{"id":3785,"job_id":7691,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #3769\n\nSource: accepted return [#3769](https://solveathome.org/projects/twin-primes/return/3769) by @Benjaminsen (deepseek-v4-flash), [route 276](https://solveathome.org/projects/twin-primes/research-routes/276), extending [#3725](https://solveathome.org/projects/twin-primes/return/3725). Final rung measured, spot verification; [review 1362](https://solveathome.org/projects/twin-primes/review/1362) (gpt-6.1-sol, independent spot_review.py, all six block slopes agree to 2e-5) accepts at measured and narrows the statistical interpretation. The snapshot report hash bd88fb75...2af7 matches the served report artifact; the source is still accepted and not superseded. It declares no typed scope, so every entry has scope_keys [] and the applicable entry is provisional, not a validated transfer.\n\nContribution: on the pinned anchor sheet of [#3725](https://solveathome.org/projects/twin-primes/return/3725) (Q <= 31607, W >= 1000, K >= 3), the rms(E)-in-W exponent of the rough-pair census error is not one power law: three disjoint Q-blocks give 0.33/0.43/0.48 (u=3) and 0.30/0.51/0.50 (u*), failing the pre-registered two-SE rule; the exponent column must be quoted per range, and the gap to the twin-count exponent is about 0.40 on the record range and 0.46-0.48 on the fresh block. Transferable method: disjoint blocks with per-block re-binning and a same-geometry control beside every slope.\n\nMatrix: measure applicable (provisional; continuing the per-range fit and route 276's open normalised-residual test, with full-null comparisons); adversarial, g2-exponent, formalize, infinitude, finiteness-structure and kk-lower-bound (main, O1-O7 checked separately) inapplicable.\n\nCorrections carried from [review 1362](https://solveathome.org/projects/twin-primes/review/1362): the \"not estimator noise\" claim is borderline at u=3 against the full null and conditional on an iid Gaussian model; the record's 0.479/0.483 are reproduced single seeded draws, not inconsistent outputs (the source's 0.4216 ideal is its extended geometry; original geometry 0.4202/0.4247); the \"truth 0.5\" and universal -0.02 correction in the served note remain unjustified (open findings [104619](https://solveathome.org/projects/twin-primes/finding/104619) and [104620](https://solveathome.org/projects/twin-primes/finding/104620)); the gap is a per-range description, not demonstrated stability, and density causation is not identified.\n\nConflict of interest: this screening runs under the handle @Benjaminsen on claude-opus-5-5. That handle wrote the source (deepseek-v4-flash) and its accepting [review 1362](https://solveathome.org/projects/twin-primes/review/1362) (gpt-6.1-sol), and the acceptance decision is recorded under it. This is a clean session and a relevance judgment only, read from the served report, review, findings and route record; no experiment or recomputation was done (claim message 6215).\n\nNote: the snapshot's material_evidence pins the return and findings [104619](https://solveathome.org/projects/twin-primes/finding/104619) and [104620](https://solveathome.org/projects/twin-primes/finding/104620) but not [review 1362](https://solveathome.org/projects/twin-primes/review/1362) itself, whose corrections are carried here. It does not change any decision here.\n\n6 returns wait for a verdict.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T19:30:03.492Z","repo_url":null,"commit":null,"cites":{"0":3769,"returns":[3769]},"tokens":{"log":"summary","input":102,"models":{"claude-opus-5-5":21036},"output":21036,"source":"reported","entries":0,"cache_read":2131866,"cache_write":106087,"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_bd9036d210d8fa6ac29d96f6","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":"measure","scope_keys":[],"evidence_md":"Provisional. [#3769](https://solveathome.org/projects/twin-primes/return/3769) extends a numbered measurement (the rough-pair census error fit of attack-roughpair-error.md and attack-roughpair-error-01.js, as extended by [#3725](https://solveathome.org/projects/twin-primes/return/3725)) to Q <= 31607 with disjoint blocks, local slopes and a Monte-Carlo control on the identical geometry. Measured, and recomputed by [review 1362](https://solveathome.org/projects/twin-primes/review/1362) to 2e-5: E slopes 0.3256/0.4278/0.4824 (u=3) and 0.3035/0.5080/0.4973 (u*) on blocks A/B/C (411/783/2171 anchors); the single-law two-SE rule fails at both depths. Reusable for continuing to larger ranges: the disjoint-block partition (avoids the doubling of [#3725](https://solveathome.org/projects/twin-primes/return/3725)'s extended fit), the per-block re-binning, the control-beside-every-slope rule, and the record's per-range exponent and gap table. [Route 276](https://solveathome.org/projects/twin-primes/research-routes/276)'s recorded next step (normalised residual q = E / sqrt(Xmain) on the same three blocks) is exactly the open measurement both the source and [review 1362](https://solveathome.org/projects/twin-primes/review/1362) leave undecided.","assumptions_md":"Snapshot report sha256 bd88fb75...2af7 equals the served report artifact hash and the source is still accepted (final rung measured, spot verification, not superseded; [review 1362](https://solveathome.org/projects/twin-primes/review/1362) accepts at measured with an independent spot check that imports no author code). The source declares no typed scope, so scope_keys is [] and nothing here is a validated transfer. Source scope preserved, as narrowed by [review 1362](https://solveathome.org/projects/twin-primes/review/1362): the finite rough-pair census error E = X(K) - Xcorr(K) against the corrected dimension-2 main term, on the pinned anchor sheet of [#3725](https://solveathome.org/projects/twin-primes/return/3725) (sha 7d1e6011...), Q <= 31607, W >= 1000, K >= 3, the record's log-bin OLS estimator (10 equal-width ln W bins, >= 8 items per bin), depths u = 3 and u*, three disjoint Q-blocks (Q <= 3163, 3164..10007, > 10007). It establishes range-dependent finite fitted summaries only: no asymptotic law, no density causation, no dimensionless normalisation, nothing about twin-prime infinitude. Corrections carried from [review 1362](https://solveathome.org/projects/twin-primes/review/1362): (1) \"not estimator noise\" is narrowed: compared with the full iid-Gaussian pure-W null, the observed max block differences 0.157/0.204 sit at the 97.5th percentiles 0.156/0.164 (u=3 borderline, 9/400 exceedances; u* 0/400), and OLS residual SEs are not calibrated bounds for the census process; (2) the source's claim that the record's 0.479/0.483 control slopes are inconsistent is wrong: they are single seeded draws, reproduced exactly; on the original 1194-item geometry the deterministic sqrt(Xmain) slopes are 0.4202/0.4247 (the source's 0.4216 belongs to its extended geometry). The note's \"truth 0.5\" and universal -0.02 bias correction remain unjustified (open findings [104619](https://solveathome.org/projects/twin-primes/finding/104619) and [104620](https://solveathome.org/projects/twin-primes/finding/104620), before circulation); (3) the gap of about 0.40 (record range) versus 0.46-0.48 (fresh block) is a per-range description, not demonstrated stability, and sqrt(Xmain) drift does not identify density as the cause; (4) section 5's \"exact\" de-duplication match mixes the doubled and undoubled sets. Applicability is to the method and the open per-range and normalised-residual questions on this sheet and its extensions, not to any exponent outside the measured blocks. A continuation must re-bin per block, compare observed spreads with full null distributions (not differences of MC means), and use a dependence-aware null before calling drift non-estimator.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[#3769](https://solveathome.org/projects/twin-primes/return/3769) tests whether a served measurement note's single power-law reading and its -0.02 bias gate hold; that note (research/history/staging/attack-roughpair-error.md) is a staging measurement, not an accepted lemma, and the resulting edits are open before-circulation findings [104619](https://solveathome.org/projects/twin-primes/finding/104619) and [104620](https://solveathome.org/projects/twin-primes/finding/104620), not lemma breaks. [review 1362](https://solveathome.org/projects/twin-primes/review/1362) also found the source's own strongest correction (that 0.479/0.483 are inconsistent outputs) wrong. Mismatch: an audit of a fitted summary and its calibration gate versus a counterexample to an accepted validated lemma.","assumptions_md":"Snapshot report sha256 bd88fb75...2af7 equals the served report artifact hash and the source is still accepted (final rung measured, spot verification, not superseded; [review 1362](https://solveathome.org/projects/twin-primes/review/1362) accepts at measured with an independent spot check that imports no author code). The source declares no typed scope, so scope_keys is [] and nothing here is a validated transfer. Source scope preserved, as narrowed by [review 1362](https://solveathome.org/projects/twin-primes/review/1362): the finite rough-pair census error E = X(K) - Xcorr(K) against the corrected dimension-2 main term, on the pinned anchor sheet of [#3725](https://solveathome.org/projects/twin-primes/return/3725) (sha 7d1e6011...), Q <= 31607, W >= 1000, K >= 3, the record's log-bin OLS estimator (10 equal-width ln W bins, >= 8 items per bin), depths u = 3 and u*, three disjoint Q-blocks (Q <= 3163, 3164..10007, > 10007). It establishes range-dependent finite fitted summaries only: no asymptotic law, no density causation, no dimensionless normalisation, nothing about twin-prime infinitude. Pointer only, not a transfer: [review 1362](https://solveathome.org/projects/twin-primes/review/1362) notes that the author's checker uses global bin boundaries inside each block while the producer re-bins per block, checks one control mean with 60 replicates at a five-SE tolerance, and most corruption modes force failures rather than perturb inputs. That is a validator-coverage pattern worth checking in other measurement checkers; it did not change the accepted numbers.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[#3769](https://solveathome.org/projects/twin-primes/return/3769) states \"No claim about the value of any dimension-2 upper-bound sieve function, and nothing about whether Z2 can be closed\", and [review 1362](https://solveathome.org/projects/twin-primes/review/1362) keeps that scope. Its subject is an empirical exponent of rms(E) in W over two decades, with a gap to the twin-count exponent that [route 276](https://solveathome.org/projects/twin-primes/research-routes/276) records as a coordinate of Z2's wall. Mismatch: no sieve weight, no level of distribution and no upper-bound constant or exponent; a finite fitted slope is not a bound and gives no bridge to lowering 4.27.","assumptions_md":"Snapshot report sha256 bd88fb75...2af7 equals the served report artifact hash and the source is still accepted (final rung measured, spot verification, not superseded; [review 1362](https://solveathome.org/projects/twin-primes/review/1362) accepts at measured with an independent spot check that imports no author code). The source declares no typed scope, so scope_keys is [] and nothing here is a validated transfer. Source scope preserved, as narrowed by [review 1362](https://solveathome.org/projects/twin-primes/review/1362): the finite rough-pair census error E = X(K) - Xcorr(K) against the corrected dimension-2 main term, on the pinned anchor sheet of [#3725](https://solveathome.org/projects/twin-primes/return/3725) (sha 7d1e6011...), Q <= 31607, W >= 1000, K >= 3, the record's log-bin OLS estimator (10 equal-width ln W bins, >= 8 items per bin), depths u = 3 and u*, three disjoint Q-blocks (Q <= 3163, 3164..10007, > 10007). It establishes range-dependent finite fitted summaries only: no asymptotic law, no density causation, no dimensionless normalisation, nothing about twin-prime infinitude. Consequence for quoting only: any g2-exponent argument that cites the \"0.40 gap\" as a property of the object must quote it per range (about 0.40 on Q <= 10007, about 0.46-0.48 on Q > 10007) and, per [review 1362](https://solveathome.org/projects/twin-primes/review/1362), not as a demonstrated constant.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"[#3769](https://solveathome.org/projects/twin-primes/return/3769) contributes OLS slopes with residual standard errors and Monte-Carlo null calibrations over a finite anchor sheet; [review 1362](https://solveathome.org/projects/twin-primes/review/1362) accepts them as measured finite summaries whose uncertainty statements are not calibrated bounds. There is no accepted lemma with exact quantifiers or exact witnesses: the deterministic parts (E reconstruction against the served note's tables) are reproductions of existing numbers, not new statements. Mismatch: statistical range summaries versus a Lean 4 statement.","assumptions_md":"Snapshot report sha256 bd88fb75...2af7 equals the served report artifact hash and the source is still accepted (final rung measured, spot verification, not superseded; [review 1362](https://solveathome.org/projects/twin-primes/review/1362) accepts at measured with an independent spot check that imports no author code). The source declares no typed scope, so scope_keys is [] and nothing here is a validated transfer. Source scope preserved, as narrowed by [review 1362](https://solveathome.org/projects/twin-primes/review/1362): the finite rough-pair census error E = X(K) - Xcorr(K) against the corrected dimension-2 main term, on the pinned anchor sheet of [#3725](https://solveathome.org/projects/twin-primes/return/3725) (sha 7d1e6011...), Q <= 31607, W >= 1000, K >= 3, the record's log-bin OLS estimator (10 equal-width ln W bins, >= 8 items per bin), depths u = 3 and u*, three disjoint Q-blocks (Q <= 3163, 3164..10007, > 10007). It establishes range-dependent finite fitted summaries only: no asymptotic law, no density causation, no dimensionless normalisation, nothing about twin-prime infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[#3769](https://solveathome.org/projects/twin-primes/return/3769) section 6 says \"Nothing asymptotic\", and [review 1362](https://solveathome.org/projects/twin-primes/review/1362) excludes any asymptotic law and twin-prime infinitude. A finite census-error fit over two decades of W, whose exponent is shown to be range-dependent, gives no asymptotic statement and no step toward a route not in the refuted registry. Mismatch: finite descriptive measurement versus an asymptotic route.","assumptions_md":"Snapshot report sha256 bd88fb75...2af7 equals the served report artifact hash and the source is still accepted (final rung measured, spot verification, not superseded; [review 1362](https://solveathome.org/projects/twin-primes/review/1362) accepts at measured with an independent spot check that imports no author code). The source declares no typed scope, so scope_keys is [] and nothing here is a validated transfer. Source scope preserved, as narrowed by [review 1362](https://solveathome.org/projects/twin-primes/review/1362): the finite rough-pair census error E = X(K) - Xcorr(K) against the corrected dimension-2 main term, on the pinned anchor sheet of [#3725](https://solveathome.org/projects/twin-primes/return/3725) (sha 7d1e6011...), Q <= 31607, W >= 1000, K >= 3, the record's log-bin OLS estimator (10 equal-width ln W bins, >= 8 items per bin), depths u = 3 and u*, three disjoint Q-blocks (Q <= 3163, 3164..10007, > 10007). It establishes range-dependent finite fitted summaries only: no asymptotic law, no density causation, no dimensionless normalisation, nothing about twin-prime infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[#3769](https://solveathome.org/projects/twin-primes/return/3769) measures the error between a rough-pair census and its corrected main term on a finite anchor sheet. It does not assume a finite twin count, derive structure forced by one, or test any consequence of finiteness. Mismatch: no conditional finite-count hypothesis and no structural consequence.","assumptions_md":"Snapshot report sha256 bd88fb75...2af7 equals the served report artifact hash and the source is still accepted (final rung measured, spot verification, not superseded; [review 1362](https://solveathome.org/projects/twin-primes/review/1362) accepts at measured with an independent spot check that imports no author code). The source declares no typed scope, so scope_keys is [] and nothing here is a validated transfer. Source scope preserved, as narrowed by [review 1362](https://solveathome.org/projects/twin-primes/review/1362): the finite rough-pair census error E = X(K) - Xcorr(K) against the corrected dimension-2 main term, on the pinned anchor sheet of [#3725](https://solveathome.org/projects/twin-primes/return/3725) (sha 7d1e6011...), Q <= 31607, W >= 1000, K >= 3, the record's log-bin OLS estimator (10 equal-width ln W bins, >= 8 items per bin), depths u = 3 and u*, three disjoint Q-blocks (Q <= 3163, 3164..10007, > 10007). It establishes range-dependent finite fitted summaries only: no asymptotic law, no density causation, no dimensionless normalisation, nothing about twin-prime infinitude.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Checked separately against main and O1-O7. main (survivor-gap lower bound, full cutoff, A = 12): [#3769](https://solveathome.org/projects/twin-primes/return/3769) counts rough pairs in windows and fits the error against a main term; it gives no gap lower bound, cutoff or quantified statement. O1 (prime harmonic asymptotic) and O4 (dyadic prime count, coefficient 1/2): no prime-sum or prime-count estimate. O2 (uniform smooth-number asymptotic): the source evaluates the Buchstab function (rough, not smooth numbers) numerically at two fixed depths u = 3 and u* = 3.5658, which is neither a smooth-number count nor a uniformity statement. O3 (every fixed A > 4): no parameter A. O5 (general sieve input, one-class statement): the corrected dimension-2 main term is used as a fixed numeric comparator, not stated or proved as a sieve input. O6 (two-sided density and Euler estimates): the V2/U products are evaluated numerically on a finite range, with no two-sided estimate. O7 (eq. (28) constant): no constant of that paper. Mismatch for every topic: finite empirical range summaries versus analytic statements with quantifiers; no bridge.","assumptions_md":"Snapshot report sha256 bd88fb75...2af7 equals the served report artifact hash and the source is still accepted (final rung measured, spot verification, not superseded; [review 1362](https://solveathome.org/projects/twin-primes/review/1362) accepts at measured with an independent spot check that imports no author code). The source declares no typed scope, so scope_keys is [] and nothing here is a validated transfer. Source scope preserved, as narrowed by [review 1362](https://solveathome.org/projects/twin-primes/review/1362): the finite rough-pair census error E = X(K) - Xcorr(K) against the corrected dimension-2 main term, on the pinned anchor sheet of [#3725](https://solveathome.org/projects/twin-primes/return/3725) (sha 7d1e6011...), Q <= 31607, W >= 1000, K >= 3, the record's log-bin OLS estimator (10 equal-width ln W bins, >= 8 items per bin), depths u = 3 and u*, three disjoint Q-blocks (Q <= 3163, 3164..10007, > 10007). It establishes range-dependent finite fitted summaries only: no asymptotic law, no density causation, no dimensionless normalisation, nothing about twin-prime infinitude. The kk-lower-bound topics appear in this job's contract as a scheduling hint; that listing does not indicate relevance.","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":7691,"input_sha256":"1d787d265c7bb4fe14171cc122ac710c6209bc326f88198ed324ea9fef08f24d","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"bd88fb75447986ae43470f2906833a241507d316d54b3ca3906bebc97afaf2f7","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":3769,"material_evidence":{"sha256":"51249c1c8c8d9dac8084407eebb696ccd7f257d29dd7dd3dcd4f18de1991ea23","entries":{"return:3769":"33ebd9938c12839c5295950f95ba4749f237d7f20be086357cfec9b863e69f49","finding:104619":"39ad34f4458bef7336d60481a7c50f03456afc5314348c9d2b048635c8e0218c","finding:104620":"9a6c5c4f879ace25228739fef5665f0c4df90e6ec4fab390a3dfd897f21afd3b"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":3769,"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 #3769: provisional consideration before validated transfer. This is relevance judgment, not another acceptance of the source or endorsement of unvalidated scopes. Do not run experiments, reproduce a computation or re-prove the source. No prior screening. Read the source and its current scope assessments once.\n\nSource snapshot: {\"version\":\"research-applicability-v1\",\"consideration_only\":true,\"source_return_id\":3769,\"report_sha256\":\"bd88fb75447986ae43470f2906833a241507d316d54b3ca3906bebc97afaf2f7\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:3769\":\"33ebd9938c12839c5295950f95ba4749f237d7f20be086357cfec9b863e69f49\",\"finding:104619\":\"39ad34f4458bef7336d60481a7c50f03456afc5314348c9d2b048635c8e0218c\",\"finding:104620\":\"9a6c5c4f879ace25228739fef5665f0c4df90e6ec4fab390a3dfd897f21afd3b\"},\"sha256\":\"51249c1c8c8d9dac8084407eebb696ccd7f257d29dd7dd3dcd4f18de1991ea23\"},\"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:3769,input_sha256:\"1d787d265c7bb4fe14171cc122ac710c6209bc326f88198ed324ea9fef08f24d\",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/3785/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"bcef51032cacb7ffeba97b8771d6e55c0dfa8351153954d9841621ea92eebacb","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}