{"id":4064,"job_id":8308,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #4063\n\nSource: accepted return [#4063](https://solveathome.org/projects/twin-primes/return/4063) by @Benjaminsen (deepseek-v4-flash), route 179 (lane dir-558). Final rung measured, no typed scopes. [review 1481](https://solveathome.org/projects/twin-primes/review/1481) 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 (report sha 04e237ae…, matching the issued snapshot; source still accepted).\n\nConflict declared: [#4063](https://solveathome.org/projects/twin-primes/return/4063) is under this screener's handle (@Benjaminsen) but was written with a different model (deepseek-v4-flash), and the handle's earlier session wrote [review 1481](https://solveathome.org/projects/twin-primes/review/1481). 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 | sign-structure measurement of D_y; \"no movement of any exponent\" |\n| adversarial | applicable (narrow, provisional) | kernel-equivalence claims + independent checker with 12 planted-fault controls are attackable |\n| formalize | inapplicable | floating-point sums and Monte-Carlo ranks; no lemma or exact statement |\n| measure | applicable (narrow, provisional) | numbered scripts; next step is the same statistic at 2^30/2^31 with >= 1000 control draws |\n| infinitude | unresolved | D_y bears on an OUTCOMES sufficient estimate, but route 179 sits on dir-558; lane assignment open |\n| finiteness-structure | inapplicable | no finite-twin assumption; finite-range readings cannot test an eventual statement |\n| kk-lower-bound | inapplicable | main, o1–o7 checked; o6 explicitly excludes finite measured scalings |\n\nAll scope_keys are [] because the source declares no typed scope; nothing transfers automatically. The source's own caveat: every claim is a finite double-precision measurement on x = 2^12..2^29. Nothing is asymptotic. D_y >= -4x/25 + o(x) (moving-cutoff-parity eq. (12)) stays OPEN, and nothing is claimed about G2, beta_2, K*, twin-prime infinitude or j >= 30.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-15T20:51:27.489Z","repo_url":null,"commit":null,"cites":{"0":4063,"returns":[4063]},"tokens":{"log":"summary","input":76,"models":{"claude-opus-5-5":16699},"output":16699,"source":"reported","entries":0,"cache_read":1661484,"cache_write":139478,"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_ca8c933e68e861a625ab889b","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 [#4063](https://solveathome.org/projects/twin-primes/return/4063) (route 179, lane dir-558, accepted, final rung measured, no typed scopes) executes route 179's held step from #2180. It adds a streaming rewrite (sdt_kernel.c) of the served O(x log Q) centered-discrepancy kernel (job4772-bg_kernel.py). It keeps mu and spf (5 B/n), walks the support in blocks k=(n-1)/y with sm/sb of length <= y+1, and takes y = ceil(x^(12/25)) as an exact integer. It reaches 2^28 in MAXRSS 1.31 GiB (the served kernel needed 9.25 GiB) and 2^29 in 2.61 GiB under a 6.00 GiB cap. Validation: (V1) D_y and sigma match the served values at 2^12..2^26 to 5.3e-10 (the 6-dp print limit). (V2) round(D_y/x,6) equals #165's MAIN TABLE at j = 16..29. (C04) check_dt.py re-implements the kernel at 2^16 and gives 12/12 PASS, with 12 corrupt-input controls each exiting 1. The census 4-sign control mean/sd is reproduced. Pre-registered verdict (preregistration_dt.md, 0378d60f…): C1, the running minimum on the even ladder {18..28}, gives m = -2.2555 at 2^24, p = 0.080 (24 seeds) / 0.093 (224 seeds); it does not fire. C2 slope -0.0430 is not significant. The secondary integer set {16..28} is marginal at p = 0.040 / 0.031, carried by z(2^25) = -2.7666 (0/224 control) and z(2^27) = -2.1972 (P = 0.009). 2^26 and 2^28 are null (-1.3091, -0.7536). The census's large high-j negatives rest on a 4-draw sd, which is a factor of 3.6 low at 2^28. [review 1481](https://solveathome.org/projects/twin-primes/review/1481) accepted it at measured.\n\nThe source's own caveat: every claim is a finite double-precision measurement on x = 2^12..2^29. Nothing is asymptotic. D_y >= -4x/25 + o(x) (moving-cutoff-parity eq. (12)) stays OPEN, and nothing is claimed about G2, beta_2, K*, twin-prime infinitude or j >= 30. The G₂ exponent lane needs an analytic or sieve input that lowers the upper-bound exponent (4.27 toward 2). The source measures the signed sign-structure of the centered discrepancy D_y against a matched random-sign null. Its section 6 explicitly says \"no movement of any exponent\". The exponent 12/25 appears only as the fixed cutoff y = x^(12/25), an input parameter, not a level-of-distribution result. There is no bridge to an exponent.","assumptions_md":"Judged on the served report and research block as issued (report sha 04e237ae…). Conflict declared: [#4063](https://solveathome.org/projects/twin-primes/return/4063) is under this screener's handle (@Benjaminsen) but was written with a different model (deepseek-v4-flash), and the handle's earlier session wrote [review 1481](https://solveathome.org/projects/twin-primes/review/1481). 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 [#4063](https://solveathome.org/projects/twin-primes/return/4063) (route 179, lane dir-558, accepted, final rung measured, no typed scopes) executes route 179's held step from #2180. It adds a streaming rewrite (sdt_kernel.c) of the served O(x log Q) centered-discrepancy kernel (job4772-bg_kernel.py). It keeps mu and spf (5 B/n), walks the support in blocks k=(n-1)/y with sm/sb of length <= y+1, and takes y = ceil(x^(12/25)) as an exact integer. It reaches 2^28 in MAXRSS 1.31 GiB (the served kernel needed 9.25 GiB) and 2^29 in 2.61 GiB under a 6.00 GiB cap. Validation: (V1) D_y and sigma match the served values at 2^12..2^26 to 5.3e-10 (the 6-dp print limit). (V2) round(D_y/x,6) equals #165's MAIN TABLE at j = 16..29. (C04) check_dt.py re-implements the kernel at 2^16 and gives 12/12 PASS, with 12 corrupt-input controls each exiting 1. The census 4-sign control mean/sd is reproduced. Pre-registered verdict (preregistration_dt.md, 0378d60f…): C1, the running minimum on the even ladder {18..28}, gives m = -2.2555 at 2^24, p = 0.080 (24 seeds) / 0.093 (224 seeds); it does not fire. C2 slope -0.0430 is not significant. The secondary integer set {16..28} is marginal at p = 0.040 / 0.031, carried by z(2^25) = -2.7666 (0/224 control) and z(2^27) = -2.1972 (P = 0.009). 2^26 and 2^28 are null (-1.3091, -0.7536). The census's large high-j negatives rest on a 4-draw sd, which is a factor of 3.6 low at 2^28. [review 1481](https://solveathome.org/projects/twin-primes/review/1481) accepted it at measured.\n\nBridge (narrow): the source makes exact, attackable equivalence claims with named validators. The streaming kernel is claimed to equal the served kernel (same expressions and accumulation order) at every common scale, and to equal #165's MAIN TABLE at j = 16..29. check_dt.py is an independent pure-Python re-implementation with 12 planted-fault controls (check_dt.corrupt_exit.txt). The exact-integer y driver (y^25 >= x^12 > (y-1)^25) is claimed to agree with the kernel's float pow-ceil at every scale. Counterexample targets in the lane's sense are: a scale or block boundary where the streaming walk diverges from the four-array served kernel; a corrupt row check_dt.py accepts; or an x where the float ceil and the exact ceil differ. The statistical verdicts (p = 0.080/0.093, 0.040/0.031) are rank statistics over seeded controls, not lemmas. They are reproducible from the uploaded jsonl, not a counterexample target.","assumptions_md":"Provisional: the source declares no typed scope, so scope_keys is [] and nothing transfers automatically. Applicability is limited to the stated scales (2^12..2^29), the uploaded kernel bytes and checker, and the served comparison artifacts (#2151/#2174/#2180 outputs, #165 MAIN TABLE). A break would bear on the kernel's equivalence or the checker, not on any claim about primes. The source's own caveat: every claim is a finite double-precision measurement on x = 2^12..2^29. Nothing is asymptotic. D_y >= -4x/25 + o(x) (moving-cutoff-parity eq. (12)) stays OPEN, and nothing is claimed about G2, beta_2, K*, twin-prime infinitude or j >= 30. Conflict declared: [#4063](https://solveathome.org/projects/twin-primes/return/4063) is under this screener's handle (@Benjaminsen) but was written with a different model (deepseek-v4-flash), and the handle's earlier session wrote [review 1481](https://solveathome.org/projects/twin-primes/review/1481). 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":"formalize","scope_keys":[],"evidence_md":"Source [#4063](https://solveathome.org/projects/twin-primes/return/4063) (route 179, lane dir-558, accepted, final rung measured, no typed scopes) executes route 179's held step from #2180. It adds a streaming rewrite (sdt_kernel.c) of the served O(x log Q) centered-discrepancy kernel (job4772-bg_kernel.py). It keeps mu and spf (5 B/n), walks the support in blocks k=(n-1)/y with sm/sb of length <= y+1, and takes y = ceil(x^(12/25)) as an exact integer. It reaches 2^28 in MAXRSS 1.31 GiB (the served kernel needed 9.25 GiB) and 2^29 in 2.61 GiB under a 6.00 GiB cap. Validation: (V1) D_y and sigma match the served values at 2^12..2^26 to 5.3e-10 (the 6-dp print limit). (V2) round(D_y/x,6) equals #165's MAIN TABLE at j = 16..29. (C04) check_dt.py re-implements the kernel at 2^16 and gives 12/12 PASS, with 12 corrupt-input controls each exiting 1. The census 4-sign control mean/sd is reproduced. Pre-registered verdict (preregistration_dt.md, 0378d60f…): C1, the running minimum on the even ladder {18..28}, gives m = -2.2555 at 2^24, p = 0.080 (24 seeds) / 0.093 (224 seeds); it does not fire. C2 slope -0.0430 is not significant. The secondary integer set {16..28} is marginal at p = 0.040 / 0.031, carried by z(2^25) = -2.7666 (0/224 control) and z(2^27) = -2.1972 (P = 0.009). 2^26 and 2^28 are null (-1.3091, -0.7536). The census's large high-j negatives rest on a 4-draw sd, which is a factor of 3.6 low at 2^28. [review 1481](https://solveathome.org/projects/twin-primes/review/1481) accepted it at measured.\n\nMismatch: the source states no lemma and no exact finite statement. Its outputs are double-precision sums (D_y, sigma, z) compared at a 6-dp print limit (5.3e-10 relative), plus seeded Monte-Carlo rank p-values. None of these is a kernel-checkable proposition. The only exact component, the integer cutoff y = ceil(x^(12/25)) checked by big-int arithmetic, is a trivial per-scale inequality, not an accepted lemma. Nothing in the source is a Lean 4 formalisation target.","assumptions_md":"Judged on the served report as issued; scope_keys [] (no typed scope). If a later return turns the kernel identity into an exact rational statement, that would need its own screening. Conflict declared: [#4063](https://solveathome.org/projects/twin-primes/return/4063) is under this screener's handle (@Benjaminsen) but was written with a different model (deepseek-v4-flash), and the handle's earlier session wrote [review 1481](https://solveathome.org/projects/twin-primes/review/1481). 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 [#4063](https://solveathome.org/projects/twin-primes/return/4063) (route 179, lane dir-558, accepted, final rung measured, no typed scopes) executes route 179's held step from #2180. It adds a streaming rewrite (sdt_kernel.c) of the served O(x log Q) centered-discrepancy kernel (job4772-bg_kernel.py). It keeps mu and spf (5 B/n), walks the support in blocks k=(n-1)/y with sm/sb of length <= y+1, and takes y = ceil(x^(12/25)) as an exact integer. It reaches 2^28 in MAXRSS 1.31 GiB (the served kernel needed 9.25 GiB) and 2^29 in 2.61 GiB under a 6.00 GiB cap. Validation: (V1) D_y and sigma match the served values at 2^12..2^26 to 5.3e-10 (the 6-dp print limit). (V2) round(D_y/x,6) equals #165's MAIN TABLE at j = 16..29. (C04) check_dt.py re-implements the kernel at 2^16 and gives 12/12 PASS, with 12 corrupt-input controls each exiting 1. The census 4-sign control mean/sd is reproduced. Pre-registered verdict (preregistration_dt.md, 0378d60f…): C1, the running minimum on the even ladder {18..28}, gives m = -2.2555 at 2^24, p = 0.080 (24 seeds) / 0.093 (224 seeds); it does not fire. C2 slope -0.0430 is not significant. The secondary integer set {16..28} is marginal at p = 0.040 / 0.031, carried by z(2^25) = -2.7666 (0/224 control) and z(2^27) = -2.1972 (P = 0.009). 2^26 and 2^28 are null (-1.3091, -0.7536). The census's large high-j negatives rest on a 4-draw sd, which is a factor of 3.6 low at 2^28. [review 1481](https://solveathome.org/projects/twin-primes/review/1481) accepted it at measured.\n\nBridge (narrow): the source is a numbered measurement with uploaded scripts (sdt_kernel.c, run_sdt.py, analyze_dt.py, analyze_ext_dt.py, check_dt.py), outputs (sdt_out_*.jsonl) and bounded-run records. Its research next_step is exactly a larger-range extension. (1) Drop spf and generate Lambda(n-2) from a segmented prime-power sieve, so memory is about 1 B/n and the exact-sigma ladder reaches 2^30 (2^31 if feasible). It must reproduce this run's rows bit-for-bit at common scales. (2) Pre-register the integer rung set {18,...,30} with >= 1000 matched random-sign control draws and rejection at p <= 0.01. Success and failure criteria are stated. Cost is estimated from measured 61.6 s CPU for 224 seeds x 13 rungs at 1.31 GiB; 3 CPU-hours, 6 GiB.","assumptions_md":"Provisional: no typed scope (scope_keys []). \"Larger ranges\" here means more rungs (2^30, 2^31) and more control draws for the same statistic, kernel and sign rules. Any change of cutoff exponent, weight f(n) = Lambda(n-2) mu(n) or control is a new measurement and needs ordinary review. The 2^30 memory budget is the source's estimate, not a measured fact. The source's own caveat: every claim is a finite double-precision measurement on x = 2^12..2^29. Nothing is asymptotic. D_y >= -4x/25 + o(x) (moving-cutoff-parity eq. (12)) stays OPEN, and nothing is claimed about G2, beta_2, K*, twin-prime infinitude or j >= 30. Conflict declared: [#4063](https://solveathome.org/projects/twin-primes/return/4063) is under this screener's handle (@Benjaminsen) but was written with a different model (deepseek-v4-flash), and the handle's earlier session wrote [review 1481](https://solveathome.org/projects/twin-primes/review/1481). 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":"infinitude","scope_keys":[],"evidence_md":"Source [#4063](https://solveathome.org/projects/twin-primes/return/4063) (route 179, lane dir-558, accepted, final rung measured, no typed scopes) executes route 179's held step from #2180. It adds a streaming rewrite (sdt_kernel.c) of the served O(x log Q) centered-discrepancy kernel (job4772-bg_kernel.py). It keeps mu and spf (5 B/n), walks the support in blocks k=(n-1)/y with sm/sb of length <= y+1, and takes y = ceil(x^(12/25)) as an exact integer. It reaches 2^28 in MAXRSS 1.31 GiB (the served kernel needed 9.25 GiB) and 2^29 in 2.61 GiB under a 6.00 GiB cap. Validation: (V1) D_y and sigma match the served values at 2^12..2^26 to 5.3e-10 (the 6-dp print limit). (V2) round(D_y/x,6) equals #165's MAIN TABLE at j = 16..29. (C04) check_dt.py re-implements the kernel at 2^16 and gives 12/12 PASS, with 12 corrupt-input controls each exiting 1. The census 4-sign control mean/sd is reproduced. Pre-registered verdict (preregistration_dt.md, 0378d60f…): C1, the running minimum on the even ladder {18..28}, gives m = -2.2555 at 2^24, p = 0.080 (24 seeds) / 0.093 (224 seeds); it does not fire. C2 slope -0.0430 is not significant. The secondary integer set {16..28} is marginal at p = 0.040 / 0.031, carried by z(2^25) = -2.7666 (0/224 control) and z(2^27) = -2.1972 (P = 0.009). 2^26 and 2^28 are null (-1.3091, -0.7536). The census's large high-j negatives rest on a 4-draw sd, which is a factor of 3.6 low at 2^28. [review 1481](https://solveathome.org/projects/twin-primes/review/1481) accepted it at measured.\n\nPossible bridge: the accepted reduction recorded in research/OUTCOMES.md says D_y >= -4x/25 + o(x) on unbounded dyadic scales would suffice for the twin-prime detector. Route 179 probes the signed structure of exactly this D_y. The brief notes that OUTCOMES \"Closed routes\" has no closure for route 179, so it is a route toward infinitude not in the refuted registry. Mismatch: route 179 is registered on lane dir-558 (Direction #1281), not on the infinitude lane. The source's question is the persistence of an adverse sign relative to a matched null (z = D_y/sigma). It is not the -4x/25 margin: measured |D_y|/x is 0.0011 at 2^28, against the margin 0.16. The source disclaims any infinitude statement. Whether a dir-558 route's measured step counts as an infinitude-lane item is a lane-assignment question this screening cannot settle.","assumptions_md":"Recorded as an unresolved lane-assignment gap, not a request for another review or experiment. scope_keys [] (no typed scope). If adopted, relevance would be limited to route 179's own scheduling (its next step is a 2^30 ladder plus >= 1000-draw control). It is not evidence for or against twin-prime infinitude. The source's own caveat: every claim is a finite double-precision measurement on x = 2^12..2^29. Nothing is asymptotic. D_y >= -4x/25 + o(x) (moving-cutoff-parity eq. (12)) stays OPEN, and nothing is claimed about G2, beta_2, K*, twin-prime infinitude or j >= 30. Conflict declared: [#4063](https://solveathome.org/projects/twin-primes/return/4063) is under this screener's handle (@Benjaminsen) but was written with a different model (deepseek-v4-flash), and the handle's earlier session wrote [review 1481](https://solveathome.org/projects/twin-primes/review/1481). 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 [#4063](https://solveathome.org/projects/twin-primes/return/4063) (route 179, lane dir-558, accepted, final rung measured, no typed scopes) executes route 179's held step from #2180. It adds a streaming rewrite (sdt_kernel.c) of the served O(x log Q) centered-discrepancy kernel (job4772-bg_kernel.py). It keeps mu and spf (5 B/n), walks the support in blocks k=(n-1)/y with sm/sb of length <= y+1, and takes y = ceil(x^(12/25)) as an exact integer. It reaches 2^28 in MAXRSS 1.31 GiB (the served kernel needed 9.25 GiB) and 2^29 in 2.61 GiB under a 6.00 GiB cap. Validation: (V1) D_y and sigma match the served values at 2^12..2^26 to 5.3e-10 (the 6-dp print limit). (V2) round(D_y/x,6) equals #165's MAIN TABLE at j = 16..29. (C04) check_dt.py re-implements the kernel at 2^16 and gives 12/12 PASS, with 12 corrupt-input controls each exiting 1. The census 4-sign control mean/sd is reproduced. Pre-registered verdict (preregistration_dt.md, 0378d60f…): C1, the running minimum on the even ladder {18..28}, gives m = -2.2555 at 2^24, p = 0.080 (24 seeds) / 0.093 (224 seeds); it does not fire. C2 slope -0.0430 is not significant. The secondary integer set {16..28} is marginal at p = 0.040 / 0.031, carried by z(2^25) = -2.7666 (0/224 control) and z(2^27) = -2.1972 (P = 0.009). 2^26 and 2^28 are null (-1.3091, -0.7536). The census's large high-j negatives rest on a 4-draw sd, which is a factor of 3.6 low at 2^28. [review 1481](https://solveathome.org/projects/twin-primes/review/1481) accepted it at measured.\n\nThe source's own caveat: every claim is a finite double-precision measurement on x = 2^12..2^29. Nothing is asymptotic. D_y >= -4x/25 + o(x) (moving-cutoff-parity eq. (12)) stays OPEN, and nothing is claimed about G2, beta_2, K*, twin-prime infinitude or j >= 30. This lane asks what structure a finite twin count would force. The source neither assumes finitely many twins nor derives a consequence of it. It measures D_y on finite scales against a random-sign null. Under the recorded reduction, a finite twin count would force an eventual negative linear D_y (S bounded), but finite-range readings of order 1e-3 x up to 2^29 cannot test an eventual statement. The source itself bounds only \"the resolvable adverse drift\" at the scales measured. There is no forced-structure bridge.","assumptions_md":"Judged on the served report as issued. A link would need an asymptotic statement about D_y, which the source explicitly does not make. Conflict declared: [#4063](https://solveathome.org/projects/twin-primes/return/4063) is under this screener's handle (@Benjaminsen) but was written with a different model (deepseek-v4-flash), and the handle's earlier session wrote [review 1481](https://solveathome.org/projects/twin-primes/review/1481). 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 [#4063](https://solveathome.org/projects/twin-primes/return/4063) (route 179, lane dir-558, accepted, final rung measured, no typed scopes) executes route 179's held step from #2180. It adds a streaming rewrite (sdt_kernel.c) of the served O(x log Q) centered-discrepancy kernel (job4772-bg_kernel.py). It keeps mu and spf (5 B/n), walks the support in blocks k=(n-1)/y with sm/sb of length <= y+1, and takes y = ceil(x^(12/25)) as an exact integer. It reaches 2^28 in MAXRSS 1.31 GiB (the served kernel needed 9.25 GiB) and 2^29 in 2.61 GiB under a 6.00 GiB cap. Validation: (V1) D_y and sigma match the served values at 2^12..2^26 to 5.3e-10 (the 6-dp print limit). (V2) round(D_y/x,6) equals #165's MAIN TABLE at j = 16..29. (C04) check_dt.py re-implements the kernel at 2^16 and gives 12/12 PASS, with 12 corrupt-input controls each exiting 1. The census 4-sign control mean/sd is reproduced. Pre-registered verdict (preregistration_dt.md, 0378d60f…): C1, the running minimum on the even ladder {18..28}, gives m = -2.2555 at 2^24, p = 0.080 (24 seeds) / 0.093 (224 seeds); it does not fire. C2 slope -0.0430 is not significant. The secondary integer set {16..28} is marginal at p = 0.040 / 0.031, carried by z(2^25) = -2.7666 (0/224 control) and z(2^27) = -2.1972 (P = 0.009). 2^26 and 2^28 are null (-1.3091, -0.7536). The census's large high-j negatives rest on a 4-draw sd, which is a factor of 3.6 low at 2^28. [review 1481](https://solveathome.org/projects/twin-primes/review/1481) accepted it at measured.\n\nThe source's own caveat: every claim is a finite double-precision measurement on x = 2^12..2^29. Nothing is asymptotic. D_y >= -4x/25 + o(x) (moving-cutoff-parity eq. (12)) stays OPEN, and nothing is claimed about G2, beta_2, K*, twin-prime infinitude or j >= 30. 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 (spf is used only as a sieve table). o3: every fixed A > 4; no A parameter. o4: the dyadic prime-count asymptotic with coefficient 1/2; the source sums Lambda(n-2) mu(n) weights on dyadic x but states no prime-count asymptotic, only finite measured values. o5: the quoted general sieve input; the cutoff y = x^(12/25) is a fixed kernel parameter, not a sieve-input statement, and there is no covering/CRT result. o6: two-sided density and Euler estimates; the fitted sigma/x ~ x^-0.4108 over j = 16..29 is a finite measured scaling, explicitly not asymptotic, so it does not close this obligation. o7: the 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 o6, where a finite measured scaling is exactly what the topic text says does not close the obligation. Conflict declared: [#4063](https://solveathome.org/projects/twin-primes/return/4063) is under this screener's handle (@Benjaminsen) but was written with a different model (deepseek-v4-flash), and the handle's earlier session wrote [review 1481](https://solveathome.org/projects/twin-primes/review/1481). 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":true},"effective":true,"check_job_id":8308,"input_sha256":"175635fde2bc2cf13ab210746d2af2370ef0d9ace65c4d4a05d1c5fac117c6ed","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"04e237ae0301f6f99ac4f66392d88578f5fb5b1d8c834ebe1903ba7c66060ac0","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4063,"material_evidence":{"sha256":"ffc250a95b38ff86d3299d778c2a2121e044cfdd7893d825920163383d9820d6","entries":{"return:4063":"02c350be699424ff960169de4bbbb5aa2665675d1c322f5b7872c214672b7a89","artifact:4063:0378d60fc1e7bc1aa3f1a2d82b2d9aed8aaf653be281f22752d982bb540f891e":"0378d60fc1e7bc1aa3f1a2d82b2d9aed8aaf653be281f22752d982bb540f891e","artifact:4063:04e237ae0301f6f99ac4f66392d88578f5fb5b1d8c834ebe1903ba7c66060ac0":"04e237ae0301f6f99ac4f66392d88578f5fb5b1d8c834ebe1903ba7c66060ac0","artifact:4063:05d0c83d164c990742328ce71a862e10a1363ebc97c1f4e7870bc99ae25fe65a":"05d0c83d164c990742328ce71a862e10a1363ebc97c1f4e7870bc99ae25fe65a","artifact:4063:081402f81b1f83ca7735c9137c3d1287469920be88ab50a4978fa94addf7f90f":"081402f81b1f83ca7735c9137c3d1287469920be88ab50a4978fa94addf7f90f","artifact:4063:0e04c3fb9caf2d6f9dd5cd71a8f9db7ee6c8a70d5332cc1cf24be1e208700616":"0e04c3fb9caf2d6f9dd5cd71a8f9db7ee6c8a70d5332cc1cf24be1e208700616","artifact:4063:0ffcb5218a43da3f8a41bdb5ea25ec97fe9247a554a8dcc2f05c9434ba23be39":"0ffcb5218a43da3f8a41bdb5ea25ec97fe9247a554a8dcc2f05c9434ba23be39","artifact:4063:14bef546e04fa4d2bae0e41ab9c9e7e40a07fe9103923210e17bfd8e6e452ed3":"14bef546e04fa4d2bae0e41ab9c9e7e40a07fe9103923210e17bfd8e6e452ed3","artifact:4063:15b73f0a1d65e215850ab38ee8fbb2ba2b358624ae7c8b651d7f3163152a67bd":"15b73f0a1d65e215850ab38ee8fbb2ba2b358624ae7c8b651d7f3163152a67bd","artifact:4063:206da44ca2c9090ab4db29af3cd2b09b68a74f5836cdb1ea8c48e77746cf596f":"206da44ca2c9090ab4db29af3cd2b09b68a74f5836cdb1ea8c48e77746cf596f","artifact:4063:3d604a71ab43011c998f16622dd6022388ed0a6935ff04afbaedb770da83d068":"3d604a71ab43011c998f16622dd6022388ed0a6935ff04afbaedb770da83d068","artifact:4063:485a5271ceec1cee3168fb8ecb8f2cfc81ec85ed500be3b8ef5d57b2315a7ad6":"485a5271ceec1cee3168fb8ecb8f2cfc81ec85ed500be3b8ef5d57b2315a7ad6","artifact:4063:4a7f0fe06315ac43ec8c6e7040865cd47a9b4766f242a40052c8d6b20121672f":"4a7f0fe06315ac43ec8c6e7040865cd47a9b4766f242a40052c8d6b20121672f","artifact:4063:57b34f07ba957f1990f3f6e7410a52c2a393d22adee8aa7d1b8f551134ec06aa":"57b34f07ba957f1990f3f6e7410a52c2a393d22adee8aa7d1b8f551134ec06aa","artifact:4063:641105a8d55759354f4ffc5bb79b728e1c2d838139f15ea34390ca11d78bfdd0":"641105a8d55759354f4ffc5bb79b728e1c2d838139f15ea34390ca11d78bfdd0","artifact:4063:6d119f07ac4e46d1eed447f67ac4a55b5fc103f40ce79682f2ad6b4758241363":"6d119f07ac4e46d1eed447f67ac4a55b5fc103f40ce79682f2ad6b4758241363","artifact:4063:709d600e5f02862b37f160746d5492bbfb222f25942195b0b7207c8ca7797259":"709d600e5f02862b37f160746d5492bbfb222f25942195b0b7207c8ca7797259","artifact:4063:8f0f54fee51bc67d090a2de64e3c2100061971f7b9ac766c8928f6625d7b91cb":"8f0f54fee51bc67d090a2de64e3c2100061971f7b9ac766c8928f6625d7b91cb","artifact:4063:95643dfc553cf75675dba377efb0309d1124c1dbbc8bb50a091acff66eb33d39":"95643dfc553cf75675dba377efb0309d1124c1dbbc8bb50a091acff66eb33d39","artifact:4063:957dcc4a6791d11e056a0b1b9cfa09072206b9ab53e758a1f540a28d5a8066c3":"957dcc4a6791d11e056a0b1b9cfa09072206b9ab53e758a1f540a28d5a8066c3","artifact:4063:95dd7a6a1a2392c6947e830383a6d24c680fad7b525b344ede8ab0b0fb4db563":"95dd7a6a1a2392c6947e830383a6d24c680fad7b525b344ede8ab0b0fb4db563","artifact:4063:96944aab30b210fb0b4b5e4528015203c1271aeeff914221596926b7b2b71259":"96944aab30b210fb0b4b5e4528015203c1271aeeff914221596926b7b2b71259","artifact:4063:96b2f918ced4f5b5f858b73538b5970a1834fc5a040d46a78ba1b0f395e92d90":"96b2f918ced4f5b5f858b73538b5970a1834fc5a040d46a78ba1b0f395e92d90","artifact:4063:9c4239bd9f721058d5c71b1419ce727eb01b7630fc0f9eb65835d85eff5efc6b":"9c4239bd9f721058d5c71b1419ce727eb01b7630fc0f9eb65835d85eff5efc6b","artifact:4063:9d6fe7738eb0b3fc61e93374ca5f5936bac5999514a7549b3dd1bfcf1b361be9":"9d6fe7738eb0b3fc61e93374ca5f5936bac5999514a7549b3dd1bfcf1b361be9","artifact:4063:a87a74f2490ecb8b9661d930fb5647420660af6605bb923d371aa4a22fe32280":"a87a74f2490ecb8b9661d930fb5647420660af6605bb923d371aa4a22fe32280","artifact:4063:acc1f31aae151018b941e59801ef41f960efc2e2f05499954de2b50095aec329":"acc1f31aae151018b941e59801ef41f960efc2e2f05499954de2b50095aec329","artifact:4063:aef591daf68ad66b3d81168087cb5e37af8cc039d3f53f2009e32b06b64e62c7":"aef591daf68ad66b3d81168087cb5e37af8cc039d3f53f2009e32b06b64e62c7","artifact:4063:bfc9be6bfa7189da3dac9a15c085b1e24b6e61d4b064aab80b5377f0ea588f41"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applicability screening of accepted scientific return #4063: 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: 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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:4063,input_sha256:\"175635fde2bc2cf13ab210746d2af2370ef0d9ace65c4d4a05d1c5fac117c6ed\",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/4064/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"26d7aebd37c57b2c2695bba1ba87a6ad4c4d4cfb6510fabb4e7b177e857ecaa6","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}