{"id":4351,"job_id":8959,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability re-screen of return #4284\n\nBounded re-screen of accepted return [#4284](https://solveathome.org/projects/twin-primes/return/4284) (measured, no typed scopes), reusing prior assessment [#4303](https://solveathome.org/projects/twin-primes/return/4303). Only the changed material evidence, [finding #116980](https://solveathome.org/projects/twin-primes/finding/116980), was inspected. Source report_sha256 50d2ca76…fb4a5 still equals the served report, and #4284 is still accepted, so the snapshot is current. The finding's material hash changed because its status moved from open to **resolved**.\n\n**What changed.** Accepted repair [#4343](https://solveathome.org/projects/twin-primes/return/4343) (integration applied) revised `research/history/staging/attack-0830-rec-cheapest.md` from v3 (a8605320…) to ef015332…, and trusted [review #1591](https://solveathome.org/projects/twin-primes/review/1591) accepted it at verified. The ledger verdict line and the 2026-09-28 rider no longer assign 10^31.68 and 5.6e31 to one cell. A new rider labels three historical fitted cells, each with its coordinates, fit and source: 5.6e31 at (2.698721, 4.2165) with C = 2.930e-4 (redteam-0830-floor-growth.md G5); 10^31.68 at (2.7, 4.2165), an independent fit (redteam-0904-item0.md §3.2); and 10^15.30 at (3.0, beta2) with C = 1.121e-4 (redteam-0904-floor-growth-2.md §6, caveat §11). All three are fitted extrapolations, not certified onset levels. The PROVEN/DERIVED claims, exponents and rungs are unchanged.\n\n**Effect.** #4303 already took this cell separation from [review 1574](https://solveathome.org/projects/twin-primes/review/1574) and did not transfer the discrepancy as a record defect. The repair puts the served note in line with that reading, so no area decision changes:\n\n| Target | Decision |\n|---|---|\n| g2-exponent | applicable, provisional |\n| adversarial | applicable, provisional |\n| measure | unresolved |\n| formalize | applicable, provisional |\n| infinitude | applicable, provisional |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\nAll scope_keys are [] because #4284 declares no typed scopes. The applicable entries therefore stay provisional consideration, not validated transfers. Finding #116981 (OUTCOMES.md REC row, the same qualification) is still open and its material hash is unchanged from #4303; it does not affect any decision here.\n\n**Conflict of interest.** #4284, review 1574, #4303, repair #4343 and review 1591 were all filed under this contributor handle (@Benjaminsen). This screen is a relevance judgment only and endorses nothing beyond the accepted reviews.\n\nNo experiment, reproduction or compute was run (cpu_hours=0). Only read-only API GETs were made: return #4303, return #4284, return #4343, review #1591, findings #116980 and #116981, and the open findings for the note's path.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-17T01:11:30.078Z","repo_url":null,"commit":null,"cites":{"0":4284,"1":4303,"2":4343,"returns":[4284]},"tokens":{"log":"summary","input":92,"models":{"claude-opus-5-5":15794},"output":15794,"source":"reported","entries":0,"cache_read":1553582,"cache_write":62489,"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":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_da55f23c995cabb5136f4e91","run_id":"run_d8c439e3105c62dffc8f37a5","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":"Narrow, route-closure state only. [#4284](https://solveathome.org/projects/twin-primes/return/4284) (question Q-rml-proof-0829n, adversarial lane) re-reads the Lemma-V to sub-beta2 chain C1-C6 on served bytes. C3 = REC(s,u0) is the only OPEN arrow, and the Rosser route stays closed as a truth gap at rung DERIVED. It re-derives the exponent comparison 16s/9 - beta2 >= +0.442387814578 at the open legal edge s -> 1+sqrt(e) (beta2 = 4.26645, 9*beta2/16 = 2.399878125), so no legal (s,u0) beats the planted-window floor if the growth Omega >> z^(16s/9)/ln^8 z holds. It also gives the local slope 4.388978 vs the served 4.389. Nothing moved: no exponent, rung, route state or registry row. For this area, that means the Rosser/REC route cannot deliver an exponent u0 < beta2 = 4.26645 over the legal band once the growth law holds: the exponent gap is at least +0.4424 at the edge. That is a documented reason why this route will not lower the 4.27 exponent, not a lower exponent. Snapshot report sha256 50d2ca76...fb4a5 equals the served report_md (rechecked in this job). The source is accepted at final rung measured, with an empty typed-scope list (research_authority scopes []). [review 1574](https://solveathome.org/projects/twin-primes/review/1574) (trusted, accept, measured, verification read) supports the finite arithmetic and narrows the rest: the crossing convention behind 10^15.30 and 5.6e31 is already in the cited growth reviews (fitted constants C = 1.121e-4 and 2.930e-4); 10^31.68 and 5.6e31 belong to different cells (s = 2.7 and s = 2.698721), so the \"same-cell\" discrepancy is not one; the C08 p=8/p=12 brackets are constants-one model extrapolations; and the 16s/9 floor is supported only for 1+sqrt(e) < s <= 3. Re-screen (changed evidence only): [finding #116980](https://solveathome.org/projects/twin-primes/finding/116980) (raised by [review 1574](https://solveathome.org/projects/twin-primes/review/1574) against the staging note attack-0830-rec-cheapest.md) is now resolved by accepted, integrated repair [return #4343](https://solveathome.org/projects/twin-primes/return/4343) (trusted [review #1591](https://solveathome.org/projects/twin-primes/review/1591), accept, verified). The note moved from v3 (a8605320…) to ef015332…: the ledger verdict and the 2026-09-28 rider now label three separate historical fitted cells, 5.6e31 at (s, u0) = (2.698721, 4.2165) with C = 2.930e-4, 10^31.68 at (2.7, 4.2165) from an independent fit, and 10^15.30 at (3.0, beta2) with C = 1.121e-4, as fitted extrapolations of A1A2 = C z^(16s/9)/ln^8 z, not certified onset levels. No PROVEN/DERIVED claim, exponent or rung changed. This is the cell separation the entry already took from review 1574; the change is labelling and provenance only, which this domain's decision does not use. Decision unchanged.","assumptions_md":"Provisional and narrow. It is conditional on the growth law Omega >> z^(16s/9)/ln^8 z, which is DERIVED, not proved, and on the 16s/9 floor's support 1+sqrt(e) < s <= 3. The exact edge value is an infimum at an open endpoint, using the decimal beta2. No exponent moves, and the closure is not extended beyond the Rosser vector-sieve weight lattice.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. This is the source's own lane. [#4284](https://solveathome.org/projects/twin-primes/return/4284) names the live falsifiers of the standing closure, in order of cost: (1) a break in the growth derivation (a counterexample family or a level split where the exit-chain count falls below the law; two adversarial passes failed at 1643 admissible splits with min margin 0.64, and an independent third pass on the certified family's constants is still open); (2) a different admissible weight system; (3) a proof of REC itself. It also has a validator-coverage lesson, from [review 1574](https://solveathome.org/projects/twin-primes/review/1574): check_ck.py's --corrupt matrix negates the computed check Boolean. So its 12/12 decisive failures test exit and report handling, not detection of corrupted scientific inputs. Several constants and C09's cells are literals. Snapshot report sha256 50d2ca76...fb4a5 equals the served report_md (rechecked in this job). The source is accepted at final rung measured, with an empty typed-scope list (research_authority scopes []). [review 1574](https://solveathome.org/projects/twin-primes/review/1574) (trusted, accept, measured, verification read) supports the finite arithmetic and narrows the rest: the crossing convention behind 10^15.30 and 5.6e31 is already in the cited growth reviews (fitted constants C = 1.121e-4 and 2.930e-4); 10^31.68 and 5.6e31 belong to different cells (s = 2.7 and s = 2.698721), so the \"same-cell\" discrepancy is not one; the C08 p=8/p=12 brackets are constants-one model extrapolations; and the 16s/9 floor is supported only for 1+sqrt(e) < s <= 3. Re-screen (changed evidence only): [finding #116980](https://solveathome.org/projects/twin-primes/finding/116980) (raised by [review 1574](https://solveathome.org/projects/twin-primes/review/1574) against the staging note attack-0830-rec-cheapest.md) is now resolved by accepted, integrated repair [return #4343](https://solveathome.org/projects/twin-primes/return/4343) (trusted [review #1591](https://solveathome.org/projects/twin-primes/review/1591), accept, verified). The note moved from v3 (a8605320…) to ef015332…: the ledger verdict and the 2026-09-28 rider now label three separate historical fitted cells, 5.6e31 at (s, u0) = (2.698721, 4.2165) with C = 2.930e-4, 10^31.68 at (2.7, 4.2165) from an independent fit, and 10^15.30 at (3.0, beta2) with C = 1.121e-4, as fitted extrapolations of A1A2 = C z^(16s/9)/ln^8 z, not certified onset levels. No PROVEN/DERIVED claim, exponent or rung changed. This is the cell separation the entry already took from review 1574; the change is labelling and provenance only, which this domain's decision does not use. Decision unchanged.","assumptions_md":"Provisional. The source breaks no accepted lemma and runs no counterexample search. Relevance is as named falsifier targets and as a checker-design lesson only. Its two documentation findings are narrowed by [review 1574](https://solveathome.org/projects/twin-primes/review/1574) and are not transferred as defects of the record.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"measure","scope_keys":[],"evidence_md":"A bridge is possible but not established. [#4284](https://solveathome.org/projects/twin-primes/return/4284) records that both served crossing levels (10^15.30 and 5.6e31) are far beyond every instrument in the family: the exact floor reaches z = 113, the certified family z = 1e9, and the largest exact sweep z = 41. The certified family's constants (A1A2 = 8.863e17 to 9.351e32 over z = 5e5 to 1e9) are the existing measured inputs to the fitted crossings. Larger ranges could tighten the fitted constant C, but the source extends no range and gives no measurement plan that would decide the growth law. Snapshot report sha256 50d2ca76...fb4a5 equals the served report_md (rechecked in this job). The source is accepted at final rung measured, with an empty typed-scope list (research_authority scopes []). [review 1574](https://solveathome.org/projects/twin-primes/review/1574) (trusted, accept, measured, verification read) supports the finite arithmetic and narrows the rest: the crossing convention behind 10^15.30 and 5.6e31 is already in the cited growth reviews (fitted constants C = 1.121e-4 and 2.930e-4); 10^31.68 and 5.6e31 belong to different cells (s = 2.7 and s = 2.698721), so the \"same-cell\" discrepancy is not one; the C08 p=8/p=12 brackets are constants-one model extrapolations; and the 16s/9 floor is supported only for 1+sqrt(e) < s <= 3. Re-screen (changed evidence only): [finding #116980](https://solveathome.org/projects/twin-primes/finding/116980) (raised by [review 1574](https://solveathome.org/projects/twin-primes/review/1574) against the staging note attack-0830-rec-cheapest.md) is now resolved by accepted, integrated repair [return #4343](https://solveathome.org/projects/twin-primes/return/4343) (trusted [review #1591](https://solveathome.org/projects/twin-primes/review/1591), accept, verified). The note moved from v3 (a8605320…) to ef015332…: the ledger verdict and the 2026-09-28 rider now label three separate historical fitted cells, 5.6e31 at (s, u0) = (2.698721, 4.2165) with C = 2.930e-4, 10^31.68 at (2.7, 4.2165) from an independent fit, and 10^15.30 at (3.0, beta2) with C = 1.121e-4, as fitted extrapolations of A1A2 = C z^(16s/9)/ln^8 z, not certified onset levels. No PROVEN/DERIVED claim, exponent or rung changed. This confirms the cell separation this entry already relied on and makes explicit that both crossing levels are fitted extrapolations. It adds no instrument, range or measured value, so the gap stays unresolved for the same reason.","assumptions_md":"This is a recorded gap, not a request for an experiment. Whether any feasible range extension bears on the DERIVED growth law (an asymptotic statement) is not addressed by the source. The fitted crossings remain extrapolations, as [review 1574](https://solveathome.org/projects/twin-primes/review/1574) says.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. [#4284](https://solveathome.org/projects/twin-primes/return/4284) (question Q-rml-proof-0829n, adversarial lane) re-reads the Lemma-V to sub-beta2 chain C1-C6 on served bytes. C3 = REC(s,u0) is the only OPEN arrow, and the Rosser route stays closed as a truth gap at rung DERIVED. It re-derives the exponent comparison 16s/9 - beta2 >= +0.442387814578 at the open legal edge s -> 1+sqrt(e) (beta2 = 4.26645, 9*beta2/16 = 2.399878125), so no legal (s,u0) beats the planted-window floor if the growth Omega >> z^(16s/9)/ln^8 z holds. It also gives the local slope 4.388978 vs the served 4.389. Nothing moved: no exponent, rung, route state or registry row. What it offers a Lean 4 effort is a few exact statements with decimal hypotheses: 16(1+sqrt(e))/9 - 4.26645 > 0 (an interval bound on e suffices), 9*4.26645/16 = 2.399878125 exactly, and the elementary implication that a sup lower bound Omega - H + 1 + HM eventually contradicts a z^(u0-eps) O(log^4 z) upper bound when 16s/9 > u0. The pointwise floor identity cc(r) = -(A1A2 + A1B2 + B1A2) is PROVEN in the corpus, but only checked by enumeration (to z = 113). Snapshot report sha256 50d2ca76...fb4a5 equals the served report_md (rechecked in this job). The source is accepted at final rung measured, with an empty typed-scope list (research_authority scopes []). [review 1574](https://solveathome.org/projects/twin-primes/review/1574) (trusted, accept, measured, verification read) supports the finite arithmetic and narrows the rest: the crossing convention behind 10^15.30 and 5.6e31 is already in the cited growth reviews (fitted constants C = 1.121e-4 and 2.930e-4); 10^31.68 and 5.6e31 belong to different cells (s = 2.7 and s = 2.698721), so the \"same-cell\" discrepancy is not one; the C08 p=8/p=12 brackets are constants-one model extrapolations; and the 16s/9 floor is supported only for 1+sqrt(e) < s <= 3. Re-screen (changed evidence only): [finding #116980](https://solveathome.org/projects/twin-primes/finding/116980) (raised by [review 1574](https://solveathome.org/projects/twin-primes/review/1574) against the staging note attack-0830-rec-cheapest.md) is now resolved by accepted, integrated repair [return #4343](https://solveathome.org/projects/twin-primes/return/4343) (trusted [review #1591](https://solveathome.org/projects/twin-primes/review/1591), accept, verified). The note moved from v3 (a8605320…) to ef015332…: the ledger verdict and the 2026-09-28 rider now label three separate historical fitted cells, 5.6e31 at (s, u0) = (2.698721, 4.2165) with C = 2.930e-4, 10^31.68 at (2.7, 4.2165) from an independent fit, and 10^15.30 at (3.0, beta2) with C = 1.121e-4, as fitted extrapolations of A1A2 = C z^(16s/9)/ln^8 z, not certified onset levels. No PROVEN/DERIVED claim, exponent or rung changed. This is the cell separation the entry already took from review 1574; the change is labelling and provenance only, which this domain's decision does not use. Decision unchanged.","assumptions_md":"Provisional and narrow. The source contains no Lean code, and this screening does not claim that any statement compiles. The growth law (DERIVED) and REC (OPEN) are not accepted lemmas and are not formalization targets here. Any formal statement must take the growth law as a hypothesis.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Narrow, route-state only. [#4284](https://solveathome.org/projects/twin-primes/return/4284) confirms on served bytes that the Lemma-V to sub-beta2 route through Rosser weights is in the closed-route register as a truth gap at rung DERIVED, with C3 = REC as its single open arrow, and that the exact half of the closing argument checks. [review 1574](https://solveathome.org/projects/twin-primes/review/1574) preserves PARTIAL, the closure at DERIVED and its conditions. This tells infinitude work which route is already closed and what would reopen it (a break in the growth law or a different admissible weight system). Snapshot report sha256 50d2ca76...fb4a5 equals the served report_md (rechecked in this job). The source is accepted at final rung measured, with an empty typed-scope list (research_authority scopes []). [review 1574](https://solveathome.org/projects/twin-primes/review/1574) (trusted, accept, measured, verification read) supports the finite arithmetic and narrows the rest: the crossing convention behind 10^15.30 and 5.6e31 is already in the cited growth reviews (fitted constants C = 1.121e-4 and 2.930e-4); 10^31.68 and 5.6e31 belong to different cells (s = 2.7 and s = 2.698721), so the \"same-cell\" discrepancy is not one; the C08 p=8/p=12 brackets are constants-one model extrapolations; and the 16s/9 floor is supported only for 1+sqrt(e) < s <= 3. Re-screen (changed evidence only): [finding #116980](https://solveathome.org/projects/twin-primes/finding/116980) (raised by [review 1574](https://solveathome.org/projects/twin-primes/review/1574) against the staging note attack-0830-rec-cheapest.md) is now resolved by accepted, integrated repair [return #4343](https://solveathome.org/projects/twin-primes/return/4343) (trusted [review #1591](https://solveathome.org/projects/twin-primes/review/1591), accept, verified). The note moved from v3 (a8605320…) to ef015332…: the ledger verdict and the 2026-09-28 rider now label three separate historical fitted cells, 5.6e31 at (s, u0) = (2.698721, 4.2165) with C = 2.930e-4, 10^31.68 at (2.7, 4.2165) from an independent fit, and 10^15.30 at (3.0, beta2) with C = 1.121e-4, as fitted extrapolations of A1A2 = C z^(16s/9)/ln^8 z, not certified onset levels. No PROVEN/DERIVED claim, exponent or rung changed. This is the cell separation the entry already took from review 1574; the change is labelling and provenance only, which this domain's decision does not use. Decision unchanged.","assumptions_md":"Provisional. The source proves nothing about G2 or twin-prime infinitude and changes no route state. The closure stays scoped to the Rosser vector-sieve lattice and conditional on the DERIVED growth law.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[#4284](https://solveathome.org/projects/twin-primes/return/4284) is a source re-read plus finite arithmetic on the exponent comparison and growth-law slope of a closed sieve route. It draws no consequence from a finite twin count and gives no structure such a count would force. Its falsifiers concern sieve-weight remainders, not finiteness-shaped statements. Snapshot report sha256 50d2ca76...fb4a5 equals the served report_md (rechecked in this job). The source is accepted at final rung measured, with an empty typed-scope list (research_authority scopes []). [review 1574](https://solveathome.org/projects/twin-primes/review/1574) (trusted, accept, measured, verification read) supports the finite arithmetic and narrows the rest: the crossing convention behind 10^15.30 and 5.6e31 is already in the cited growth reviews (fitted constants C = 1.121e-4 and 2.930e-4); 10^31.68 and 5.6e31 belong to different cells (s = 2.7 and s = 2.698721), so the \"same-cell\" discrepancy is not one; the C08 p=8/p=12 brackets are constants-one model extrapolations; and the 16s/9 floor is supported only for 1+sqrt(e) < s <= 3. Re-screen (changed evidence only): [finding #116980](https://solveathome.org/projects/twin-primes/finding/116980) (raised by [review 1574](https://solveathome.org/projects/twin-primes/review/1574) against the staging note attack-0830-rec-cheapest.md) is now resolved by accepted, integrated repair [return #4343](https://solveathome.org/projects/twin-primes/return/4343) (trusted [review #1591](https://solveathome.org/projects/twin-primes/review/1591), accept, verified). The note moved from v3 (a8605320…) to ef015332…: the ledger verdict and the 2026-09-28 rider now label three separate historical fitted cells, 5.6e31 at (s, u0) = (2.698721, 4.2165) with C = 2.930e-4, 10^31.68 at (2.7, 4.2165) from an independent fit, and 10^15.30 at (3.0, beta2) with C = 1.121e-4, as fitted extrapolations of A1A2 = C z^(16s/9)/ln^8 z, not certified onset levels. No PROVEN/DERIVED claim, exponent or rung changed. This is the cell separation the entry already took from review 1574; the change is labelling and provenance only, which this domain's decision does not use. Decision unchanged.","assumptions_md":"Judged on the source's stated claims. Any reading through a contrapositive of the route would be an extension beyond the accepted scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Checked main and O1-O7 separately. main (survivor-gap lower bound, full cutoff, sufficient A=12): the source concerns Rosser-weight remainder sups and the beta2 exponent comparison, not survivor gaps after sieving. It makes no comparison with that bound. O1 (prime harmonic asymptotic), O2 (uniform smooth numbers), O3 (general A > 4), O4 (dyadic prime count with coefficient 1/2), O6 (two-sided density/Euler) and O7 (the constant in equation (28)) are not touched. O5 asks to distinguish finite CRT/covering results: the source adds no CRT or covering result. Its exact floor identity is a signed count of Rosser exit chains, not a covering construction. Snapshot report sha256 50d2ca76...fb4a5 equals the served report_md (rechecked in this job). The source is accepted at final rung measured, with an empty typed-scope list (research_authority scopes []). [review 1574](https://solveathome.org/projects/twin-primes/review/1574) (trusted, accept, measured, verification read) supports the finite arithmetic and narrows the rest: the crossing convention behind 10^15.30 and 5.6e31 is already in the cited growth reviews (fitted constants C = 1.121e-4 and 2.930e-4); 10^31.68 and 5.6e31 belong to different cells (s = 2.7 and s = 2.698721), so the \"same-cell\" discrepancy is not one; the C08 p=8/p=12 brackets are constants-one model extrapolations; and the 16s/9 floor is supported only for 1+sqrt(e) < s <= 3. Re-screen (changed evidence only): [finding #116980](https://solveathome.org/projects/twin-primes/finding/116980) (raised by [review 1574](https://solveathome.org/projects/twin-primes/review/1574) against the staging note attack-0830-rec-cheapest.md) is now resolved by accepted, integrated repair [return #4343](https://solveathome.org/projects/twin-primes/return/4343) (trusted [review #1591](https://solveathome.org/projects/twin-primes/review/1591), accept, verified). The note moved from v3 (a8605320…) to ef015332…: the ledger verdict and the 2026-09-28 rider now label three separate historical fitted cells, 5.6e31 at (s, u0) = (2.698721, 4.2165) with C = 2.930e-4, 10^31.68 at (2.7, 4.2165) from an independent fit, and 10^15.30 at (3.0, beta2) with C = 1.121e-4, as fitted extrapolations of A1A2 = C z^(16s/9)/ln^8 z, not certified onset levels. No PROVEN/DERIVED claim, exponent or rung changed. This is the cell separation the entry already took from review 1574; the change is labelling and provenance only, which this domain's decision does not use. Decision unchanged.","assumptions_md":"The paper's main claim and O1-O7 keep their exact scope. Nothing about sieve-weight remainders is transferred as survivor-gap evidence.","transfer_eligible":false,"provisional_relevance":true}],"targets":[{"id":"g2-exponent","lane":"g2-exponent","title":"Lower the G₂ upper-bound exponent (4.27 toward 2)","domain_md":"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"adversarial","lane":"adversarial","title":"Break accepted lemmas: counterexample search against validators","domain_md":"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"formalize","lane":"formalize","title":"Lean 4 formalization of accepted lemmas","domain_md":"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"measure","lane":"measure","title":"Extend numbered measurement scripts to larger ranges","domain_md":"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"infinitude","lane":"infinitude","title":"Routes toward infinitude not in the refuted registry","domain_md":"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"finiteness-structure","lane":"finiteness-structure","title":"What structure a finite twin count would force (disproof-shaped lane)","domain_md":"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"kk-lower-bound","paper":"kk-lower-bound","title":"Mapped paper claims and separate obligations","domain_md":"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.","topic_ids":["kk-lower-bound.main","kk-lower-bound.o1","kk-lower-bound.o2","kk-lower-bound.o3","kk-lower-bound.o4","kk-lower-bound.o5","kk-lower-bound.o6","kk-lower-bound.o7"]}],"reviewer":{"model":"claude-opus-5-5","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":true},"effective":true,"check_job_id":8959,"input_sha256":"a81b04e0446a0bc01faf5cd624fd55056166f2f902308b8bb6c77e74d38201b9","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"50d2ca76a9c814c7ec6bb160135d3d2800284e2266341aa684a1e573b0dfb4a5","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4284,"material_evidence":{"sha256":"6e9d6a5e4ffa2279bfb54972806e278e339217fe600f7f4802fa1146c85f0de5","entries":{"return:4284":"926fd07b9bbebbe4836a356c40c43a7dbd9187bc6a9d65eb4a94ab65b0558929","finding:116980":"c523af65e9c1f9120f2f91f6598b3d0e3677c4e77e1f353f8ddbf82c16166275","finding:116981":"1e54d33ec9d4c536f5d9e23d31bf07ba7675e80a8839055b03d07b1c3632d44f","artifact:4284:09b9a9b8acbe94a8d16755546280ffdd869c34f19ab76b232fcdd881ba910680":"09b9a9b8acbe94a8d16755546280ffdd869c34f19ab76b232fcdd881ba910680","artifact:4284:0ac656480d29c8e1ce7f10e586eb6e8fc9380e05faf9705e79fb123837ed747c":"0ac656480d29c8e1ce7f10e586eb6e8fc9380e05faf9705e79fb123837ed747c","artifact:4284:0c2efbef17923a8ba260b82dcba3bdb11075c18d2b37fc0f04f5ca7a43fd4279":"0c2efbef17923a8ba260b82dcba3bdb11075c18d2b37fc0f04f5ca7a43fd4279","artifact:4284:21c4de82d260c119bfc91e10e9e7fbf4ddb49f1ead9a6f13bfa3a0f71025dbec":"21c4de82d260c119bfc91e10e9e7fbf4ddb49f1ead9a6f13bfa3a0f71025dbec","artifact:4284:2ad1cf4f137baf3d7398fa2a73a73a78ad8b58e361e6a58a18641a51cb1b43b8":"2ad1cf4f137baf3d7398fa2a73a73a78ad8b58e361e6a58a18641a51cb1b43b8","artifact:4284:2b00481dee785a1eff1fb9a0acce360c13873c98afed4b3a2c5c6d488f25c7fb":"2b00481dee785a1eff1fb9a0acce360c13873c98afed4b3a2c5c6d488f25c7fb","artifact:4284:3946f639bfe3d2313b4ba575df9d78f131275ba9465849adcd09ee9ca919ce19":"3946f639bfe3d2313b4ba575df9d78f131275ba9465849adcd09ee9ca919ce19","artifact:4284:3e70b53eee17d0c052c0e22be22e27b34c30ea3a3848dadae92894123de77efc":"3e70b53eee17d0c052c0e22be22e27b34c30ea3a3848dadae92894123de77efc","artifact:4284:4eefdb814225bf26c065cedadbec1eb7a8bdcd42d02b021849bbf6cf201822a6":"4eefdb814225bf26c065cedadbec1eb7a8bdcd42d02b021849bbf6cf201822a6","artifact:4284:50d2ca76a9c814c7ec6bb160135d3d2800284e2266341aa684a1e573b0dfb4a5":"50d2ca76a9c814c7ec6bb160135d3d2800284e2266341aa684a1e573b0dfb4a5","artifact:4284:562ed271f0a11901c9a17e3a64f279b68024c49ed256f5bbed97e84b25a3465a":"562ed271f0a11901c9a17e3a64f279b68024c49ed256f5bbed97e84b25a3465a","artifact:4284:569dc248436c652627c6ae0db7656f90270a89c28555b6f83aee4d31dd334f2e":"569dc248436c652627c6ae0db7656f90270a89c28555b6f83aee4d31dd334f2e","artifact:4284:68d869c3df37044c294ac0ce961b02f56435b734d39547f1b0adf86b6eabb377":"68d869c3df37044c294ac0ce961b02f56435b734d39547f1b0adf86b6eabb377","artifact:4284:818496fd105faaef95c60518b9637cad966668c83be7953a9ccb8ece7fa719fb":"818496fd105faaef95c60518b9637cad966668c83be7953a9ccb8ece7fa719fb","artifact:4284:8e212ad34d1c03ef4a6115202360da0e7bf25c0357ca6167267beb5d101d2bf7":"8e212ad34d1c03ef4a6115202360da0e7bf25c0357ca6167267beb5d101d2bf7","artifact:4284:94fdd9a479d28ae397084b1a53ab4132ac1ee6d14199efa7c2153046a5b016fe":"94fdd9a479d28ae397084b1a53ab4132ac1ee6d14199efa7c2153046a5b016fe","artifact:4284:9b313dcaddb9962950705a9a1465957d18ae48473245ae064b39cfe878763698":"9b313dcaddb9962950705a9a1465957d18ae48473245ae064b39cfe878763698","artifact:4284:9cab1ada328e5ced54b55daf2de3e773ed074213fe98f53c01e13ec0e569aa78":"9cab1ada328e5ced54b55daf2de3e773ed074213fe98f53c01e13ec0e569aa78","artifact:4284:a8605320611a7d002d29837dd5ca7fe4b26ccf2e343e03b3326d2e2325d18b8c":"a8605320611a7d002d29837dd5ca7fe4b26ccf2e343e03b3326d2e2325d18b8c","artifact:4284:ad7efa96a9b2419092916f3964e7e9baa980d99ab0011ae89926d41343ce2db6":"ad7efa96a9b2419092916f3964e7e9baa980d99ab0011ae89926d41343ce2db6","artifact:4284:afdd7bdd2d924c0dd2c989ba87b9e69caa8765b44ca3a937d6eb335c46ea6050":"afdd7bdd2d924c0dd2c989ba87b9e69caa8765b44ca3a937d6eb335c46ea6050","artifact:4284:d22d8d0eb37c2b48254d915a582a6126a58685706f43192292e588186fc8bf38":"d22d8d0eb37c2b48254d915a582a6126a58685706f43192292e588186fc8bf38","artifact:4284:d347905469202ab8846dc22f64b8b2847f5b2d4aada81da1eaf657159df9b832":"d347905469202ab8846dc22f64b8b2847f5b2d4aada81da1eaf657159df9b832","artifact:4284:d3d70e79f566505b1d465a481f725d47ed50abbdad83f0886cb2a7a34cfd6816":"d3d70e79f566505b1d465a481f725d47ed50abbdad83f0886cb2a7a34cfd6816","artifact:4284:e0d04b3dfe90d3045e484fccddcadaf831278693f425458173979d9aa96821fe":"e0d04b3dfe90d3045e484fccddcadaf831278693f425458173979d9aa96821fe","artifact:4284:ed4f76200c3b0f466a83b9520a886b4112fd859c0e890f374175e808f965408b":"ed4f76200c3b0f466a83b9520a886b4112fd859c0e890f374175e808f965408b"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4284,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":4303},"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 #4284: 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. Prior assessment return #4303: [{\"target_id\":\"g2-exponent\",\"decision\":\"applicable\",\"scope_keys\":[]},{\"target_id\":\"adversarial\",\"decision\":\"applicable\",\"scope_keys\":[]},{\"target_id\":\"measure\",\"decision\":\"unresolved\",\"scope_keys\":[]},{\"target_id\":\"formalize\",\"decision\":\"applicable\",\"scope_keys\":[]},{\"target_id\":\"infinitude\",\"decision\":\"applicable\",\"scope_keys\":[]},{\"target_id\":\"finiteness-structure\",\"decision\":\"inapplicable\",\"scope_keys\":[]},{\"target_id\":\"kk-lower-bound\",\"decision\":\"inapplicable\",\"scope_keys\":[]}]. Read its full conditions at GET <project>/return/4303. Reuse unchanged entries; inspect only changed source evidence: finding:116980.\n\nSource snapshot: {\"version\":\"research-applicability-v1\",\"consideration_only\":true,\"source_return_id\":4284,\"report_sha256\":\"50d2ca76a9c814c7ec6bb160135d3d2800284e2266341aa684a1e573b0dfb4a5\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4284\":\"926fd07b9bbebbe4836a356c40c43a7dbd9187bc6a9d65eb4a94ab65b0558929\",\"finding:116980\":\"c523af65e9c1f9120f2f91f6598b3d0e3677c4e77e1f353f8ddbf82c16166275\",\"finding:116981\":\"1e54d33ec9d4c536f5d9e23d31bf07ba7675e80a8839055b03d07b1c3632d44f\",\"artifact:4284:09b9a9b8acbe94a8d16755546280ffdd869c34f19ab76b232fcdd881ba910680\":\"09b9a9b8acbe94a8d16755546280ffdd869c34f19ab76b232fcdd881ba910680\",\"artifact:4284:0ac656480d29c8e1ce7f10e586eb6e8fc9380e05faf9705e79fb123837ed747c\":\"0ac656480d29c8e1ce7f10e586eb6e8fc9380e05faf9705e79fb123837ed747c\",\"artifact:4284:0c2efbef17923a8ba260b82dcba3bdb11075c18d2b37fc0f04f5ca7a43fd4279\":\"0c2efbef17923a8ba260b82dcba3bdb11075c18d2b37fc0f04f5ca7a43fd4279\",\"artifact:4284:21c4de82d260c119bfc91e10e9e7fbf4ddb49f1ead9a6f13bfa3a0f71025dbec\":\"21c4de82d260c119bfc91e10e9e7fbf4ddb49f1ead9a6f13bfa3a0f71025dbec\",\"artifact:4284:2ad1cf4f137baf3d7398fa2a73a73a78ad8b58e361e6a58a18641a51cb1b43b8\":\"2ad1cf4f137baf3d7398fa2a73a73a78ad8b58e361e6a58a18641a51cb1b43b8\",\"artifact:4284:2b00481dee785a1eff1fb9a0acce360c13873c98afed4b3a2c5c6d488f25c7fb\":\"2b00481dee785a1eff1fb9a0acce360c13873c98afed4b3a2c5c6d488f25c7fb\",\"artifact:4284:3946f639bfe3d2313b4ba575df9d78f131275ba9465849adcd09ee9ca919ce19\":\"3946f639bfe3d2313b4ba575df9d78f131275ba9465849adcd09ee9ca919ce19\",\"artifact:4284:3e70b53eee17d0c052c0e22be22e27b34c30ea3a3848dadae92894123de77efc\":\"3e70b53eee17d0c052c0e22be22e27b34c30ea3a3848dadae92894123de77efc\",\"artifact:4284:4eefdb814225bf26c065cedadbec1eb7a8bdcd42d02b021849bbf6cf201822a6\":\"4eefdb814225bf26c065cedadbec1eb7a8bdcd42d02b021849bbf6cf201822a6\",\"artifact:4284:50d2ca76a9c814c7ec6bb160135d3d2800284e2266341aa684a1e573b0dfb4a5\":\"50d2ca76a9c814c7ec6bb160135d3d2800284e2266341aa684a1e573b0dfb4a5\",\"artifact:4284:562ed271f0a11901c9a17e3a64f279b68024c49ed256f5bbed97e84b25a3465a\":\"562ed271f0a11901c9a17e3a64f279b68024c49ed256f5bbed97e84b25a3465a\",\"artifact:4284:569dc248436c652627c6ae0db7656f90270a89c28555b6f83aee4d31dd334f2e\":\"569dc248436c652627c6ae0db7656f90270a89c28555b6f83aee4d31dd334f2e\",\"artifact:4284:68d869c3df37044c294ac0ce961b02f56435b734d39547f1b0adf86b6eabb377\":\"68d869c3df37044c294ac0ce961b02f56435b734d39547f1b0adf86b6eabb377\",\"artifact:4284:818496fd105faaef95c60518b9637cad966668c83be7953a9ccb8ece7fa719fb\":\"818496fd105faaef95c60518b9637cad966668c83be7953a9ccb8ece7fa719fb\",\"artifact:4284:8e212ad34d1c03ef4a6115202360da0e7bf25c0357ca6167267beb5d101d2bf7\":\"8e212ad34d1c03ef4a6115202360da0e7bf25c0357ca6167267beb5d101d2bf7\",\"artifact:4284:94fdd9a479d28ae397084b1a53ab4132ac1ee6d14199efa7c2153046a5b016fe\":\"94fdd9a479d28ae397084b1a53ab4132ac1ee6d14199efa7c2153046a5b016fe\",\"artifact:4284:9b313dcaddb9962950705a9a1465957d18ae48473245ae064b39cfe878763698\":\"9b313dcaddb9962950705a9a1465957d18ae48473245ae064b39cfe878763698\",\"artifact:4284:9cab1ada328e5ced54b55daf2de3e773ed074213fe98f53c01e13ec0e569aa78\":\"9cab1ada328e5ced54b55daf2de3e773ed074213fe98f53c01e13ec0e569aa78\",\"artifact:4284:a8605320611a7d002d29837dd5ca7fe4b26ccf2e343e03b3326d2e2325d18b8c\":\"a8605320611a7d002d29837dd5ca7fe4b26ccf2e343e03b3326d2e2325d18b8c\",\"artifact:4284:ad7efa96a9b2419092916f3964e7e9baa980d99ab0011ae89926d41343ce2db6\":\"ad7efa96a9b2419092916f3964e7e9baa980d99ab0011ae89926d41343ce2db6\",\"artifact:4284:afdd7bdd2d924c0dd2c989ba87b9e69caa8765b44ca3a937d6eb335c46ea6050\":\"afdd7bdd2d924c0dd2c989ba87b9e69caa8765b44ca3a937d6eb335c46ea6050\",\"artifact:4284:d22d8d0eb37c2b48254d915a582a6126a58685706f43192292e588186fc8bf38\":\"d22d8d0eb37c2b48254d915a582a6126a58685706f43192292e588186fc8bf38\",\"artifact:4284:d347905469202ab8846dc22f64b8b2847f5b2d4aada81da1eaf657159df9b832\":\"d347905469202ab8846dc22f64b8b2847f5b2d4aada81da1eaf657159df9b832\",\"artifact:4284:d3d70e79f566505b1d465a481f725d47ed50abbdad83f0886cb2a7a34cfd6816\":\"d3d70e79f566505b1d465a481f725d47ed50abbdad83f0886cb2a7a34cfd6816\",\"artifact:4284:e0d04b3dfe90d3045e484fccddcadaf831278693f425458173979d9aa96821fe\":\"e0d04b3dfe90d3045e484fccddcadaf831278693f425458173979d9aa96821fe\",\"artifact:4284:ed4f76200c3b0f466a83b9520a886b4112fd859c0e890f374175e808f965408b\":\"ed4f76200c3b0f466a83b9520a886b4112fd859c0e890f374175e808f965408b\"},\"sha256\":\"6e9d6a5e4ffa2279bfb54972806e278e339217fe600f7f4802fa1146c85f0de5\"},\"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:4284,input_sha256:\"a81b04e0446a0bc01faf5cd624fd55056166f2f902308b8bb6c77e74d38201b9\",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/4351/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"f976989bc19d49a7aef829b39c6b9e7108c5c179370d2f5616e3a13979b9b788","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}