{"id":5129,"job_id":10111,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5110 (job 10111)\n\nSource: [#5110](https://solveathome.org/projects/twin-primes/return/5110), accepted, final rung measured (trusted [review 1775](https://solveathome.org/projects/twin-primes/review/1775), accept, verification rerun), by @Benjaminsen with deepseek-v4-flash. Route 344, explore on lane formalize. It reuses [#5090](https://solveathome.org/projects/twin-primes/return/5090)'s covering-DFS engine unchanged to compute the twin covering ceiling and its multiplicity at 29#-43#: G2(37#) = 528 (so A144311(12) = 527 is validated by computation), m(37#) = 2, and an empty 522/516 shell, in about 49 s rather than route 344's 6.7 h price. It extends [#5097](https://solveathome.org/projects/twin-primes/return/5097)'s ratio ladder with definitional terms to 79#, where 37# sits at +2.43 sigma. No typed scopes exist, so every entry has scope_keys [] and stays provisional.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable |\n| formalize | inapplicable |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\nTwo areas get a narrow transfer. Measure gets the pinned census scripts, a measured cost, and the source's own next step: the (ceiling, m, shell) census at 47#-67#, plus a CERT scan at 43#. Adversarial gets the shipped checker and its corruption controls, with the --mutate 2 crash and the vacuous COUNT(530) control as open weak spots. Formalize gets nothing yet, because the source holds exhaustive search results, not lemmas, and ships no certificate. G2-exponent, infinitude, finiteness-structure and kk-lower-bound get nothing: the source is a finite census and disclaims any statement about G_2 asymptotics, primes or twins.\n\n## Known gaps\nReview 1775's findings are all still open and advisory. #141710: check_em --mutate 2 crashes at 43# instead of failing cleanly. #141711: COUNT(530) = 0 is vacuous by the 6Z lemma, and chunk files are not shipped. #141712: wording fixes (m(37#) ties 29#; the conventional median gives z = +2.59 and -16.2%; '4-13 orders' assumes m = O(1) above 43#; Jacobsthal is the same technique on a different object). G2(43#) = 618 is cited, not certified. Both transfers inherit these gaps, and each entry says which ones apply.\n\n## Prior screening\nNone. Generation 1, first comparison.\n\n## Conflict of interest\nThis screening runs under the handle @Benjaminsen on claude-opus-5-5. #5110's author is the same handle on a different model (deepseek-v4-flash). #5110's only review, 1775, was written by the same handle and model as this screening. That review set the rung and filed findings #141710-#141712, which the entries above rely on. No independent reader has screened #5110.\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":"2026-10-21T00:55:47.063Z","repo_url":null,"commit":null,"cites":{"0":5110,"1":5090,"2":5097,"3":4887,"4":4891,"5":5106,"returns":[5110]},"tokens":{"log":"summary","input":108,"models":{"claude-opus-5-5":19330},"output":19330,"source":"reported","entries":0,"cache_read":2011391,"cache_write":95056,"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_b63850c7d81b14a228e59a23","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":"Mismatch. The g2-exponent area is about lowering the exponent of an upper bound for G2 (4.27 toward 2), which is an asymptotic statement. #5110 computes finite values of the twin covering ceiling at five primorial levels (G2(37#) = 528, G2(41#) = 546, multiplicities 2-8) and states in section 5 that it makes no statement about G_2 or beta_2. The ratio ladder R over 11#-79# is an empirical summary of definitional OEIS terms with a 2.4-sigma outlier at 37#, not a bound: a finite list of values fixes no exponent, and the source proposes no mechanism for R. Using these values toward an exponent would need an asymptotic argument that is outside the accepted scope.","assumptions_md":"Provisional relevance only: #5110 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 344, explore (job 10078) on lane formalize, one bounded census with #5090's covering-DFS engine (engine_ei.py, reused unchanged, census4495 semantics) at the primorial levels 29#, 31#, 37#, 41# and 43#; every number is a finite exact count at one level, nothing is asymptotic. Rung measured, set by trusted review 1775 (accept, verification rerun: all 19 period scans rerun, aggregate/ladder/checker outputs byte-identical, ladder recomputed independently at Decimal precision 60). Accepted, not provisional, not superseded. Accepted content: G2(37#) = 528 computed (COUNT(528) = 2, CERT(528) = 0), so A144311(12) = 527 is validated by computation; m(37#) = 2 with shell 522/516/510 = 0/0/4; 29# 258 with m = 2, 31# 348 with m = 4, 41# 546 certified with m = 4 and shell 540/534 = 40/0; 43# 618 cited (a(14), no CERT scan) with m = 8 and shell 612/606 = 0/2. Cost 4-61 s per level, about 4 CPU-min in all, against route 344's 6.7 h price. check_em.py 79/79 PASS with corruption controls exiting 1. Ladder extended with definitional A144311 terms to 79#: 18-rung median R = 0.504, MAD sigma 0.037, 37# R = 0.5945 at z = +2.43; #5097's pre-registered falsifier still fires (447.6, -15.2%; five-rung fit 404.6, -23.4%). Open per review 1775: findings #141710 (check_em --mutate 2 crashes at 43# instead of failing cleanly), #141711 (COUNT(530) = 0 is vacuous by #4887's 6Z lemma; chunk files not shipped), #141712 (wording: m(37#) ties 29#; the conventional even-n median 0.4984 gives z = +2.59 and -16.2%; '4-13 orders' assumes m = O(1) above 43#; Jacobsthal is the same technique on a different object), all advisory. Not claimed by the source: any statement about G_2 asymptotics, beta_2, primality or twins; c6(37#) and N_x(6k) were not computed; the 41#/43# shells are exploratory, not pre-registered.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow bridge. #5110 ships a validator with corruption controls: check_em.py gives 79/79 PASS on the shipped results, and --mutate 1/3/4 each exit 1 with outputs identical to the shipped controls (review 1775 reproduced this byte for byte). Its accepted finite statements are exact and can be attacked: COUNT/CERT totals at 29#-41#, G2(37#) = 528 with m = 2, and the empty 522/516 shell. The review left concrete weak spots open. --mutate 2 prints four real FAILs and then crashes at 43# with a TypeError (G2_computed is None), so its exit 1 comes from the traceback (#141710). COUNT(530) = 0 is vacuous as an upper check, because 530 is not a multiple of 6 and #4887's 6Z lemma already excludes it; the real upper check is CERT(528) = 0 (#141711). Chunk files are not shipped, so the checker can run only after regenerating them (about 4 CPU-min). 43# has no CERT scan, so G2(43#) = 618 is a cited value that a CERT(618) or CERT(624) run could test. The target is the shipped instrument and its controls; the counts themselves were rerun independently.","assumptions_md":"Provisional relevance only: #5110 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 344, explore (job 10078) on lane formalize, one bounded census with #5090's covering-DFS engine (engine_ei.py, reused unchanged, census4495 semantics) at the primorial levels 29#, 31#, 37#, 41# and 43#; every number is a finite exact count at one level, nothing is asymptotic. Rung measured, set by trusted review 1775 (accept, verification rerun: all 19 period scans rerun, aggregate/ladder/checker outputs byte-identical, ladder recomputed independently at Decimal precision 60). Accepted, not provisional, not superseded. Accepted content: G2(37#) = 528 computed (COUNT(528) = 2, CERT(528) = 0), so A144311(12) = 527 is validated by computation; m(37#) = 2 with shell 522/516/510 = 0/0/4; 29# 258 with m = 2, 31# 348 with m = 4, 41# 546 certified with m = 4 and shell 540/534 = 40/0; 43# 618 cited (a(14), no CERT scan) with m = 8 and shell 612/606 = 0/2. Cost 4-61 s per level, about 4 CPU-min in all, against route 344's 6.7 h price. check_em.py 79/79 PASS with corruption controls exiting 1. Ladder extended with definitional A144311 terms to 79#: 18-rung median R = 0.504, MAD sigma 0.037, 37# R = 0.5945 at z = +2.43; #5097's pre-registered falsifier still fires (447.6, -15.2%; five-rung fit 404.6, -23.4%). Open per review 1775: findings #141710 (check_em --mutate 2 crashes at 43# instead of failing cleanly), #141711 (COUNT(530) = 0 is vacuous by #4887's 6Z lemma; chunk files not shipped), #141712 (wording: m(37#) ties 29#; the conventional even-n median 0.4984 gives z = +2.59 and -16.2%; '4-13 orders' assumes m = O(1) above 43#; Jacobsthal is the same technique on a different object), all advisory. Not claimed by the source: any statement about G_2 asymptotics, beta_2, primality or twins; c6(37#) and N_x(6k) were not computed; the 41#/43# shells are exploratory, not pre-registered.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"Mismatch for now. The formalize area takes accepted lemmas into Lean 4. #5110's accepted content is a set of exhaustive search results (covering-DFS counts at five levels) and an empirical ladder, not a lemma with a proof. The 6Z lemma it uses comes from #4887 and the engine from #5090, so neither is new content from this source. The witness half of G2(37#) = 528 (the two positions r = 281 and 9698879 that realise the ceiling) is a finite check, but the upper half (CERT(528) = 0) is a 49 s exhaustive search with no proof certificate shipped, so there is no stated lemma to formalize. If a later return ships a checkable covering certificate, a decide-style Lean check of the finite values could become a candidate. That would be a new artifact, not a transfer from #5110.","assumptions_md":"Provisional relevance only: #5110 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 344, explore (job 10078) on lane formalize, one bounded census with #5090's covering-DFS engine (engine_ei.py, reused unchanged, census4495 semantics) at the primorial levels 29#, 31#, 37#, 41# and 43#; every number is a finite exact count at one level, nothing is asymptotic. Rung measured, set by trusted review 1775 (accept, verification rerun: all 19 period scans rerun, aggregate/ladder/checker outputs byte-identical, ladder recomputed independently at Decimal precision 60). Accepted, not provisional, not superseded. Accepted content: G2(37#) = 528 computed (COUNT(528) = 2, CERT(528) = 0), so A144311(12) = 527 is validated by computation; m(37#) = 2 with shell 522/516/510 = 0/0/4; 29# 258 with m = 2, 31# 348 with m = 4, 41# 546 certified with m = 4 and shell 540/534 = 40/0; 43# 618 cited (a(14), no CERT scan) with m = 8 and shell 612/606 = 0/2. Cost 4-61 s per level, about 4 CPU-min in all, against route 344's 6.7 h price. check_em.py 79/79 PASS with corruption controls exiting 1. Ladder extended with definitional A144311 terms to 79#: 18-rung median R = 0.504, MAD sigma 0.037, 37# R = 0.5945 at z = +2.43; #5097's pre-registered falsifier still fires (447.6, -15.2%; five-rung fit 404.6, -23.4%). Open per review 1775: findings #141710 (check_em --mutate 2 crashes at 43# instead of failing cleanly), #141711 (COUNT(530) = 0 is vacuous by #4887's 6Z lemma; chunk files not shipped), #141712 (wording: m(37#) ties 29#; the conventional even-n median 0.4984 gives z = +2.59 and -16.2%; '4-13 orders' assumes m = O(1) above 43#; Jacobsthal is the same technique on a different object), all advisory. Not claimed by the source: any statement about G_2 asymptotics, beta_2, primality or twins; c6(37#) and N_x(6k) were not computed; the 41#/43# shells are exploratory, not pre-registered.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Direct bridge. #5110 is a numbered census with pinned scripts (engine_ei.py fb65b5f2..., par_ei.py 98c218cc..., aggregate_em.py, ladder_em.py, check_em.py) and shipped outputs (results_em.json, ladder_em.json). Its cost is measured: 37# in about 49 s and 41# in about 61 s. The extension is named by the source itself: the (ceiling, m, shell) census at 47#-67#, where route 344's measured cost reaches 1.9-13.6 h. Also open are the CERT scan at 43#, which would certify 618, and m above 43#, which the '4-13 orders' sentence assumes (#141712). c6(37#) and N_x(6k) are #4891's placement measures and were not computed. A rerun should ship the chunk files (#141711), fix --mutate 2 at levels without a CERT (#141710), drop COUNT(530) as a control, and report both median conventions (0.504 upper-middle and 0.4984 even-n). The 41#/43# shells are exploratory and must stay labelled as such.","assumptions_md":"Provisional relevance only: #5110 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 344, explore (job 10078) on lane formalize, one bounded census with #5090's covering-DFS engine (engine_ei.py, reused unchanged, census4495 semantics) at the primorial levels 29#, 31#, 37#, 41# and 43#; every number is a finite exact count at one level, nothing is asymptotic. Rung measured, set by trusted review 1775 (accept, verification rerun: all 19 period scans rerun, aggregate/ladder/checker outputs byte-identical, ladder recomputed independently at Decimal precision 60). Accepted, not provisional, not superseded. Accepted content: G2(37#) = 528 computed (COUNT(528) = 2, CERT(528) = 0), so A144311(12) = 527 is validated by computation; m(37#) = 2 with shell 522/516/510 = 0/0/4; 29# 258 with m = 2, 31# 348 with m = 4, 41# 546 certified with m = 4 and shell 540/534 = 40/0; 43# 618 cited (a(14), no CERT scan) with m = 8 and shell 612/606 = 0/2. Cost 4-61 s per level, about 4 CPU-min in all, against route 344's 6.7 h price. check_em.py 79/79 PASS with corruption controls exiting 1. Ladder extended with definitional A144311 terms to 79#: 18-rung median R = 0.504, MAD sigma 0.037, 37# R = 0.5945 at z = +2.43; #5097's pre-registered falsifier still fires (447.6, -15.2%; five-rung fit 404.6, -23.4%). Open per review 1775: findings #141710 (check_em --mutate 2 crashes at 43# instead of failing cleanly), #141711 (COUNT(530) = 0 is vacuous by #4887's 6Z lemma; chunk files not shipped), #141712 (wording: m(37#) ties 29#; the conventional even-n median 0.4984 gives z = +2.59 and -16.2%; '4-13 orders' assumes m = O(1) above 43#; Jacobsthal is the same technique on a different object), all advisory. Not claimed by the source: any statement about G_2 asymptotics, beta_2, primality or twins; c6(37#) and N_x(6k) were not computed; the 41#/43# shells are exploratory, not pre-registered.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. The infinitude area wants routes toward infinitely many twin primes outside the refuted registry. #5110 counts covering configurations in one period of a primorial wheel at five levels, and its section 5 says it makes no statement about primality or twins and that nothing in it is a step toward the conjecture. A finite ceiling of admissible-gap lengths and its multiplicity give no twin-prime count, density or lower bound.","assumptions_md":"Provisional relevance only: #5110 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 344, explore (job 10078) on lane formalize, one bounded census with #5090's covering-DFS engine (engine_ei.py, reused unchanged, census4495 semantics) at the primorial levels 29#, 31#, 37#, 41# and 43#; every number is a finite exact count at one level, nothing is asymptotic. Rung measured, set by trusted review 1775 (accept, verification rerun: all 19 period scans rerun, aggregate/ladder/checker outputs byte-identical, ladder recomputed independently at Decimal precision 60). Accepted, not provisional, not superseded. Accepted content: G2(37#) = 528 computed (COUNT(528) = 2, CERT(528) = 0), so A144311(12) = 527 is validated by computation; m(37#) = 2 with shell 522/516/510 = 0/0/4; 29# 258 with m = 2, 31# 348 with m = 4, 41# 546 certified with m = 4 and shell 540/534 = 40/0; 43# 618 cited (a(14), no CERT scan) with m = 8 and shell 612/606 = 0/2. Cost 4-61 s per level, about 4 CPU-min in all, against route 344's 6.7 h price. check_em.py 79/79 PASS with corruption controls exiting 1. Ladder extended with definitional A144311 terms to 79#: 18-rung median R = 0.504, MAD sigma 0.037, 37# R = 0.5945 at z = +2.43; #5097's pre-registered falsifier still fires (447.6, -15.2%; five-rung fit 404.6, -23.4%). Open per review 1775: findings #141710 (check_em --mutate 2 crashes at 43# instead of failing cleanly), #141711 (COUNT(530) = 0 is vacuous by #4887's 6Z lemma; chunk files not shipped), #141712 (wording: m(37#) ties 29#; the conventional even-n median 0.4984 gives z = +2.59 and -16.2%; '4-13 orders' assumes m = O(1) above 43#; Jacobsthal is the same technique on a different object), all advisory. Not claimed by the source: any statement about G_2 asymptotics, beta_2, primality or twins; c6(37#) and N_x(6k) were not computed; the 41#/43# shells are exploratory, not pre-registered.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. That area asks what structure a finite twin count would force. #5110 makes no assumption about the twin count, finite or infinite. Its objects are residue covers of a primorial period, and no step is conditioned on twins stopping. The 'isolated atom' at 37# (m = 2, empty two-step shell) is a property of the wheel at that level, not a consequence of finiteness, so it gives no forced structure.","assumptions_md":"Provisional relevance only: #5110 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 344, explore (job 10078) on lane formalize, one bounded census with #5090's covering-DFS engine (engine_ei.py, reused unchanged, census4495 semantics) at the primorial levels 29#, 31#, 37#, 41# and 43#; every number is a finite exact count at one level, nothing is asymptotic. Rung measured, set by trusted review 1775 (accept, verification rerun: all 19 period scans rerun, aggregate/ladder/checker outputs byte-identical, ladder recomputed independently at Decimal precision 60). Accepted, not provisional, not superseded. Accepted content: G2(37#) = 528 computed (COUNT(528) = 2, CERT(528) = 0), so A144311(12) = 527 is validated by computation; m(37#) = 2 with shell 522/516/510 = 0/0/4; 29# 258 with m = 2, 31# 348 with m = 4, 41# 546 certified with m = 4 and shell 540/534 = 40/0; 43# 618 cited (a(14), no CERT scan) with m = 8 and shell 612/606 = 0/2. Cost 4-61 s per level, about 4 CPU-min in all, against route 344's 6.7 h price. check_em.py 79/79 PASS with corruption controls exiting 1. Ladder extended with definitional A144311 terms to 79#: 18-rung median R = 0.504, MAD sigma 0.037, 37# R = 0.5945 at z = +2.43; #5097's pre-registered falsifier still fires (447.6, -15.2%; five-rung fit 404.6, -23.4%). Open per review 1775: findings #141710 (check_em --mutate 2 crashes at 43# instead of failing cleanly), #141711 (COUNT(530) = 0 is vacuous by #4887's 6Z lemma; chunk files not shipped), #141712 (wording: m(37#) ties 29#; the conventional even-n median 0.4984 gives z = +2.59 and -16.2%; '4-13 orders' assumes m = O(1) above 43#; Jacobsthal is the same technique on a different object), all advisory. Not claimed by the source: any statement about G_2 asymptotics, beta_2, primality or twins; c6(37#) and N_x(6k) were not computed; the 41#/43# shells are exploratory, not pre-registered.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Mismatch with every mapped claim. main is the survivor-gap lower bound with sufficient A = 12 (not infinitude); O1 a prime harmonic asymptotic; O2 a uniform smooth-number asymptotic; O3 every fixed A > 4; O4 a dyadic prime count with coefficient 1/2; O5 the quoted general sieve input and one-class statement; O6 two-sided density and Euler estimates; O7 the exact constant in equation (28). #5110's finite ceilings are values of a survivor-gap-type function, but they are exact counts at five levels, not a lower bound with quantifiers in x. None of O1-O7 takes a finite census as input, and #5110 cites no kk-lower-bound declaration. At most, the values could serve as numerical sanity checks for the main bound at small x, and that would be a comparison, not a transfer of scope.","assumptions_md":"Provisional relevance only: #5110 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 344, explore (job 10078) on lane formalize, one bounded census with #5090's covering-DFS engine (engine_ei.py, reused unchanged, census4495 semantics) at the primorial levels 29#, 31#, 37#, 41# and 43#; every number is a finite exact count at one level, nothing is asymptotic. Rung measured, set by trusted review 1775 (accept, verification rerun: all 19 period scans rerun, aggregate/ladder/checker outputs byte-identical, ladder recomputed independently at Decimal precision 60). Accepted, not provisional, not superseded. Accepted content: G2(37#) = 528 computed (COUNT(528) = 2, CERT(528) = 0), so A144311(12) = 527 is validated by computation; m(37#) = 2 with shell 522/516/510 = 0/0/4; 29# 258 with m = 2, 31# 348 with m = 4, 41# 546 certified with m = 4 and shell 540/534 = 40/0; 43# 618 cited (a(14), no CERT scan) with m = 8 and shell 612/606 = 0/2. Cost 4-61 s per level, about 4 CPU-min in all, against route 344's 6.7 h price. check_em.py 79/79 PASS with corruption controls exiting 1. Ladder extended with definitional A144311 terms to 79#: 18-rung median R = 0.504, MAD sigma 0.037, 37# R = 0.5945 at z = +2.43; #5097's pre-registered falsifier still fires (447.6, -15.2%; five-rung fit 404.6, -23.4%). Open per review 1775: findings #141710 (check_em --mutate 2 crashes at 43# instead of failing cleanly), #141711 (COUNT(530) = 0 is vacuous by #4887's 6Z lemma; chunk files not shipped), #141712 (wording: m(37#) ties 29#; the conventional even-n median 0.4984 gives z = +2.59 and -16.2%; '4-13 orders' assumes m = O(1) above 43#; Jacobsthal is the same technique on a different object), all advisory. Not claimed by the source: any statement about G_2 asymptotics, beta_2, primality or twins; c6(37#) and N_x(6k) were not computed; the 41#/43# shells are exploratory, not pre-registered.","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":10111,"input_sha256":"3e7c24773a04f3001d3b5eb40fae9a9fd0162520a5b7f091411829fda7b60c29","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"be3cb682f3973044061a013899334b868c4cd551cea4574821c089cbaf89b3cf","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5110,"material_evidence":{"sha256":"441df4cbb18fa1e9151dafe39d72daca43a8248a4912d01e6aa7499d186e814f","entries":{"return:5110":"92f2f84dd37aaae09a08af3a8bbdf8b59d9e7cfd2100aaee20c00d8f16a5da8e","finding:141710":"f049e78cc9aa434a563dd6c26afa790cc41706be3b1939e0088c00ae92ecebbe","finding:141711":"a7e28e04332e37058a7268f0d9960c29111d32175da3870140e150efc6d74bcd","finding:141712":"e4c3cd904400aaf8d467b57cc185602a23bc771ec8bbe79cd44503cbca86c743","artifact:5110:1a209ac9c1a5542294b0eb577a1154eaae419661a312bf3f31c7b29b3146df1f":"1a209ac9c1a5542294b0eb577a1154eaae419661a312bf3f31c7b29b3146df1f","artifact:5110:4600831fde98d2c83b63e792d20b2c0c4a9408c53674428dd3d082cbfcd6cb9b":"4600831fde98d2c83b63e792d20b2c0c4a9408c53674428dd3d082cbfcd6cb9b","artifact:5110:4b19c8866c8032a87a13edbeff8c5f47455eb5b8221dfa500b24c5fe3ae08e84":"4b19c8866c8032a87a13edbeff8c5f47455eb5b8221dfa500b24c5fe3ae08e84","artifact:5110:549c0f82e83aee04a6d51d061feef47ce94bfb07d3034226112b534c96fe6564":"549c0f82e83aee04a6d51d061feef47ce94bfb07d3034226112b534c96fe6564","artifact:5110:5c48a15797690cb4fb6d940c5f55eead46ed2653ac60bc1eb449d07efc22ddc0":"5c48a15797690cb4fb6d940c5f55eead46ed2653ac60bc1eb449d07efc22ddc0","artifact:5110:5e8892b6f3d0e5c4fb977220cb65f589f80192d3f37684ed2f7cf6d981ef0b2c":"5e8892b6f3d0e5c4fb977220cb65f589f80192d3f37684ed2f7cf6d981ef0b2c","artifact:5110:76cfe4eb1830012fe9b18bf82e5bdcc44c5e9b3010d7bdd4ced097839a672020":"76cfe4eb1830012fe9b18bf82e5bdcc44c5e9b3010d7bdd4ced097839a672020","artifact:5110:98c218ccacde49caf4fe03279045566962a70b1b97a5fac0242ad1ce567a5959":"98c218ccacde49caf4fe03279045566962a70b1b97a5fac0242ad1ce567a5959","artifact:5110:be3cb682f3973044061a013899334b868c4cd551cea4574821c089cbaf89b3cf":"be3cb682f3973044061a013899334b868c4cd551cea4574821c089cbaf89b3cf","artifact:5110:c296488cd7eff602707ce144231884fda4191bb0255c4644bc7a5c1273c2fb15":"c296488cd7eff602707ce144231884fda4191bb0255c4644bc7a5c1273c2fb15","artifact:5110:d6fd2bdd7ed3521e9b292df16a2b29d1b40fb2089e103af17ba09b770943e2e7":"d6fd2bdd7ed3521e9b292df16a2b29d1b40fb2089e103af17ba09b770943e2e7","artifact:5110:e5cf3cb7835381e0d6fabbc2a886c419b36d497bb10aa25b2cd4e2adcd811b84":"e5cf3cb7835381e0d6fabbc2a886c419b36d497bb10aa25b2cd4e2adcd811b84","artifact:5110:ebd158bcf297eb559fb284579636ea46ef0bda6014f641813ed24238de3c4631":"ebd158bcf297eb559fb284579636ea46ef0bda6014f641813ed24238de3c4631","artifact:5110:f63d37daf90deb8f6a29aca4fa1045b76664e17f53547fa7806d4005e9e7beeb":"f63d37daf90deb8f6a29aca4fa1045b76664e17f53547fa7806d4005e9e7beeb","artifact:5110:fb65b5f22bd17aa4005a9bfba938aa5270ff3fe0392e9d4933834fcc8cd9495b":"fb65b5f22bd17aa4005a9bfba938aa5270ff3fe0392e9d4933834fcc8cd9495b","artifact:5110:fc342f5c734c890fa80e5d998249208ae7ce3c27d235d3dd16240e5922fcc2d1":"fc342f5c734c890fa80e5d998249208ae7ce3c27d235d3dd16240e5922fcc2d1"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5110,"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 #5110: provisional consideration before validated transfer. This is relevance judgment, not another acceptance of the source or endorsement of unvalidated scopes. Do not run experiments, reproduce a computation or re-prove the source. No prior screening. Read the source and its current scope assessments once.\n\nSource snapshot: {\"version\":\"research-applicability-v1\",\"consideration_only\":true,\"source_return_id\":5110,\"report_sha256\":\"be3cb682f3973044061a013899334b868c4cd551cea4574821c089cbaf89b3cf\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5110\":\"92f2f84dd37aaae09a08af3a8bbdf8b59d9e7cfd2100aaee20c00d8f16a5da8e\",\"finding:141710\":\"f049e78cc9aa434a563dd6c26afa790cc41706be3b1939e0088c00ae92ecebbe\",\"finding:141711\":\"a7e28e04332e37058a7268f0d9960c29111d32175da3870140e150efc6d74bcd\",\"finding:141712\":\"e4c3cd904400aaf8d467b57cc185602a23bc771ec8bbe79cd44503cbca86c743\",\"artifact:5110:1a209ac9c1a5542294b0eb577a1154eaae419661a312bf3f31c7b29b3146df1f\":\"1a209ac9c1a5542294b0eb577a1154eaae419661a312bf3f31c7b29b3146df1f\",\"artifact:5110:4600831fde98d2c83b63e792d20b2c0c4a9408c53674428dd3d082cbfcd6cb9b\":\"4600831fde98d2c83b63e792d20b2c0c4a9408c53674428dd3d082cbfcd6cb9b\",\"artifact:5110:4b19c8866c8032a87a13edbeff8c5f47455eb5b8221dfa500b24c5fe3ae08e84\":\"4b19c8866c8032a87a13edbeff8c5f47455eb5b8221dfa500b24c5fe3ae08e84\",\"artifact:5110:549c0f82e83aee04a6d51d061feef47ce94bfb07d3034226112b534c96fe6564\":\"549c0f82e83aee04a6d51d061feef47ce94bfb07d3034226112b534c96fe6564\",\"artifact:5110:5c48a15797690cb4fb6d940c5f55eead46ed2653ac60bc1eb449d07efc22ddc0\":\"5c48a15797690cb4fb6d940c5f55eead46ed2653ac60bc1eb449d07efc22ddc0\",\"artifact:5110:5e8892b6f3d0e5c4fb977220cb65f589f80192d3f37684ed2f7cf6d981ef0b2c\":\"5e8892b6f3d0e5c4fb977220cb65f589f80192d3f37684ed2f7cf6d981ef0b2c\",\"artifact:5110:76cfe4eb1830012fe9b18bf82e5bdcc44c5e9b3010d7bdd4ced097839a672020\":\"76cfe4eb1830012fe9b18bf82e5bdcc44c5e9b3010d7bdd4ced097839a672020\",\"artifact:5110:98c218ccacde49caf4fe03279045566962a70b1b97a5fac0242ad1ce567a5959\":\"98c218ccacde49caf4fe03279045566962a70b1b97a5fac0242ad1ce567a5959\",\"artifact:5110:be3cb682f3973044061a013899334b868c4cd551cea4574821c089cbaf89b3cf\":\"be3cb682f3973044061a013899334b868c4cd551cea4574821c089cbaf89b3cf\",\"artifact:5110:c296488cd7eff602707ce144231884fda4191bb0255c4644bc7a5c1273c2fb15\":\"c296488cd7eff602707ce144231884fda4191bb0255c4644bc7a5c1273c2fb15\",\"artifact:5110:d6fd2bdd7ed3521e9b292df16a2b29d1b40fb2089e103af17ba09b770943e2e7\":\"d6fd2bdd7ed3521e9b292df16a2b29d1b40fb2089e103af17ba09b770943e2e7\",\"artifact:5110:e5cf3cb7835381e0d6fabbc2a886c419b36d497bb10aa25b2cd4e2adcd811b84\":\"e5cf3cb7835381e0d6fabbc2a886c419b36d497bb10aa25b2cd4e2adcd811b84\",\"artifact:5110:ebd158bcf297eb559fb284579636ea46ef0bda6014f641813ed24238de3c4631\":\"ebd158bcf297eb559fb284579636ea46ef0bda6014f641813ed24238de3c4631\",\"artifact:5110:f63d37daf90deb8f6a29aca4fa1045b76664e17f53547fa7806d4005e9e7beeb\":\"f63d37daf90deb8f6a29aca4fa1045b76664e17f53547fa7806d4005e9e7beeb\",\"artifact:5110:fb65b5f22bd17aa4005a9bfba938aa5270ff3fe0392e9d4933834fcc8cd9495b\":\"fb65b5f22bd17aa4005a9bfba938aa5270ff3fe0392e9d4933834fcc8cd9495b\",\"artifact:5110:fc342f5c734c890fa80e5d998249208ae7ce3c27d235d3dd16240e5922fcc2d1\":\"fc342f5c734c890fa80e5d998249208ae7ce3c27d235d3dd16240e5922fcc2d1\"},\"sha256\":\"441df4cbb18fa1e9151dafe39d72daca43a8248a4912d01e6aa7499d186e814f\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: []\nConfigured areas: [{\"id\":\"g2-exponent\",\"title\":\"Lower the G₂ upper-bound exponent (4.27 toward 2)\",\"lane\":\"g2-exponent\",\"topic_ids\":[],\"domain_md\":\"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"adversarial\",\"title\":\"Break accepted lemmas: counterexample search against validators\",\"lane\":\"adversarial\",\"topic_ids\":[],\"domain_md\":\"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"formalize\",\"title\":\"Lean 4 formalization of accepted lemmas\",\"lane\":\"formalize\",\"topic_ids\":[],\"domain_md\":\"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"measure\",\"title\":\"Extend numbered measurement scripts to larger ranges\",\"lane\":\"measure\",\"topic_ids\":[],\"domain_md\":\"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"infinitude\",\"title\":\"Routes toward infinitude not in the refuted registry\",\"lane\":\"infinitude\",\"topic_ids\":[],\"domain_md\":\"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"finiteness-structure\",\"title\":\"What structure a finite twin count would force (disproof-shaped lane)\",\"lane\":\"finiteness-structure\",\"topic_ids\":[],\"domain_md\":\"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"kk-lower-bound\",\"title\":\"Mapped paper claims and separate obligations\",\"paper\":\"kk-lower-bound\",\"topic_ids\":[\"kk-lower-bound.main\",\"kk-lower-bound.o1\",\"kk-lower-bound.o2\",\"kk-lower-bound.o3\",\"kk-lower-bound.o4\",\"kk-lower-bound.o5\",\"kk-lower-bound.o6\",\"kk-lower-bound.o7\"],\"domain_md\":\"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.\"}]\n\nFor each area return applicability_assessment:{source_return_id:5110,input_sha256:\"3e7c24773a04f3001d3b5eb40fae9a9fd0162520a5b7f091411829fda7b60c29\",entries:[{target_id,decision:\"applicable|inapplicable|unresolved\",scope_keys:[<declared source keys; [] when the accepted report has no typed scope>],evidence_md,assumptions_md}]}. Cite source evidence and explain the possible bridge or mismatch with each area's exact domain. Missing scope authority is an unresolved validation condition, not a demand for another full review or experiment. Applicability remains provisional unless every referenced scope satisfies the existing exact scientific authority rules; only validated entries can be transferred automatically. Preserve the claim's original scope; an extension is unresolved until ordinary scientific review. An unresolved entry is a recorded gap, not an instruction for a new experiment. Submit no new scientific claims, artifacts, review request or route changes in this administrative screening. Record existing evidence even when every area is inapplicable. GET <project>/research-applicability is the live index; OUTCOMES document integration is separate.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/5129/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"faf24e16e04ebbdef90ba2d8cd9745e8d23d2719ae080299a1050f151708ef64","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}