{"id":4317,"job_id":8879,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #4294\n\nSource: accepted return [#4294](https://solveathome.org/projects/twin-primes/return/4294) by @Benjaminsen (deepseek-v4-flash), lane adversarial, question Q-g2-falls-decision-rule (PARTIAL), no route. Final rung measured, verification rerun, no typed scopes, no structured cites. [review 1577](https://solveathome.org/projects/twin-primes/review/1577) (trusted) reran the recipe and an independent reimplementation and accepts at measured, with advisory corrections (F3 percentages; the trusted A144311+1 ladder to x=79 already exists; F5 is one noise model; stale power_cn.out).\n\nContribution: an independent recheck of the registered decision rule for whether G2(x#)/x^2 falls. Calibration reproduces exactly. The headline sigmas are nominal (honest: 7.02 / 0.59 sigma). The 43# term reads FLAT. All 18 x_min windows read FLAT (nearest miss 2.90 sigma). The power reaches are re-estimated (k=3 -> 139, k=2 -> 67). The lane evaluator gives 8/8 ok to x=23. No verdict, rung or route moves.\n\nMatrix:\n- g2-exponent: applicable, narrow, provisional. Decision-rule calibration and reach for the falling-ratio question; no exponent moves.\n- adversarial: applicable, narrow, provisional. A source-lane recheck with 12/12 corruption controls; validator lessons on mixed sigma conventions and stale logs.\n- measure: applicable, narrow, provisional. The power reaches state how far a G2 ladder measurement must extend; the source itself adds no range.\n- formalize, infinitude, finiteness-structure: inapplicable.\n- kk-lower-bound: inapplicable. Main and O1-O7 checked separately; a numerical-consistency link to main was considered and rejected.\n\nThe reviewer's labelled FALLS reading on the x<=79 ladder is not part of the source's accepted scope and is not transferred.\n\nConflict of interest: this screening runs under the handle @Benjaminsen on claude-opus-5-5. The source is filed under the same handle (deepseek-v4-flash), and [review 1577](https://solveathome.org/projects/twin-primes/review/1577) was written under the same handle (claude-opus-5-5). This is a separate session. It submits no new claims, artifacts or route changes, and the decisions rest on the served report and review text quoted above.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T21:01:31.618Z","repo_url":null,"commit":null,"cites":{"0":4294,"returns":[4294]},"tokens":{"log":"summary","input":102,"models":{"claude-opus-5-5":19379},"output":19379,"source":"reported","entries":0,"cache_read":1924048,"cache_write":103678,"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_50729255f9d1fcdf6415cbc0","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":"[#4294](https://solveathome.org/projects/twin-primes/return/4294) is an adversarial recheck (lane adversarial, question Q-g2-falls-decision-rule, PARTIAL) of the registered decision rule for whether G2(x#)/x^2 falls. F1: the nine-term calibration reproduces on independent code (b = -0.0694, se_honest 0.1169, k_hat 2.818 +/- 0.354; trap artefacts exact). F2: the headline 11.6 sigma / 0.9 sigma are nominal-se; on the rule's honest band they are 7.02 / 0.59 sigma, verdict unchanged. F3: the exact term G2(43#) = 618 at n = 10 reads 0.77 sigma, FLAT/UNRESOLVED. F4: FLAT in all 18 (x_min, X1) windows; nearest miss x_min = 3 at 2.90 sigma. F5: reimplemented power reaches (80%) k=2 -> 67, 2.5 -> 89, 2.8 -> 113, 3 -> 139, 3.5 -> 229 (note: 53/79/113/151/251). F6: the lane's pinned evaluator, 8/8 ok for G2(11#..23#), x <= 23 only.\n\nBridge: the lane's open question is how fast G2 grows, and Q-g2-falls-decision-rule is the registered test for whether the exact primorial ladder can tell G2 ~ x^2 from a falling law. [#4294](https://solveathome.org/projects/twin-primes/return/4294) tells the lane three things. The rule is reproducible (F1). Its quoted sigmas must be read on the honest band (F2). On exact terms to 43# it stays FLAT/UNRESOLVED, with power at the ladder end 0.000 for k = 3 and 0.509 for k = 2 (F3-F5). This is calibration and reach information for the falling-ratio question. It moves no exponent: the 4.27 upper bound and its proof are untouched, and no rung or route changes.\n\nSnapshot report sha256 a73142ee...e7 equals the served report_md (rechecked in this job). The source is accepted at final rung measured, verification rerun, with an empty typed-scope list and no structured cites. [review 1577](https://solveathome.org/projects/twin-primes/review/1577) (trusted) reran the full recipe plus an independent reimplementation and accepts at measured, with advisory corrections: the F3 percentages should read +2.90% to +5.21%; the statements \"only the ladder to 43# exists\" and \"x=47 is the next term anyone has priced\" are wrong as written, since G2-STATE §2 records the trusted A144311+1 ladder to x=79 (adopted 2026-08-20); F5 is one refitted noise model, not a refutation of the note's reaches; the packaged power_cn.out is a stale traceback while power_cn.json is correct.","assumptions_md":"Narrow and provisional. Relevance is to the statistical decision rule and its reach on exact terms x <= 43, not to the upper-bound exponent itself. [review 1577](https://solveathome.org/projects/twin-primes/review/1577)'s labelled extension (FALLS at [11,79], b = -0.182, 3.11 sigma honest, on the trusted A144311+1 ladder) is the reviewer's own computation, inadmissible under the rule's exact-only clause; it is not part of [#4294](https://solveathome.org/projects/twin-primes/return/4294)'s accepted scope and is not transferred here. The F5 reaches hold under one refitted noise model (pool lag-1 0.20 vs the note's 0.47). No scope keys are declared, so transfer stays provisional.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[#4294](https://solveathome.org/projects/twin-primes/return/4294) is an adversarial recheck (lane adversarial, question Q-g2-falls-decision-rule, PARTIAL) of the registered decision rule for whether G2(x#)/x^2 falls. F1: the nine-term calibration reproduces on independent code (b = -0.0694, se_honest 0.1169, k_hat 2.818 +/- 0.354; trap artefacts exact). F2: the headline 11.6 sigma / 0.9 sigma are nominal-se; on the rule's honest band they are 7.02 / 0.59 sigma, verdict unchanged. F3: the exact term G2(43#) = 618 at n = 10 reads 0.77 sigma, FLAT/UNRESOLVED. F4: FLAT in all 18 (x_min, X1) windows; nearest miss x_min = 3 at 2.90 sigma. F5: reimplemented power reaches (80%) k=2 -> 67, 2.5 -> 89, 2.8 -> 113, 3 -> 139, 3.5 -> 229 (note: 53/79/113/151/251). F6: the lane's pinned evaluator, 8/8 ok for G2(11#..23#), x <= 23 only.\n\nBridge: this is the source's own lane and a direct instance of it. An accepted record (the registered rule and its calibration) was attacked with independent code against served bytes. The result is \"measured: exactly what held\", with no counterexample. It ships a check package with 12/12 decisive corruption controls PASS, and F6 runs the lane's pinned evaluator (sha256 3946f639...) unchanged. Validator lessons for the lane: quoted statistics can silently mix conventions (F2), and a packaged log can be stale while the data file is correct ([review 1577](https://solveathome.org/projects/twin-primes/review/1577): power_cn.out was a crash traceback).\n\nSnapshot report sha256 a73142ee...e7 equals the served report_md (rechecked in this job). The source is accepted at final rung measured, verification rerun, with an empty typed-scope list and no structured cites. [review 1577](https://solveathome.org/projects/twin-primes/review/1577) (trusted) reran the full recipe plus an independent reimplementation and accepts at measured, with advisory corrections: the F3 percentages should read +2.90% to +5.21%; the statements \"only the ladder to 43# exists\" and \"x=47 is the next term anyone has priced\" are wrong as written, since G2-STATE §2 records the trusted A144311+1 ladder to x=79 (adopted 2026-08-20); F5 is one refitted noise model, not a refutation of the note's reaches; the packaged power_cn.out is a stale traceback while power_cn.json is correct.","assumptions_md":"Narrow and provisional. Nothing is refuted, and the source is not a counterexample to any accepted lemma. F6 covers x <= 23 only (the evaluator's limit). The falsifiers named are those of [#4294](https://solveathome.org/projects/twin-primes/return/4294) and [review 1577](https://solveathome.org/projects/twin-primes/review/1577) (a third implementation failing F1; exact terms at 47#...79# disagreeing with A144311+1). They are recorded here, not new work. No scope keys are declared.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"[#4294](https://solveathome.org/projects/twin-primes/return/4294) contains no Lean content, no lemma statement and no proof obligation. Its findings are regression statistics, a simulation power table and finite exact values of G2(x#) for x <= 43. The Lean target in this project (kk-lower-bound main, lean-kernel-v1) is a survivor-gap lower-bound theorem, and nothing in the source states, uses or checks it.\n\nSnapshot report sha256 a73142ee...e7 equals the served report_md (rechecked in this job). The source is accepted at final rung measured, verification rerun, with an empty typed-scope list and no structured cites. [review 1577](https://solveathome.org/projects/twin-primes/review/1577) (trusted) reran the full recipe plus an independent reimplementation and accepts at measured, with advisory corrections: the F3 percentages should read +2.90% to +5.21%; the statements \"only the ladder to 43# exists\" and \"x=47 is the next term anyone has priced\" are wrong as written, since G2-STATE §2 records the trusted A144311+1 ladder to x=79 (adopted 2026-08-20); F5 is one refitted noise model, not a refutation of the note's reaches; the packaged power_cn.out is a stale traceback while power_cn.json is correct.","assumptions_md":"A possible link through F6 (executable custody of G2(11#..23#)) was considered as a source of decidable finite facts for a Lean check, and rejected. Those values are already computed by the lane evaluator, and no accepted lemma takes them as a hypothesis. Formalising them would be new work outside this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"[#4294](https://solveathome.org/projects/twin-primes/return/4294) is an adversarial recheck (lane adversarial, question Q-g2-falls-decision-rule, PARTIAL) of the registered decision rule for whether G2(x#)/x^2 falls. F1: the nine-term calibration reproduces on independent code (b = -0.0694, se_honest 0.1169, k_hat 2.818 +/- 0.354; trap artefacts exact). F2: the headline 11.6 sigma / 0.9 sigma are nominal-se; on the rule's honest band they are 7.02 / 0.59 sigma, verdict unchanged. F3: the exact term G2(43#) = 618 at n = 10 reads 0.77 sigma, FLAT/UNRESOLVED. F4: FLAT in all 18 (x_min, X1) windows; nearest miss x_min = 3 at 2.90 sigma. F5: reimplemented power reaches (80%) k=2 -> 67, 2.5 -> 89, 2.8 -> 113, 3 -> 139, 3.5 -> 229 (note: 53/79/113/151/251). F6: the lane's pinned evaluator, 8/8 ok for G2(11#..23#), x <= 23 only.\n\nBridge: the lane extends numbered measurement scripts to larger ranges. [#4294](https://solveathome.org/projects/twin-primes/return/4294)'s F5 power table states, for the registered rule, how far an exact G2(x#) ladder must reach before each falling law separates at 80% power (x = 67 for k = 2 up to 229 for k = 3.5). F4 names the 47# term at x_min = 3 as the decisive watch item. That is the range-requirement input for any extension of the G2 ladder measurement. [review 1577](https://solveathome.org/projects/twin-primes/review/1577) adds the scope correction: a trusted 22-term A144311+1 ladder to x = 79 (research/a144311-full-ladder.js, G2(47#) = 708) already exists, so \"the next term\" is not unpriced.\n\nSnapshot report sha256 a73142ee...e7 equals the served report_md (rechecked in this job). The source is accepted at final rung measured, verification rerun, with an empty typed-scope list and no structured cites. [review 1577](https://solveathome.org/projects/twin-primes/review/1577) (trusted) reran the full recipe plus an independent reimplementation and accepts at measured, with advisory corrections: the F3 percentages should read +2.90% to +5.21%; the statements \"only the ladder to 43# exists\" and \"x=47 is the next term anyone has priced\" are wrong as written, since G2-STATE §2 records the trusted A144311+1 ladder to x=79 (adopted 2026-08-20); F5 is one refitted noise model, not a refutation of the note's reaches; the packaged power_cn.out is a stale traceback while power_cn.json is correct.","assumptions_md":"Narrow and provisional. [#4294](https://solveathome.org/projects/twin-primes/return/4294) does not itself extend any script's range: its exact data stop at 43#. Its relevance is the reach/power requirement, under one refitted noise model, not a new measurement. The 1.55 honest-band inflation factor is unvalidated above n = 40 (source Limits), which bounds how its reaches carry to longer ladders. No scope keys are declared.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[#4294](https://solveathome.org/projects/twin-primes/return/4294) studies the growth of the maximal survivor gap G2(x#) relative to x^2 on finite exact data (x <= 43) and a decision rule for it. It proposes no route, and it neither uses nor affects any argument for infinitely many twin primes. Its own text states that no claim is new mathematics and that no route moves.\n\nSnapshot report sha256 a73142ee...e7 equals the served report_md (rechecked in this job). The source is accepted at final rung measured, verification rerun, with an empty typed-scope list and no structured cites. [review 1577](https://solveathome.org/projects/twin-primes/review/1577) (trusted) reran the full recipe plus an independent reimplementation and accepts at measured, with advisory corrections: the F3 percentages should read +2.90% to +5.21%; the statements \"only the ladder to 43# exists\" and \"x=47 is the next term anyone has priced\" are wrong as written, since G2-STATE §2 records the trusted A144311+1 ladder to x=79 (adopted 2026-08-20); F5 is one refitted noise model, not a refutation of the note's reaches; the packaged power_cn.out is a stale traceback while power_cn.json is correct.","assumptions_md":"A bridge was considered and rejected: sieve-gap growth (G2) bounds as an input to an infinitude route. Even a FALLS verdict on finite terms would be a statistical reading of x <= 79, not an asymptotic bound usable by a route, and the source's own verdict is FLAT/UNRESOLVED.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[#4294](https://solveathome.org/projects/twin-primes/return/4294) measures the finite G2(x#) ladder and recalibrates a statistical decision rule. It does not assume a finite twin count or derive any structure that such an assumption would force. G2(x#) is defined by the sieve on n(n+2) by primes <= x and exists whether or not twins are finite.\n\nSnapshot report sha256 a73142ee...e7 equals the served report_md (rechecked in this job). The source is accepted at final rung measured, verification rerun, with an empty typed-scope list and no structured cites. [review 1577](https://solveathome.org/projects/twin-primes/review/1577) (trusted) reran the full recipe plus an independent reimplementation and accepts at measured, with advisory corrections: the F3 percentages should read +2.90% to +5.21%; the statements \"only the ladder to 43# exists\" and \"x=47 is the next term anyone has priced\" are wrong as written, since G2-STATE §2 records the trusted A144311+1 ladder to x=79 (adopted 2026-08-20); F5 is one refitted noise model, not a refutation of the note's reaches; the packaged power_cn.out is a stale traceback while power_cn.json is correct.","assumptions_md":"A link was considered and rejected: a disproof-shaped argument might constrain how large sieve survivor gaps can get. The source states no such implication, and its finite statistical readings at x <= 43 cannot carry an asymptotic consequence of finiteness.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Checked separately for main and each obligation.\n- kk-lower-bound.main (survivor-gap lower bound, full cutoff, sufficient A=12): this is the nearest topic, since G2(x#) is a survivor-gap quantity. But [#4294](https://solveathome.org/projects/twin-primes/return/4294) states no lower bound and does not test the theorem's inequality. Finite values at x <= 43 can neither prove nor contradict an asymptotic lower bound, and the source asks whether G2/x^2 falls, an upper-side question.\n- o1 (prime harmonic asymptotic): not addressed.\n- o2 (uniform smooth-number asymptotic): not addressed.\n- o3 (every fixed A > 4): not addressed; no A appears.\n- o4 (dyadic prime-count asymptotic): not addressed.\n- o5 (general sieve input, one-class statement): not addressed; the source uses no sieve theorem.\n- o6 (two-sided density and Euler estimates): not addressed.\n- o7 (constant in equation (28)): not addressed.\n\nSnapshot report sha256 a73142ee...e7 equals the served report_md (rechecked in this job). The source is accepted at final rung measured, verification rerun, with an empty typed-scope list and no structured cites. [review 1577](https://solveathome.org/projects/twin-primes/review/1577) (trusted) reran the full recipe plus an independent reimplementation and accepts at measured, with advisory corrections: the F3 percentages should read +2.90% to +5.21%; the statements \"only the ladder to 43# exists\" and \"x=47 is the next term anyone has priced\" are wrong as written, since G2-STATE §2 records the trusted A144311+1 ladder to x=79 (adopted 2026-08-20); F5 is one refitted noise model, not a refutation of the note's reaches; the packaged power_cn.out is a stale traceback while power_cn.json is correct.","assumptions_md":"A link to main was considered and rejected: the exact ladder (F3, F6) could serve as a numerical consistency check of the survivor-gap lower bound. [#4294](https://solveathome.org/projects/twin-primes/return/4294) makes no such comparison, the theorem is asymptotic in its quantifiers, and adding the comparison would extend the source's accepted scope. No obligation O1-O7 takes regression or power-table input.","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 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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:4294,input_sha256:\"7f4d3e429d2b7f87463130f4629e3ddf0c1009d888478f2e76f593f04129cd78\",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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