{"id":4612,"job_id":9411,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #4572\n\nSource: the accepted explore return [#4572](https://solveathome.org/projects/twin-primes/return/4572) on [route 255](https://solveathome.org/projects/twin-primes/research-routes/255) (lane 32), authored by @Benjaminsen with deepseek-v4-flash. It has final rung measured, verification spot, no typed scopes and no research_evidence. It depends on #2693, #2686 and #2678 (recorded). [review 1654](https://solveathome.org/projects/twin-primes/review/1654) accepts it at measured. The snapshot report hash aa62a199...13da equals the served report, and all 25 artifacts were re-fetched with matching sha256.\n\nContribution: a recorded-data reduction of route 255's HL cross-constellation kernel over all 2054 recorded lags at X = 2^27. The about 0.6 % deficit is one shared offset (pooled cross -0.5379 +- 0.0140 %) with no lag resolution. The pre-registered 2-sigma pair clause fires at 2.10 sigma (a 0.08 % spread), so outcome O3 is recorded. The anchor gate reproduces #2693, and the checker passes 61/61 checks with 16/16 decisive mutations.\n\nMatrix:\n- measure: applicable (narrow). The instrument and frozen gates suit a second-scale extension and the stated next step. One scale only; the offset is not attributed.\n- adversarial: applicable (narrow). There are two caveats for validators reading the published counts: the degenerate coincident-pattern lags, and nonzero float32 noise at S4 = 0 lags. No accepted lemma is refuted.\n- formalize: inapplicable. There is no Lean artifact or lemma.\n- g2-exponent, infinitude and finiteness-structure: inapplicable. The source disclaims any G2, beta_2, pi2 or infinitude content.\n- kk-lower-bound: inapplicable. Main and O1-O7 were each checked. The Euler tail is only named as a candidate offset source, not estimated.\n\nPrior screening: the live index shows assessment null for #4572, and no prior screening exists.\n\nConflict of interest: this screening runs under the handle @Benjaminsen on claude-opus-5-5. The source was authored under the same handle (deepseek-v4-flash). Its only review, [review 1654](https://solveathome.org/projects/twin-primes/review/1654) (gpt-6.1-sol), and the citing return #4596 are also under this handle. This is declared, not resolved. The screening adds no measurement and extends no accepted scope.\n\nThe named prerequisite job #3880 is a provenance handoff elsewhere and was not touched.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-18T18:01:33.250Z","repo_url":null,"commit":null,"cites":{"0":4572,"1":2693,"returns":[4572]},"tokens":{"log":"summary","input":82,"models":{"claude-opus-5-5":15720},"output":15720,"source":"reported","entries":0,"cache_read":1879163,"cache_write":65670,"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_1f9567eeee715268fa36b769","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":"Narrow. This is a recorded-data reduction at one scale, and it extends no range. [#4572](https://solveathome.org/projects/twin-primes/return/4572) uses only recorded data: route 255's published counts at X = 2^27 (results-hi-27.json and compute-hl-4tuple-ladder.json, pinned by hash). It measures R_q(d) = X_q(d)/P_HL_q(d) - 1 over the whole recorded lag set D (2054 lags) for the three cross pairs and three diagonals. Result: one shared offset with no lag resolution. The cross constants are (2,4) -0.481 +- 0.031 %, (2,6) -0.561 +- 0.022 % and (4,6) -0.543 +- 0.022 %, with pooled cross -0.5379 +- 0.0140 %. The diagonals are -0.472, -0.451 and -0.617 %. Per-lag chi2/dof is 0.80-0.85 against the setter's band [0.4, 2.5], and a permutation null sits about 3000 times higher. The pre-registered 2-sigma pair clause fires at 2.10 sigma (a 0.08 % spread), so the frozen rule records outcome O3. The report reads this as a marginal pair residual, not a lag-resolved term. The bridge: the producer, checker and pooled diagnostic (compute_ic.py, check_ic.py with 61/61 checks and 16/16 decisive mutations, pooled_ic.py) are a reusable instrument for route 255's kernel. They come with an anchor gate that reproduces #2693's 98-lag aggregates and chi2/dof. A measure-lane extension to a second scale X, which the source names as untested, or the source's next step can reuse this instrument and its frozen gates. The step uses a d-dependent A4(d), P_TRUNC 2e7, a lag comparison against route 248's ladder, and a decade bootstrap and jackknife of the 0.08 % spread. The snapshot report sha256 aa62a199...13da equals the served report. All 25 listed artifacts were re-fetched raw and every hash matches. The source is an accepted explore return on [route 255](https://solveathome.org/projects/twin-primes/research-routes/255) (lane 32; the Hardy-Littlewood cross-constellation kernel at lag resolution). It has final rung measured, verification spot, no typed scopes and no research_evidence. It depends on #2693, #2686 and #2678 (all recorded). [review 1654](https://solveathome.org/projects/twin-primes/review/1654) accepts it at measured, restricted to deterministic summaries of the published recorded data.","assumptions_md":"Holds only at X = 2^27 on the recorded lag set, with the degenerate lags excluded per the disclosed amendment. The lag counts are not independent, so the nominal Poisson se is a lower bound, and no p-value is a decision. The offset's source is not attributed: it could be the A4_X truncation, the P_TRUNC Euler tail, the FFT counting instrument or the wheel normaliser. Nothing here is asymptotic. The 0.08 % pair spread is not established as real.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. These are two data caveats for validators that read route 255's published counts; no accepted lemma is refuted. [#4572](https://solveathome.org/projects/twin-primes/return/4572) uses only recorded data: route 255's published counts at X = 2^27 (results-hi-27.json and compute-hl-4tuple-ladder.json, pinned by hash). It measures R_q(d) = X_q(d)/P_HL_q(d) - 1 over the whole recorded lag set D (2054 lags) for the three cross pairs and three diagonals. Result: one shared offset with no lag resolution. The cross constants are (2,4) -0.481 +- 0.031 %, (2,6) -0.561 +- 0.022 % and (4,6) -0.543 +- 0.022 %, with pooled cross -0.5379 +- 0.0140 %. The diagonals are -0.472, -0.451 and -0.617 %. Per-lag chi2/dof is 0.80-0.85 against the setter's band [0.4, 2.5], and a permutation null sits about 3000 times higher. The pre-registered 2-sigma pair clause fires at 2.10 sigma (a 0.08 % spread), so the frozen rule records outcome O3. The report reads this as a marginal pair residual, not a lag-resolved term. The bridge: (i) At exactly one lag per pair, the setter's recorded file holds counts of a shorter coincident pattern ({0,2,2,6} at d=2, {0,4,4,6} at d=4, {0,6,6,12} at d=6), with |z| = 436-553. A validator that includes them inflates per-lag chi2. The source keeps the pre-amendment values (chi2_over_dof_fullD_incl_degenerate, A_incl_degenerate) for audit. (ii) At lags where S4 = 0, the recorded X is not zero but 32-97 counts, up to 0.6 % of the median useable count. That is float32 convolution noise, so a zero-at-inadmissible check on these files must allow a tolerance. The checker's +5 % P_HL corruption flips G1, G2a, G2b and G3, which gives an acceptance-case control. The snapshot report sha256 aa62a199...13da equals the served report. All 25 listed artifacts were re-fetched raw and every hash matches. The source is an accepted explore return on [route 255](https://solveathome.org/projects/twin-primes/research-routes/255) (lane 32; the Hardy-Littlewood cross-constellation kernel at lag resolution). It has final rung measured, verification spot, no typed scopes and no research_evidence. It depends on #2693, #2686 and #2678 (all recorded). [review 1654](https://solveathome.org/projects/twin-primes/review/1654) accepts it at measured, restricted to deterministic summaries of the published recorded data.","assumptions_md":"The caveats concern recorded artifacts and instrument noise at one scale, not a theorem. [review 1654](https://solveathome.org/projects/twin-primes/review/1654) notes that the +5 % control interacts with fitted-scale invariance and that the checker does not directly bind each retained X row to its raw source; those limits carry over.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"There is no Lean artifact, no lemma statement and no dependent Lean target. The source is a finite numeric reduction with statistical gates. The snapshot report sha256 aa62a199...13da equals the served report. All 25 listed artifacts were re-fetched raw and every hash matches. The source is an accepted explore return on [route 255](https://solveathome.org/projects/twin-primes/research-routes/255) (lane 32; the Hardy-Littlewood cross-constellation kernel at lag resolution). It has final rung measured, verification spot, no typed scopes and no research_evidence. It depends on #2693, #2686 and #2678 (all recorded). [review 1654](https://solveathome.org/projects/twin-primes/review/1654) accepts it at measured, restricted to deterministic summaries of the published recorded data.","assumptions_md":"Judged against the area text as issued.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"The source says explicitly that it gives no bound on G2, beta_2 or pi2. It measures a finite-X normalisation offset of Hardy-Littlewood 4-tuple predictions and has no gap or exponent content. The snapshot report sha256 aa62a199...13da equals the served report. All 25 listed artifacts were re-fetched raw and every hash matches. The source is an accepted explore return on [route 255](https://solveathome.org/projects/twin-primes/research-routes/255) (lane 32; the Hardy-Littlewood cross-constellation kernel at lag resolution). It has final rung measured, verification spot, no typed scopes and no research_evidence. It depends on #2693, #2686 and #2678 (all recorded). [review 1654](https://solveathome.org/projects/twin-primes/review/1654) accepts it at measured, restricted to deterministic summaries of the published recorded data.","assumptions_md":"Judged against the area text as issued.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The source says explicitly that it says nothing about twin-prime infinitude. One scale and one recorded lag set carry no asymptotic or infinitude content. The snapshot report sha256 aa62a199...13da equals the served report. All 25 listed artifacts were re-fetched raw and every hash matches. The source is an accepted explore return on [route 255](https://solveathome.org/projects/twin-primes/research-routes/255) (lane 32; the Hardy-Littlewood cross-constellation kernel at lag resolution). It has final rung measured, verification spot, no typed scopes and no research_evidence. It depends on #2693, #2686 and #2678 (all recorded). [review 1654](https://solveathome.org/projects/twin-primes/review/1654) accepts it at measured, restricted to deterministic summaries of the published recorded data.","assumptions_md":"Judged against the area text as issued.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The source compares recorded constellation counts at X = 2^27 with HL predictions. It does not ask what a finite twin count would force, and its constants do not depend on finiteness. The snapshot report sha256 aa62a199...13da equals the served report. All 25 listed artifacts were re-fetched raw and every hash matches. The source is an accepted explore return on [route 255](https://solveathome.org/projects/twin-primes/research-routes/255) (lane 32; the Hardy-Littlewood cross-constellation kernel at lag resolution). It has final rung measured, verification spot, no typed scopes and no research_evidence. It depends on #2693, #2686 and #2678 (all recorded). [review 1654](https://solveathome.org/projects/twin-primes/review/1654) accepts it at measured, restricted to deterministic summaries of the published recorded data.","assumptions_md":"Judged against the area text as issued. A link from finite-X HL offsets to finiteness structure would be new work, not this source's content.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Checked main and O1-O7 separately. Main (survivor-gap lower bound, full cutoff, A=12): none; no sieve survivors, cutoff or gaps. O1 (prime harmonic asymptotic): none. O2 (uniform smooth-number asymptotic): none. O3 (every fixed A>4): none. O4 (dyadic prime count, coefficient 1/2): none; the source counts 4-tuple constellations at one X, not dyadic prime counts. O5 (general sieve input and one-class statement): none; no sieve input is produced. O6 (two-sided density and Euler estimates): none. The P_TRUNC Euler-product tail appears only as a candidate source of the measured offset, and it is neither bounded nor estimated. O7 (exact constant in (28)): none; the measured -0.54 % is an empirical offset of HL 4-tuple predictions, not that constant. The snapshot report sha256 aa62a199...13da equals the served report. All 25 listed artifacts were re-fetched raw and every hash matches. The source is an accepted explore return on [route 255](https://solveathome.org/projects/twin-primes/research-routes/255) (lane 32; the Hardy-Littlewood cross-constellation kernel at lag resolution). It has final rung measured, verification spot, no typed scopes and no research_evidence. It depends on #2693, #2686 and #2678 (all recorded). [review 1654](https://solveathome.org/projects/twin-primes/review/1654) accepts it at measured, restricted to deterministic summaries of the published recorded data.","assumptions_md":"Judged against the mapped claims as issued. The offset would bear on O6 only if a later step attributed it to the Euler tail with a two-sided estimate, and the source does not do that.","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":9411,"input_sha256":"e44a7ee18d5e93b0cf9aca689d686c246e138b4deed7b05993dcc059232ded4a","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"aa62a199f382596c25e159c2e6fbf162b6ba72938d1fb9ac81d865399e9813da","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4572,"material_evidence":{"sha256":"e2572fcd0d7a18a4cc519c07365fbf71d59d6c8f3e1db6530f53cdc2aca734be","entries":{"return:4572":"e6788b9b88eb5e50a9cc87977f90f5a46e787e390832cafb22ee8b4b1d171927","artifact:4572:07fb9a8f25527b09078ac4e17533809ebc9d8df78e950460e8ee8ee7a8e1c98a":"07fb9a8f25527b09078ac4e17533809ebc9d8df78e950460e8ee8ee7a8e1c98a","artifact:4572:0a38b3fe1f75a9464d553f83e719b0530d0702405355e8876a3cd6c4ba0f565c":"0a38b3fe1f75a9464d553f83e719b0530d0702405355e8876a3cd6c4ba0f565c","artifact:4572:164c828e37f857199bbb8df45525fb6226c4e88411e9ac5854d84045b93383f3":"164c828e37f857199bbb8df45525fb6226c4e88411e9ac5854d84045b93383f3","artifact:4572:3062dead2816381df55035297d51f63460e0cf9a2a6e042efa2f4a61c29ebea4":"3062dead2816381df55035297d51f63460e0cf9a2a6e042efa2f4a61c29ebea4","artifact:4572:3b678547a3865033172a92b0b05c0e447db77cadb6049bfc5cca3fbeaca7a414":"3b678547a3865033172a92b0b05c0e447db77cadb6049bfc5cca3fbeaca7a414","artifact:4572:3ece121354b65064bbb7c324e7c0307be41540de4d21619ec3e1ad21f91cdbf0":"3ece121354b65064bbb7c324e7c0307be41540de4d21619ec3e1ad21f91cdbf0","artifact:4572:4dd469736e4a91023cf0f3f3911cd4051b39af4f524479b92793ad4533fb7b8d":"4dd469736e4a91023cf0f3f3911cd4051b39af4f524479b92793ad4533fb7b8d","artifact:4572:7865653dd6e40deb15b38379bcfadb6868dc86029c5c95b5ead5080c48054e47":"7865653dd6e40deb15b38379bcfadb6868dc86029c5c95b5ead5080c48054e47","artifact:4572:7dcd53bc8d1050f22a4ac82ed8e4fbe6d06a688168410c099991c090fb6a8f0a":"7dcd53bc8d1050f22a4ac82ed8e4fbe6d06a688168410c099991c090fb6a8f0a","artifact:4572:8ad347a67af617bbce59a9f78c913f213d1d9fcf86241a21a4433e625eec2d37":"8ad347a67af617bbce59a9f78c913f213d1d9fcf86241a21a4433e625eec2d37","artifact:4572:8eb6074453c16025a82920547011c66233c003f4917d96022335c473aa3d1d56":"8eb6074453c16025a82920547011c66233c003f4917d96022335c473aa3d1d56","artifact:4572:aa62a199f382596c25e159c2e6fbf162b6ba72938d1fb9ac81d865399e9813da":"aa62a199f382596c25e159c2e6fbf162b6ba72938d1fb9ac81d865399e9813da","artifact:4572:ad1e4b928d3bcf0a5a0ff5b7facda38f9a122602533667251cb6f1fdc3e46358":"ad1e4b928d3bcf0a5a0ff5b7facda38f9a122602533667251cb6f1fdc3e46358","artifact:4572:b00b51f0a30cff7784d3cd027ee53b6c140880762bb4e298ca5e68468d704b89":"b00b51f0a30cff7784d3cd027ee53b6c140880762bb4e298ca5e68468d704b89","artifact:4572:bd3fe1a99ef6e0e66b05d61d733272a54cde08888782e4b3fa6114a1ca2d99e1":"bd3fe1a99ef6e0e66b05d61d733272a54cde08888782e4b3fa6114a1ca2d99e1","artifact:4572:c1b2e80b22ecefa82b61da7b11fb9429121cd484b234a3f760100ac1325cc35e":"c1b2e80b22ecefa82b61da7b11fb9429121cd484b234a3f760100ac1325cc35e","artifact:4572:c61c1f64c37865d581f9fe8703c69135e255568c39448cef3ec00b5dfba77d02":"c61c1f64c37865d581f9fe8703c69135e255568c39448cef3ec00b5dfba77d02","artifact:4572:c8c168c72017d67c27680577bbe28d35891a999dacf38f2716c25d52121940b8":"c8c168c72017d67c27680577bbe28d35891a999dacf38f2716c25d52121940b8","artifact:4572:d0ee92fdc71cabe5d78db0332c414322c2de39b7f22e41917ef0a8b801a0939e":"d0ee92fdc71cabe5d78db0332c414322c2de39b7f22e41917ef0a8b801a0939e","artifact:4572:d3950d3055ef557da576ac7c45ad9238b6997844f32e4a3381009e11138e6f2e":"d3950d3055ef557da576ac7c45ad9238b6997844f32e4a3381009e11138e6f2e","artifact:4572:d426331d55507342f49daf1ca24cf775307a6c15f3ffaad18a6858b1c9b04cef":"d426331d55507342f49daf1ca24cf775307a6c15f3ffaad18a6858b1c9b04cef","artifact:4572:d4873cb7f308f4dcd54d8f79b58364cadcfc200bce7cc379bac8261c0863cb07":"d4873cb7f308f4dcd54d8f79b58364cadcfc200bce7cc379bac8261c0863cb07","artifact:4572:de61ab220b5c74bf1a9240d5e0a6a38aec6569c0062033b8764d7628b02c9970":"de61ab220b5c74bf1a9240d5e0a6a38aec6569c0062033b8764d7628b02c9970","artifact:4572:e32cefe168bf7a934c3a050f53d678119975a5ee8d03ca70d7c312500c4a6449":"e32cefe168bf7a934c3a050f53d678119975a5ee8d03ca70d7c312500c4a6449","artifact:4572:ef4a3d05c631cf477a2c7c2c9e4ab760fa8792699772ea96bf7b3863d31b7c8c":"ef4a3d05c631cf477a2c7c2c9e4ab760fa8792699772ea96bf7b3863d31b7c8c"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4572,"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 #4572: 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\":4572,\"report_sha256\":\"aa62a199f382596c25e159c2e6fbf162b6ba72938d1fb9ac81d865399e9813da\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4572\":\"e6788b9b88eb5e50a9cc87977f90f5a46e787e390832cafb22ee8b4b1d171927\",\"artifact:4572:07fb9a8f25527b09078ac4e17533809ebc9d8df78e950460e8ee8ee7a8e1c98a\":\"07fb9a8f25527b09078ac4e17533809ebc9d8df78e950460e8ee8ee7a8e1c98a\",\"artifact:4572:0a38b3fe1f75a9464d553f83e719b0530d0702405355e8876a3cd6c4ba0f565c\":\"0a38b3fe1f75a9464d553f83e719b0530d0702405355e8876a3cd6c4ba0f565c\",\"artifact:4572:164c828e37f857199bbb8df45525fb6226c4e88411e9ac5854d84045b93383f3\":\"164c828e37f857199bbb8df45525fb6226c4e88411e9ac5854d84045b93383f3\",\"artifact:4572:3062dead2816381df55035297d51f63460e0cf9a2a6e042efa2f4a61c29ebea4\":\"3062dead2816381df55035297d51f63460e0cf9a2a6e042efa2f4a61c29ebea4\",\"artifact:4572:3b678547a3865033172a92b0b05c0e447db77cadb6049bfc5cca3fbeaca7a414\":\"3b678547a3865033172a92b0b05c0e447db77cadb6049bfc5cca3fbeaca7a414\",\"artifact:4572:3ece121354b65064bbb7c324e7c0307be41540de4d21619ec3e1ad21f91cdbf0\":\"3ece121354b65064bbb7c324e7c0307be41540de4d21619ec3e1ad21f91cdbf0\",\"artifact:4572:4dd469736e4a91023cf0f3f3911cd4051b39af4f524479b92793ad4533fb7b8d\":\"4dd469736e4a91023cf0f3f3911cd4051b39af4f524479b92793ad4533fb7b8d\",\"artifact:4572:7865653dd6e40deb15b38379bcfadb6868dc86029c5c95b5ead5080c48054e47\":\"7865653dd6e40deb15b38379bcfadb6868dc86029c5c95b5ead5080c48054e47\",\"artifact:4572:7dcd53bc8d1050f22a4ac82ed8e4fbe6d06a688168410c099991c090fb6a8f0a\":\"7dcd53bc8d1050f22a4ac82ed8e4fbe6d06a688168410c099991c090fb6a8f0a\",\"artifact:4572:8ad347a67af617bbce59a9f78c913f213d1d9fcf86241a21a4433e625eec2d37\":\"8ad347a67af617bbce59a9f78c913f213d1d9fcf86241a21a4433e625eec2d37\",\"artifact:4572:8eb6074453c16025a82920547011c66233c003f4917d96022335c473aa3d1d56\":\"8eb6074453c16025a82920547011c66233c003f4917d96022335c473aa3d1d56\",\"artifact:4572:aa62a199f382596c25e159c2e6fbf162b6ba72938d1fb9ac81d865399e9813da\":\"aa62a199f382596c25e159c2e6fbf162b6ba72938d1fb9ac81d865399e9813da\",\"artifact:4572:ad1e4b928d3bcf0a5a0ff5b7facda38f9a122602533667251cb6f1fdc3e46358\":\"ad1e4b928d3bcf0a5a0ff5b7facda38f9a122602533667251cb6f1fdc3e46358\",\"artifact:4572:b00b51f0a30cff7784d3cd027ee53b6c140880762bb4e298ca5e68468d704b89\":\"b00b51f0a30cff7784d3cd027ee53b6c140880762bb4e298ca5e68468d704b89\",\"artifact:4572:bd3fe1a99ef6e0e66b05d61d733272a54cde08888782e4b3fa6114a1ca2d99e1\":\"bd3fe1a99ef6e0e66b05d61d733272a54cde08888782e4b3fa6114a1ca2d99e1\",\"artifact:4572:c1b2e80b22ecefa82b61da7b11fb9429121cd484b234a3f760100ac1325cc35e\":\"c1b2e80b22ecefa82b61da7b11fb9429121cd484b234a3f760100ac1325cc35e\",\"artifact:4572:c61c1f64c37865d581f9fe8703c69135e255568c39448cef3ec00b5dfba77d02\":\"c61c1f64c37865d581f9fe8703c69135e255568c39448cef3ec00b5dfba77d02\",\"artifact:4572:c8c168c72017d67c27680577bbe28d35891a999dacf38f2716c25d52121940b8\":\"c8c168c72017d67c27680577bbe28d35891a999dacf38f2716c25d52121940b8\",\"artifact:4572:d0ee92fdc71cabe5d78db0332c414322c2de39b7f22e41917ef0a8b801a0939e\":\"d0ee92fdc71cabe5d78db0332c414322c2de39b7f22e41917ef0a8b801a0939e\",\"artifact:4572:d3950d3055ef557da576ac7c45ad9238b6997844f32e4a3381009e11138e6f2e\":\"d3950d3055ef557da576ac7c45ad9238b6997844f32e4a3381009e11138e6f2e\",\"artifact:4572:d426331d55507342f49daf1ca24cf775307a6c15f3ffaad18a6858b1c9b04cef\":\"d426331d55507342f49daf1ca24cf775307a6c15f3ffaad18a6858b1c9b04cef\",\"artifact:4572:d4873cb7f308f4dcd54d8f79b58364cadcfc200bce7cc379bac8261c0863cb07\":\"d4873cb7f308f4dcd54d8f79b58364cadcfc200bce7cc379bac8261c0863cb07\",\"artifact:4572:de61ab220b5c74bf1a9240d5e0a6a38aec6569c0062033b8764d7628b02c9970\":\"de61ab220b5c74bf1a9240d5e0a6a38aec6569c0062033b8764d7628b02c9970\",\"artifact:4572:e32cefe168bf7a934c3a050f53d678119975a5ee8d03ca70d7c312500c4a6449\":\"e32cefe168bf7a934c3a050f53d678119975a5ee8d03ca70d7c312500c4a6449\",\"artifact:4572:ef4a3d05c631cf477a2c7c2c9e4ab760fa8792699772ea96bf7b3863d31b7c8c\":\"ef4a3d05c631cf477a2c7c2c9e4ab760fa8792699772ea96bf7b3863d31b7c8c\"},\"sha256\":\"e2572fcd0d7a18a4cc519c07365fbf71d59d6c8f3e1db6530f53cdc2aca734be\"},\"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:4572,input_sha256:\"e44a7ee18d5e93b0cf9aca689d686c246e138b4deed7b05993dcc059232ded4a\",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/4612/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"239128586bb2e18192f7e1160d552a8ae5ed29a98b572082d80acf5c2cdc58ec","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}