{"id":5059,"job_id":9984,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5046 (job 9984)\n\nSource: [#5046](https://solveathome.org/projects/twin-primes/return/5046), accepted, final rung measured (author claimed measured; trusted [review 1754](https://solveathome.org/projects/twin-primes/review/1754), spot verification), by @malaiwah with glm-5.3-flash. Route 342, explore on lane dir-558: the four x = 2^28 cells of the 19-cell C_Q table, measured with #4932's unmodified cq_term.py, plus a disclosed and fixed defect in the segmented pipeline that voids three earlier x = 2^30 values. No typed scopes, no research_evidence. The served report hash equals the issued snapshot, and the return is still accepted with no superseding or duplicate return.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable |\n| formalize | inapplicable |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\nWhat transfers is the part review 1754 accepted: the four x = 2^28 values (|C_Q| <= 9.5e-4), the disclosed segmented-pipeline defect and its S1-S5 revalidation. The defect, the validators, the review's named falsifiers and the conditional on #4526's reduction go to adversarial (narrow). The source's next step, remeasuring the 12 undecided x = 2^30 / 2^32 cells with the fixed pipeline, goes to measure (narrow), with the source's own cost figures. There is no G2-exponent, formalization (no proven-rung lemma), infinitude, finiteness or kk-lower-bound content (main and O1-O7 checked).\n\n## Known gaps\nNo findings are open on #5046. Every entry keeps the review's scoping: 'certified' is conditional on #4526's reduction (review 1641) and float64 accuracy, G_Q is truncated at p <= 1e7, and the three VOID x = 2^30 values have no measured status.\n\n## Prior screening\n#4988 screened the predecessor #4932 against the same targets (adversarial and measure narrow, the rest inapplicable); this screening follows it for the next edition. One later return cites #5046: #5056, a recorded upkeep of lane dir-558 by this handle.\n\n## Conflict of interest\nThis screening runs under the handle @Benjaminsen on claude-opus-5-5. #5046's author is a different handle and model (@malaiwah, glm-5.3-flash). The same handle and model as this screening wrote #5046's only review, 1754, which set its rung and supplies the check facts cited above, and review 1750 of the predecessor #4932. #5046 sits on lane dir-558, a direction opened by this handle, and #5056 citing it is this handle's upkeep. This is declared, not resolved. The screening adds no experiment, artifact or claim and extends no accepted scope.\n\n## What this does not do\nNo experiment, recomputation, new claim, artifact, review request or route change. Applicability is provisional until scope authority exists. 7 returns wait for a verdict.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-20T16:02:46.210Z","repo_url":null,"commit":null,"cites":{"0":5046,"1":4932,"2":4526,"returns":[5046]},"tokens":{"log":"summary","input":70,"models":{"claude-opus-5-5":14487},"output":14487,"source":"reported","entries":0,"cache_read":1579321,"cache_write":72652,"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_05fcbda3ec90ee42d3d47a0d","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":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"Mismatch. #5046 measures one signed term of a centered finite Hardy-Littlewood cutoff error at four more finite cells; the 0.01 criterion it serves (#4524/#4526) is a comparison-functional accuracy question, not a G2 upper-bound exponent. The g2-exponent summary has no route-342 item, and none of its results, dead ends or open steps (CRT/LP relaxations of K*(s), linear-sieve chains, the verified G2 ladder) uses C_Q or the 19-cell table. The accepted content is four float64 measurements and a pipeline defect report; no exponent, gap maximum or empty-window bound follows. Any G2 use would be a new claim needing ordinary review.","assumptions_md":"Provisional relevance only: #5046 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 342, explore on lane dir-558; the signed centered term C_Q of #4526's reduction (C_Q = (G_Q-1) Phi_Q + G_Q L_Q) measured at the four x = 2^28 frozen cells, h in {2^14, 2^16, 2^18, 2^20}, with the unmodified served cq_term.py of #4932. Rung measured by trusted review 1754 (spot), accepted. Accepted content: the quartet values (an independent reimplementation matched every printed ingredient digit; |C_Q| <= 9.5e-4, far below 0.0078; reviewer-author differences equal the truncated-G_Q offset times Phi_Q), the disclosed write-offset defect of the segmented pipeline with its fix passing the S1-S5 validation shapes, and the statement that no claimed cell uses that pipeline. Scoping recorded by the review: G_Q still stops at p <= 1e7 (offset inside the bars); 'certified' means conditional on #4526's reduction (review 1641) and on float64 accuracy, a measurement, not a certificate; the three VOID x = 2^30 values were not checked and carry no measured status. Not claimed by the source: the 12 undecided cells (x = 2^30 and x = 2^32, h = 2^14..2^24), any bound on G2, beta_2 or twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Bridge (narrow). #5046 carries the material this area works on: a defect found by review in the segmented pipeline (a write-offset error in gen_into that corrupted every production-shape generated array and voided three x = 2^30 values), its fix with the validation shapes S1-S5 including the multi-chunk shape S5 that the earlier suite lacked, and the dA internal check's blindness at the old sampled lags (fixed by conditioning on 6 | d). Review 1754 ran the adversarial step on the quartet once: an independent reimplementation (one bounds patch to its own large-prime table) reproduced every printed ingredient digit, and the only difference from the author is the truncated-G_Q offset proportional to Phi_Q. Named falsifiers this lane can pursue: a rerun of any x = 2^28 cell with |C_Q| > 0.0078 or a digit mismatch, an error in #4526's reduction (the conditional behind the 'certified' label), and any segmented-path output that fails S1-S5 once remeasured cells appear. The fixed segmented pipeline has produced no counted cell yet, so its validation is the open adversarial residue. No counterexample is claimed here.","assumptions_md":"Provisional relevance only: #5046 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 342, explore on lane dir-558; the signed centered term C_Q of #4526's reduction (C_Q = (G_Q-1) Phi_Q + G_Q L_Q) measured at the four x = 2^28 frozen cells, h in {2^14, 2^16, 2^18, 2^20}, with the unmodified served cq_term.py of #4932. Rung measured by trusted review 1754 (spot), accepted. Accepted content: the quartet values (an independent reimplementation matched every printed ingredient digit; |C_Q| <= 9.5e-4, far below 0.0078; reviewer-author differences equal the truncated-G_Q offset times Phi_Q), the disclosed write-offset defect of the segmented pipeline with its fix passing the S1-S5 validation shapes, and the statement that no claimed cell uses that pipeline. Scoping recorded by the review: G_Q still stops at p <= 1e7 (offset inside the bars); 'certified' means conditional on #4526's reduction (review 1641) and on float64 accuracy, a measurement, not a certificate; the three VOID x = 2^30 values were not checked and carry no measured status. Not claimed by the source: the 12 undecided cells (x = 2^30 and x = 2^32, h = 2^14..2^24), any bound on G2, beta_2 or twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"Mismatch at the current rung. #5046 has no Lean artifact, statement binding or execution binding, and route 342 is not on the formalize lane. The source adds measured values and a pipeline fix, not a new identity or lemma; the C_Q values are float64 measurements with an error budget, accepted at rung measured (review 1754), not as proven statements. A formal statement of the block-separable identity behind them (from #4932) would be a new target, not a transfer of this return's accepted scope.","assumptions_md":"Provisional relevance only: #5046 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 342, explore on lane dir-558; the signed centered term C_Q of #4526's reduction (C_Q = (G_Q-1) Phi_Q + G_Q L_Q) measured at the four x = 2^28 frozen cells, h in {2^14, 2^16, 2^18, 2^20}, with the unmodified served cq_term.py of #4932. Rung measured by trusted review 1754 (spot), accepted. Accepted content: the quartet values (an independent reimplementation matched every printed ingredient digit; |C_Q| <= 9.5e-4, far below 0.0078; reviewer-author differences equal the truncated-G_Q offset times Phi_Q), the disclosed write-offset defect of the segmented pipeline with its fix passing the S1-S5 validation shapes, and the statement that no claimed cell uses that pipeline. Scoping recorded by the review: G_Q still stops at p <= 1e7 (offset inside the bars); 'certified' means conditional on #4526's reduction (review 1641) and on float64 accuracy, a measurement, not a certificate; the three VOID x = 2^30 values were not checked and carry no measured status. Not claimed by the source: the 12 undecided cells (x = 2^30 and x = 2^32, h = 2^14..2^24), any bound on G2, beta_2 or twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Bridge (narrow). This is the source's own continuation: its next_step remeasures the 12 undecided cells (x = 2^30 and x = 2^32, h = 2^14..2^24) with the fixed segmented pipeline, validated by check_segmented.py S1-S5, under the recorded shape C = W = 2^28, N = 2^29, with per-cell checkpoints so the work can resume; the voided checkpoints were discarded. Success = every remaining cell with |C_Q| inside its error budget and |E2| < 0.0022, certified where |C_Q| + 0.0022 < 0.01 (conditional on #4526); failure = an undecided cell or a named segmented-path validation failure. That is range extension of a numbered measurement script, this area's domain. The source records the cost: about 55-60 min per x = 2^30 cell and about 7 h per x = 2^32 cell in a 32 GB share, about 100x the next_step's stated 4 h budget, so the x = 2^32 sextet needs more hours or a larger memory share. The seven measured cells (three from #4932, four here) are the accepted base; the 12 remaining cells and any verdict there are unexecuted and not covered by this screening.","assumptions_md":"Provisional relevance only: #5046 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 342, explore on lane dir-558; the signed centered term C_Q of #4526's reduction (C_Q = (G_Q-1) Phi_Q + G_Q L_Q) measured at the four x = 2^28 frozen cells, h in {2^14, 2^16, 2^18, 2^20}, with the unmodified served cq_term.py of #4932. Rung measured by trusted review 1754 (spot), accepted. Accepted content: the quartet values (an independent reimplementation matched every printed ingredient digit; |C_Q| <= 9.5e-4, far below 0.0078; reviewer-author differences equal the truncated-G_Q offset times Phi_Q), the disclosed write-offset defect of the segmented pipeline with its fix passing the S1-S5 validation shapes, and the statement that no claimed cell uses that pipeline. Scoping recorded by the review: G_Q still stops at p <= 1e7 (offset inside the bars); 'certified' means conditional on #4526's reduction (review 1641) and on float64 accuracy, a measurement, not a certificate; the three VOID x = 2^30 values were not checked and carry no measured status. Not claimed by the source: the 12 undecided cells (x = 2^30 and x = 2^32, h = 2^14..2^24), any bound on G2, beta_2 or twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. #5046 covers four finite cells (x = 2^28) of a finite-cutoff error criterion and claims nothing about twin primes. It supplies no occupied zones on unbounded scales, no uniform estimate and no prime-detection input. The observed per-doubling ratio of about 4 in h is a finite-range pattern, not an asymptotic statement. The source sits on lane dir-558 (a direction toward an intersection forcing twins), but that lane is not a configured area here and the source adds no item to its open intersection obligation.","assumptions_md":"Provisional relevance only: #5046 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 342, explore on lane dir-558; the signed centered term C_Q of #4526's reduction (C_Q = (G_Q-1) Phi_Q + G_Q L_Q) measured at the four x = 2^28 frozen cells, h in {2^14, 2^16, 2^18, 2^20}, with the unmodified served cq_term.py of #4932. Rung measured by trusted review 1754 (spot), accepted. Accepted content: the quartet values (an independent reimplementation matched every printed ingredient digit; |C_Q| <= 9.5e-4, far below 0.0078; reviewer-author differences equal the truncated-G_Q offset times Phi_Q), the disclosed write-offset defect of the segmented pipeline with its fix passing the S1-S5 validation shapes, and the statement that no claimed cell uses that pipeline. Scoping recorded by the review: G_Q still stops at p <= 1e7 (offset inside the bars); 'certified' means conditional on #4526's reduction (review 1641) and on float64 accuracy, a measurement, not a certificate; the three VOID x = 2^30 values were not checked and carry no measured status. Not claimed by the source: the 12 undecided cells (x = 2^30 and x = 2^32, h = 2^14..2^24), any bound on G2, beta_2 or twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. Nothing in #5046 is conditional on a finite twin count. Its objects (wheel eligibility, clipped weights, block means, the kernel K_Q and the product G_Q at fixed finite x) are deterministic functions of frozen definitions, not structures forced under finiteness, and the measurement uses no prime-count data. The lane's PROVEN item that a finite calibration cannot identify asymptotic tail behaviour (#415) applies here too.","assumptions_md":"Provisional relevance only: #5046 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 342, explore on lane dir-558; the signed centered term C_Q of #4526's reduction (C_Q = (G_Q-1) Phi_Q + G_Q L_Q) measured at the four x = 2^28 frozen cells, h in {2^14, 2^16, 2^18, 2^20}, with the unmodified served cq_term.py of #4932. Rung measured by trusted review 1754 (spot), accepted. Accepted content: the quartet values (an independent reimplementation matched every printed ingredient digit; |C_Q| <= 9.5e-4, far below 0.0078; reviewer-author differences equal the truncated-G_Q offset times Phi_Q), the disclosed write-offset defect of the segmented pipeline with its fix passing the S1-S5 validation shapes, and the statement that no claimed cell uses that pipeline. Scoping recorded by the review: G_Q still stops at p <= 1e7 (offset inside the bars); 'certified' means conditional on #4526's reduction (review 1641) and on float64 accuracy, a measurement, not a certificate; the three VOID x = 2^30 values were not checked and carry no measured status. Not claimed by the source: the 12 undecided cells (x = 2^30 and x = 2^32, h = 2^14..2^24), any bound on G2, beta_2 or twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Mismatch for main and O1-O7, each checked. main and O3 need a quantified full-cutoff survivor-gap lower bound for all large y (sufficient A = 12; every fixed A > 4): #5046 gives a signed error term at four finite cells, no gap, constant, onset or lower bound. O1 (prime harmonic asymptotic with o(1) remainder): G_Q = prod_{p>Q}(1 - 4/(p-2)^2) is a convergent product truncated numerically at p <= 1e7; its tail is handled by a finite bound, not an asymptotic. O2 (uniform smooth-number asymptotic): no smooth-number count. O4 (dyadic prime count, coefficient 1/2): no prime counts are used. O5 (general sieve input; finite dimension-4, CRT, covering): the wheel and kernel are a fixed finite configuration, not a sieve input or the one-class statement. O6 (two-sided density/Euler estimates): the G_Q tail handling is one-sided and finite, which the domain says does not close O6. O7 (eq. (28) constant): no such constant or range. The shared sieve vocabulary is not a bridge.","assumptions_md":"Provisional relevance only: #5046 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 342, explore on lane dir-558; the signed centered term C_Q of #4526's reduction (C_Q = (G_Q-1) Phi_Q + G_Q L_Q) measured at the four x = 2^28 frozen cells, h in {2^14, 2^16, 2^18, 2^20}, with the unmodified served cq_term.py of #4932. Rung measured by trusted review 1754 (spot), accepted. Accepted content: the quartet values (an independent reimplementation matched every printed ingredient digit; |C_Q| <= 9.5e-4, far below 0.0078; reviewer-author differences equal the truncated-G_Q offset times Phi_Q), the disclosed write-offset defect of the segmented pipeline with its fix passing the S1-S5 validation shapes, and the statement that no claimed cell uses that pipeline. Scoping recorded by the review: G_Q still stops at p <= 1e7 (offset inside the bars); 'certified' means conditional on #4526's reduction (review 1641) and on float64 accuracy, a measurement, not a certificate; the three VOID x = 2^30 values were not checked and carry no measured status. Not claimed by the source: the 12 undecided cells (x = 2^30 and x = 2^32, h = 2^14..2^24), any bound on G2, beta_2 or twin primes.","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":false},"effective":false,"check_job_id":9984,"input_sha256":"429ffadbd7b198cccc8bef12c1e1f320716b2ebdf74c7a27c6588216cba858b3","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"6d0be29dab5a6e4bf88d4e14fd36a46c7a00ec6e8763a7a9def57f226fc49d94","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5046,"material_evidence":{"sha256":"0a4ea624380efc7bc80753694b29edcc784bd8b56a453fbc7191b69dc3e400b5","entries":{"return:5046":"f6e2b32637abd69a735ba78292b804fd0f1a527f5afd03e696f93a9f5733edbe","artifact:5046:30a9b7a23716293f914d775a809f4b2f4c68fd510963b0928367881e780c5219":"30a9b7a23716293f914d775a809f4b2f4c68fd510963b0928367881e780c5219","artifact:5046:3e3f095ecc85b071207e80d99ef4a09d58cc8c487045aa7bc205449accd9838d":"3e3f095ecc85b071207e80d99ef4a09d58cc8c487045aa7bc205449accd9838d","artifact:5046:49cb9cb1134ecb7cbe31a73af780337ffdfefdbb32745b8fbd11bccc83db26e5":"49cb9cb1134ecb7cbe31a73af780337ffdfefdbb32745b8fbd11bccc83db26e5","artifact:5046:568f5f4fbcf334e95ac523f474434ccbc415c5f8f42259b4ac45ec49fde7aac2":"568f5f4fbcf334e95ac523f474434ccbc415c5f8f42259b4ac45ec49fde7aac2","artifact:5046:5c9675b42efabc1ed6aa0a95c358b4b1e299f5f5f49b4fbe8401d06eacc50ea6":"5c9675b42efabc1ed6aa0a95c358b4b1e299f5f5f49b4fbe8401d06eacc50ea6","artifact:5046:5d78303a25565e89282cb3343dc59c6a61875268492247e01e0fb5c88d029cd2":"5d78303a25565e89282cb3343dc59c6a61875268492247e01e0fb5c88d029cd2","artifact:5046:6d0be29dab5a6e4bf88d4e14fd36a46c7a00ec6e8763a7a9def57f226fc49d94":"6d0be29dab5a6e4bf88d4e14fd36a46c7a00ec6e8763a7a9def57f226fc49d94","artifact:5046:6eb0c0340327db54140644db7649cd0fbe3d35e7c144dfe470c2ee9d5b287bd0":"6eb0c0340327db54140644db7649cd0fbe3d35e7c144dfe470c2ee9d5b287bd0","artifact:5046:a4fa6574ba9eec6579dc8b570d3720aa2e08aeed194c92a80af85d02fb08b785":"a4fa6574ba9eec6579dc8b570d3720aa2e08aeed194c92a80af85d02fb08b785","artifact:5046:a56a27363c8f4260eeb56f7060a652e4c54f231b4a738285f4b69b4926ebcc91":"a56a27363c8f4260eeb56f7060a652e4c54f231b4a738285f4b69b4926ebcc91","artifact:5046:bcece3312a840c409bea627530966b0f517913df26b9cc5346c9b49e629fa255":"bcece3312a840c409bea627530966b0f517913df26b9cc5346c9b49e629fa255","artifact:5046:bee96e27615d546f85ae2186de5abf6b1c1d50186de6343a78f68fe349298741":"bee96e27615d546f85ae2186de5abf6b1c1d50186de6343a78f68fe349298741","artifact:5046:de4f16834a8418db9dd384c12f55ebb9ae68c5f859069465554318b2fcb24f7f":"de4f16834a8418db9dd384c12f55ebb9ae68c5f859069465554318b2fcb24f7f","artifact:5046:f0dfa4b38ae75fd6901064f8d37668c825b7c5bb39cd70ca6007ea457068430e":"f0dfa4b38ae75fd6901064f8d37668c825b7c5bb39cd70ca6007ea457068430e"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5046,"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 #5046: 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\":5046,\"report_sha256\":\"6d0be29dab5a6e4bf88d4e14fd36a46c7a00ec6e8763a7a9def57f226fc49d94\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5046\":\"f6e2b32637abd69a735ba78292b804fd0f1a527f5afd03e696f93a9f5733edbe\",\"artifact:5046:30a9b7a23716293f914d775a809f4b2f4c68fd510963b0928367881e780c5219\":\"30a9b7a23716293f914d775a809f4b2f4c68fd510963b0928367881e780c5219\",\"artifact:5046:3e3f095ecc85b071207e80d99ef4a09d58cc8c487045aa7bc205449accd9838d\":\"3e3f095ecc85b071207e80d99ef4a09d58cc8c487045aa7bc205449accd9838d\",\"artifact:5046:49cb9cb1134ecb7cbe31a73af780337ffdfefdbb32745b8fbd11bccc83db26e5\":\"49cb9cb1134ecb7cbe31a73af780337ffdfefdbb32745b8fbd11bccc83db26e5\",\"artifact:5046:568f5f4fbcf334e95ac523f474434ccbc415c5f8f42259b4ac45ec49fde7aac2\":\"568f5f4fbcf334e95ac523f474434ccbc415c5f8f42259b4ac45ec49fde7aac2\",\"artifact:5046:5c9675b42efabc1ed6aa0a95c358b4b1e299f5f5f49b4fbe8401d06eacc50ea6\":\"5c9675b42efabc1ed6aa0a95c358b4b1e299f5f5f49b4fbe8401d06eacc50ea6\",\"artifact:5046:5d78303a25565e89282cb3343dc59c6a61875268492247e01e0fb5c88d029cd2\":\"5d78303a25565e89282cb3343dc59c6a61875268492247e01e0fb5c88d029cd2\",\"artifact:5046:6d0be29dab5a6e4bf88d4e14fd36a46c7a00ec6e8763a7a9def57f226fc49d94\":\"6d0be29dab5a6e4bf88d4e14fd36a46c7a00ec6e8763a7a9def57f226fc49d94\",\"artifact:5046:6eb0c0340327db54140644db7649cd0fbe3d35e7c144dfe470c2ee9d5b287bd0\":\"6eb0c0340327db54140644db7649cd0fbe3d35e7c144dfe470c2ee9d5b287bd0\",\"artifact:5046:a4fa6574ba9eec6579dc8b570d3720aa2e08aeed194c92a80af85d02fb08b785\":\"a4fa6574ba9eec6579dc8b570d3720aa2e08aeed194c92a80af85d02fb08b785\",\"artifact:5046:a56a27363c8f4260eeb56f7060a652e4c54f231b4a738285f4b69b4926ebcc91\":\"a56a27363c8f4260eeb56f7060a652e4c54f231b4a738285f4b69b4926ebcc91\",\"artifact:5046:bcece3312a840c409bea627530966b0f517913df26b9cc5346c9b49e629fa255\":\"bcece3312a840c409bea627530966b0f517913df26b9cc5346c9b49e629fa255\",\"artifact:5046:bee96e27615d546f85ae2186de5abf6b1c1d50186de6343a78f68fe349298741\":\"bee96e27615d546f85ae2186de5abf6b1c1d50186de6343a78f68fe349298741\",\"artifact:5046:de4f16834a8418db9dd384c12f55ebb9ae68c5f859069465554318b2fcb24f7f\":\"de4f16834a8418db9dd384c12f55ebb9ae68c5f859069465554318b2fcb24f7f\",\"artifact:5046:f0dfa4b38ae75fd6901064f8d37668c825b7c5bb39cd70ca6007ea457068430e\":\"f0dfa4b38ae75fd6901064f8d37668c825b7c5bb39cd70ca6007ea457068430e\"},\"sha256\":\"0a4ea624380efc7bc80753694b29edcc784bd8b56a453fbc7191b69dc3e400b5\"},\"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:5046,input_sha256:\"429ffadbd7b198cccc8bef12c1e1f320716b2ebdf74c7a27c6588216cba858b3\",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/5059/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"118b89f1a8ffb24747f2b94c55077756bb4f5d010bebf4f965a1f8f6eb213a74","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}