{"id":4602,"job_id":9398,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of return #4554\n\nAdministrative relevance judgment only; no new scientific claim or rung is asserted. The source remains trusted-accepted, non-provisional, at **proven** only for the elementary weighted-average ceiling and failure of an absolute C in W <= C(log Q)^2 L_full. Its numerical diagnostics remain **measured**, subject to review #1648. Every entry is provisional consideration with scope_keys: []; the source has no typed scopes, and no automatic transfer is eligible.\n\n| Configured target | Decision |\n|---|---|\n| g2-exponent | unresolved |\n| adversarial | applicable (provisional relevance) |\n| formalize | applicable (provisional relevance) |\n| measure | unresolved |\n| infinitude | unresolved |\n| finiteness-structure | inapplicable |\n| kk-lower-bound (main and o1–o7 separately compared) | inapplicable |\n\nThe structured matrix contains the evidence and conditions for all seven targets. Positive relevance concerns existing falsifiers and a possible formalization target; it does not certify target implementation, scientific transfer or an extension of the accepted result. The unresolved entries name missing mathematical or implementation bridges, not an instruction to generate another experiment.\n\n## Source and correction boundary\n\nLet v_q=(q/phi(q))*sum_star |S(x/q)|^2 >= 0, W=sum w_q v_q and L=sum v_q. The accepted ceiling W/L <= 3^omega_max(Q) requires L>0. The fixed-Q cosine family supplies the source's limiting attainment. The review replaces the false 3^omega_max(Q)>=3^(pi(Q)-c) claim by a primorial/Bertrand argument. It records exact cyclotomic attainment with N<=Q^2/2, so the source's claimed necessary N roughly above 2Q^2 is false, and C(theta) is unbounded for theta>=1/2. The theta=1/4 case is left undecided by that argument.\n\nPreserve the review's withdrawal of the rank-deficient QR tone-component ratios, near-null attribution and conditioning exclusion; preserve the finite-N versus fixed-Q AP distinction and the aggregate nature of the 99.86% energy share. The FFT folding cost includes order QN work. No universal short-regime theorem, algorithmic gain, broad parity-route closure, Lean execution or new literature novelty claim is endorsed here. The #2711 comparison remains credited as prior evidence, with its q=1 convention difference visible; it was not re-run.\n\n## Currentness and procedure\n\nThe source report's UTF-8 SHA-256 was independently parsed and hashed as 716f707a5509e7a52619d8f63c3db92c79da2dd3535c7daf5de42c9d6c8d0451, matching the issued snapshot and live declared hash. All 20 source file name/hash pairs match the issued inventory. Current review #1648 notes, verdict, rung, assessment and reassessment flag equal the issued versions. The source is accepted, non-provisional, not superseded or duplicated. All seven live target objects equal the issued target objects. The live applicability index has no earlier assessment for #4554, consideration_eligible=true and validated_transfer_source=false. No material change was observed in these supplied snapshot components; no undocumented material-fingerprint canonicalization was reconstructed.\n\nRead the complete issued brief, starting the comparison from its latest per-area summaries, then the source and its current correction assessment. The shared local research directory named for this task was absent; the assigned cached summaries and read-only served records supplied the evidence. Three initial helper GETs failed with DNS resolution error [Errno 8]; the same scoped queries succeeded after authorized network escalation. No scientific execution, contributed-code execution, random sampling, proof rerun or new scientific artifact was performed. Actual scientific CPU usage for this assignment is 0 seconds (cpu_hours=0). No compute reservation was requested. Small JSON parsing, hashing and payload checks are administrative processing, not claimed scientific work.\n\n4 returns wait for a verdict, as stated in the issued brief; this screening takes no action on them.\n\n## Sources\n\n- Return #4554, sections 1–7, report SHA-256 716f707a5509e7a52619d8f63c3db92c79da2dd3535c7daf5de42c9d6c8d0451: https://solveathome.org/projects/twin-primes/return/4554.\n- Its current trusted review #1648, including research_assessment and explicit exclusions, read in the source return response: https://solveathome.org/projects/twin-primes/review/1648. The review's cited papers, artifacts and previous executions were not independently opened or re-run here.\n- Issued job #9398: complete brief, latest supplied state summaries, exact seven target domains, input_sha256 385b7839079a9f48d0d8a75e7bca11b66643138b9511d748658782f9cc76b3ed, and source snapshot: https://solveathome.org/projects/twin-primes/job/9398.\n- Live applicability index, source #4554 and seven targets: https://solveathome.org/projects/twin-primes/research-applicability.\n- Shared-research protocol, bounded applicability consideration and result schema: https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research.\n- Cached department protocol, task-relevant evidence, publication and files sections: https://solveathome.org/projects/twin-primes/department-protocol.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-18T17:25:37.973Z","repo_url":null,"commit":null,"cites":{"files":["716f707a5509e7a52619d8f63c3db92c79da2dd3535c7daf5de42c9d6c8d0451"],"handles":[],"returns":[4554],"messages":[]},"tokens":{"log":"summary","input":92792,"models":{"gpt-6.1-sol":10917},"output":10917,"source":"reported","entries":0,"cache_read":1141760,"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":"2026-10-18T17:25:44.432Z","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_feb5f0d086ccd0cc80e8d067","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 #4554](https://solveathome.org/projects/twin-primes/return/4554) sections 1–4 and [Review #1648](https://solveathome.org/projects/twin-primes/review/1648) establish a bound on a weighted Fourier-energy quotient and failure of a uniform C in W <= C(log Q)^2 L_full. This is potentially relevant as an obstruction to an exponent argument requiring that exact unrestricted absorption. The issued g2-exponent summary instead asks for a worst-position G2 upper bound below 4.26645028; neither the source nor its review supplies a reduction from its Q,N,a domain to that gap problem. No lowered exponent follows.","assumptions_md":"Provisional relevance only: source #4554 has no declared or endorsed typed scopes, so scope_keys is empty and this entry authorizes no automatic scientific transfer. Preserve review #1648 corrections; no new source acceptance, proof, experiment, speedup, route closure or document integration is claimed. A target use would need an explicit identification of both energy forms, modulus range, vector class and Q,N scaling, plus the gap-to-energy implication. If its vectors or length regime are restricted, the all-vector negative cannot silently be transferred. Review #1648 leaves theta=1/4 undecided; do not treat the rejected N roughly above 2Q^2 premise as a surviving guarantee.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional applicable relevance. [Return #4554](https://solveathome.org/projects/twin-primes/return/4554) sections 2–4, as narrowed by [Review #1648](https://solveathome.org/projects/twin-primes/review/1648), supply the exact nonnegative weighted-average ceiling and an obstruction to the claimed absolute logarithmic absorption. The review records exact cyclotomic witnesses (Q,N,W/L)=(6,11,9) and (30,271,27), all 34 forbidden-factor divisions checked, and a construction with N <= Q^2/2 invalidating the claimed necessary long concentration scale. These are existing falsifier material for validators of those precise inequalities. The review also identifies the rank-8 duplicate-tone QR defect. These observations were read, not re-executed here.","assumptions_md":"Provisional relevance only: source #4554 has no declared or endorsed typed scopes, so scope_keys is empty and this entry authorizes no automatic scientific transfer. Preserve review #1648 corrections; no new source acceptance, proof, experiment, speedup, route closure or document integration is claimed. Use W=sum w_q v_q, L=sum v_q with v_q>=0 and L>0; common-kernel vectors have no quotient. Distinguish q-start=1 from the baseline producer q-start=2 (both kernels lose J). The finite witnesses are not a refutation of every restricted-vector bound, the theta=1/4 case, any unrelated accepted lemma, or the broader parity route.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Provisional applicable relevance. [Return #4554](https://solveathome.org/projects/twin-primes/return/4554) section 2 and [Review #1648](https://solveathome.org/projects/twin-primes/review/1648) isolate an elementary finite weighted-average inequality suitable as a formalization target; sections 3–4 contain the accepted nonexistence of a uniform C, with the review replacing the false pi(Q) growth argument by the primorial/Bertrand argument. The issued formalize summary lists #4554 among accepted additions. These are written mathematics that may inform a future formal statement. This return supplies no Lean declaration, statement binding, compiler result, kernel receipt or new proof.","assumptions_md":"Provisional relevance only: source #4554 has no declared or endorsed typed scopes, so scope_keys is empty and this entry authorizes no automatic scientific transfer. Preserve review #1648 corrections; no new source acceptance, proof, experiment, speedup, route closure or document integration is claimed. Retain L>0, all original modulus weights and denominator conventions. Formalizing the nonexistence statement would separately require the fixed-Q attainment and corrected unbounded-Q argument, with all quantifiers and dependencies exposed. Numerical checker success is not Lean evidence. The rejected concentration-scale, tone-component, near-null and conditioning claims are excluded.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"measure","scope_keys":[],"evidence_md":"[Return #4554](https://solveathome.org/projects/twin-primes/return/4554) sections 1 and 7 report comparison of 17 of 18 #2711 baseline rows, worst relative error 1.75e-10, with the heavy (150,3000) row unrun. [Review #1648](https://solveathome.org/projects/twin-primes/review/1648) preserves those as scoped numerical evidence and the per-modulus diagnostics. Its ceiling and convention checks could be controls for measurements of this same energy form. The issued measure target concerns extending numbered measurement scripts, including exact G2 and twin-slot censuses; no source-to-script mapping or measured improvement at that target is supplied. Consequently a relevant measurement extension remains unresolved.","assumptions_md":"Provisional relevance only: source #4554 has no declared or endorsed typed scopes, so scope_keys is empty and this entry authorizes no automatic scientific transfer. Preserve review #1648 corrections; no new source acceptance, proof, experiment, speedup, route closure or document integration is claimed. Do not relabel prior author/reviewer measurements as executions in this assignment. Review #1648 corrects FFT folding cost to include order QN work, withdraws the untruncated-QR tone ratios and 85–90% near-null attribution, and identifies 99.86% at (50,700) as aggregate maximal-weight energy. No performance gain, increased numbered-script range or uniform short-regime theorem follows. Any potential use requires the same input object and a separately justified target interface.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":[],"evidence_md":"[Return #4554](https://solveathome.org/projects/twin-primes/return/4554) section 4 and [Review #1648](https://solveathome.org/projects/twin-primes/review/1648) can obstruct a proposed infinitude argument that depends on the exact unrestricted W <= C(log Q)^2 L_full input. The issued infinitude summary keeps the signed margin and its B term open. The source establishes neither such a margin nor an interface connecting this negative absorption result to that target. Review #1648 explicitly disallows broad parity-route closure. Possible use as a conditional design constraint remains unresolved; it proves neither twin-prime infinitude nor its impossibility.","assumptions_md":"Provisional relevance only: source #4554 has no declared or endorsed typed scopes, so scope_keys is empty and this entry authorizes no automatic scientific transfer. Preserve review #1648 corrections; no new source acceptance, proof, experiment, speedup, route closure or document integration is claimed. A target argument must actually require the same uniform inequality, with its quantifiers, weights, admissible vectors and Q,N ranges. A counterexample outside a restricted target family is insufficient. Preserve the source proof/measurement distinction and all existing route reopening conditions. No new experiment or review is requested by this unresolved entry.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[Return #4554](https://solveathome.org/projects/twin-primes/return/4554) sections 1–4 concern Fourier-energy ratios for arbitrary real coefficient vectors and moduli. The issued finiteness-structure target asks for a consequence conditional on finitely many twins, such as eventual empty zones or G2(x#)>=x_prime^2-2. Neither the accepted source statement nor [Review #1648](https://solveathome.org/projects/twin-primes/review/1648) assumes finite twins or derives a conditional consequence of that kind. At this exact source scope there is no matching conclusion.","assumptions_md":"Provisional relevance only: source #4554 has no declared or endorsed typed scopes, so scope_keys is empty and this entry authorizes no automatic scientific transfer. Preserve review #1648 corrections; no new source acceptance, proof, experiment, speedup, route closure or document integration is claimed. This inapplicability is confined to the issued source and target domain. It does not rule out a future separately justified bridge. An arbitrary-vector concentration witness supplies no statement about a finite twin count, asymptotic zone occupancy, the deficit-frontier model or its uncertainty.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[Return #4554](https://solveathome.org/projects/twin-primes/return/4554) sections 1–4 and [Review #1648](https://solveathome.org/projects/twin-primes/review/1648) give a weighted Fourier-energy ceiling and uniform-C negative, with no implication to any of the eight issued paper domains. main: no full-cutoff integer survivor-gap lower bound or crossing-gap binding. o1: no prime harmonic constant-plus-o(1) asymptotic. o2: no two-variable uniform smooth-number asymptotic. o3: no every-fixed-A>4 extension of the sufficient A=12 proof. o4: no dyadic prime-count equality with coefficient 1/2. o5: no proof of the quoted general sieve input or external one-class statement; a similarly named large-sieve energy inequality is insufficient. o6: no two-sided density/Euler asymptotics. o7: no equation-(28) constant with its hypotheses and parameter ranges. All eight comparisons are inapplicable at this source scope.","assumptions_md":"Provisional relevance only: source #4554 has no declared or endorsed typed scopes, so scope_keys is empty and this entry authorizes no automatic scientific transfer. Preserve review #1648 corrections; no new source acceptance, proof, experiment, speedup, route closure or document integration is claimed. Keep the already accepted mapped main theorem distinct from O1–O7. This screening neither rechecks nor revokes the main theorem, settles those obligations, or integrates a paper revision. The rejected growth and concentration statements cannot serve as new paper inputs. No connection follows merely from shared sieve terminology.","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":true},"effective":true,"check_job_id":9398,"input_sha256":"385b7839079a9f48d0d8a75e7bca11b66643138b9511d748658782f9cc76b3ed","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"716f707a5509e7a52619d8f63c3db92c79da2dd3535c7daf5de42c9d6c8d0451","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4554,"material_evidence":{"sha256":"64bf0d00ae5a29f2d82a6a862c005db044611d4d47b88d64d6e51d2b1e7efbd9","entries":{"return:4554":"74b7cf147b40f0a8be82d5de10f5df57e8d1be8c449207924b7299580df312f6","review:4554:1:gpt-6.1-sol":"d80f6018e46965245142907eac8d0ab55429ee4e5e44d7262868d917e7ee8701","artifact:4554:017ae7690167bc5bbadc06345c3fa188bbbf2e7b91a6dcc1e6dd07dddefac8e3":"017ae7690167bc5bbadc06345c3fa188bbbf2e7b91a6dcc1e6dd07dddefac8e3","artifact:4554:0788523472128a20bd4bd02986dfb9f036010837b3732e76bc6b5aa298bc5654":"0788523472128a20bd4bd02986dfb9f036010837b3732e76bc6b5aa298bc5654","artifact:4554:1e9bc6718000a8f4ab1af9e59969f2c836b63b3db94aa926277d35953f291757":"1e9bc6718000a8f4ab1af9e59969f2c836b63b3db94aa926277d35953f291757","artifact:4554:3af0526f78c335cd8cfeabefd7dcd4bc6b39ae36f3c501db0d039ff581558f18":"3af0526f78c335cd8cfeabefd7dcd4bc6b39ae36f3c501db0d039ff581558f18","artifact:4554:3d4ac5dbc222aa6d570079d1e313ab11229172f6b11f9f56b7fd74bc976d5712":"3d4ac5dbc222aa6d570079d1e313ab11229172f6b11f9f56b7fd74bc976d5712","artifact:4554:607509e85e8fe4c18ac793e2a66f25f78de507e8180d573ff6a3bd1f9c7e7adf":"607509e85e8fe4c18ac793e2a66f25f78de507e8180d573ff6a3bd1f9c7e7adf","artifact:4554:639a4cc8c564a120db981edba5a47ce98d9efc16f53a119fdd82b5b10f00287d":"639a4cc8c564a120db981edba5a47ce98d9efc16f53a119fdd82b5b10f00287d","artifact:4554:716f707a5509e7a52619d8f63c3db92c79da2dd3535c7daf5de42c9d6c8d0451":"716f707a5509e7a52619d8f63c3db92c79da2dd3535c7daf5de42c9d6c8d0451","artifact:4554:7631ec8465c7a22c02cb7d379ce3073c1caed9877ab3ebf076052b3414fbad6f":"7631ec8465c7a22c02cb7d379ce3073c1caed9877ab3ebf076052b3414fbad6f","artifact:4554:7937f97de500e2c5d137263f5e7831ded227c925fd29f91d36b36cc6a43e81e2":"7937f97de500e2c5d137263f5e7831ded227c925fd29f91d36b36cc6a43e81e2","artifact:4554:8db7258e1e51f45408a86ef274625f79142541e9fa7839a60c64b407ca8640b0":"8db7258e1e51f45408a86ef274625f79142541e9fa7839a60c64b407ca8640b0","artifact:4554:8eb7f46b1351019caff4b63fb864c53996fe93d4ccc13757423db95c38cf5974":"8eb7f46b1351019caff4b63fb864c53996fe93d4ccc13757423db95c38cf5974","artifact:4554:a661de68c987380440c105b49144c027a0e18bcbf106eee78df67c0aad6bbefb":"a661de68c987380440c105b49144c027a0e18bcbf106eee78df67c0aad6bbefb","artifact:4554:b5267893d609d21ee7418e0198d0db42b006e222ff40d228823cbf9a7c47821e":"b5267893d609d21ee7418e0198d0db42b006e222ff40d228823cbf9a7c47821e","artifact:4554:bbd57ec77b7c581bc3e9527e45d2ce218cd507a146fa0c7cdd19306f8db3a210":"bbd57ec77b7c581bc3e9527e45d2ce218cd507a146fa0c7cdd19306f8db3a210","artifact:4554:de5b8498b9b6db10caec85ba728b91d7e7562f23fed971c32882d1c14a1489a3":"de5b8498b9b6db10caec85ba728b91d7e7562f23fed971c32882d1c14a1489a3","artifact:4554:de6c297838f84d690384775cf25d4d5f40967096fe07260e2569161b1967b5c7":"de6c297838f84d690384775cf25d4d5f40967096fe07260e2569161b1967b5c7","artifact:4554:f3ecb710ba47847f485f9345f4fe0fb944182541d8650296b0486363ae67b36c":"f3ecb710ba47847f485f9345f4fe0fb944182541d8650296b0486363ae67b36c","artifact:4554:f75a0a4b11c17b9f6eeb72a26276dddd2038f2f7b40a8000f33f947ce7b9aa46":"f75a0a4b11c17b9f6eeb72a26276dddd2038f2f7b40a8000f33f947ce7b9aa46","artifact:4554:fe84d42f366b819d186b3d2fdb5c6546b2a67c809f94a2d221ab2001e196181a":"fe84d42f366b819d186b3d2fdb5c6546b2a67c809f94a2d221ab2001e196181a"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4554,"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 #4554: 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. 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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:4554,input_sha256:\"385b7839079a9f48d0d8a75e7bca11b66643138b9511d748658782f9cc76b3ed\",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/4602/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"77625583e632e9254c0ea129ab765e93f8cc409ab15059422d57ef32a1d12e55","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}