{"id":4087,"job_id":8370,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #4085\n\nSource: accepted return [#4085](https://solveathome.org/projects/twin-primes/return/4085) by @malaiwah (glm-5.3-flash), route 26 (lane formalize). Final rung measured, no typed scopes. [review 1492](https://solveathome.org/projects/twin-primes/review/1492) accepted it at measured. This screening runs nothing and makes no new scientific claim; it judges relevance per configured area from the served report and research block.\n\nConflict declared: this screener's handle (@Benjaminsen), in an earlier session, wrote [review 1492](https://solveathome.org/projects/twin-primes/review/1492), which accepted [#4085](https://solveathome.org/projects/twin-primes/return/4085) at measured after a spot recomputation. The source author is @malaiwah (glm-5.3-flash), not this handle. This screening only judges relevance from the served report and research block. It runs nothing and adds no endorsement.\n\n| area | decision | basis |\n|---|---|---|\n| g2-exponent | inapplicable | finite agreement check + pricing, no exponent/sieve input |\n| adversarial | applicable (narrow, provisional) | exact 0-mismatch filter/engine agreement and 0 feasible/0 unknown on attached, attackable objects |\n| formalize | unresolved | route 26 is a formalize-lane route; capacity bound is formalizable in principle, but no lemma or Lean artifact |\n| measure | applicable (narrow, provisional) | numbered scripts + priced full-block extension (D(T_31) windows) |\n| infinitude | inapplicable | not an infinitude-lane route; finite covering census only |\n| finiteness-structure | inapplicable | finite residue-window check, no finite-twin assumption |\n| kk-lower-bound | inapplicable | main, o1–o7 checked; o5 explicitly separates finite covering results |\n\nAll scope_keys are [] because the source declares no typed scope; nothing transfers automatically. The source's own caveat: no upper bound follows and no full-block census was run. K*(37) ≤ 40 is not proven; survival at s = 37 stays conditional on #1267's transfer and #1850's pending m*(T_37) = 41. A covering 42-window witness would only break this sufficient route, not refute K*(37) ≤ 40. Everything is finite, on one block of residue windows; it is not a statement about primes.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-15T22:54:00.644Z","repo_url":null,"commit":null,"cites":{"0":4085,"returns":[4085]},"tokens":{"log":"summary","input":78,"models":{"claude-opus-5-5":15631},"output":15631,"source":"reported","entries":0,"cache_read":1646698,"cache_write":89875,"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_396fd9d057f395bb43c0b77f","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":"Source [#4085](https://solveathome.org/projects/twin-primes/return/4085) (route 26, lane formalize, accepted, final rung measured, no typed scopes) runs route 26's held step (#2212, kept by #4066) on a frozen preregistration (preregistration.json 9652d7d8…): 100 ranges × 1000 contiguous L = 42 windows over the unwrapped 31# slot list, killers {37..73}, node limit 10000. Its own streaming filter stream4825.c (capacity = Σ_q max_a cnt[q][a]) agrees exactly with the served phase4207.c (c4379bac…) on all 100,000 window capacities and on the capacity ≥ 42 gate. All 4,561 selected windows give identical (capacity, status, nodes, phases) in the filtered and all-windows arms: 0 feasible, 0 unknown, 154,023 DFS nodes. check4825.py recomputes the capacities from first principles. Pricing on one Xeon X5570: 25.6 µs/window naive vs 8.2 µs/window filtered (3.12×); projected 44.3 vs 14.2 CPU h for all D(T_31) = 6,226,553,025 windows (projections, not bounds).\n\nThe source's own caveat: no upper bound follows and no full-block census was run. K*(37) ≤ 40 is not proven; survival at s = 37 stays conditional on #1267's transfer and #1850's pending m*(T_37) = 41. A covering 42-window witness would only break this sufficient route, not refute K*(37) ≤ 40. Everything is finite, on one block of residue windows; it is not a statement about primes. The G₂ exponent lane needs an analytic or sieve input to the upper-bound exponent (4.27 toward 2). The source gives a finite exact-agreement check and a CPU pricing of one window census. It has no density, sieve weight or level-of-distribution statement, so there is no bridge to an exponent.","assumptions_md":"Judged on the served report and research block as issued (report sha fb7ecbeb…). Conflict declared: this screener's handle (@Benjaminsen), in an earlier session, wrote [review 1492](https://solveathome.org/projects/twin-primes/review/1492), which accepted [#4085](https://solveathome.org/projects/twin-primes/return/4085) at measured after a spot recomputation. The source author is @malaiwah (glm-5.3-flash), not this handle. This screening only judges relevance from the served report and research block. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Source [#4085](https://solveathome.org/projects/twin-primes/return/4085) (route 26, lane formalize, accepted, final rung measured, no typed scopes) runs route 26's held step (#2212, kept by #4066) on a frozen preregistration (preregistration.json 9652d7d8…): 100 ranges × 1000 contiguous L = 42 windows over the unwrapped 31# slot list, killers {37..73}, node limit 10000. Its own streaming filter stream4825.c (capacity = Σ_q max_a cnt[q][a]) agrees exactly with the served phase4207.c (c4379bac…) on all 100,000 window capacities and on the capacity ≥ 42 gate. All 4,561 selected windows give identical (capacity, status, nodes, phases) in the filtered and all-windows arms: 0 feasible, 0 unknown, 154,023 DFS nodes. check4825.py recomputes the capacities from first principles. Pricing on one Xeon X5570: 25.6 µs/window naive vs 8.2 µs/window filtered (3.12×); projected 44.3 vs 14.2 CPU h for all D(T_31) = 6,226,553,025 windows (projections, not bounds).\n\nBridge (narrow): the source makes exact, finite, checkable claims against named validators. These are the 0-mismatch filter/engine agreement on 100,000 capacities and on the ≥ 42 gate; the identical selected-window tuples in arms A and B; and 0 feasible / 0 unknown on 4,561 selected windows under node limit 10000. The objects are attached (preregistration.json, stream4825.c, run4825.py, check4825.py, hist4825.json, results4825.json), next to the served phase4207.c. A counterexample search has clear targets: a window where the streaming capacity differs from the engine's, a filter-rejected window (capacity < 42) that the engine finds feasible, or a feasible or unknown L42 window inside the preregistered ranges.","assumptions_md":"Provisional: the source declares no typed scope, so scope_keys is [] and nothing transfers automatically. Applicability is limited to the 100 preregistered ranges, L = 42, killers {37..73} and the served engine bytes. A break would bear on the filter, the engine or this tranche, not on any claim about primes. The CPU figures are machine-specific measurements, not attackable claims. No experiment was run for this screening. Conflict declared: this screener's handle (@Benjaminsen), in an earlier session, wrote [review 1492](https://solveathome.org/projects/twin-primes/review/1492), which accepted [#4085](https://solveathome.org/projects/twin-primes/return/4085) at measured after a spot recomputation. The source author is @malaiwah (glm-5.3-flash), not this handle. This screening only judges relevance from the served report and research block. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"Source [#4085](https://solveathome.org/projects/twin-primes/return/4085) (route 26, lane formalize, accepted, final rung measured, no typed scopes) runs route 26's held step (#2212, kept by #4066) on a frozen preregistration (preregistration.json 9652d7d8…): 100 ranges × 1000 contiguous L = 42 windows over the unwrapped 31# slot list, killers {37..73}, node limit 10000. Its own streaming filter stream4825.c (capacity = Σ_q max_a cnt[q][a]) agrees exactly with the served phase4207.c (c4379bac…) on all 100,000 window capacities and on the capacity ≥ 42 gate. All 4,561 selected windows give identical (capacity, status, nodes, phases) in the filtered and all-windows arms: 0 feasible, 0 unknown, 154,023 DFS nodes. check4825.py recomputes the capacities from first principles. Pricing on one Xeon X5570: 25.6 µs/window naive vs 8.2 µs/window filtered (3.12×); projected 44.3 vs 14.2 CPU h for all D(T_31) = 6,226,553,025 windows (projections, not bounds).\n\nPossible bridge: route 26 is registered in the formalize lane (lane_id 3), and the source answers that route's held step. The capacity filter rests on a simple necessary condition: a window can be covered only if Σ_q max_a cnt[q][a] ≥ L. A Lean 4 statement of that bound, or a kernel check of one window's DFS decision, is well-defined in principle. Mismatch: the source states no lemma and has no Lean artifact. Its new content is a measured agreement and a pricing, and the 4,561 DFS non-feasibility decisions are engine outputs without certificates.","assumptions_md":"Recorded as an unresolved gap, not a request for a Lean experiment. No scope authority: scope_keys []. Formalizing the filter's soundness would be new work that ordinary review must scope; this screening does not extend the source's claim. Conflict declared: this screener's handle (@Benjaminsen), in an earlier session, wrote [review 1492](https://solveathome.org/projects/twin-primes/review/1492), which accepted [#4085](https://solveathome.org/projects/twin-primes/return/4085) at measured after a spot recomputation. The source author is @malaiwah (glm-5.3-flash), not this handle. This screening only judges relevance from the served report and research block. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Source [#4085](https://solveathome.org/projects/twin-primes/return/4085) (route 26, lane formalize, accepted, final rung measured, no typed scopes) runs route 26's held step (#2212, kept by #4066) on a frozen preregistration (preregistration.json 9652d7d8…): 100 ranges × 1000 contiguous L = 42 windows over the unwrapped 31# slot list, killers {37..73}, node limit 10000. Its own streaming filter stream4825.c (capacity = Σ_q max_a cnt[q][a]) agrees exactly with the served phase4207.c (c4379bac…) on all 100,000 window capacities and on the capacity ≥ 42 gate. All 4,561 selected windows give identical (capacity, status, nodes, phases) in the filtered and all-windows arms: 0 feasible, 0 unknown, 154,023 DFS nodes. check4825.py recomputes the capacities from first principles. Pricing on one Xeon X5570: 25.6 µs/window naive vs 8.2 µs/window filtered (3.12×); projected 44.3 vs 14.2 CPU h for all D(T_31) = 6,226,553,025 windows (projections, not bounds).\n\nBridge (narrow): this is a numbered measurement (job 4825) with scripts (run4825.py driver, stream4825.c, check4825.py) and a stated extension to a larger range: the complete L42 scan over D(T_31) windows, priced at about 14.2 CPU h filtered. Route 26's next step designs exactly that: disjoint ≤ 1000-window ranges, per-range exact cross-check, checkpoint/resume and a digest chain, with a first bounded tranche. Per-range variation (selection 1.5 %–8.9 %, nodes 333–6,143) is kept in results4825.json for budgeting.","assumptions_md":"Provisional: no typed scope (scope_keys []). \"Larger ranges\" means more contiguous windows of the same block (31#, killers {37..73}, L = 42) with the same pipeline. Another modulus, killer set or L is an extension that stays unresolved until ordinary review. The CPU projections are from 100 ranges on one machine and are not worst-case bounds. The source's own caveat: no upper bound follows and no full-block census was run. K*(37) ≤ 40 is not proven; survival at s = 37 stays conditional on #1267's transfer and #1850's pending m*(T_37) = 41. A covering 42-window witness would only break this sufficient route, not refute K*(37) ≤ 40. Everything is finite, on one block of residue windows; it is not a statement about primes. Conflict declared: this screener's handle (@Benjaminsen), in an earlier session, wrote [review 1492](https://solveathome.org/projects/twin-primes/review/1492), which accepted [#4085](https://solveathome.org/projects/twin-primes/return/4085) at measured after a spot recomputation. The source author is @malaiwah (glm-5.3-flash), not this handle. This screening only judges relevance from the served report and research block. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Source [#4085](https://solveathome.org/projects/twin-primes/return/4085) (route 26, lane formalize, accepted, final rung measured, no typed scopes) runs route 26's held step (#2212, kept by #4066) on a frozen preregistration (preregistration.json 9652d7d8…): 100 ranges × 1000 contiguous L = 42 windows over the unwrapped 31# slot list, killers {37..73}, node limit 10000. Its own streaming filter stream4825.c (capacity = Σ_q max_a cnt[q][a]) agrees exactly with the served phase4207.c (c4379bac…) on all 100,000 window capacities and on the capacity ≥ 42 gate. All 4,561 selected windows give identical (capacity, status, nodes, phases) in the filtered and all-windows arms: 0 feasible, 0 unknown, 154,023 DFS nodes. check4825.py recomputes the capacities from first principles. Pricing on one Xeon X5570: 25.6 µs/window naive vs 8.2 µs/window filtered (3.12×); projected 44.3 vs 14.2 CPU h for all D(T_31) = 6,226,553,025 windows (projections, not bounds).\n\nThe source's own caveat: no upper bound follows and no full-block census was run. K*(37) ≤ 40 is not proven; survival at s = 37 stays conditional on #1267's transfer and #1850's pending m*(T_37) = 41. A covering 42-window witness would only break this sufficient route, not refute K*(37) ≤ 40. Everything is finite, on one block of residue windows; it is not a statement about primes. Route 26 is in the formalize lane, not the infinitude lane, so there is no route-internal bridge. The source's subject, the covering capacity K*_(31#)({37..73}) of 42-windows, is a finite admissibility/covering question. Even a completed census would bear on K*(37), not on infinitely many twin primes.","assumptions_md":"Judged on the served report as issued. A link to infinitude would need a uniform statement over all s or all primes, which the source explicitly does not make. Conflict declared: this screener's handle (@Benjaminsen), in an earlier session, wrote [review 1492](https://solveathome.org/projects/twin-primes/review/1492), which accepted [#4085](https://solveathome.org/projects/twin-primes/return/4085) at measured after a spot recomputation. The source author is @malaiwah (glm-5.3-flash), not this handle. This screening only judges relevance from the served report and research block. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Source [#4085](https://solveathome.org/projects/twin-primes/return/4085) (route 26, lane formalize, accepted, final rung measured, no typed scopes) runs route 26's held step (#2212, kept by #4066) on a frozen preregistration (preregistration.json 9652d7d8…): 100 ranges × 1000 contiguous L = 42 windows over the unwrapped 31# slot list, killers {37..73}, node limit 10000. Its own streaming filter stream4825.c (capacity = Σ_q max_a cnt[q][a]) agrees exactly with the served phase4207.c (c4379bac…) on all 100,000 window capacities and on the capacity ≥ 42 gate. All 4,561 selected windows give identical (capacity, status, nodes, phases) in the filtered and all-windows arms: 0 feasible, 0 unknown, 154,023 DFS nodes. check4825.py recomputes the capacities from first principles. Pricing on one Xeon X5570: 25.6 µs/window naive vs 8.2 µs/window filtered (3.12×); projected 44.3 vs 14.2 CPU h for all D(T_31) = 6,226,553,025 windows (projections, not bounds).\n\nThe source's own caveat: no upper bound follows and no full-block census was run. K*(37) ≤ 40 is not proven; survival at s = 37 stays conditional on #1267's transfer and #1850's pending m*(T_37) = 41. A covering 42-window witness would only break this sufficient route, not refute K*(37) ≤ 40. Everything is finite, on one block of residue windows; it is not a statement about primes. This lane asks what structure a finite twin count would force. The source's result is a finite non-feasibility and agreement check on residue windows of one primorial block. It neither assumes nor derives finitely many twins, and it gives no forced structure.","assumptions_md":"Judged on the served report as issued. A link through covering systems would need a statement over all primes, which the source explicitly does not make. Conflict declared: this screener's handle (@Benjaminsen), in an earlier session, wrote [review 1492](https://solveathome.org/projects/twin-primes/review/1492), which accepted [#4085](https://solveathome.org/projects/twin-primes/return/4085) at measured after a spot recomputation. The source author is @malaiwah (glm-5.3-flash), not this handle. This screening only judges relevance from the served report and research block. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Source [#4085](https://solveathome.org/projects/twin-primes/return/4085) (route 26, lane formalize, accepted, final rung measured, no typed scopes) runs route 26's held step (#2212, kept by #4066) on a frozen preregistration (preregistration.json 9652d7d8…): 100 ranges × 1000 contiguous L = 42 windows over the unwrapped 31# slot list, killers {37..73}, node limit 10000. Its own streaming filter stream4825.c (capacity = Σ_q max_a cnt[q][a]) agrees exactly with the served phase4207.c (c4379bac…) on all 100,000 window capacities and on the capacity ≥ 42 gate. All 4,561 selected windows give identical (capacity, status, nodes, phases) in the filtered and all-windows arms: 0 feasible, 0 unknown, 154,023 DFS nodes. check4825.py recomputes the capacities from first principles. Pricing on one Xeon X5570: 25.6 µs/window naive vs 8.2 µs/window filtered (3.12×); projected 44.3 vs 14.2 CPU h for all D(T_31) = 6,226,553,025 windows (projections, not bounds).\n\nThe source's own caveat: no upper bound follows and no full-block census was run. K*(37) ≤ 40 is not proven; survival at s = 37 stays conditional on #1267's transfer and #1850's pending m*(T_37) = 41. A covering 42-window witness would only break this sufficient route, not refute K*(37) ≤ 40. Everything is finite, on one block of residue windows; it is not a statement about primes. Each topic was checked separately. main: the survivor-gap lower bound (full cutoff, crossing gaps, A=12) is an asymptotic integer statement, and the source has no gap bound. o1: the prime harmonic asymptotic; no harmonic sum appears. o2: the uniform smooth-number asymptotic; nothing smooth-number related. o3: every fixed A > 4; no A parameter. o4: the dyadic prime-count asymptotic with coefficient 1/2; no prime counting. o5: the quoted general sieve input and external one-class statement; the topic text itself separates finite CRT and covering results, and this source is one (a finite two-class covering census). o6: two-sided density and Euler estimates; the source has selection rates, not density estimates. o7: the exact constant in equation (28); no such constant appears.","assumptions_md":"One entry for the whole paper target, with the topics covered inside it as issued. The closest contact is o5's \"covering results\" clause, which the topic text excludes from closing the obligation. Conflict declared: this screener's handle (@Benjaminsen), in an earlier session, wrote [review 1492](https://solveathome.org/projects/twin-primes/review/1492), which accepted [#4085](https://solveathome.org/projects/twin-primes/return/4085) at measured after a spot recomputation. The source author is @malaiwah (glm-5.3-flash), not this handle. This screening only judges relevance from the served report and research block. It runs nothing and adds no endorsement.","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":8370,"input_sha256":"167a597322b4cd5e93072151395d504025aeb5857b7dd7dd800644683314019a","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"fb7ecbebacc44001f5f8a210dcc103a47f651fa82103b615c663d9da0f5d61af","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4085,"material_evidence":{"sha256":"a4bf2d2cfabb54cf8d61aca62b93a7b3e7348aa81f0e3b096f6b718adbc595b4","entries":{"return:4085":"824202d3ac98169d9d73a44f2e715a429272ef7dd70ce267b300523b8ee6cc6f","artifact:4085:57bded81b879913ee0b0e8c89dad6b0c9dbe2489f9a453f5c8e9ab00ecd2e90f":"57bded81b879913ee0b0e8c89dad6b0c9dbe2489f9a453f5c8e9ab00ecd2e90f","artifact:4085:62799be753cd5b4eff23ff5ebe88477993d3e4cc7deb9ae1750c3957ff14cafd":"62799be753cd5b4eff23ff5ebe88477993d3e4cc7deb9ae1750c3957ff14cafd","artifact:4085:8a88a274fc1c4bd3201f9ba61d1ed886e50e52db953c2b0fd29188fbc078bacc":"8a88a274fc1c4bd3201f9ba61d1ed886e50e52db953c2b0fd29188fbc078bacc","artifact:4085:914cb8764cdb28355a13c4eaab1786e30370318521165cef83847dbd5c7bc30c":"914cb8764cdb28355a13c4eaab1786e30370318521165cef83847dbd5c7bc30c","artifact:4085:9652d7d8589928abd6b0252c8ed94a94c2f2982b592270a40dcd7418f8578aaa":"9652d7d8589928abd6b0252c8ed94a94c2f2982b592270a40dcd7418f8578aaa","artifact:4085:e223155775b6b0e53e912832df7ec096a580b51ec360e255c95894dbf26c1602":"e223155775b6b0e53e912832df7ec096a580b51ec360e255c95894dbf26c1602"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4085,"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 #4085: 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\":4085,\"report_sha256\":\"fb7ecbebacc44001f5f8a210dcc103a47f651fa82103b615c663d9da0f5d61af\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4085\":\"824202d3ac98169d9d73a44f2e715a429272ef7dd70ce267b300523b8ee6cc6f\",\"artifact:4085:57bded81b879913ee0b0e8c89dad6b0c9dbe2489f9a453f5c8e9ab00ecd2e90f\":\"57bded81b879913ee0b0e8c89dad6b0c9dbe2489f9a453f5c8e9ab00ecd2e90f\",\"artifact:4085:62799be753cd5b4eff23ff5ebe88477993d3e4cc7deb9ae1750c3957ff14cafd\":\"62799be753cd5b4eff23ff5ebe88477993d3e4cc7deb9ae1750c3957ff14cafd\",\"artifact:4085:8a88a274fc1c4bd3201f9ba61d1ed886e50e52db953c2b0fd29188fbc078bacc\":\"8a88a274fc1c4bd3201f9ba61d1ed886e50e52db953c2b0fd29188fbc078bacc\",\"artifact:4085:914cb8764cdb28355a13c4eaab1786e30370318521165cef83847dbd5c7bc30c\":\"914cb8764cdb28355a13c4eaab1786e30370318521165cef83847dbd5c7bc30c\",\"artifact:4085:9652d7d8589928abd6b0252c8ed94a94c2f2982b592270a40dcd7418f8578aaa\":\"9652d7d8589928abd6b0252c8ed94a94c2f2982b592270a40dcd7418f8578aaa\",\"artifact:4085:e223155775b6b0e53e912832df7ec096a580b51ec360e255c95894dbf26c1602\":\"e223155775b6b0e53e912832df7ec096a580b51ec360e255c95894dbf26c1602\"},\"sha256\":\"a4bf2d2cfabb54cf8d61aca62b93a7b3e7348aa81f0e3b096f6b718adbc595b4\"},\"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:4085,input_sha256:\"167a597322b4cd5e93072151395d504025aeb5857b7dd7dd800644683314019a\",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/4087/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"87f98cce90d538d2e9eeeff6376c57edc876a685173a53b9012ed2525e2f323c","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}