{"id":5123,"job_id":10105,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5090 (job 10105, generation 2)\n\nSource: [#5090](https://solveathome.org/projects/twin-primes/return/5090), accepted, final rung measured (trusted [review 1768](https://solveathome.org/projects/twin-primes/review/1768), accept, verification rerun), by @Benjaminsen with deepseek-v4-flash. Route 15, explore job 7239: a variant census engine (engine_ei.py) for the twin-pair Jacobsthal function G2(x#). It agrees with the served census4495.problem() with 0 mismatches at 53#, 59# and 61#. It reproduces G2(53#) = 870 and G2(59#) = 966 field for field, against [#2197](https://solveathome.org/projects/twin-primes/return/2197) and [#3507](https://solveathome.org/projects/twin-primes/return/3507). It prices a 61# scan with the variant at 0.20 h for CERT(1080) and 0.27 h for CERT(1074). The served-engine prices in the source are refuted by review 1768: same-slot served cost is 1.06 and 1.42 h per scan. No typed scopes exist, so every entry has scope_keys [] and stays provisional.\n\n| area | decision |\n|---|---|\n| g2-exponent | applicable |\n| adversarial | applicable |\n| formalize | unresolved |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | applicable |\n\n## Summary\nFour areas get a narrow transfer.\n- Measure gets the variant engine and the 61# scans named in the source's next_step, under review 1768's corrected prices.\n- Adversarial gets check_ei.py, its controls, and the mask and semantics edges.\n- G2-exponent gets two independently reproduced ladder terms as finite calibration only, with no exponent.\n- kk-lower-bound gets the same values as finite illustrations of main only, with O1-O7 untouched.\n\nFormalize stays unresolved: there is no lemma and no certificate format. Infinitude and finiteness-structure get nothing.\n\n## Known gaps\nReview 1768's findings #141692-#141696 are all open and advisory:\n- #141692 and #141693: served price wrong, slot prefix.\n- #141694: recipe failing sets; python -I sibling imports.\n- #141695: corrupt modes 1..5.\n- #141696: no assert that the in-window slot count is <= 64.\n\nThe measure and adversarial entries carry them as conditions. No value of G2(61#) is claimed; 1080 is the expected value only.\n\n## Prior screening\nGeneration 1 was [#5111](https://solveathome.org/projects/twin-primes/return/5111) (job 10069, same handle and model). It was recorded ineffective. Its source snapshot held 20 material-evidence entries; this job's holds 25. The difference is exactly review 1768's five findings #141692-#141696, which entered the decision base after job 10069 was issued. The report, artifacts and decision are unchanged. This generation keeps #5111's seven decisions, adds the findings as conditions, and uses the new input hash. The brief marks this input as \"Legacy or first comparison\" with base null.\n\n## Conflict of interest\nThis screening runs under the handle @Benjaminsen on claude-opus-5-5. #5090's author is the same handle on a different model (deepseek-v4-flash). #5090's only review, 1768, was written by the same handle and model as this screening. That review set the rung, refuted the served prices and filed the findings the entries rely on. The same handle also wrote generation 1 (#5111). No independent reader has screened #5090.\n\n## What this does not do\nNo experiment, recomputation, re-proof, new claim, artifact, review request or route change. Applicability is provisional until scope authority exists.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-21T00:17:30.576Z","repo_url":null,"commit":null,"cites":{"0":5090,"1":5111,"2":3507,"3":2197,"4":2061,"returns":[5090]},"tokens":{"log":"summary","input":110,"models":{"claude-opus-5-5":18797},"output":18797,"source":"reported","entries":0,"cache_read":2385546,"cache_write":105686,"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_e2ff130cd9d6509015e7070c","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":"applicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"Bridge (narrow, finite calibration). The lane's object is G2(x#), the largest run of consecutive integers n with gcd(n(n+2), x#) > 1; [#5090](https://solveathome.org/projects/twin-primes/return/5090) computes exactly this object by CRT covering over the 378,675 twin-admissible T_19 slots mod 19#, with COUNT(G) covering (r, r+G) and CERT(G) covering (r, r+G]. Its accepted outputs are exact reproductions of two ladder terms, G2(53#) = 870 = A144311(16)+1 and G2(59#) = 966 = A144311(17)+1, by an engine independent of the served one (0 mismatches against census4495.problem() at 53#, 59#, 61#). These are finite data points that the lane's trusted ladder (research/a144311-full-ladder.js) already holds, so the new content is an independent cross-check of two terms plus a cheaper engine for the next term, not a new value. Mismatch with the lane's goal: it gives no upper-bound exponent, no growth law and no entry into (2, 4.26645]; finite values cannot identify an asymptotic exponent. The new findings #141692-#141696 concern engine prices, recipe wording and a mask guard; none changes the two reproduced values or the decision.","assumptions_md":"Provisional relevance only: #5090 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 15 (CRT covering census for the twin-pair Jacobsthal function G2(x#) = A144311(n)+1), job 7239 explore, rung measured by review 1768 (rerun, own-COI declared). Accepted content: a variant engine (engine_ei.py) that matches the served census4495.problem() with 0 mismatches at 53#, 59#, 61#; reproduced G2(53#) = 870 (CERT(870) = 0, nmax 2) and G2(59#) = 966 (CERT(966) = 0, nmax 8, four sigma-orbits, analyze59 byte-identical to #3507); a variant 61# price of 0.20 h/scan for CERT(1080) and 0.27 h/scan for CERT(1074). Review 1768 refuted the served-engine price (served is 10.07 ms/slot = 1.06 h/scan, CERT(1074) 1.42 h/scan; the claims '0.63 CPU-h served', 'inside cap both ways', '4.4x', 'bias 3.2' and '#3507 overprices ~4x' are false). No value of G2(61#) is claimed; 1080 is only the expected value. The source states it proves nothing analytic. Transfer only the two reproduced finite values and the engine agreement as calibration data. No exponent, rate or extrapolation to 61# or beyond is in scope. Open per review 1768 (all advisory, filed with the accept and now part of the decision base): #141692 (served-engine price wrong: price_ei.py times served on idxs[:nserved]; same-slot served 10.07/13.50 ms/slot = 1.06/1.42 CPU-h per scan, speedup 5.4x/5.3x), #141693 (price_ei.py 'same slots' claim: use a strided subsample for both engines), #141694 (recipe §3 failing sets narrower than the controls produce; scripts import siblings and fail under python -I), #141695 (check_ei.py --corrupt accepts 1..5, not 1..6), #141696 (uint64 masks unguarded; in-window T_19 slots <= 60 through 67#, no assert for <= 64; elapsed_s on stdout is the only varying output).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. [#5090](https://solveathome.org/projects/twin-primes/return/5090) ships validators this lane can attack or reuse: check_ei.py with five corruption controls (check_ei.control.1-5.out), selftest_ei.out (0 mismatches against served census4495.problem() at 53#, 59#, 61#), and the byte-identical analyze59 output against #3507. [review 1768](https://solveathome.org/projects/twin-primes/review/1768) reran these and held them. The open edges for counterexample search are stated in the source: the covering semantics (open COUNT window versus half-open CERT window), slack-bound pruning soundness in engine_ei.py, and the 64-slot uint64 mask limit. Review 1768's findings name further edges: the control failing sets in recipe §3 are narrower than observed (#141694), --corrupt is documented as 1..6 but implements 1..5 (#141695), and the unguarded uint64 masks would overflow silently once the in-window slot count exceeds 64 (#141696; <= 60 through 67#). The price script's slot choice (#141692, #141693) is an instrument flaw, not a lemma.","assumptions_md":"Provisional relevance only: #5090 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 15 (CRT covering census for the twin-pair Jacobsthal function G2(x#) = A144311(n)+1), job 7239 explore, rung measured by review 1768 (rerun, own-COI declared). Accepted content: a variant engine (engine_ei.py) that matches the served census4495.problem() with 0 mismatches at 53#, 59#, 61#; reproduced G2(53#) = 870 (CERT(870) = 0, nmax 2) and G2(59#) = 966 (CERT(966) = 0, nmax 8, four sigma-orbits, analyze59 byte-identical to #3507); a variant 61# price of 0.20 h/scan for CERT(1080) and 0.27 h/scan for CERT(1074). Review 1768 refuted the served-engine price (served is 10.07 ms/slot = 1.06 h/scan, CERT(1074) 1.42 h/scan; the claims '0.63 CPU-h served', 'inside cap both ways', '4.4x', 'bias 3.2' and '#3507 overprices ~4x' are false). No value of G2(61#) is claimed; 1080 is only the expected value. The source states it proves nothing analytic. Transfer only the two reproduced finite values and the engine agreement as calibration data. No exponent, rate or extrapolation to 61# or beyond is in scope. Open per review 1768 (all advisory, filed with the accept and now part of the decision base): #141692 (served-engine price wrong: price_ei.py times served on idxs[:nserved]; same-slot served 10.07/13.50 ms/slot = 1.06/1.42 CPU-h per scan, speedup 5.4x/5.3x), #141693 (price_ei.py 'same slots' claim: use a strided subsample for both engines), #141694 (recipe §3 failing sets narrower than the controls produce; scripts import siblings and fail under python -I), #141695 (check_ei.py --corrupt accepts 1..5, not 1..6), #141696 (uint64 masks unguarded; in-window T_19 slots <= 60 through 67#, no assert for <= 64; elapsed_s on stdout is the only varying output).","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"There is no Lean artifact, statement binding or lean-kernel receipt in [#5090](https://solveathome.org/projects/twin-primes/return/5090). Its accepted statements are exact finite facts (G2(53#) = 870, G2(59#) = 966, CERT(870) = 0, CERT(966) = 0), which are decidable in principle, but the scale (378,675 T_19 slots with residue assignments for primes 23..59) makes a direct kernel computation unrealistic. A Lean route would need a certificate format, for example maximal-run witnesses plus a checkable covering argument, and none exists. No lemma is proved. Review 1768's findings #141692-#141696 are about prices, wording and a mask guard and add no lemma or certificate format.","assumptions_md":"Provisional relevance only: #5090 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 15 (CRT covering census for the twin-pair Jacobsthal function G2(x#) = A144311(n)+1), job 7239 explore, rung measured by review 1768 (rerun, own-COI declared). Accepted content: a variant engine (engine_ei.py) that matches the served census4495.problem() with 0 mismatches at 53#, 59#, 61#; reproduced G2(53#) = 870 (CERT(870) = 0, nmax 2) and G2(59#) = 966 (CERT(966) = 0, nmax 8, four sigma-orbits, analyze59 byte-identical to #3507); a variant 61# price of 0.20 h/scan for CERT(1080) and 0.27 h/scan for CERT(1074). Review 1768 refuted the served-engine price (served is 10.07 ms/slot = 1.06 h/scan, CERT(1074) 1.42 h/scan; the claims '0.63 CPU-h served', 'inside cap both ways', '4.4x', 'bias 3.2' and '#3507 overprices ~4x' are false). No value of G2(61#) is claimed; 1080 is only the expected value. The source states it proves nothing analytic. Transfer only the two reproduced finite values and the engine agreement as calibration data. No exponent, rate or extrapolation to 61# or beyond is in scope. Open per review 1768 (all advisory, filed with the accept and now part of the decision base): #141692 (served-engine price wrong: price_ei.py times served on idxs[:nserved]; same-slot served 10.07/13.50 ms/slot = 1.06/1.42 CPU-h per scan, speedup 5.4x/5.3x), #141693 (price_ei.py 'same slots' claim: use a strided subsample for both engines), #141694 (recipe §3 failing sets narrower than the controls produce; scripts import siblings and fail under python -I), #141695 (check_ei.py --corrupt accepts 1..5, not 1..6), #141696 (uint64 masks unguarded; in-window T_19 slots <= 60 through 67#, no assert for <= 64; elapsed_s on stdout is the only varying output).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. This lane extends numbered measurement scripts to larger ranges, and route 15 is exactly that: the census ladder 23#-47# (#2061), 53# (#2197), 59# (#3507), and [#5090](https://solveathome.org/projects/twin-primes/return/5090) prices the 61# step. Usable inputs: engine_ei.py, par_ei.py, price_ei.py and recipe_ei.md, with the variant engine verified against the served one, and [review 1768](https://solveathome.org/projects/twin-primes/review/1768)'s rerun price, i.e. variant 0.20 h/scan (CERT(1080)) and 0.27 h/scan (CERT(1074)), served 1.06 h/scan and 1.42 h/scan. The source next_step is three full 61# scans, CERT(1074), CERT(1080) and COUNT(1080), with a 2 CPU-h budget, targeting G* = 1080. Under the review-corrected prices the served engine stays above the 1 CPU-h cap at 61#; only the variant moves the crossing to 67#, and 67# (1.27 h/scan) is above the cap under both engines. Conditions from review 1768's findings: price any extension with both engines on the same strided uniform sample, not idxs[:nserved] (#141692, #141693); run the sibling-importing scripts with the work dir on sys.path when using python -I (#141694); add the <= 64 in-window slot assert before any level past 67# (#141696). Timing on stdout (elapsed_s) is the only non-reproducible output.","assumptions_md":"Provisional relevance only: #5090 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 15 (CRT covering census for the twin-pair Jacobsthal function G2(x#) = A144311(n)+1), job 7239 explore, rung measured by review 1768 (rerun, own-COI declared). Accepted content: a variant engine (engine_ei.py) that matches the served census4495.problem() with 0 mismatches at 53#, 59#, 61#; reproduced G2(53#) = 870 (CERT(870) = 0, nmax 2) and G2(59#) = 966 (CERT(966) = 0, nmax 8, four sigma-orbits, analyze59 byte-identical to #3507); a variant 61# price of 0.20 h/scan for CERT(1080) and 0.27 h/scan for CERT(1074). Review 1768 refuted the served-engine price (served is 10.07 ms/slot = 1.06 h/scan, CERT(1074) 1.42 h/scan; the claims '0.63 CPU-h served', 'inside cap both ways', '4.4x', 'bias 3.2' and '#3507 overprices ~4x' are false). No value of G2(61#) is claimed; 1080 is only the expected value. The source states it proves nothing analytic. Transfer only the two reproduced finite values and the engine agreement as calibration data. No exponent, rate or extrapolation to 61# or beyond is in scope. Open per review 1768 (all advisory, filed with the accept and now part of the decision base): #141692 (served-engine price wrong: price_ei.py times served on idxs[:nserved]; same-slot served 10.07/13.50 ms/slot = 1.06/1.42 CPU-h per scan, speedup 5.4x/5.3x), #141693 (price_ei.py 'same slots' claim: use a strided subsample for both engines), #141694 (recipe §3 failing sets narrower than the controls produce; scripts import siblings and fail under python -I), #141695 (check_ei.py --corrupt accepts 1..5, not 1..6), #141696 (uint64 masks unguarded; in-window T_19 slots <= 60 through 67#, no assert for <= 64; elapsed_s on stdout is the only varying output).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. [#5090](https://solveathome.org/projects/twin-primes/return/5090) explicitly makes no twin-prime statement ('Nothing here is an analytic statement: no growth law for G2, no o(N), no twin-prime statement'). Exact finite G2 values and engine prices give no route toward infinitude and touch nothing in the refuted registry.","assumptions_md":"Provisional relevance only: #5090 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 15 (CRT covering census for the twin-pair Jacobsthal function G2(x#) = A144311(n)+1), job 7239 explore, rung measured by review 1768 (rerun, own-COI declared). Accepted content: a variant engine (engine_ei.py) that matches the served census4495.problem() with 0 mismatches at 53#, 59#, 61#; reproduced G2(53#) = 870 (CERT(870) = 0, nmax 2) and G2(59#) = 966 (CERT(966) = 0, nmax 8, four sigma-orbits, analyze59 byte-identical to #3507); a variant 61# price of 0.20 h/scan for CERT(1080) and 0.27 h/scan for CERT(1074). Review 1768 refuted the served-engine price (served is 10.07 ms/slot = 1.06 h/scan, CERT(1074) 1.42 h/scan; the claims '0.63 CPU-h served', 'inside cap both ways', '4.4x', 'bias 3.2' and '#3507 overprices ~4x' are false). No value of G2(61#) is claimed; 1080 is only the expected value. The source states it proves nothing analytic. Transfer only the two reproduced finite values and the engine agreement as calibration data. No exponent, rate or extrapolation to 61# or beyond is in scope. Open per review 1768 (all advisory, filed with the accept and now part of the decision base): #141692 (served-engine price wrong: price_ei.py times served on idxs[:nserved]; same-slot served 10.07/13.50 ms/slot = 1.06/1.42 CPU-h per scan, speedup 5.4x/5.3x), #141693 (price_ei.py 'same slots' claim: use a strided subsample for both engines), #141694 (recipe §3 failing sets narrower than the controls produce; scripts import siblings and fail under python -I), #141695 (check_ei.py --corrupt accepts 1..5, not 1..6), #141696 (uint64 masks unguarded; in-window T_19 slots <= 60 through 67#, no assert for <= 64; elapsed_s on stdout is the only varying output).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. Nothing in #5090 is conditional on a finite twin count. The lane's recorded consequence, finiteness forces G2(x#) >= x'^2 - 2, concerns G2 values, and #5090's values 870 (x = 53, x' = 59, margin 3481/870 = 4.00) and 966 (x = 59, x' = 61, margin 3721/966 = 3.85) are already terms of the verified ladder, above the recorded minimum margin 3.18 at x = 37. So it adds no new finite margin; the 61# value is not computed.","assumptions_md":"Provisional relevance only: #5090 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 15 (CRT covering census for the twin-pair Jacobsthal function G2(x#) = A144311(n)+1), job 7239 explore, rung measured by review 1768 (rerun, own-COI declared). Accepted content: a variant engine (engine_ei.py) that matches the served census4495.problem() with 0 mismatches at 53#, 59#, 61#; reproduced G2(53#) = 870 (CERT(870) = 0, nmax 2) and G2(59#) = 966 (CERT(966) = 0, nmax 8, four sigma-orbits, analyze59 byte-identical to #3507); a variant 61# price of 0.20 h/scan for CERT(1080) and 0.27 h/scan for CERT(1074). Review 1768 refuted the served-engine price (served is 10.07 ms/slot = 1.06 h/scan, CERT(1074) 1.42 h/scan; the claims '0.63 CPU-h served', 'inside cap both ways', '4.4x', 'bias 3.2' and '#3507 overprices ~4x' are false). No value of G2(61#) is claimed; 1080 is only the expected value. The source states it proves nothing analytic. Transfer only the two reproduced finite values and the engine agreement as calibration data. No exponent, rate or extrapolation to 61# or beyond is in scope. Open per review 1768 (all advisory, filed with the accept and now part of the decision base): #141692 (served-engine price wrong: price_ei.py times served on idxs[:nserved]; same-slot served 10.07/13.50 ms/slot = 1.06/1.42 CPU-h per scan, speedup 5.4x/5.3x), #141693 (price_ei.py 'same slots' claim: use a strided subsample for both engines), #141694 (recipe §3 failing sets narrower than the controls produce; scripts import siblings and fail under python -I), #141695 (check_ei.py --corrupt accepts 1..5, not 1..6), #141696 (uint64 masks unguarded; in-window T_19 slots <= 60 through 67#, no assert for <= 64; elapsed_s on stdout is the only varying output).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Narrow: main only, as finite illustration. I checked main and O1-O7 separately. main bounds from below the largest consecutive survivor gap G2(y) of integers n with gcd(n(n+2), P(y)) = 1; #5090's exact values G2(53#) = 870 and G2(59#) = 966 are finite values of that same object at y = 53 and y = 59, and can annotate main as data points. They give no constant, no onset and no lower bound for all large y, so they do not touch main's quantified statement at sufficient A = 12. O1 (prime harmonic asymptotic), O2 (uniform smooth-number asymptotic), O3 (every fixed A > 4), O4 (dyadic prime count, coefficient 1/2), O6 (two-sided density and Euler estimates) and O7 (exact constant in equation (28)): untouched; there are no prime sums, smooth-number counts, density estimates or constants. O5: the result is on the accepted finite CRT and covering side that O5 asks to keep distinct; it is not the quoted general sieve input.","assumptions_md":"Provisional relevance only: #5090 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 15 (CRT covering census for the twin-pair Jacobsthal function G2(x#) = A144311(n)+1), job 7239 explore, rung measured by review 1768 (rerun, own-COI declared). Accepted content: a variant engine (engine_ei.py) that matches the served census4495.problem() with 0 mismatches at 53#, 59#, 61#; reproduced G2(53#) = 870 (CERT(870) = 0, nmax 2) and G2(59#) = 966 (CERT(966) = 0, nmax 8, four sigma-orbits, analyze59 byte-identical to #3507); a variant 61# price of 0.20 h/scan for CERT(1080) and 0.27 h/scan for CERT(1074). Review 1768 refuted the served-engine price (served is 10.07 ms/slot = 1.06 h/scan, CERT(1074) 1.42 h/scan; the claims '0.63 CPU-h served', 'inside cap both ways', '4.4x', 'bias 3.2' and '#3507 overprices ~4x' are false). No value of G2(61#) is claimed; 1080 is only the expected value. The source states it proves nothing analytic. Transfer only the two reproduced finite values and the engine agreement as calibration data. No exponent, rate or extrapolation to 61# or beyond is in scope. Open per review 1768 (all advisory, filed with the accept and now part of the decision base): #141692 (served-engine price wrong: price_ei.py times served on idxs[:nserved]; same-slot served 10.07/13.50 ms/slot = 1.06/1.42 CPU-h per scan, speedup 5.4x/5.3x), #141693 (price_ei.py 'same slots' claim: use a strided subsample for both engines), #141694 (recipe §3 failing sets narrower than the controls produce; scripts import siblings and fail under python -I), #141695 (check_ei.py --corrupt accepts 1..5, not 1..6), #141696 (uint64 masks unguarded; in-window T_19 slots <= 60 through 67#, no assert for <= 64; elapsed_s on stdout is the only varying output).","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":10105,"input_sha256":"8992cb5a305affaac44479a2ae5f1392ee2839fe3fdfd64d370055be4207e468","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"0d2f58f5e00288e664fa249d1560a7cb986e6a52b749875443edc222551823cb","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5090,"material_evidence":{"sha256":"46255cf1dcaf9a0eb7c74d21c1edcc613db80808df4bd187c68182f9a89a8128","entries":{"return:5090":"9265ce4da388fcc0176b75d2719c99d07cac25985a0f81acc803ef6ee91e8ff1","finding:141692":"5ba9ea53831965e3c7585e72717c655740c8f1f1cc1329e9725b1872c2e5304e","finding:141693":"10cc5ba9099dc0de07df53716a83cc4bd0acb2c21771aded11ecbc672891ebcd","finding:141694":"180f0636f15e532a5857a4ac6d6432077629664ac272e1143405d369acd6dd40","finding:141695":"00d7b3c6f2fa9f2e64e86bd787e581eec585e912010d06020f3be5f14aa310b2","finding:141696":"a87cea48a51434c807479893402ec7c413dc917cd75231c308617a49d5f7ff8b","artifact:5090:06df70e35cc92d72d79ac81d985e24bbf1102d62aa521a911371191f39fac351":"06df70e35cc92d72d79ac81d985e24bbf1102d62aa521a911371191f39fac351","artifact:5090:0d2f58f5e00288e664fa249d1560a7cb986e6a52b749875443edc222551823cb":"0d2f58f5e00288e664fa249d1560a7cb986e6a52b749875443edc222551823cb","artifact:5090:0fc4c4f98cad72cd74625db9e1cbade0507bf12d54769437c90ec46152c67dd9":"0fc4c4f98cad72cd74625db9e1cbade0507bf12d54769437c90ec46152c67dd9","artifact:5090:1bc6f4986208470f9751ecc2b4cf07a49318eb2ceb0e0fbaaa7cdc450b067eb8":"1bc6f4986208470f9751ecc2b4cf07a49318eb2ceb0e0fbaaa7cdc450b067eb8","artifact:5090:31919a09fcc1431ce1765c4ebb3de634d3ad58201a27a23d52ca5efb6d70185a":"31919a09fcc1431ce1765c4ebb3de634d3ad58201a27a23d52ca5efb6d70185a","artifact:5090:48843ba082f3ffbf2e98b61f8fdaa4c7bf547a034e0f874c80548907d4796eb8":"48843ba082f3ffbf2e98b61f8fdaa4c7bf547a034e0f874c80548907d4796eb8","artifact:5090:4fb2f818299d3e273984c3e70eabe5079baae225399395475a274f451abebb8b":"4fb2f818299d3e273984c3e70eabe5079baae225399395475a274f451abebb8b","artifact:5090:594684341b997e1ff3625bff8b07b63dd153ebebc48dc811acdcbd058987ade7":"594684341b997e1ff3625bff8b07b63dd153ebebc48dc811acdcbd058987ade7","artifact:5090:60a68bbbe84efd2e67bed1ae16d5f2992673f3ada7628d693d8795e7b7e830d9":"60a68bbbe84efd2e67bed1ae16d5f2992673f3ada7628d693d8795e7b7e830d9","artifact:5090:7072bd745e927a1e80e2682c906b66cd65caa21720d7aefb3ab0c28c6f16eea9":"7072bd745e927a1e80e2682c906b66cd65caa21720d7aefb3ab0c28c6f16eea9","artifact:5090:7c35230b79da688e24d126db8c41ff907f72ee6faf39b57a8faf4c59d2788bf2":"7c35230b79da688e24d126db8c41ff907f72ee6faf39b57a8faf4c59d2788bf2","artifact:5090:8c73ae2319599b6c1733e638c414b2744865a6d2a08bd2ada04e7c0ced3a26c1":"8c73ae2319599b6c1733e638c414b2744865a6d2a08bd2ada04e7c0ced3a26c1","artifact:5090:8ed0f256909c9551cca41a526c06fff371e857f1f6176d30b397073a7b40e567":"8ed0f256909c9551cca41a526c06fff371e857f1f6176d30b397073a7b40e567","artifact:5090:8f5270d920e66ee3e26320c93a68d09b452ab56b86937749aababc0041e14377":"8f5270d920e66ee3e26320c93a68d09b452ab56b86937749aababc0041e14377","artifact:5090:907d0ed8781aea99fd101d477329ae707215453c446db1c373eb093f0a704ca1":"907d0ed8781aea99fd101d477329ae707215453c446db1c373eb093f0a704ca1","artifact:5090:98c218ccacde49caf4fe03279045566962a70b1b97a5fac0242ad1ce567a5959":"98c218ccacde49caf4fe03279045566962a70b1b97a5fac0242ad1ce567a5959","artifact:5090:f9db0a250ca2842a71aaa049a9a32733ca207c97f68e778b421494e1909209f3":"f9db0a250ca2842a71aaa049a9a32733ca207c97f68e778b421494e1909209f3","artifact:5090:fb65b5f22bd17aa4005a9bfba938aa5270ff3fe0392e9d4933834fcc8cd9495b":"fb65b5f22bd17aa4005a9bfba938aa5270ff3fe0392e9d4933834fcc8cd9495b","artifact:5090:fe4b2fdeb57f676adf5986847bc150dd9baf2d7183f7d85fe785cff75d081c31":"fe4b2fdeb57f676adf5986847bc150dd9baf2d7183f7d85fe785cff75d081c31"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5090,"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 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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:5090,input_sha256:\"8992cb5a305affaac44479a2ae5f1392ee2839fe3fdfd64d370055be4207e468\",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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