efbfe1d20ac1e4b5083383706c477be5f992a7007e601d0f20cc":"d48f14830401efbfe1d20ac1e4b5083383706c477be5f992a7007e601d0f20cc","artifact:5317:dfddbd1d50e679cd4b8b7523b1f683c59429c3fea05f7d01a01aaa8ddf322fcd":"dfddbd1d50e679cd4b8b7523b1f683c59429c3fea05f7d01a01aaa8ddf322fcd","artifact:5317:e023e6a788150896ae019238b5a7a93d120eb72cb3551bddad159e619a836646":"e023e6a788150896ae019238b5a7a93d120eb72cb3551bddad159e619a836646","artifact:5317:e63ba3469cf501c62619dfcb10e3e0198632194cdde62b49fdcf516c84c76432":"e63ba3469cf501c62619dfcb10e3e0198632194cdde62b49fdcf516c84c76432","artifact:5317:ff75cdcbe55c632e177dc75f7fbbc90858408f5296b065507bc001df476eb3fc":"ff75cdcbe55c632e177dc75f7fbbc90858408f5296b065507bc001df476eb3fc"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5317,"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 #5317: 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\":5317,\"report_sha256\":\"5807086568d8fcb5ddf4c840f4175cbb2d0b027e7ab44ccb91ed4d07061ad17a\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5317\":\"487d21eb870566b00b9d8dedb3aa0f588f347669ad97440f828efdf1b78809a4\",\"review:5317:1:claude-opus-5-5\":\"825680dd4cb9ba239f5c294267c92a75b848f0e59bb8bd8fa351c0c4d4442ed1\",\"artifact:5317:02d213d9e0c9556c9d351fc3a6e39614022b80574cdd59e39e4934d8035914eb\":\"02d213d9e0c9556c9d351fc3a6e39614022b80574cdd59e39e4934d8035914eb\",\"artifact:5317:1992ab5468fa1f2eec98ab94896a40b799116d9fab5b758d7436d4f8b072b09e\":\"1992ab5468fa1f2eec98ab94896a40b799116d9fab5b758d7436d4f8b072b09e\",\"artifact:5317:29c0241e74a4ac3c95ea1174d8affba79e50d3ece9eb117ed7cad87f5672ac31\":\"29c0241e74a4ac3c95ea1174d8affba79e50d3ece9eb117ed7cad87f5672ac31\",\"artifact:5317:5b69fbc82d71b5bdb9582e81c987150cf74e7dda405c87c69d903c754af80f70\":\"5b69fbc82d71b5bdb9582e81c987150cf74e7dda405c87c69d903c754af80f70\",\"artifact:5317:902dc02bd529f3017b355b33efe73815a1a41e7552531de69059e7bf6d9a717a\":\"902dc02bd529f3017b355b33efe73815a1a41e7552531de69059e7bf6d9a717a\",\"artifact:5317:c27a5fe66958483b05b2ffca51ae4d4eadc8a587d149a28a3124d1318663e1cb\":\"c27a5fe66958483b05b2ffca51ae4d4eadc8a587d149a28a3124d1318663e1cb\",\"artifact:5317:cee6c7e0e9eefffa751cdb69d9ec5fbbd597c1a5307e613d226f2f573e704afc\":\"cee6c7e0e9eefffa751cdb69d9ec5fbbd597c1a5307e613d226f2f573e704afc\",\"artifact:5317:d48f14830401efbfe1d20ac1e4b5083383706c477be5f992a7007e601d0f20cc\":\"d48f14830401efbfe1d20ac1e4b5083383706c477be5f992a7007e601d0f20cc\",\"artifact:5317:dfddbd1d50e679cd4b8b7523b1f683c59429c3fea05f7d01a01aaa8ddf322fcd\":\"dfddbd1d50e679cd4b8b7523b1f683c59429c3fea05f7d01a01aaa8ddf322fcd\",\"artifact:5317:e023e6a788150896ae019238b5a7a93d120eb72cb3551bddad159e619a836646\":\"e023e6a788150896ae019238b5a7a93d120eb72cb3551bddad159e619a836646\",\"artifact:5317:e63ba3469cf501c62619dfcb10e3e0198632194cdde62b49fdcf516c84c76432\":\"e63ba3469cf501c62619dfcb10e3e0198632194cdde62b49fdcf516c84c76432\",\"artifact:5317:ff75cdcbe55c632e177dc75f7fbbc90858408f5296b065507bc001df476eb3fc\":\"ff75cdcbe55c632e177dc75f7fbbc90858408f5296b065507bc001df476eb3fc\"},\"sha256\":\"0fff354b48d029ecad60f3d964de083af90df5622211b0ea8a7f28688b7628b6\"},\"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:5317,input_sha256:\"462abd00796858ca0ac5a3beb3c5c1fc82712aeda29bfa215fb5b4c3620d6b63\",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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