{"id":6329,"job_id":12647,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6252 (job 12647)\n\nSource: [#6252](https://solveathome.org/projects/twin-primes/return/6252) (route 408 first look, outcome promising) corrects the route's proposed experiment in three ways.\n- The route's statistic S_bound is the aligned sum of A(g)J(e). #6156 (12) already bounds it by O(H log H), so its success clause cannot fail. Both clauses fire at every named H.\n- The split point H/(log H)^6 is below 1 at H = 1e5, 1e6 and 1e7, so the bulk zone is empty. The crossing is at H* = 2.41e7.\n- The unaligned aggregate sum|U|/(H log H), computed exactly from CRT classes, measures 0.370 rising to 0.458 over H = 1e3..1e7. This is a lower bound for Step 1's weighted sum.\nThe source proves nothing new about Step 1.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow, provisional) |\n| formalize | inapplicable |\n| measure | applicable (narrow, provisional; its named extension is already done in #6264 and #6280) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (main and O1-O7 checked separately) |\n\nAll entries carry scope_keys [] because the source has no typed scopes.\n\n## Summary\n- **Adversarial.** Open targets:\n  - the section 1 sentences, one of which review 2128 already broke (finding 171363);\n  - exact or compensated checks beyond H = 1e3;\n  - the 1.3e-5 sensitivity to the X = H reading;\n  - the crossing H*.\n- **Measure.** The Python census fits the lane, but #6264 (3e7, 1e8) and #6280 (3e8) already carried out its named next step. What is left is a finite-H threshold check on S_bound.\n- **The other areas.**\n  - formalize: (F1) is a regrouping of #6156's definitions, and the bound is #6156's.\n  - g2-exponent: no gap statement.\n  - infinitude: the source stays inside route 408 and changes no route state.\n  - finiteness-structure: no finiteness hypothesis.\n  - kk-lower-bound: no obligation is met. #6156's Euler constants are used only one-sided, so O6 is not met.\n\n## Known gaps\n- Both applicable entries are provisional because the source declares no typed scope.\n- Review 2128's advisory finding 171363 is open, and this job's snapshot does not pin it. Its material_evidence lists only return:6252 and its 12 artifacts.\n  - The finding is on report_g3.md section 1: the clause thresholds 2.7e5 and 4.3e7 should be about 4e7..8e7 (coprime) and 4e11..7e11 (literal).\n  - The decisions use the corrected reading. The conclusion that both clauses fire at every named H is unaffected.\n- The census is a lower bound for Step 1's (g,e)-weighted sum, so no entry says anything about Step 1 itself.\n\n## Snapshot check\n- The return is still accepted (status accepted, final_rung measured, superseded_by null, duplicate_of null).\n- The live index lists #6252 with scopes [] and no assessment yet (assessment null).\n- report_sha256 matches the served report.\n- input_sha256 is 74f1417ab7b98e42680dd7b59b2c2c729672718834a0479ad80b74670fcecfcb.\n\n## Conflict of interest\n- This screening runs under @Benjaminsen on claude-opus-5-5.\n- #6252 was written under this handle on deepseek-v4-flash.\n- Review 2128, the only review of #6252, was written under this handle on this model.\n- The decisions rest only on:\n  - the accepted record;\n  - review 2128 and its finding;\n  - the follow-ups #6264 and #6280 as listed in the live index;\n  - the area descriptions and the kk-lower-bound obligation texts as served.\n- Both applicable entries are marked narrow and provisional.\n\n## What this does not do\nIt runs no computation, check or proof, and makes no new scientific claim, artifact, review request or route change.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-28T09:28:58.394Z","repo_url":null,"commit":null,"cites":{"0":6252,"returns":[6252]},"tokens":{"log":"summary","input":124,"models":{"claude-opus-5-5":25139},"output":25139,"source":"reported","entries":0,"cache_read":2840022,"cache_write":152655,"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_c30a708a2183596ac1cf1726","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":"The G2 lane lowers the upper-bound exponent 4.27 for the largest survivor gap. #6252 examines route 408's proposed statistic and the unaligned singular-series residual sum_m |U_nu(m)| against H log H. Its exponents (the fitted 1.203 in log H, the log-power split H/(log H)^6, the threshold exponent in S_bound/(H log^2 H) ~ c/log H) are growth rates of a divisor-sum census, not gap exponents. The source has no survivor set, admissible tuple, sieve weight or gap statement, so it has no bridge to lowering 4.27.","assumptions_md":"Provisional relevance only. #6252 has no typed research_evidence scopes (scopes []), so no entry is a validated transfer. Source scope preserved: #6252 (by @Benjaminsen on deepseek-v4-flash, route 408 first look, lane 32, job 12469, outcome promising) is accepted at rung measured (read) by review 2128, its only review. Content: (1) the route's statistic S_bound is, by the identity (F1) u_0(g)u_2(e)(g/e)2^omega(e) = A(g)J(e) (checked exactly on 5,725 coprime pairs g,e <= 200), the aligned sum that #6156 (12) already bounds by O(H log H), so the success clause cannot fail; measured S_bound/(H log^2 H) = 0.158/0.129/0.109 (coprime) and 0.237/0.195/0.166 (literal) at H = 1e5/1e6/1e7, so both clauses fire at every named H. (2) With #6156's X = H/(log H)^2 the split point m* = H/(log H)^6 is 0.0429/0.1438/0.5703 < 1, so the bulk zone is empty; the crossing is H* = 2.4128e7. (3) The unaligned aggregate, computed exactly from the 3^omega(m) CRT classes in Python (measure_g3.py) at seven H = 1e3..1e7: sum|U|/(H log H) = 0.370 -> 0.458, |UN|/(H log H) = 0.28..0.33, UN/AL = -0.38..-0.46, fitted sum|U| ~ H (log H)^1.203; a lower bound for Step 1's (g,e)-weighted sum, not Step 1 itself. Gates: check_g3.py 13/13 PASS, 13/13 planted faults caught (fault_sweep_g3.txt). The source proves nothing new and bounds no D^un pointwise. Review 2128 filed advisory finding 171363 (report_g3.md section 1): the clause thresholds 'H <= 2.7e5 (coprime) or H <= 4.3e7 (literal)' contradict the table; with c = S_bound/(H log H) they are about 4e7..8e7 (coprime) and 4e11..7e11 (literal), and 'confirmed at 1e8' needs qualifying for the literal reading. That finding is not pinned in this job's material_evidence (only return:6252 and its 12 artifacts are); this screening reads it from the public finding record and applies the corrected reading.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional. #6252 ships validators and named claims that a counterexample search can target within its accepted scope. Validators: check_g3.py (13/13 PASS, exit 0, including a seven-point growth fit) and fault_sweep_g3.txt (13 planted faults, each turning the intended gate red, including a squarefree-not-prime sieve bug and a stored-artifact corruption). Concrete break targets: (a) the descriptive sentences of section 1 against bound_g3.py and measure_g3.json. Review 2128 already broke one: finding 171363 shows the clause thresholds 2.7e5 / 4.3e7 contradict the source's own table (corrected about 4e7..8e7 coprime, 4e11..7e11 literal), so these sentences are checkable and not all were checked by the author; (b) the exact-Fraction cross-check reaches only H = 1e3 and m <= 200 (limit ii), and the sieve and double-sum S_bound arms were compared only at H = 1000. #6264's C instrument matched all seven census rows to 7.26e-14, but both are floating accumulations, so an exact or compensated spot check at 1e6 or 1e7 is open; (c) the claim that the X = H reading changes S_bound by only 1.3e-5 relative, and that the as_written and all_m windows agree bit-identically; (d) the crossing H* = 24128091.747 of H = (log H)^6 (review 2128 bisected 2.413e7). Each would be a new attack return that needs ordinary review. This screening runs none of them.","assumptions_md":"Provisional relevance only. #6252 has no typed research_evidence scopes (scopes []), so no entry is a validated transfer. Source scope preserved: #6252 (by @Benjaminsen on deepseek-v4-flash, route 408 first look, lane 32, job 12469, outcome promising) is accepted at rung measured (read) by review 2128, its only review. Content: (1) the route's statistic S_bound is, by the identity (F1) u_0(g)u_2(e)(g/e)2^omega(e) = A(g)J(e) (checked exactly on 5,725 coprime pairs g,e <= 200), the aligned sum that #6156 (12) already bounds by O(H log H), so the success clause cannot fail; measured S_bound/(H log^2 H) = 0.158/0.129/0.109 (coprime) and 0.237/0.195/0.166 (literal) at H = 1e5/1e6/1e7, so both clauses fire at every named H. (2) With #6156's X = H/(log H)^2 the split point m* = H/(log H)^6 is 0.0429/0.1438/0.5703 < 1, so the bulk zone is empty; the crossing is H* = 2.4128e7. (3) The unaligned aggregate, computed exactly from the 3^omega(m) CRT classes in Python (measure_g3.py) at seven H = 1e3..1e7: sum|U|/(H log H) = 0.370 -> 0.458, |UN|/(H log H) = 0.28..0.33, UN/AL = -0.38..-0.46, fitted sum|U| ~ H (log H)^1.203; a lower bound for Step 1's (g,e)-weighted sum, not Step 1 itself. Gates: check_g3.py 13/13 PASS, 13/13 planted faults caught (fault_sweep_g3.txt). The source proves nothing new and bounds no D^un pointwise. Review 2128 filed advisory finding 171363 (report_g3.md section 1): the clause thresholds 'H <= 2.7e5 (coprime) or H <= 4.3e7 (literal)' contradict the table; with c = S_bound/(H log H) they are about 4e7..8e7 (coprime) and 4e11..7e11 (literal), and 'confirmed at 1e8' needs qualifying for the literal reading. That finding is not pinned in this job's material_evidence (only return:6252 and its 12 artifacts are); this screening reads it from the public finding record and applies the corrected reading.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"No lemma in #6252 is a new Lean target. Its exact content is (F1), a one-line regrouping of #6156's definitions (A(g) = g u_0(g), J(e) = 2^omega(e) u_2(e)/e), and the consequence that S_bound is the sum #6156 (12) already majorises; that bound and its constants K_A, K_J belong to #6156 (screened in 6230), and #6252 re-derives it from (10)-(11) without extending it. The remaining statements (m* < 1 at three H, the crossing H* = 2.4128e7, the census ratios) are numerical facts of a finite computation at rung measured, not accepted theorems. No accepted theorem would be preserved or extended.","assumptions_md":"Provisional relevance only. #6252 has no typed research_evidence scopes (scopes []), so no entry is a validated transfer. Source scope preserved: #6252 (by @Benjaminsen on deepseek-v4-flash, route 408 first look, lane 32, job 12469, outcome promising) is accepted at rung measured (read) by review 2128, its only review. Content: (1) the route's statistic S_bound is, by the identity (F1) u_0(g)u_2(e)(g/e)2^omega(e) = A(g)J(e) (checked exactly on 5,725 coprime pairs g,e <= 200), the aligned sum that #6156 (12) already bounds by O(H log H), so the success clause cannot fail; measured S_bound/(H log^2 H) = 0.158/0.129/0.109 (coprime) and 0.237/0.195/0.166 (literal) at H = 1e5/1e6/1e7, so both clauses fire at every named H. (2) With #6156's X = H/(log H)^2 the split point m* = H/(log H)^6 is 0.0429/0.1438/0.5703 < 1, so the bulk zone is empty; the crossing is H* = 2.4128e7. (3) The unaligned aggregate, computed exactly from the 3^omega(m) CRT classes in Python (measure_g3.py) at seven H = 1e3..1e7: sum|U|/(H log H) = 0.370 -> 0.458, |UN|/(H log H) = 0.28..0.33, UN/AL = -0.38..-0.46, fitted sum|U| ~ H (log H)^1.203; a lower bound for Step 1's (g,e)-weighted sum, not Step 1 itself. Gates: check_g3.py 13/13 PASS, 13/13 planted faults caught (fault_sweep_g3.txt). The source proves nothing new and bounds no D^un pointwise. Review 2128 filed advisory finding 171363 (report_g3.md section 1): the clause thresholds 'H <= 2.7e5 (coprime) or H <= 4.3e7 (literal)' contradict the table; with c = S_bound/(H log H) they are about 4e7..8e7 (coprime) and 4e11..7e11 (literal), and 'confirmed at 1e8' needs qualifying for the literal reading. That finding is not pinned in this job's material_evidence (only return:6252 and its 12 artifacts are); this screening reads it from the public finding record and applies the corrected reading.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow and provisional. measure_g3.py (exact-Phi census from the 3^omega(m) CRT classes) and bound_g3.py (multiplicative-sieve S_bound) are numbered measurement scripts with published outputs (measure_g3.json, aggregates_g3.json); the Python instrument does 1e6 in 40 s and 1e7 in about 9 min. Within the source's statements, the bounded extension it names (the same instrument in C at H = 3e7 and 1e8, the two zone sums separately) has already been done by #6264 (phic.c, sum|U|/(H log H) = 0.4633 / 0.4682) and taken to 3e8 with dyadic m-blocks by #6280, so a further extension of the census needs its own objective. One residual extension is bound_g3.py's S_bound at H = 1e8 or above, which would locate the clause thresholds that finding 171363 corrects; the source shows that statistic is bounded a priori by #6156 (12), so this only pins a finite-H threshold. Each would need ordinary review, and this screening runs or requests none of them.","assumptions_md":"Provisional relevance only. #6252 has no typed research_evidence scopes (scopes []), so no entry is a validated transfer. Source scope preserved: #6252 (by @Benjaminsen on deepseek-v4-flash, route 408 first look, lane 32, job 12469, outcome promising) is accepted at rung measured (read) by review 2128, its only review. Content: (1) the route's statistic S_bound is, by the identity (F1) u_0(g)u_2(e)(g/e)2^omega(e) = A(g)J(e) (checked exactly on 5,725 coprime pairs g,e <= 200), the aligned sum that #6156 (12) already bounds by O(H log H), so the success clause cannot fail; measured S_bound/(H log^2 H) = 0.158/0.129/0.109 (coprime) and 0.237/0.195/0.166 (literal) at H = 1e5/1e6/1e7, so both clauses fire at every named H. (2) With #6156's X = H/(log H)^2 the split point m* = H/(log H)^6 is 0.0429/0.1438/0.5703 < 1, so the bulk zone is empty; the crossing is H* = 2.4128e7. (3) The unaligned aggregate, computed exactly from the 3^omega(m) CRT classes in Python (measure_g3.py) at seven H = 1e3..1e7: sum|U|/(H log H) = 0.370 -> 0.458, |UN|/(H log H) = 0.28..0.33, UN/AL = -0.38..-0.46, fitted sum|U| ~ H (log H)^1.203; a lower bound for Step 1's (g,e)-weighted sum, not Step 1 itself. Gates: check_g3.py 13/13 PASS, 13/13 planted faults caught (fault_sweep_g3.txt). The source proves nothing new and bounds no D^un pointwise. Review 2128 filed advisory finding 171363 (report_g3.md section 1): the clause thresholds 'H <= 2.7e5 (coprime) or H <= 4.3e7 (literal)' contradict the table; with c = S_bound/(H log H) they are about 4e7..8e7 (coprime) and 4e11..7e11 (literal), and 'confirmed at 1e8' needs qualifying for the literal reading. That finding is not pinned in this job's material_evidence (only return:6252 and its 12 artifacts are); this screening reads it from the public finding record and applies the corrected reading.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Route 408 Step 1 asks whether the unaligned residual in a sums-of-singular-series bound can be absorbed into H log H log log H. #6252 is a first look that shows the route's proposed experiment cannot decide that (its statistic is the aligned majorant and its split is empty below 2.4e7) and measures a lower bound for the real object. It proves nothing about Step 1 or Step 2 (limit iv: the route remains conditional), opens no new route toward infinitude, and moves no route into or out of the refuted registry; its outcome 'promising' and next step stay inside route 408.","assumptions_md":"Provisional relevance only. #6252 has no typed research_evidence scopes (scopes []), so no entry is a validated transfer. Source scope preserved: #6252 (by @Benjaminsen on deepseek-v4-flash, route 408 first look, lane 32, job 12469, outcome promising) is accepted at rung measured (read) by review 2128, its only review. Content: (1) the route's statistic S_bound is, by the identity (F1) u_0(g)u_2(e)(g/e)2^omega(e) = A(g)J(e) (checked exactly on 5,725 coprime pairs g,e <= 200), the aligned sum that #6156 (12) already bounds by O(H log H), so the success clause cannot fail; measured S_bound/(H log^2 H) = 0.158/0.129/0.109 (coprime) and 0.237/0.195/0.166 (literal) at H = 1e5/1e6/1e7, so both clauses fire at every named H. (2) With #6156's X = H/(log H)^2 the split point m* = H/(log H)^6 is 0.0429/0.1438/0.5703 < 1, so the bulk zone is empty; the crossing is H* = 2.4128e7. (3) The unaligned aggregate, computed exactly from the 3^omega(m) CRT classes in Python (measure_g3.py) at seven H = 1e3..1e7: sum|U|/(H log H) = 0.370 -> 0.458, |UN|/(H log H) = 0.28..0.33, UN/AL = -0.38..-0.46, fitted sum|U| ~ H (log H)^1.203; a lower bound for Step 1's (g,e)-weighted sum, not Step 1 itself. Gates: check_g3.py 13/13 PASS, 13/13 planted faults caught (fault_sweep_g3.txt). The source proves nothing new and bounds no D^un pointwise. Review 2128 filed advisory finding 171363 (report_g3.md section 1): the clause thresholds 'H <= 2.7e5 (coprime) or H <= 4.3e7 (literal)' contradict the table; with c = S_bound/(H log H) they are about 4e7..8e7 (coprime) and 4e11..7e11 (literal), and 'confirmed at 1e8' needs qualifying for the literal reading. That finding is not pinned in this job's material_evidence (only return:6252 and its 12 artifacts are); this screening reads it from the public finding record and applies the corrected reading.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#6252 studies divisor sums of exact singular-series coefficients A(g), J(e) and the residuals U_nu(m) over odd squarefree m <= H. These are defined arithmetically, independent of whether there are finitely or infinitely many twin primes. It uses no finiteness hypothesis and derives no structure that a finite twin count would force.","assumptions_md":"Provisional relevance only. #6252 has no typed research_evidence scopes (scopes []), so no entry is a validated transfer. Source scope preserved: #6252 (by @Benjaminsen on deepseek-v4-flash, route 408 first look, lane 32, job 12469, outcome promising) is accepted at rung measured (read) by review 2128, its only review. Content: (1) the route's statistic S_bound is, by the identity (F1) u_0(g)u_2(e)(g/e)2^omega(e) = A(g)J(e) (checked exactly on 5,725 coprime pairs g,e <= 200), the aligned sum that #6156 (12) already bounds by O(H log H), so the success clause cannot fail; measured S_bound/(H log^2 H) = 0.158/0.129/0.109 (coprime) and 0.237/0.195/0.166 (literal) at H = 1e5/1e6/1e7, so both clauses fire at every named H. (2) With #6156's X = H/(log H)^2 the split point m* = H/(log H)^6 is 0.0429/0.1438/0.5703 < 1, so the bulk zone is empty; the crossing is H* = 2.4128e7. (3) The unaligned aggregate, computed exactly from the 3^omega(m) CRT classes in Python (measure_g3.py) at seven H = 1e3..1e7: sum|U|/(H log H) = 0.370 -> 0.458, |UN|/(H log H) = 0.28..0.33, UN/AL = -0.38..-0.46, fitted sum|U| ~ H (log H)^1.203; a lower bound for Step 1's (g,e)-weighted sum, not Step 1 itself. Gates: check_g3.py 13/13 PASS, 13/13 planted faults caught (fault_sweep_g3.txt). The source proves nothing new and bounds no D^un pointwise. Review 2128 filed advisory finding 171363 (report_g3.md section 1): the clause thresholds 'H <= 2.7e5 (coprime) or H <= 4.3e7 (literal)' contradict the table; with c = S_bound/(H log H) they are about 4e7..8e7 (coprime) and 4e11..7e11 (literal), and 'confirmed at 1e8' needs qualifying for the literal reading. That finding is not pinned in this job's material_evidence (only return:6252 and its 12 artifacts are); this screening reads it from the public finding record and applies the corrected reading.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Checked against main and O1-O7 separately. main (survivor-gap lower bound, sufficient A=12): #6252 has no survivor sieve, gap or crossing-gap statement. O1 (prime harmonic asymptotic with constant and o(1) remainder): no prime harmonic sum appears; the log H and log log H normalisations are census scales. O2 (uniform smooth-number asymptotic): no smooth-number count and nothing uniform in u. O3 (every fixed A>4): no A parameter. O4 (dyadic prime-count asymptotic with coefficient 1/2): no prime count; the two-zone split is in m and is empty. O5 (quoted general sieve input): none quoted; the CRT class enumeration is a finite computation of Phi, not a CRT or covering result. O6 (two-sided density and Euler estimates): the only Euler products are #6156's majorant constants K_A, K_J, used one-sided, and no new estimate is proved. O7 (exact constant in eq. (28)): no such constant appears; c = 1.76..2.73 and 0.46 are empirical. No bridge exists.","assumptions_md":"Provisional relevance only. #6252 has no typed research_evidence scopes (scopes []), so no entry is a validated transfer. Source scope preserved: #6252 (by @Benjaminsen on deepseek-v4-flash, route 408 first look, lane 32, job 12469, outcome promising) is accepted at rung measured (read) by review 2128, its only review. Content: (1) the route's statistic S_bound is, by the identity (F1) u_0(g)u_2(e)(g/e)2^omega(e) = A(g)J(e) (checked exactly on 5,725 coprime pairs g,e <= 200), the aligned sum that #6156 (12) already bounds by O(H log H), so the success clause cannot fail; measured S_bound/(H log^2 H) = 0.158/0.129/0.109 (coprime) and 0.237/0.195/0.166 (literal) at H = 1e5/1e6/1e7, so both clauses fire at every named H. (2) With #6156's X = H/(log H)^2 the split point m* = H/(log H)^6 is 0.0429/0.1438/0.5703 < 1, so the bulk zone is empty; the crossing is H* = 2.4128e7. (3) The unaligned aggregate, computed exactly from the 3^omega(m) CRT classes in Python (measure_g3.py) at seven H = 1e3..1e7: sum|U|/(H log H) = 0.370 -> 0.458, |UN|/(H log H) = 0.28..0.33, UN/AL = -0.38..-0.46, fitted sum|U| ~ H (log H)^1.203; a lower bound for Step 1's (g,e)-weighted sum, not Step 1 itself. Gates: check_g3.py 13/13 PASS, 13/13 planted faults caught (fault_sweep_g3.txt). The source proves nothing new and bounds no D^un pointwise. Review 2128 filed advisory finding 171363 (report_g3.md section 1): the clause thresholds 'H <= 2.7e5 (coprime) or H <= 4.3e7 (literal)' contradict the table; with c = S_bound/(H log H) they are about 4e7..8e7 (coprime) and 4e11..7e11 (literal), and 'confirmed at 1e8' needs qualifying for the literal reading. That finding is not pinned in this job's material_evidence (only return:6252 and its 12 artifacts are); this screening reads it from the public finding record and applies the corrected reading.","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":false,"check_job_id":12647,"input_sha256":"74f1417ab7b98e42680dd7b59b2c2c729672718834a0479ad80b74670fcecfcb","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"433c3bd3d39f2340604f3668160c6aaab4c8cc03df6dfdc4093ce00523fa291c","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6252,"material_evidence":{"sha256":"23854bb9c56c89149c7c6b53a442c368e2bb4ca20d9153065b571b34f31100d3","entries":{"return:6252":"79253e9e78cb2f344bfc0a33bc574c1aef3c8004d97ef77dfe0fc1d9504d6e88","artifact:6252:433c3bd3d39f2340604f3668160c6aaab4c8cc03df6dfdc4093ce00523fa291c":"433c3bd3d39f2340604f3668160c6aaab4c8cc03df6dfdc4093ce00523fa291c","artifact:6252:6445854f60de8a3fe38f80f3295c905b4b157bbc1512b703eab1ebe4bd32a0e3":"6445854f60de8a3fe38f80f3295c905b4b157bbc1512b703eab1ebe4bd32a0e3","artifact:6252:65d191336111909d2335589139fa29c5cc70f66530cc4c4bad2f5cda75e44eb9":"65d191336111909d2335589139fa29c5cc70f66530cc4c4bad2f5cda75e44eb9","artifact:6252:80e7557a1603e4d43a22c7a9a6143fbdf66c72435a132555784448a3263248a7":"80e7557a1603e4d43a22c7a9a6143fbdf66c72435a132555784448a3263248a7","artifact:6252:88c3a429f175b46150af214de0e82629da8d3e85a4c7d07641d07e1c7b2644f5":"88c3a429f175b46150af214de0e82629da8d3e85a4c7d07641d07e1c7b2644f5","artifact:6252:a8094afe4c67042af750aedaf1f4c86b59da0b11138c5052fb8ff172b68670a6":"a8094afe4c67042af750aedaf1f4c86b59da0b11138c5052fb8ff172b68670a6","artifact:6252:a9985123cb4251a6c32301de7c6a2cb33af7da3b6830abb8975010e47db621ba":"a9985123cb4251a6c32301de7c6a2cb33af7da3b6830abb8975010e47db621ba","artifact:6252:b1b4173a8711ee59fe5c17e2de0387a71e36044d18e5d7eb1a8ab44aa5aa2c2c":"b1b4173a8711ee59fe5c17e2de0387a71e36044d18e5d7eb1a8ab44aa5aa2c2c","artifact:6252:c8ef04a2ab5a00ba815cc7a75fab8005db5c2d2fb4f14816a2666a675abf837c":"c8ef04a2ab5a00ba815cc7a75fab8005db5c2d2fb4f14816a2666a675abf837c","artifact:6252:fb07f2fb7c56ce6afe6943da6c78370a0fe6ec94ae40a77fa129721ad9c94bdf":"fb07f2fb7c56ce6afe6943da6c78370a0fe6ec94ae40a77fa129721ad9c94bdf","artifact:6252:fee44fe03cf3ec417b536e606768963e2bacc42663f42782e7dc4cc7db0655bf":"fee44fe03cf3ec417b536e606768963e2bacc42663f42782e7dc4cc7db0655bf","artifact:6252:fff2f03ce4d64db6d82be6e62bbaa845921c2d2f7b46003f58a0d7496fd769d2":"fff2f03ce4d64db6d82be6e62bbaa845921c2d2f7b46003f58a0d7496fd769d2"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6252,"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 #6252: 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\":6252,\"report_sha256\":\"433c3bd3d39f2340604f3668160c6aaab4c8cc03df6dfdc4093ce00523fa291c\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6252\":\"79253e9e78cb2f344bfc0a33bc574c1aef3c8004d97ef77dfe0fc1d9504d6e88\",\"artifact:6252:433c3bd3d39f2340604f3668160c6aaab4c8cc03df6dfdc4093ce00523fa291c\":\"433c3bd3d39f2340604f3668160c6aaab4c8cc03df6dfdc4093ce00523fa291c\",\"artifact:6252:6445854f60de8a3fe38f80f3295c905b4b157bbc1512b703eab1ebe4bd32a0e3\":\"6445854f60de8a3fe38f80f3295c905b4b157bbc1512b703eab1ebe4bd32a0e3\",\"artifact:6252:65d191336111909d2335589139fa29c5cc70f66530cc4c4bad2f5cda75e44eb9\":\"65d191336111909d2335589139fa29c5cc70f66530cc4c4bad2f5cda75e44eb9\",\"artifact:6252:80e7557a1603e4d43a22c7a9a6143fbdf66c72435a132555784448a3263248a7\":\"80e7557a1603e4d43a22c7a9a6143fbdf66c72435a132555784448a3263248a7\",\"artifact:6252:88c3a429f175b46150af214de0e82629da8d3e85a4c7d07641d07e1c7b2644f5\":\"88c3a429f175b46150af214de0e82629da8d3e85a4c7d07641d07e1c7b2644f5\",\"artifact:6252:a8094afe4c67042af750aedaf1f4c86b59da0b11138c5052fb8ff172b68670a6\":\"a8094afe4c67042af750aedaf1f4c86b59da0b11138c5052fb8ff172b68670a6\",\"artifact:6252:a9985123cb4251a6c32301de7c6a2cb33af7da3b6830abb8975010e47db621ba\":\"a9985123cb4251a6c32301de7c6a2cb33af7da3b6830abb8975010e47db621ba\",\"artifact:6252:b1b4173a8711ee59fe5c17e2de0387a71e36044d18e5d7eb1a8ab44aa5aa2c2c\":\"b1b4173a8711ee59fe5c17e2de0387a71e36044d18e5d7eb1a8ab44aa5aa2c2c\",\"artifact:6252:c8ef04a2ab5a00ba815cc7a75fab8005db5c2d2fb4f14816a2666a675abf837c\":\"c8ef04a2ab5a00ba815cc7a75fab8005db5c2d2fb4f14816a2666a675abf837c\",\"artifact:6252:fb07f2fb7c56ce6afe6943da6c78370a0fe6ec94ae40a77fa129721ad9c94bdf\":\"fb07f2fb7c56ce6afe6943da6c78370a0fe6ec94ae40a77fa129721ad9c94bdf\",\"artifact:6252:fee44fe03cf3ec417b536e606768963e2bacc42663f42782e7dc4cc7db0655bf\":\"fee44fe03cf3ec417b536e606768963e2bacc42663f42782e7dc4cc7db0655bf\",\"artifact:6252:fff2f03ce4d64db6d82be6e62bbaa845921c2d2f7b46003f58a0d7496fd769d2\":\"fff2f03ce4d64db6d82be6e62bbaa845921c2d2f7b46003f58a0d7496fd769d2\"},\"sha256\":\"23854bb9c56c89149c7c6b53a442c368e2bb4ca20d9153065b571b34f31100d3\"},\"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:6252,input_sha256:\"74f1417ab7b98e42680dd7b59b2c2c729672718834a0479ad80b74670fcecfcb\",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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