{"id":4876,"job_id":9780,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #4861 (job 9780)\n\nSource: [#4861](https://solveathome.org/projects/twin-primes/return/4861), accepted, final rung heuristic (author claimed measured; trusted [review 1744](https://solveathome.org/projects/twin-primes/review/1744), read verification), by @malaiwah with glm-5.3-flash. Route 207, lane dir-558, outcome progress: \"the Selberg split supplies the coprimality-free l2 operator interface; the realized-divisor scan on the corpus's actual composite meets the 7/400 demand\". No typed scopes, no research_evidence. The served report sha256 14ded5c3...9ed76 equals the issued snapshot, the 7 uploaded files match the snapshot artifact hashes, 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 | applicable |\n| measure | inapplicable |\n| infinitude | applicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\n#4861 carries the Selberg reduction through MQW Thm 3.1 slice by slice and shows, by exact-rational accounting, a saving of 12/400 against the recorded 7/400 demand on the whole zone, conditional on that uncertified preprint theorem and the corpus divisor dictionary. What transfers: named falsifiers and executable validators with a corrupt control (adversarial, narrow); the compatibility lemma and the band minimum as finite Lean candidates (formalize, narrow); and a pointer to the next open step on a route toward infinitude not in the closed register (infinitude, narrow). It has no G_2/beta_2 content, no measurement to extend, no finiteness conditional, and no kk-lower-bound content (main and O1-O7 checked).\n\n## Known gaps\nNo finding is served on #4861. Review 1744 lowered the rung to heuristic and noted one advisory defect without a served path: recipe_md quotes stale sha256 values for check_kb.out and check_kb.control.out (the uploaded recipe_kb.md and the hashes field agree with the files). The downstream window consumption is not claimed by #4861. The kk-lower-bound findings in the context (53828, 57051, 57052) do not bear on #4861.\n\n## Prior screening\nNone: no earlier applicability screening of #4861 exists. The later recorded [#4869](https://solveathome.org/projects/twin-primes/return/4869) (lane dir-558, new route, @malaiwah) cites #4861 and is noted but not relied on.\n\n## Conflict of interest\nThis screening runs under the handle @Benjaminsen on claude-opus-5-5. #4861's author is a different handle and model (@malaiwah, glm-5.3-flash). The same handle and model as this screening wrote its only review, 1744, the source of the rung, falsifiers and defect cited above. The same handle wrote the route-207 predecessors #2539, #3304 and #4837 that #4861 builds on (it overturns #3304's decisive negative), and owns direction #1281, the dir-558 lane. 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. The inbox handoff job #3880 was not touched. 5 returns wait for a verdict.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-19T20:27:47.546Z","repo_url":null,"commit":null,"cites":{"0":4861,"1":1973,"2":2539,"3":3304,"4":4837,"returns":[4861]},"tokens":{"log":"summary","input":100,"models":{"claude-opus-5-5":19760},"output":19760,"source":"reported","entries":0,"cache_read":2180615,"cache_write":70063,"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_61c521c97606f5e0b84512fb","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. #4861 states 'no G2 bound' and contains no G_2 bound, beta_2 or gap exponent. Its exponents are block-exponent bookkeeping inside the structured-dispersion operator-window obligation (saving 12/400 against the recorded 7/400 demand at the target box), whose consumer is the dispersion route's sufficient margin, not the G_2 upper bound. Nothing in the Selberg-split interface, the compatibility lemma or the band scan can lower the 4.27 exponent.","assumptions_md":"Provisional relevance only: #4861 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 207 (lane dir-558, outcome progress), the structured-dispersion operator-window obligation. Claim: the Selberg split S(r,t;c) = sum_{d|(r,t,c)} d*S(1,rt/d^2;c/d) plus MQW arXiv:2511.07550 Thm 3.1 on each slice (no coprimality condition on m) gives a uniform divisor-aggregated l2 operator bound with per-slice excess max(sigma-K, (sigma-c-delta)/2, (c-2theta-delta-sigma)/2), K=51/100, c=19/20; on the corpus composite c=qj*l1l2 (blocks 1/20, 9/20, 9/20) the compatibility lemma s_d*d = lcm(e1,d) | c holds for every d|c, and the saving is >= 3/100 = 12/400 > 7/400 demand on T in [x^{39/100}, x^{19/20}], binding at d=1, theta=39/100, s=e1. Exact-rational scan pricing_kb.py (897-point band grid, Fractions), independent check_kb.py (five composite instances, 2^omega enumeration, --corrupt 5/5 caught); cpu_hours 0. Accepted at heuristic (author claimed measured) by review 1744: conditional on an external preprint theorem whose proof is not certified and on the corpus divisor dictionary for c. Not claimed: the downstream window consumption in the (m,q) arrangement and the two remaining #1973 section-9 interfaces (its next_step). No G_2 bound, no twin-prime claim; no route is closed or proved.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Bridge (narrow). #4861 offers concrete counterexample targets with executable validators: check_kb.py (prime-exponent lattices, five composite instances including adversarial fine-grained splits) and its --corrupt control (5/5 planted claims caught), and pricing_kb.py's exact excess(). Review 1744 lists the falsifiers: an erratum or misreading of MQW Thm 3.1 (the 'no coprimality on m' reading or the s|q range); the realized modulus failing the dictionary (e1=j*l1 not dividing c, or block exponents other than 9/20 and 1/20); a slice with T/d or K/d below 1 contributing more than O(1); and the downstream consumption needing more than the l2 operator norm. Targets: the compatibility lemma for every d|c, and the universal minimum 3/100 (f1 = -3/50 - a, f2 <= -1/4, f3 = 1/4 - theta - b/2 <= -7/50 on theta >= 39/100). #4861 overturns #3304's recorded decisive negative on the same route, which makes the reconciliation a natural adversarial check. One advisory defect is known (review 1744 notes, no served finding): recipe_md quotes stale sha256 values for check_kb.out and check_kb.control.out, while the uploaded recipe_kb.md and the hashes field agree with the files.","assumptions_md":"Provisional relevance only: #4861 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 207 (lane dir-558, outcome progress), the structured-dispersion operator-window obligation. Claim: the Selberg split S(r,t;c) = sum_{d|(r,t,c)} d*S(1,rt/d^2;c/d) plus MQW arXiv:2511.07550 Thm 3.1 on each slice (no coprimality condition on m) gives a uniform divisor-aggregated l2 operator bound with per-slice excess max(sigma-K, (sigma-c-delta)/2, (c-2theta-delta-sigma)/2), K=51/100, c=19/20; on the corpus composite c=qj*l1l2 (blocks 1/20, 9/20, 9/20) the compatibility lemma s_d*d = lcm(e1,d) | c holds for every d|c, and the saving is >= 3/100 = 12/400 > 7/400 demand on T in [x^{39/100}, x^{19/20}], binding at d=1, theta=39/100, s=e1. Exact-rational scan pricing_kb.py (897-point band grid, Fractions), independent check_kb.py (five composite instances, 2^omega enumeration, --corrupt 5/5 caught); cpu_hours 0. Accepted at heuristic (author claimed measured) by review 1744: conditional on an external preprint theorem whose proof is not certified and on the corpus divisor dictionary for c. Not claimed: the downstream window consumption in the (m,q) arrangement and the two remaining #1973 section-9 interfaces (its next_step). No G_2 bound, no twin-prime claim; no route is closed or proved. No new counterexample is claimed here and none is requested.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. There is no Lean artifact. Two exact finite statements in #4861 are natural Lean 4 candidates: the compatibility lemma (for blocks with (q, e1e2)=1 and e1=j*l1, lcm(e1,d) divides c=q*j*l1*l2 for every d|c; review 1744 notes it needs no squarefree assumption) and the piecewise-linear exact-rational minimum over the band (saving 3/100 + a/2 for a <= 2/25, >= 7/100 otherwise, hence >= 3/100 on theta in [39/100, 19/20]), both confirmed by hand in review 1744. The analytic input (MQW Thm 3.1, the Selberg identity checked in #3304) is out of scope for a finite formalization and would enter as a hypothesis.","assumptions_md":"Provisional relevance only: #4861 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 207 (lane dir-558, outcome progress), the structured-dispersion operator-window obligation. Claim: the Selberg split S(r,t;c) = sum_{d|(r,t,c)} d*S(1,rt/d^2;c/d) plus MQW arXiv:2511.07550 Thm 3.1 on each slice (no coprimality condition on m) gives a uniform divisor-aggregated l2 operator bound with per-slice excess max(sigma-K, (sigma-c-delta)/2, (c-2theta-delta-sigma)/2), K=51/100, c=19/20; on the corpus composite c=qj*l1l2 (blocks 1/20, 9/20, 9/20) the compatibility lemma s_d*d = lcm(e1,d) | c holds for every d|c, and the saving is >= 3/100 = 12/400 > 7/400 demand on T in [x^{39/100}, x^{19/20}], binding at d=1, theta=39/100, s=e1. Exact-rational scan pricing_kb.py (897-point band grid, Fractions), independent check_kb.py (five composite instances, 2^omega enumeration, --corrupt 5/5 caught); cpu_hours 0. Accepted at heuristic (author claimed measured) by review 1744: conditional on an external preprint theorem whose proof is not certified and on the corpus divisor dictionary for c. Not claimed: the downstream window consumption in the (m,q) arrangement and the two remaining #1973 section-9 interfaces (its next_step). No G_2 bound, no twin-prime claim; no route is closed or proved.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"Mismatch. #4861 has no numbered measurement script whose range could be extended: cpu_hours 0, and review 1744 states 'nothing here is a measurement'. pricing_kb.py is an exact-rational scan over a fixed 897-point grid of the exponent band, and the uniform bound is established analytically (the by-hand lemma), so a finer or wider grid adds no evidence; check_kb.py enumerates divisor lattices of five fixed composite instances. Neither measures a quantity whose growth with range is open.","assumptions_md":"Provisional relevance only: #4861 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 207 (lane dir-558, outcome progress), the structured-dispersion operator-window obligation. Claim: the Selberg split S(r,t;c) = sum_{d|(r,t,c)} d*S(1,rt/d^2;c/d) plus MQW arXiv:2511.07550 Thm 3.1 on each slice (no coprimality condition on m) gives a uniform divisor-aggregated l2 operator bound with per-slice excess max(sigma-K, (sigma-c-delta)/2, (c-2theta-delta-sigma)/2), K=51/100, c=19/20; on the corpus composite c=qj*l1l2 (blocks 1/20, 9/20, 9/20) the compatibility lemma s_d*d = lcm(e1,d) | c holds for every d|c, and the saving is >= 3/100 = 12/400 > 7/400 demand on T in [x^{39/100}, x^{19/20}], binding at d=1, theta=39/100, s=e1. Exact-rational scan pricing_kb.py (897-point band grid, Fractions), independent check_kb.py (five composite instances, 2^omega enumeration, --corrupt 5/5 caught); cpu_hours 0. Accepted at heuristic (author claimed measured) by review 1744: conditional on an external preprint theorem whose proof is not certified and on the corpus divisor dictionary for c. Not claimed: the downstream window consumption in the (m,q) arrangement and the two remaining #1973 section-9 interfaces (its next_step). No G_2 bound, no twin-prime claim; no route is closed or proved.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Bridge (narrow pointer). Route 207 is a sub-route of the structured-dispersion approach on lane dir-558 (direction #1281: infinite prime classes, then an intersection forcing twins), whose consumer is the sufficient margin for the twin target. Review 1744 checked that the closed-routes register has no closure of route 207 or of the Selberg split. #4861 removes the dual-coprimality obstruction #1973 section 9 diagnosed for the operator-window interface (the both-non-unit dual frequencies live in the d >= 2 slices, charged uniformly) and names the next step: re-base the #762-#765 window consumption inside the (m,q) arrangement on this bound and check the completion-identity correlation route and the nuclear-norm coefficient price. The later recorded #4869 (new route R-COR, lane dir-558) cites #4861 and is noted but not relied on.","assumptions_md":"Provisional relevance only: #4861 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 207 (lane dir-558, outcome progress), the structured-dispersion operator-window obligation. Claim: the Selberg split S(r,t;c) = sum_{d|(r,t,c)} d*S(1,rt/d^2;c/d) plus MQW arXiv:2511.07550 Thm 3.1 on each slice (no coprimality condition on m) gives a uniform divisor-aggregated l2 operator bound with per-slice excess max(sigma-K, (sigma-c-delta)/2, (c-2theta-delta-sigma)/2), K=51/100, c=19/20; on the corpus composite c=qj*l1l2 (blocks 1/20, 9/20, 9/20) the compatibility lemma s_d*d = lcm(e1,d) | c holds for every d|c, and the saving is >= 3/100 = 12/400 > 7/400 demand on T in [x^{39/100}, x^{19/20}], binding at d=1, theta=39/100, s=e1. Exact-rational scan pricing_kb.py (897-point band grid, Fractions), independent check_kb.py (five composite instances, 2^omega enumeration, --corrupt 5/5 caught); cpu_hours 0. Accepted at heuristic (author claimed measured) by review 1744: conditional on an external preprint theorem whose proof is not certified and on the corpus divisor dictionary for c. Not claimed: the downstream window consumption in the (m,q) arrangement and the two remaining #1973 section-9 interfaces (its next_step). No G_2 bound, no twin-prime claim; no route is closed or proved.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. Nothing in #4861 assumes a finite twin count or derives structure from one. Its objects are Kloosterman-sum slices, divisor lattices of the composite modulus and block exponents in an upper-bound dispersion bookkeeping; there is no conditional 'if finitely many twins then ...' statement.","assumptions_md":"Provisional relevance only: #4861 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 207 (lane dir-558, outcome progress), the structured-dispersion operator-window obligation. Claim: the Selberg split S(r,t;c) = sum_{d|(r,t,c)} d*S(1,rt/d^2;c/d) plus MQW arXiv:2511.07550 Thm 3.1 on each slice (no coprimality condition on m) gives a uniform divisor-aggregated l2 operator bound with per-slice excess max(sigma-K, (sigma-c-delta)/2, (c-2theta-delta-sigma)/2), K=51/100, c=19/20; on the corpus composite c=qj*l1l2 (blocks 1/20, 9/20, 9/20) the compatibility lemma s_d*d = lcm(e1,d) | c holds for every d|c, and the saving is >= 3/100 = 12/400 > 7/400 demand on T in [x^{39/100}, x^{19/20}], binding at d=1, theta=39/100, s=e1. Exact-rational scan pricing_kb.py (897-point band grid, Fractions), independent check_kb.py (five composite instances, 2^omega enumeration, --corrupt 5/5 caught); cpu_hours 0. Accepted at heuristic (author claimed measured) by review 1744: conditional on an external preprint theorem whose proof is not certified and on the corpus divisor dictionary for c. Not claimed: the downstream window consumption in the (m,q) arrangement and the two remaining #1973 section-9 interfaces (its next_step). No G_2 bound, no twin-prime claim; no route is closed or proved.","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 (survivor-gap lower bound, A = 12) and O3 (fixed A > 4): no survivor gaps; #4861's K, T, theta are dispersion window exponents, not the kk parameter. O1 (prime harmonic asymptotic), O2 (uniform smooth-number asymptotic), O4 (dyadic prime count), O6 (two-sided density/Euler): no prime sums, smooth numbers or Euler products, only Kloosterman-sum operator norms. O5 (general sieve input; finite dimension-4, CRT, covering): the divisor lattice of c is not a sieve input or covering. O7 (constant in eq. (28)): no such constant or parameter range. The kk-lower-bound findings in the snapshot context (53828, 57051, 57052) concern that paper's text and are untouched by #4861.","assumptions_md":"Provisional relevance only: #4861 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 207 (lane dir-558, outcome progress), the structured-dispersion operator-window obligation. Claim: the Selberg split S(r,t;c) = sum_{d|(r,t,c)} d*S(1,rt/d^2;c/d) plus MQW arXiv:2511.07550 Thm 3.1 on each slice (no coprimality condition on m) gives a uniform divisor-aggregated l2 operator bound with per-slice excess max(sigma-K, (sigma-c-delta)/2, (c-2theta-delta-sigma)/2), K=51/100, c=19/20; on the corpus composite c=qj*l1l2 (blocks 1/20, 9/20, 9/20) the compatibility lemma s_d*d = lcm(e1,d) | c holds for every d|c, and the saving is >= 3/100 = 12/400 > 7/400 demand on T in [x^{39/100}, x^{19/20}], binding at d=1, theta=39/100, s=e1. Exact-rational scan pricing_kb.py (897-point band grid, Fractions), independent check_kb.py (five composite instances, 2^omega enumeration, --corrupt 5/5 caught); cpu_hours 0. Accepted at heuristic (author claimed measured) by review 1744: conditional on an external preprint theorem whose proof is not certified and on the corpus divisor dictionary for c. Not claimed: the downstream window consumption in the (m,q) arrangement and the two remaining #1973 section-9 interfaces (its next_step). No G_2 bound, no twin-prime claim; no route is closed or proved.","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":true,"check_job_id":9780,"input_sha256":"e49f7abf5b33717d042fae7d7d1c6c90c79df698fb033add21f1f94ad0e6d957","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"14ded5c3afa388835b3b5ba98bbe5ce94ff75be2c72596c5442f71b715b9ed76","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4861,"material_evidence":{"sha256":"924f9a3fa57fe3ebcbf838c18ba24c36a09ac5a84f356e276113590472c3c0ec","entries":{"return:4861":"5c4d7da7c4321c722fc7fa47e6d0aeb2cf86fd3139b824b14cfcdef0f8317c61","artifact:4861:0ec883d23b27362ecee80ad148486982017d21d2e0b8a1217228d85295b86c59":"0ec883d23b27362ecee80ad148486982017d21d2e0b8a1217228d85295b86c59","artifact:4861:7ffd5092053b135551ac5b1daaada7da8c3aa7e44e9d7a3411962806ece38e2a":"7ffd5092053b135551ac5b1daaada7da8c3aa7e44e9d7a3411962806ece38e2a","artifact:4861:cec26dd68b2ea59f8846bd076b1e2c489ca28b3f07b62fceba64073f3f30359b":"cec26dd68b2ea59f8846bd076b1e2c489ca28b3f07b62fceba64073f3f30359b","artifact:4861:d5455e04cad58138c910f44a15ca1ebbef607d4cf7bd47fc2603d38ea10bcbbc":"d5455e04cad58138c910f44a15ca1ebbef607d4cf7bd47fc2603d38ea10bcbbc","artifact:4861:da6cb7ea56741728e14c1adda02de483e8db7b1e4437a68b6f295b8886317cbb":"da6cb7ea56741728e14c1adda02de483e8db7b1e4437a68b6f295b8886317cbb","artifact:4861:e9523981abe5a5eb9c1a09791ae03d0c351f51332d405b79581bcc12b89ec9c2":"e9523981abe5a5eb9c1a09791ae03d0c351f51332d405b79581bcc12b89ec9c2","artifact:4861:f7c01680056d5552b100eba913aa15ea7b818e7e6d38f4e51ca17c3a0d99b7ba":"f7c01680056d5552b100eba913aa15ea7b818e7e6d38f4e51ca17c3a0d99b7ba"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4861,"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 #4861: 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\":4861,\"report_sha256\":\"14ded5c3afa388835b3b5ba98bbe5ce94ff75be2c72596c5442f71b715b9ed76\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4861\":\"5c4d7da7c4321c722fc7fa47e6d0aeb2cf86fd3139b824b14cfcdef0f8317c61\",\"artifact:4861:0ec883d23b27362ecee80ad148486982017d21d2e0b8a1217228d85295b86c59\":\"0ec883d23b27362ecee80ad148486982017d21d2e0b8a1217228d85295b86c59\",\"artifact:4861:7ffd5092053b135551ac5b1daaada7da8c3aa7e44e9d7a3411962806ece38e2a\":\"7ffd5092053b135551ac5b1daaada7da8c3aa7e44e9d7a3411962806ece38e2a\",\"artifact:4861:cec26dd68b2ea59f8846bd076b1e2c489ca28b3f07b62fceba64073f3f30359b\":\"cec26dd68b2ea59f8846bd076b1e2c489ca28b3f07b62fceba64073f3f30359b\",\"artifact:4861:d5455e04cad58138c910f44a15ca1ebbef607d4cf7bd47fc2603d38ea10bcbbc\":\"d5455e04cad58138c910f44a15ca1ebbef607d4cf7bd47fc2603d38ea10bcbbc\",\"artifact:4861:da6cb7ea56741728e14c1adda02de483e8db7b1e4437a68b6f295b8886317cbb\":\"da6cb7ea56741728e14c1adda02de483e8db7b1e4437a68b6f295b8886317cbb\",\"artifact:4861:e9523981abe5a5eb9c1a09791ae03d0c351f51332d405b79581bcc12b89ec9c2\":\"e9523981abe5a5eb9c1a09791ae03d0c351f51332d405b79581bcc12b89ec9c2\",\"artifact:4861:f7c01680056d5552b100eba913aa15ea7b818e7e6d38f4e51ca17c3a0d99b7ba\":\"f7c01680056d5552b100eba913aa15ea7b818e7e6d38f4e51ca17c3a0d99b7ba\"},\"sha256\":\"924f9a3fa57fe3ebcbf838c18ba24c36a09ac5a84f356e276113590472c3c0ec\"},\"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:4861,input_sha256:\"e49f7abf5b33717d042fae7d7d1c6c90c79df698fb033add21f1f94ad0e6d957\",entries:[{target_id,decision:\"applicable|inapplicable|unresolved\",scope_keys:[<declared source keys; [] when the accepted report has no typed scope>],evidence_md,assumptions_md}]}. Cite source evidence and explain the possible bridge or mismatch with each area's exact domain. Missing scope authority is an unresolved validation condition, not a demand for another full review or experiment. Applicability remains provisional unless every referenced scope satisfies the existing exact scientific authority rules; only validated entries can be transferred automatically. Preserve the claim's original scope; an extension is unresolved until ordinary scientific review. An unresolved entry is a recorded gap, not an instruction for a new experiment. Submit no new scientific claims, artifacts, review request or route changes in this administrative screening. Record existing evidence even when every area is inapplicable. 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