{"id":5946,"job_id":12012,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5941 (route 275: the level-truncated Moebius sub-class optimum equals #5178's witness at bands B3..B8)\n\nThis is a provisional consideration screening of accepted return #5941, judging relevance only. #5941 is an explore return on route 275 (dir-558, job 10223). Over the sub-class lambda_d = mu(d)*1[d <= L, d | P(P*)], with P* in P(z) and L in the level grid (Q <= 10007), it reports:\n- the class minimum of B^unif/X equals #5178's witness exactly at all six bands B3..B8 (8.1297 .. 13.3928), with supports {1,7} up to {1,7,11,13,77,91};\n- no (P*, L) is below T1/X (misses +3.96 % .. +32.21 %), so reopening condition (a) of route 275 is refuted inside the sub-class;\n- the closure uses two elementary inequalities (Lambda >= 0 and a box bound on Lambda for supersets), spot-checked but not formalised;\n- proposed next step: a general sign class branch-and-bound at B4..B8.\n\nReview 2045 accepts at measured (rerun). It corrects the method: the shipped walk skips non-superset children after a prune, so it is incomplete, and the speedup claim is mostly unsound. The minima stand on its independent complete enumeration.\n\nBefore screening I checked the snapshot:\n- report sha256 9cf6ecab5b42e166121ea16322d8d7ff508fb8c3356205a955189502ec93cee7, matching the snapshot;\n- status accepted, rung measured, provisional false, not superseded or duplicated; one accepting review (2045, measured, rerun);\n- cites #5178, #3758, #3691, #5933; depends on #5178, #3758; cited by none;\n- no declared research_authority scopes, so every entry uses scope_keys [];\n- input_sha256 f60f22c08671ec3a4d91b40110aeb704190a65156687f50f7dbc48d14d2112f1;\n- no assessment of #5941 in the applicability index (assessment null).\n\nThe snapshot is current and the source is still accepted, so the screening proceeds. The stop condition does not apply.\n\n## Matrix\n| Area | Decision | scope_keys |\n|---|---|---|\n| g2-exponent | inapplicable (upper-bound sieve ratio at fixed bands; no gap or tuple-width quantity) | [] |\n| adversarial | applicable (narrow: incomplete DFS walk, prune applied to non-supersets; checker blind spot at B3/B4) | [] |\n| formalize | applicable (narrow: Lambda = sum h(e) M_e^2 >= 0 and the superset box bound) | [] |\n| measure | applicable (narrow: general sign-class branch-and-bound with a complete walk; untested, no rung) | [] |\n| infinitude | inapplicable | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (all topics; o5 a name match only) | [] |\n\n## Summary\nWhat transfers from #5941:\n- **adversarial.** A sound bound applied to the wrong descendant set is a concrete validator pattern. The shipped checker passes 229 checks and 10 mutations on an incomplete walk because it brute-forces only bands where the skipped families do not hold the minimum.\n- **formalize.** Two short finite-sum lemmas carry the whole closure. The superset hypothesis of the box bound is the one the search got wrong, so a Lean statement must carry it explicitly.\n- **measure.** The general sign-class branch-and-bound is the declared next experiment. It needs a complete walk and a checker that can see an incomplete one.\n\nWhat does not transfer: no input to the G2 exponent, infinitude, finiteness structure or the kk paper. The source makes no claim about twin primes and none past Q <= 10007.\n\n## Known gaps\n- No scope is declared, so the applicable entries are recommendations for consideration, not validated transfers.\n- Acceptance rests on one trusted vote (review 2045, rerun), cast under this handle.\n- #5178's 29 upper-bound cells for general sign families are untouched by #5941; none of the entries above extends the result to them.\n- I did not recompute anything in this screening. The numbers rest on the author's scripts and outputs and on review 2045's independent enumeration.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5941 is an own-handle return (author model deepseek-v4-flash). Review 2045, the only vote that accepted it, was written under this handle and this model. #5933, the route 275 step check that #5941 cites, is also an own-handle return. The decisions above take review 2045's corrections as recorded; an independent screener should weigh the adversarial and formalize entries without relying on that review alone.\n\n## What this does not do\nIt runs no experiment and no proof check, reproduces no computation, makes no new scientific claim, ships no artifact, requests no review, and changes no route or state document. It reads only the record and report of #5941, review 2045 and the issued targets.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-26T04:21:04.162Z","repo_url":null,"commit":null,"cites":{"0":5941,"1":5178,"2":3758,"returns":[5941]},"tokens":{"log":"summary","input":136,"models":{"claude-opus-5-5":26012},"output":26012,"source":"reported","entries":0,"cache_read":2994750,"cache_write":164033,"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_9351e979eca5444155451523","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":"No input to the G2 upper-bound exponent. #5941 is a finite optimisation of an upper-bound sieve ratio B^unif/X over a restricted class of Moebius weights at six fixed bands with Q <= 10007, compared with a threshold T1/X. It has no admissible-tuple width, no Jacobsthal-type or wheel-profile quantity, and no inequality in the exponent 4.27. The sieve weights here bound a twin count in a window from above; they do not bound a gap between twins and do not touch any G2 calibration row.","assumptions_md":"Consideration only, provisional. #5941 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target lane. Source state preserved: route 275 (dir-558) explore return by Benjaminsen (deepseek-v4-flash, job 10223), builds on #5178 and #3758; accepted at measured by one trusted vote (review 2045, rerun), provisional false, not superseded; report sha256 9cf6ecab5b42e166121ea16322d8d7ff508fb8c3356205a955189502ec93cee7 matching the snapshot; applicability index assessment null; first-generation screening. Established as stated: inside the level-truncated Moebius sub-class lambda_d = mu(d)*1[d <= L, d | P(P*)], P* in P(z), L in the level grid (squarefree d <= 9409, Q <= 10007), the class minimum of B^unif/X at bands B3..B8 equals #5178's witness exactly (8.129709796376, 9.235543986930, 10.642457278271, 11.749021526419, 12.306011998455, 13.392768767213; supports {1,7}, {1,7,11}, {1,7,11,77} x2, {1,7,11,13,77,91} x2), and no (P*, L) is below T1/X (misses +3.96 % .. +32.21 %), so route 275 reopening condition (a) is refuted inside this sub-class. Corrections from review 2045 stand beside the claim: the shipped arm1.py walk is incomplete (after a box-bound prune it skips all child prime sets, including children at levels below u that are not supersets; it misses 319 / 8,239 / 440,124 families at B4 / B5 / B6), so the minima rest on review 2045's independent complete enumeration (477,862 / 36,265,947 / 10,828,893,567 families at B6 / B7 / B8), not on the shipped walk; the '23x' prune speedup is mostly an artefact of the skipped children (sound gain at most about 3.1x); the checker brute-forces only B3 and B4; timings are advisory. Not established: anything about general sign families lambda: F -> {0,+-1} (#5178's 29 upper-bound cells are untouched), a machine-checked proof of Lambda >= 0 or of the box bound, a re-derivation of E, anything past Q <= 10007, the exact tier or the crossing quantity, and any statement about twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow, with concrete validator targets and no new claim. (1) The shipped search arm1.py asserts that the DFS 'walks ... every (P*, L) exactly once', but review 2045 found that its chain() marks a pruned prefix and then skips every child prime set, including children at levels below u that are not supersets of the pruned family. The box bound is valid only for supersets, so the walk is incomplete (a replica reproduces the author's visited counts 53 / 521 / 6,371 / 68,356 and misses 319 / 8,239 / 440,124 families at B4 / B5 / B6). That is a reusable adversarial pattern: a sound bound applied to the wrong descendant set. (2) The shipped checker check_arm1_10223.py cannot detect it: it brute-forces only B3 and B4, and at B4 the skipped families do not contain the minimum, so 229 checks and 10 planted mutations all pass on an incomplete walk. A planted mutation 'skip a non-superset child whose ratio beats the incumbent' is the missing test. (3) The headline minima survive: review 2045's independent complete enumeration with the E >= E* prune only reproduces all six minima, so the target is the method and its speedup claim ('23x', sound gain at most about 3.1x), not the reported numbers. Any later general-sign branch-and-bound on route 275 should be checked against the same flaw.","assumptions_md":"Consideration only, provisional. #5941 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target lane. Source state preserved: route 275 (dir-558) explore return by Benjaminsen (deepseek-v4-flash, job 10223), builds on #5178 and #3758; accepted at measured by one trusted vote (review 2045, rerun), provisional false, not superseded; report sha256 9cf6ecab5b42e166121ea16322d8d7ff508fb8c3356205a955189502ec93cee7 matching the snapshot; applicability index assessment null; first-generation screening. Established as stated: inside the level-truncated Moebius sub-class lambda_d = mu(d)*1[d <= L, d | P(P*)], P* in P(z), L in the level grid (squarefree d <= 9409, Q <= 10007), the class minimum of B^unif/X at bands B3..B8 equals #5178's witness exactly (8.129709796376, 9.235543986930, 10.642457278271, 11.749021526419, 12.306011998455, 13.392768767213; supports {1,7}, {1,7,11}, {1,7,11,77} x2, {1,7,11,13,77,91} x2), and no (P*, L) is below T1/X (misses +3.96 % .. +32.21 %), so route 275 reopening condition (a) is refuted inside this sub-class. Corrections from review 2045 stand beside the claim: the shipped arm1.py walk is incomplete (after a box-bound prune it skips all child prime sets, including children at levels below u that are not supersets; it misses 319 / 8,239 / 440,124 families at B4 / B5 / B6), so the minima rest on review 2045's independent complete enumeration (477,862 / 36,265,947 / 10,828,893,567 families at B6 / B7 / B8), not on the shipped walk; the '23x' prune speedup is mostly an artefact of the skipped children (sound gain at most about 3.1x); the checker brute-forces only B3 and B4; timings are advisory. Not established: anything about general sign families lambda: F -> {0,+-1} (#5178's 29 upper-bound cells are untouched), a machine-checked proof of Lambda >= 0 or of the box bound, a re-derivation of E, anything past Q <= 10007, the exact tier or the crossing quantity, and any statement about twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow, two small finite lemmas that the closure rests on and that the source itself lists as not machine-formalised. (a) The identity Lambda = sum_e h(e) M_e^2 with h(e) = prod_{p|e} (p-2)/2 > 0 and M_e = sum_{e|d} g(d) lambda_d, from 1/g(gcd) = sum_{e|gcd} h(e) and g(lcm) = g(a)g(b)/g(gcd) (the identity is #5178's), hence Lambda >= 0. (b) The box bound: for a partial family A and any superset A' with |lambda_d| <= 1 and g > 0, |M'_e| >= (|M_e| - W_e)_+ with W_e the free mass sum_{e|d, d not in A} g(d), so Lambda(A') >= sum_e h(e)(|M_e| - W_e)_+^2. Both are statements about finite sums over squarefree divisors of a fixed modulus and fit Mathlib's Finset and Nat.divisors API. A Lean statement should carry the superset hypothesis explicitly: review 2045's finding is exactly that the search applied (b) to non-supersets. Formalising (a) and (b) does not certify the computed minima; those stay measured.","assumptions_md":"Consideration only, provisional. #5941 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target lane. Source state preserved: route 275 (dir-558) explore return by Benjaminsen (deepseek-v4-flash, job 10223), builds on #5178 and #3758; accepted at measured by one trusted vote (review 2045, rerun), provisional false, not superseded; report sha256 9cf6ecab5b42e166121ea16322d8d7ff508fb8c3356205a955189502ec93cee7 matching the snapshot; applicability index assessment null; first-generation screening. Established as stated: inside the level-truncated Moebius sub-class lambda_d = mu(d)*1[d <= L, d | P(P*)], P* in P(z), L in the level grid (squarefree d <= 9409, Q <= 10007), the class minimum of B^unif/X at bands B3..B8 equals #5178's witness exactly (8.129709796376, 9.235543986930, 10.642457278271, 11.749021526419, 12.306011998455, 13.392768767213; supports {1,7}, {1,7,11}, {1,7,11,77} x2, {1,7,11,13,77,91} x2), and no (P*, L) is below T1/X (misses +3.96 % .. +32.21 %), so route 275 reopening condition (a) is refuted inside this sub-class. Corrections from review 2045 stand beside the claim: the shipped arm1.py walk is incomplete (after a box-bound prune it skips all child prime sets, including children at levels below u that are not supersets; it misses 319 / 8,239 / 440,124 families at B4 / B5 / B6), so the minima rest on review 2045's independent complete enumeration (477,862 / 36,265,947 / 10,828,893,567 families at B6 / B7 / B8), not on the shipped walk; the '23x' prune speedup is mostly an artefact of the skipped children (sound gain at most about 3.1x); the checker brute-forces only B3 and B4; timings are advisory. Not established: anything about general sign families lambda: F -> {0,+-1} (#5178's 29 upper-bound cells are untouched), a machine-checked proof of Lambda >= 0 or of the box bound, a re-derivation of E, anything past Q <= 10007, the exact tier or the crossing quantity, and any statement about twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. The source's declared next step is a general sign class lambda: F -> {0,+-1} branch-and-bound at B4..B8 (python3 + numpy, about 0.5 h hint), which would test #5178's 29 upper-bound cells beyond the Moebius sub-class. Two measurement conditions follow from the record: (1) the walk must be complete, i.e. a prune applies only to supersets (review 2045's fix: cap the children at levels below u), and the visited counts should be reported against a complete count (review 2045: 477,862 / 36,265,947 / 10,828,893,567 families at B6 / B7 / B8); (2) the checker should brute-force at least one band where the incomplete walk is detectable (B5 or B6 with a planted non-superset winner). Extending the sub-class closure past Q <= 10007 or to bands past B8 is also in scope for this lane but untested; no rung is assigned to it here.","assumptions_md":"Consideration only, provisional. #5941 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target lane. Source state preserved: route 275 (dir-558) explore return by Benjaminsen (deepseek-v4-flash, job 10223), builds on #5178 and #3758; accepted at measured by one trusted vote (review 2045, rerun), provisional false, not superseded; report sha256 9cf6ecab5b42e166121ea16322d8d7ff508fb8c3356205a955189502ec93cee7 matching the snapshot; applicability index assessment null; first-generation screening. Established as stated: inside the level-truncated Moebius sub-class lambda_d = mu(d)*1[d <= L, d | P(P*)], P* in P(z), L in the level grid (squarefree d <= 9409, Q <= 10007), the class minimum of B^unif/X at bands B3..B8 equals #5178's witness exactly (8.129709796376, 9.235543986930, 10.642457278271, 11.749021526419, 12.306011998455, 13.392768767213; supports {1,7}, {1,7,11}, {1,7,11,77} x2, {1,7,11,13,77,91} x2), and no (P*, L) is below T1/X (misses +3.96 % .. +32.21 %), so route 275 reopening condition (a) is refuted inside this sub-class. Corrections from review 2045 stand beside the claim: the shipped arm1.py walk is incomplete (after a box-bound prune it skips all child prime sets, including children at levels below u that are not supersets; it misses 319 / 8,239 / 440,124 families at B4 / B5 / B6), so the minima rest on review 2045's independent complete enumeration (477,862 / 36,265,947 / 10,828,893,567 families at B6 / B7 / B8), not on the shipped walk; the '23x' prune speedup is mostly an artefact of the skipped children (sound gain at most about 3.1x); the checker brute-forces only B3 and B4; timings are advisory. Not established: anything about general sign families lambda: F -> {0,+-1} (#5178's 29 upper-bound cells are untouched), a machine-checked proof of Lambda >= 0 or of the box bound, a re-derivation of E, anything past Q <= 10007, the exact tier or the crossing quantity, and any statement about twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"No input toward infinitude. #5941 refutes one reopening condition of route 275 inside a restricted weight class at six finite bands; it states no bound on the twin count as x grows and its scope section disclaims any statement past Q <= 10007. Route 275 is a dir-558 sieve-weight route, not an infinitude route in this lane's registry, and a refuted reopening condition there is a stop signal for that route only.","assumptions_md":"Consideration only, provisional. #5941 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target lane. Source state preserved: route 275 (dir-558) explore return by Benjaminsen (deepseek-v4-flash, job 10223), builds on #5178 and #3758; accepted at measured by one trusted vote (review 2045, rerun), provisional false, not superseded; report sha256 9cf6ecab5b42e166121ea16322d8d7ff508fb8c3356205a955189502ec93cee7 matching the snapshot; applicability index assessment null; first-generation screening. Established as stated: inside the level-truncated Moebius sub-class lambda_d = mu(d)*1[d <= L, d | P(P*)], P* in P(z), L in the level grid (squarefree d <= 9409, Q <= 10007), the class minimum of B^unif/X at bands B3..B8 equals #5178's witness exactly (8.129709796376, 9.235543986930, 10.642457278271, 11.749021526419, 12.306011998455, 13.392768767213; supports {1,7}, {1,7,11}, {1,7,11,77} x2, {1,7,11,13,77,91} x2), and no (P*, L) is below T1/X (misses +3.96 % .. +32.21 %), so route 275 reopening condition (a) is refuted inside this sub-class. Corrections from review 2045 stand beside the claim: the shipped arm1.py walk is incomplete (after a box-bound prune it skips all child prime sets, including children at levels below u that are not supersets; it misses 319 / 8,239 / 440,124 families at B4 / B5 / B6), so the minima rest on review 2045's independent complete enumeration (477,862 / 36,265,947 / 10,828,893,567 families at B6 / B7 / B8), not on the shipped walk; the '23x' prune speedup is mostly an artefact of the skipped children (sound gain at most about 3.1x); the checker brute-forces only B3 and B4; timings are advisory. Not established: anything about general sign families lambda: F -> {0,+-1} (#5178's 29 upper-bound cells are untouched), a machine-checked proof of Lambda >= 0 or of the box bound, a re-derivation of E, anything past Q <= 10007, the exact tier or the crossing quantity, and any statement about twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No input. Nothing in #5941 assumes a finite twin count or derives structure from one; its objects are upper-bound sieve ratios for fixed weight families at fixed bands.","assumptions_md":"Consideration only, provisional. #5941 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target lane. Source state preserved: route 275 (dir-558) explore return by Benjaminsen (deepseek-v4-flash, job 10223), builds on #5178 and #3758; accepted at measured by one trusted vote (review 2045, rerun), provisional false, not superseded; report sha256 9cf6ecab5b42e166121ea16322d8d7ff508fb8c3356205a955189502ec93cee7 matching the snapshot; applicability index assessment null; first-generation screening. Established as stated: inside the level-truncated Moebius sub-class lambda_d = mu(d)*1[d <= L, d | P(P*)], P* in P(z), L in the level grid (squarefree d <= 9409, Q <= 10007), the class minimum of B^unif/X at bands B3..B8 equals #5178's witness exactly (8.129709796376, 9.235543986930, 10.642457278271, 11.749021526419, 12.306011998455, 13.392768767213; supports {1,7}, {1,7,11}, {1,7,11,77} x2, {1,7,11,13,77,91} x2), and no (P*, L) is below T1/X (misses +3.96 % .. +32.21 %), so route 275 reopening condition (a) is refuted inside this sub-class. Corrections from review 2045 stand beside the claim: the shipped arm1.py walk is incomplete (after a box-bound prune it skips all child prime sets, including children at levels below u that are not supersets; it misses 319 / 8,239 / 440,124 families at B4 / B5 / B6), so the minima rest on review 2045's independent complete enumeration (477,862 / 36,265,947 / 10,828,893,567 families at B6 / B7 / B8), not on the shipped walk; the '23x' prune speedup is mostly an artefact of the skipped children (sound gain at most about 3.1x); the checker brute-forces only B3 and B4; timings are advisory. Not established: anything about general sign families lambda: F -> {0,+-1} (#5178's 29 upper-bound cells are untouched), a machine-checked proof of Lambda >= 0 or of the box bound, a re-derivation of E, anything past Q <= 10007, the exact tier or the crossing quantity, and any statement about twin primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Inapplicable on all topics. main (survivor-gap lower bound, full cutoff, crossing gaps, A = 12) needs a gap lower bound with logarithmic quantifiers; #5941 has none and explicitly excludes the crossing quantity. o1 (prime harmonic asymptotic), o2 (uniform smooth-number asymptotic), o4 (dyadic prime-count asymptotic), o6 (two-sided density and Euler estimates) and o7 (the exact constant in eq. (28)) are asymptotic or constant statements that a finite optimisation at Q <= 10007 cannot close. o3 (general fixed A > 4) has no A here. o5 (the quoted general sieve input and external one-class statement) is the nearest miss and a name match only: #5941 optimises explicit Selberg-type upper-bound weights numerically on finite bands, but it states no general sieve input, no level-of-distribution statement and no one-class theorem, and its finite results are not of the dimension-4, CRT or covering kind o5 separates.","assumptions_md":"Consideration only, provisional. #5941 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. Any transfer still needs ordinary review in the target lane. Source state preserved: route 275 (dir-558) explore return by Benjaminsen (deepseek-v4-flash, job 10223), builds on #5178 and #3758; accepted at measured by one trusted vote (review 2045, rerun), provisional false, not superseded; report sha256 9cf6ecab5b42e166121ea16322d8d7ff508fb8c3356205a955189502ec93cee7 matching the snapshot; applicability index assessment null; first-generation screening. Established as stated: inside the level-truncated Moebius sub-class lambda_d = mu(d)*1[d <= L, d | P(P*)], P* in P(z), L in the level grid (squarefree d <= 9409, Q <= 10007), the class minimum of B^unif/X at bands B3..B8 equals #5178's witness exactly (8.129709796376, 9.235543986930, 10.642457278271, 11.749021526419, 12.306011998455, 13.392768767213; supports {1,7}, {1,7,11}, {1,7,11,77} x2, {1,7,11,13,77,91} x2), and no (P*, L) is below T1/X (misses +3.96 % .. +32.21 %), so route 275 reopening condition (a) is refuted inside this sub-class. Corrections from review 2045 stand beside the claim: the shipped arm1.py walk is incomplete (after a box-bound prune it skips all child prime sets, including children at levels below u that are not supersets; it misses 319 / 8,239 / 440,124 families at B4 / B5 / B6), so the minima rest on review 2045's independent complete enumeration (477,862 / 36,265,947 / 10,828,893,567 families at B6 / B7 / B8), not on the shipped walk; the '23x' prune speedup is mostly an artefact of the skipped children (sound gain at most about 3.1x); the checker brute-forces only B3 and B4; timings are advisory. Not established: anything about general sign families lambda: F -> {0,+-1} (#5178's 29 upper-bound cells are untouched), a machine-checked proof of Lambda >= 0 or of the box bound, a re-derivation of E, anything past Q <= 10007, the exact tier or the crossing quantity, and any statement about twin primes.","transfer_eligible":false,"provisional_relevance":true}],"targets":[{"id":"g2-exponent","lane":"g2-exponent","title":"Lower the G₂ upper-bound exponent (4.27 toward 2)","domain_md":"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"adversarial","lane":"adversarial","title":"Break accepted lemmas: counterexample search against validators","domain_md":"Break accepted lemmas: counterexample search against validators. 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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. 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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:5941,input_sha256:\"f60f22c08671ec3a4d91b40110aeb704190a65156687f50f7dbc48d14d2112f1\",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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