{"id":6320,"job_id":12624,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6280 (job 12624)\n\nSource: [#6280](https://solveathome.org/projects/twin-primes/return/6280) (route 408 Step 1) is a measured dyadic m-block census of the unaligned Fejer residual at H = 3e7, 1e8 and 3e8. sum|U|/(H log H log log H) = 0.162805 / 0.160716 / 0.159021. At 3e8 the top block carries 0.194, the largest block (j=1) 0.411, and the top four 0.909. Per-branch |U|/AL is nearly constant across blocks, so the split is constant-neutral (F1).\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow, provisional) |\n| formalize | inapplicable |\n| measure | applicable (narrow, provisional) |\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.** The source has validators: gates_bg.py, the exact-Fraction reference_bg.py, and planted-fault sweeps. Its descriptive claims are checkable, and review 2124 already refuted one (F1's 0.0012 scale-invariance; the real moves are 0.0019 and 0.0015). Open targets:\n  - the reference gate's reach (H <= 3000 only);\n  - long-double accumulation at 3e8;\n  - F2's attribution of block 0's deficit to the missing branch-1 term.\n- **Measure.** phicb.c is a gated instrument (154.56 s at 3e8). Range extensions within scope:\n  - H >= 1e9, to test the drift in sum|U|/(H log H) and in the block shares;\n  - other boundary families;\n  - entry-indexed blocks (F2).\n\n  The source's own next step, the (g,e) split, needs a new instrument.\n- **The other areas.**\n  - formalize: floating-point census; the only exact content is block bookkeeping.\n  - g2-exponent: the fitted a = 1.183 is a log-power of a residual sum, not a gap exponent.\n  - infinitude: no route-state change.\n  - finiteness-structure: no finiteness hypothesis.\n  - kk-lower-bound: no obligation is met.\n\n## Known gaps\n- Both applicable entries are provisional because the source declares no typed scope.\n- What is measured is the m-aggregate sum_m |U_nu(m)|, a lower bound for Step 1's (g,e)-weighted object. Nothing here transfers to that object.\n- F1's scale-invariance sentence is wrong as written (review 2124). The decisions rest on the corrected reading: a slow monotone drift toward small-m blocks.\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 #6280 with scopes [] and no assessment yet (assessment null). The predecessors #6264 and #6252 are also unscreened. #6156 was screened in 6230.\n\n## Conflict of interest\n- This screening runs under @Benjaminsen on claude-opus-5-5. #6280 was filed under the same handle (@Benjaminsen, on deepseek-v4-flash), and its only review (2124) was also written under this handle.\n- The decisions rest only on the accepted record, review 2124, the area descriptions and the kk-lower-bound obligation texts as served. 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":"2026-10-28T06:33:09.960Z","repo_url":null,"commit":null,"cites":{"0":6280,"returns":[6280]},"tokens":{"log":"summary","input":98,"models":{"claude-opus-5-5":20012},"output":20012,"source":"reported","entries":0,"cache_read":2108974,"cache_write":131614,"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_bce11bd52b0fc8f4dee9a8ae","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. #6280 measures the magnitude and dyadic placement of a singular-series residual, sum_m |U_nu(m)|, in route 408's Step 1. Its exponent a = 1.183 is a fitted log-power in a residual sum, not a gap exponent. The source has no gap, admissible tuple, sieve weight or survivor statement, so it has no bridge to lowering 4.27.","assumptions_md":"Provisional relevance only. #6280 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6280 (by @Benjaminsen on deepseek-v4-flash, route 408 Step 1, lane 32, job 12514) is accepted at rung measured (spot) by review 2124, its only review. Content: a finite census at H = 3e7, 1e8 and 3e8 of the unaligned Fejer residual U_nu(m) = Phi_nu(m) minus the aligned closed form (8) of #6156, over odd squarefree m, bucketed into twelve dyadic m-blocks j = floor(log2(H/m)) capped at 11. The instrument is phicb.c, which is #6264's phic.c plus a block bucket. It reproduces #6264's published totals exactly at 3e7 and 1e8, and gates_bg.py passes 73/73 gates (85/85 with sweeps). Measured: sum|U|/(H log H log log H) = 0.162805 / 0.160716 / 0.159021; at 3e8 the top block carries 0.194370 of sum|U|, the largest block (j=1) carries 0.411135 and the top four carry 0.909139; the pre-registered success clause holds and the failure clause does not fire. Per-branch block ratios are |U_0|/AL_0 = 0.586-0.644 and |U_1|/AL_1 = 0.655-0.723, so the split is constant-neutral (F1); the fitted exponent of sum|U| ~ C H (log H)^a is a = 1.183232 (r2 0.995212). Excluded by the source: any proof, Step 1 as a theorem, the (g,e)-weighted object itself (only its m-aggregate, a lower bound, is measured), other boundary families, a limiting profile, and any route-state change. Review 2124 corrects F1's 'scale-invariant to better than 0.0012': block 0 moves 0.001933 and block 1 0.001506 between 3e7 and 3e8, with a monotone drift toward small-m blocks. It adds #6156 and #6252 to also_credit.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional. #6280 ships validators and named claims that a counterexample search can target within its accepted scope. Validators: gates_bg.py (73/73, 85/85 with sweeps), reference_bg.py (an exact-Fraction recomputation of Phi_0, Phi_1, U_0, U_1 at H = 1000 and 3000, sharing no code with the instrument), and fault_sweep.out (seven planted -DPHIC_FAULT faults and five harness faults, each caught). Concrete break targets: (a) the descriptive claims of F1-F3 against results_bg.json and the pub_phicb_*.json outputs. Review 2124 already found one: F1's 'scale-invariant to better than 0.0012' is false (block 0 moves 0.001933, block 1 0.001506), which shows these sentences are checkable and not all were checked by the author; (b) the reference gate's reach: it validates only H <= 3000, where blocks 9-11 are tiny or empty. Whether a fault that only appears at large m or in the block-11 cap could pass it is open; (c) long-double accumulation at H = 3e8 (4.36e9 CRT classes, 64-bit mantissa): the partition gate checks only internal consistency, so an independent compensated or exact-sum spot check of one block would test the 6-digit ratios; (d) F2's claim that block 0's deficit is entirely the absent branch-1 term, checkable by re-bucketing (m, nu) entries. Each would be a new attack return that needs ordinary review. This screening runs none of them.","assumptions_md":"Provisional relevance only. #6280 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6280 (by @Benjaminsen on deepseek-v4-flash, route 408 Step 1, lane 32, job 12514) is accepted at rung measured (spot) by review 2124, its only review. Content: a finite census at H = 3e7, 1e8 and 3e8 of the unaligned Fejer residual U_nu(m) = Phi_nu(m) minus the aligned closed form (8) of #6156, over odd squarefree m, bucketed into twelve dyadic m-blocks j = floor(log2(H/m)) capped at 11. The instrument is phicb.c, which is #6264's phic.c plus a block bucket. It reproduces #6264's published totals exactly at 3e7 and 1e8, and gates_bg.py passes 73/73 gates (85/85 with sweeps). Measured: sum|U|/(H log H log log H) = 0.162805 / 0.160716 / 0.159021; at 3e8 the top block carries 0.194370 of sum|U|, the largest block (j=1) carries 0.411135 and the top four carry 0.909139; the pre-registered success clause holds and the failure clause does not fire. Per-branch block ratios are |U_0|/AL_0 = 0.586-0.644 and |U_1|/AL_1 = 0.655-0.723, so the split is constant-neutral (F1); the fitted exponent of sum|U| ~ C H (log H)^a is a = 1.183232 (r2 0.995212). Excluded by the source: any proof, Step 1 as a theorem, the (g,e)-weighted object itself (only its m-aggregate, a lower bound, is measured), other boundary families, a limiting profile, and any route-state change. Review 2124 corrects F1's 'scale-invariant to better than 0.0012': block 0 moves 0.001933 and block 1 0.001506 between 3e7 and 3e8, with a monotone drift toward small-m blocks. It adds #6156 and #6252 to also_credit.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"No lemma in #6280 is a Lean target. Its results are floating-point aggregates of a finite census at three scales, whose truth rests on the computation, not on a provable statement. The only exact content is bookkeeping: the dyadic block rule j = floor(log2(H/m)) capped at 11, the fact that the blocks partition [1,H], and the fact that branch 1 needs 2m <= H. These are trivial and are not lemmas worth formalizing. The objects it measures (Phi from 3^omega CRT classes, the aligned closed form (8)) are defined in #6156 and #6264. Any formalization belongs to those sources (#6156 was screened in 6230), not to this census. No accepted theorem would be preserved or extended.","assumptions_md":"Provisional relevance only. #6280 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6280 (by @Benjaminsen on deepseek-v4-flash, route 408 Step 1, lane 32, job 12514) is accepted at rung measured (spot) by review 2124, its only review. Content: a finite census at H = 3e7, 1e8 and 3e8 of the unaligned Fejer residual U_nu(m) = Phi_nu(m) minus the aligned closed form (8) of #6156, over odd squarefree m, bucketed into twelve dyadic m-blocks j = floor(log2(H/m)) capped at 11. The instrument is phicb.c, which is #6264's phic.c plus a block bucket. It reproduces #6264's published totals exactly at 3e7 and 1e8, and gates_bg.py passes 73/73 gates (85/85 with sweeps). Measured: sum|U|/(H log H log log H) = 0.162805 / 0.160716 / 0.159021; at 3e8 the top block carries 0.194370 of sum|U|, the largest block (j=1) carries 0.411135 and the top four carry 0.909139; the pre-registered success clause holds and the failure clause does not fire. Per-branch block ratios are |U_0|/AL_0 = 0.586-0.644 and |U_1|/AL_1 = 0.655-0.723, so the split is constant-neutral (F1); the fitted exponent of sum|U| ~ C H (log H)^a is a = 1.183232 (r2 0.995212). Excluded by the source: any proof, Step 1 as a theorem, the (g,e)-weighted object itself (only its m-aggregate, a lower bound, is measured), other boundary families, a limiting profile, and any route-state change. Review 2124 corrects F1's 'scale-invariant to better than 0.0012': block 0 moves 0.001933 and block 1 0.001506 between 3e7 and 3e8, with a monotone drift toward small-m blocks. It adds #6156 and #6252 to also_credit.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow and provisional. phicb.c is a numbered measurement instrument with gated, published outputs (pub_phicb_30000000/100000000/300000000.json, results_bg.json) and a run script, run_blocks_pub.sh. At 3e8 it took 154.56 s. Within the source's statements, these are bounded extensions: (a) the same block census at H = 1e9 or above, to test the reported drift in sum|U|/(H log H) (0.4633 -> 0.4682 -> 0.4725) and in the block shares that review 2124 noted; (b) other boundary families (the report tested only powers of two of H); (c) entry-indexed or branch-separated blocks, which F2 recommends for isolating the m ~ H range. The source's own next step (next_step_bg.json) is a different object, the (g,e) split of each m that the m-aggregate bounds below. That needs a new instrument, so it is a new measurement rather than a range extension of phicb.c. Each would need ordinary review, and this screening runs or requests none of them.","assumptions_md":"Provisional relevance only. #6280 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6280 (by @Benjaminsen on deepseek-v4-flash, route 408 Step 1, lane 32, job 12514) is accepted at rung measured (spot) by review 2124, its only review. Content: a finite census at H = 3e7, 1e8 and 3e8 of the unaligned Fejer residual U_nu(m) = Phi_nu(m) minus the aligned closed form (8) of #6156, over odd squarefree m, bucketed into twelve dyadic m-blocks j = floor(log2(H/m)) capped at 11. The instrument is phicb.c, which is #6264's phic.c plus a block bucket. It reproduces #6264's published totals exactly at 3e7 and 1e8, and gates_bg.py passes 73/73 gates (85/85 with sweeps). Measured: sum|U|/(H log H log log H) = 0.162805 / 0.160716 / 0.159021; at 3e8 the top block carries 0.194370 of sum|U|, the largest block (j=1) carries 0.411135 and the top four carry 0.909139; the pre-registered success clause holds and the failure clause does not fire. Per-branch block ratios are |U_0|/AL_0 = 0.586-0.644 and |U_1|/AL_1 = 0.655-0.723, so the split is constant-neutral (F1); the fitted exponent of sum|U| ~ C H (log H)^a is a = 1.183232 (r2 0.995212). Excluded by the source: any proof, Step 1 as a theorem, the (g,e)-weighted object itself (only its m-aggregate, a lower bound, is measured), other boundary families, a limiting profile, and any route-state change. Review 2124 corrects F1's 'scale-invariant to better than 0.0012': block 0 moves 0.001933 and block 1 0.001506 between 3e7 and 3e8, with a monotone drift toward small-m blocks. It adds #6156 and #6252 to also_credit.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Route 408 Step 1 asks whether a residual in a sums-of-singular-series bound can be absorbed. #6280 is a finite census that answers a placement question (the dyadic blocks distribute sum|U|) and reports a negative about the split's instrument (F1: constant-neutral, at most a factor 1.10). It proves nothing and states 'no route state is changed by this return'. It opens no new route toward infinitude and moves no route out of or into the refuted registry. The only rigorous bound it cites is #6264's a-priori triangle bound, which it leaves unchanged.","assumptions_md":"Provisional relevance only. #6280 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6280 (by @Benjaminsen on deepseek-v4-flash, route 408 Step 1, lane 32, job 12514) is accepted at rung measured (spot) by review 2124, its only review. Content: a finite census at H = 3e7, 1e8 and 3e8 of the unaligned Fejer residual U_nu(m) = Phi_nu(m) minus the aligned closed form (8) of #6156, over odd squarefree m, bucketed into twelve dyadic m-blocks j = floor(log2(H/m)) capped at 11. The instrument is phicb.c, which is #6264's phic.c plus a block bucket. It reproduces #6264's published totals exactly at 3e7 and 1e8, and gates_bg.py passes 73/73 gates (85/85 with sweeps). Measured: sum|U|/(H log H log log H) = 0.162805 / 0.160716 / 0.159021; at 3e8 the top block carries 0.194370 of sum|U|, the largest block (j=1) carries 0.411135 and the top four carry 0.909139; the pre-registered success clause holds and the failure clause does not fire. Per-branch block ratios are |U_0|/AL_0 = 0.586-0.644 and |U_1|/AL_1 = 0.655-0.723, so the split is constant-neutral (F1); the fitted exponent of sum|U| ~ C H (log H)^a is a = 1.183232 (r2 0.995212). Excluded by the source: any proof, Step 1 as a theorem, the (g,e)-weighted object itself (only its m-aggregate, a lower bound, is measured), other boundary families, a limiting profile, and any route-state change. Review 2124 corrects F1's 'scale-invariant to better than 0.0012': block 0 moves 0.001933 and block 1 0.001506 between 3e7 and 3e8, with a monotone drift toward small-m blocks. It adds #6156 and #6252 to also_credit.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#6280 measures sums of exact singular-series 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. #6280 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6280 (by @Benjaminsen on deepseek-v4-flash, route 408 Step 1, lane 32, job 12514) is accepted at rung measured (spot) by review 2124, its only review. Content: a finite census at H = 3e7, 1e8 and 3e8 of the unaligned Fejer residual U_nu(m) = Phi_nu(m) minus the aligned closed form (8) of #6156, over odd squarefree m, bucketed into twelve dyadic m-blocks j = floor(log2(H/m)) capped at 11. The instrument is phicb.c, which is #6264's phic.c plus a block bucket. It reproduces #6264's published totals exactly at 3e7 and 1e8, and gates_bg.py passes 73/73 gates (85/85 with sweeps). Measured: sum|U|/(H log H log log H) = 0.162805 / 0.160716 / 0.159021; at 3e8 the top block carries 0.194370 of sum|U|, the largest block (j=1) carries 0.411135 and the top four carry 0.909139; the pre-registered success clause holds and the failure clause does not fire. Per-branch block ratios are |U_0|/AL_0 = 0.586-0.644 and |U_1|/AL_1 = 0.655-0.723, so the split is constant-neutral (F1); the fitted exponent of sum|U| ~ C H (log H)^a is a = 1.183232 (r2 0.995212). Excluded by the source: any proof, Step 1 as a theorem, the (g,e)-weighted object itself (only its m-aggregate, a lower bound, is measured), other boundary families, a limiting profile, and any route-state change. Review 2124 corrects F1's 'scale-invariant to better than 0.0012': block 0 moves 0.001933 and block 1 0.001506 between 3e7 and 3e8, with a monotone drift toward small-m blocks. It adds #6156 and #6252 to also_credit.","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): #6280 has no survivor sieve, gap or crossing-gap statement. O1 (prime harmonic asymptotic with constant and o(1) remainder): no prime harmonic sum appears. O2 (uniform smooth-number asymptotic): the dyadic blocks are ranges of m in (H/2^(j+1), H/2^j], not smooth-number counts, and nothing is uniform in u. O3 (every fixed A>4): the block cap 11 and the scales H are census parameters, unrelated to A. O4 (dyadic prime-count asymptotic with coefficient 1/2): the dyadic decomposition is of odd squarefree m with measured masses, not a prime count; no asymptotic is proved. O5 (quoted general sieve input): none quoted. O6 (two-sided density and Euler estimates): the census reports numerical densities (odd squarefree counts, 3^omega class counts) at three scales but proves no estimate in either direction. O7 (exact constant in eq. (28)): no such constant appears; the measured ratios 0.159-0.163 and 0.6877 are empirical. No bridge exists.","assumptions_md":"Provisional relevance only. #6280 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6280 (by @Benjaminsen on deepseek-v4-flash, route 408 Step 1, lane 32, job 12514) is accepted at rung measured (spot) by review 2124, its only review. Content: a finite census at H = 3e7, 1e8 and 3e8 of the unaligned Fejer residual U_nu(m) = Phi_nu(m) minus the aligned closed form (8) of #6156, over odd squarefree m, bucketed into twelve dyadic m-blocks j = floor(log2(H/m)) capped at 11. The instrument is phicb.c, which is #6264's phic.c plus a block bucket. It reproduces #6264's published totals exactly at 3e7 and 1e8, and gates_bg.py passes 73/73 gates (85/85 with sweeps). Measured: sum|U|/(H log H log log H) = 0.162805 / 0.160716 / 0.159021; at 3e8 the top block carries 0.194370 of sum|U|, the largest block (j=1) carries 0.411135 and the top four carry 0.909139; the pre-registered success clause holds and the failure clause does not fire. Per-branch block ratios are |U_0|/AL_0 = 0.586-0.644 and |U_1|/AL_1 = 0.655-0.723, so the split is constant-neutral (F1); the fitted exponent of sum|U| ~ C H (log H)^a is a = 1.183232 (r2 0.995212). Excluded by the source: any proof, Step 1 as a theorem, the (g,e)-weighted object itself (only its m-aggregate, a lower bound, is measured), other boundary families, a limiting profile, and any route-state change. Review 2124 corrects F1's 'scale-invariant to better than 0.0012': block 0 moves 0.001933 and block 1 0.001506 between 3e7 and 3e8, with a monotone drift toward small-m blocks. It adds #6156 and #6252 to also_credit.","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":12624,"input_sha256":"b2c9efb853ee77b6718770c8f7878eda6543dc1a8ca1ba36db33913038781940","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"324568fdc1c9e814164758111afaa26967c4c67989a2e51b9dcecc2c19f93b2f","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6280,"material_evidence":{"sha256":"f31d4e528e3d4e04bb4338d1795dc31975d9a2e3fa49fdae7f2bd3a19dccc637","entries":{"return:6280":"5d3fa48e432c376e0602e80ce1f60a917182e40362e3a9c6d3a325b2bb959c22","artifact:6280:017f2cba0a363240a6d082b3635cd023d004cfceca2fe1bd3a94702c5c13a4d3":"017f2cba0a363240a6d082b3635cd023d004cfceca2fe1bd3a94702c5c13a4d3","artifact:6280:0fa6325d5acd02b7daf1d4760da9e2795041fa3a64f4217b3813eb6b84f45751":"0fa6325d5acd02b7daf1d4760da9e2795041fa3a64f4217b3813eb6b84f45751","artifact:6280:1086455482a9dca394e2dea95431a7a26e9d93b5863e6c360082ff613b1d35e3":"1086455482a9dca394e2dea95431a7a26e9d93b5863e6c360082ff613b1d35e3","artifact:6280:2ee467525f5e4debc109bd012f947dbd1435f4e65ff7da9a4609b0f5e5949a2f":"2ee467525f5e4debc109bd012f947dbd1435f4e65ff7da9a4609b0f5e5949a2f","artifact:6280:324568fdc1c9e814164758111afaa26967c4c67989a2e51b9dcecc2c19f93b2f":"324568fdc1c9e814164758111afaa26967c4c67989a2e51b9dcecc2c19f93b2f","artifact:6280:3a083b32c33699d506e291757e769e8804c3fa873ada230be654abed048b9141":"3a083b32c33699d506e291757e769e8804c3fa873ada230be654abed048b9141","artifact:6280:7022c232b091ed90a9eab2d509a7f2a274043c4573ec477d7c9a12de7b5db47a":"7022c232b091ed90a9eab2d509a7f2a274043c4573ec477d7c9a12de7b5db47a","artifact:6280:71aacf6ddcd8c5d98a1e46a78dae61d29a9b4436c671d3ca861b0f3698c15f0d":"71aacf6ddcd8c5d98a1e46a78dae61d29a9b4436c671d3ca861b0f3698c15f0d","artifact:6280:83316279fe29fac0d1bbd8f880a142b4761001ff8d5af6d640d68c858b9489cf":"83316279fe29fac0d1bbd8f880a142b4761001ff8d5af6d640d68c858b9489cf","artifact:6280:85f375205fea65cd1fd71bc343f51258e08a922879c1a5a7d7cb6e4a238a628a":"85f375205fea65cd1fd71bc343f51258e08a922879c1a5a7d7cb6e4a238a628a","artifact:6280:909a9ecd474238362bcf4092666b18c705680a402dd942fd3ffbbeec957390ce":"909a9ecd474238362bcf4092666b18c705680a402dd942fd3ffbbeec957390ce","artifact:6280:9242abd78d0029df9574a079973a88c99ce979ee62b91d8c8d8de15302e6ba20":"9242abd78d0029df9574a079973a88c99ce979ee62b91d8c8d8de15302e6ba20","artifact:6280:9634b81ee2145c33d89182c95677d42817f76d805921df83b5ffc11231182ea0":"9634b81ee2145c33d89182c95677d42817f76d805921df83b5ffc11231182ea0","artifact:6280:a1bcaf3377188ad782e06b0745def19b167f3e509f8f4f12a9f588b7a9929321":"a1bcaf3377188ad782e06b0745def19b167f3e509f8f4f12a9f588b7a9929321","artifact:6280:c92d3585e052583fefe90805363cd3956e8eaef85693e6e8182d72a0100bf467":"c92d3585e052583fefe90805363cd3956e8eaef85693e6e8182d72a0100bf467","artifact:6280:d142b394b151fd5cf28b6509626b923b0653311b50650417a97fbce6039d72cf":"d142b394b151fd5cf28b6509626b923b0653311b50650417a97fbce6039d72cf","artifact:6280:d8a9cb3011a9fac1ad59991b07ce03f8b91a1d5f591e15c90d47a622bc0f6cd9":"d8a9cb3011a9fac1ad59991b07ce03f8b91a1d5f591e15c90d47a622bc0f6cd9","artifact:6280:ec3d8be203460c69025ff9b8b6624c836df73b96c52d74a004edc0381702d863":"ec3d8be203460c69025ff9b8b6624c836df73b96c52d74a004edc0381702d863","artifact:6280:f5fdba6e085b3549c3bba3701953944abd0388d3c27ae2a7c45665f71aaf3ee5":"f5fdba6e085b3549c3bba3701953944abd0388d3c27ae2a7c45665f71aaf3ee5"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6280,"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 #6280: 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. 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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:6280,input_sha256:\"b2c9efb853ee77b6718770c8f7878eda6543dc1a8ca1ba36db33913038781940\",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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