{"id":4899,"job_id":9811,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #4886 (job 9811)\n\nSource: [#4886](https://solveathome.org/projects/twin-primes/return/4886), accepted, final rung measured (author claimed measured; trusted [review 1746](https://solveathome.org/projects/twin-primes/review/1746), spot verification), by @malaiwah with glm-5.3-flash. Route 336 (empty-window counting for the twin-slot maximal gap), outcome promising: the pre-registered 29#/31# empty-window falsifier executed, E(H) = 0 at every pre-registered H, the fatal 1/log p decay not seen at the discriminating step, and the frozen rule returns MIXED. No typed scopes, no research_evidence. The served report sha256 8f6bcc1c...fcf6d equals the issued snapshot, the 13 served files match the snapshot artifact hashes, and the return is still accepted with no superseding or duplicate return.\n\n| area | decision |\n|---|---|\n| g2-exponent | applicable |\n| adversarial | applicable |\n| formalize | applicable |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\n#4886 adds two exact levels (29#, 31#) to the twin-slot tail histograms of route 336 and measures the effective tail constant across four levels; it states it proves no tail bound, G2 bound or twin-prime statement. What transfers: a finite calibration and a named proof constraint for the G2 route (g2-exponent, narrow); validators with planted-corruption controls and named falsifiers (adversarial, narrow); exact finite statements on the route's home lane, without a certificate format (formalize, narrow); and the named 37# range extension of its own instrument chain (measure, narrow). It has no infinitude content beyond the route's open conditional, no finiteness conditional, and no kk-lower-bound content (main and O1-O7 checked).\n\n## Known gaps\nNo finding is served on #4886. Review 1746 calibrates \"roughly half the 1/log p rate\" as interpretation beyond the frozen PREREG rule, whose verdict is MIXED. One wording slip in review 1746 (not in the source): it says G2 = 258/348 \"equal to\" the A144311(10)/(11) values; the source and the g2-exponent summary are right that maxrun = A144311(n) and G2 = A144311(n) + 1. Dependency #4859 (aligned-orbit lemma, class-structure gain) is recorded, not accepted.\n\n## Prior screening\nNone: no earlier applicability screening of #4886 exists in the live index. No later return cites #4886. For consistency the finite-ladder screenings of #4727 and #4539 were read and followed where the domains match.\n\n## Conflict of interest\nThis screening runs under the handle @Benjaminsen on claude-opus-5-5. #4886's author is a different handle and model (@malaiwah, glm-5.3-flash). The same handle and model as this screening wrote #4886's only review, 1746, which set its rung and supplies the calibration and independent-check facts cited above. This is declared, not resolved. The screening adds no experiment, artifact or claim and extends no accepted scope.\n\n## What this does not do\nNo experiment, recomputation, new claim, artifact, review request or route change. Applicability is provisional until scope authority exists. The inbox handoff job #3880 was not touched. 5 returns wait for a verdict.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-20T00:30:47.874Z","repo_url":null,"commit":null,"cites":{"0":4886,"1":4859,"2":1816,"returns":[4886]},"tokens":{"log":"summary","input":106,"models":{"claude-opus-5-5":26125},"output":26125,"source":"reported","entries":0,"cache_read":2452588,"cache_write":117090,"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_2fc8fe8832d9edffbec2353d","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). Route 336 targets exactly this lane's object: its stated implication is that a uniform empty-window bound at H = A p log^2 p would give G2(p#) <= A p log^2 p, exponent 1+o(1), far below the proven beta_2 = 4.26645028 (g2-exponent summary). #4886 executes the route's pre-registered falsifier at 29# and 31#: the fatal failure mode (c_eff decaying like 1/log p) does not occur at the discriminating 23#->29# step, E(H_A) = 0 at every pre-registered H, and the A = 1 margin is quantified (maxrun/H_1 = 0.948 at 31#, the closest approach in the record). Its section 6 names the constraint any proof attempt on the repulsion must respect: a level-independent constant is contradicted at matched depth; decay slower than 1/log p at the measured per-step rates is consistent with all four levels. Mismatch to keep: nothing here lowers 4.27 or proves any bound. The G2 values 258/348 are already on the verified ladder (A144311 + 1, exact terms to 43#), so the new content is the tail histogram and c_eff, not a ladder point. The finiteness-structure summary records as PROVEN that a finite calibration cannot identify the tail log exponent (#415), so the measured decline rate is a heuristic target for a proof, not evidence about the asymptotic rate. Review 1746 calibrates 'roughly half the 1/log p rate' as interpretation beyond the frozen rule (MIXED).","assumptions_md":"Provisional relevance only: #4886 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 336 (empty-window counting for the twin-slot maximal gap), outcome promising, rung measured by review 1746 (spot). Accepted content: the exact run-length histograms of the twin-slot set mod 29# and 31# (gaps29.csv, gaps31.csv; census 214,708,725 and 6,226,553,025 = prod(p-2); maxrun 257 = A144311(10) and 347 = A144311(11), so G2 = maxrun+1 = 258 and 348); the exact empty-window count E(H) = 0 at the pre-registered H_A = A p log^2 p, A in {1,2,4}, at all four levels 19#-31#; and the effective constant c_eff(H) = -ln(E(H)/P)/(H d) at matched depth, declining 1.6-3.0 % per step at 23#->29# (1/log p predicts 6.9 %) and 3.4-8.4 % cumulatively over 23#->31# (prediction 8.7 %), non-monotone at the deepest anchor; the frozen PREREG rule returns MIXED. Not claimed: any tail bound, G2 bound, exponent or statement about twin primes; the route's implication (uniform E(H) <= P exp(-cHd) => G2 <= A p log^2 p) stays open. Four levels and three matchings only; the deepest-anchor counts are single digits. The aligned-orbit lemma and class-structure gain belong to #4859 (recorded, not accepted) and are not part of this source's accepted scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Bridge (narrow). #4886 ships executable validators and counterexample targets: check_9760.py re-derives every reported number from the raw CSVs (check_9760.out, 69/69) and check_9760.corrupt.out records six planted-corruption controls caught; evaluate.py and evaluate_output.json implement the frozen PREREG.md decision rule. Review 1746 added an independent CRT lift 23#->29#->31# that reproduced the served gaps29.csv and gaps31.csv byte-identically, and an exact-integer recompute of E(H) and c_eff. Falsification targets the source names itself: a level with E(H_A) > 0, or c_eff decline consistent with 1/log p (route failure clause); the instrument gapdist_big.c is equivalent to the served gapdist.c by validation at n = 8/9 and by the OEIS/census/#1816 anchors at n = 10/11, not by proof. The adversarial summary already records that the Chebyshev empty-window bound is not monotone and that the monotone-hazard reading fails at 23# (#2330, #37); #4886's non-monotone deepest-anchor c_eff is consistent with that, and a claim of a monotone constant would be an obvious target.","assumptions_md":"Provisional relevance only: #4886 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 336 (empty-window counting for the twin-slot maximal gap), outcome promising, rung measured by review 1746 (spot). Accepted content: the exact run-length histograms of the twin-slot set mod 29# and 31# (gaps29.csv, gaps31.csv; census 214,708,725 and 6,226,553,025 = prod(p-2); maxrun 257 = A144311(10) and 347 = A144311(11), so G2 = maxrun+1 = 258 and 348); the exact empty-window count E(H) = 0 at the pre-registered H_A = A p log^2 p, A in {1,2,4}, at all four levels 19#-31#; and the effective constant c_eff(H) = -ln(E(H)/P)/(H d) at matched depth, declining 1.6-3.0 % per step at 23#->29# (1/log p predicts 6.9 %) and 3.4-8.4 % cumulatively over 23#->31# (prediction 8.7 %), non-monotone at the deepest anchor; the frozen PREREG rule returns MIXED. Not claimed: any tail bound, G2 bound, exponent or statement about twin primes; the route's implication (uniform E(H) <= P exp(-cHd) => G2 <= A p log^2 p) stays open. Four levels and three matchings only; the deepest-anchor counts are single digits. The aligned-orbit lemma and class-structure gain belong to #4859 (recorded, not accepted) and are not part of this source's accepted scope. No new counterexample is claimed here and none is requested.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. Route 336 is filed on this lane (the formalize summary lists #4886 as its newest accepted return, not yet folded in). There is no Lean artifact, statement binding or execution binding. #4886's accepted statements are exact finite facts about the twin-slot set mod p# (maxrun 257 at 29#, 347 at 31#; E(H_A) = 0 at the stated H; census = prod(p-2)), which are finite formalization targets in the same sense as the screened ladder value of #4727. Their scale (6,469,693,230 and 200,560,490,130 residues) makes a direct kernel computation unrealistic, so a Lean route would need a certificate format (for example the per-level maximal-run witnesses plus a covering argument); none exists. The proved aligned-orbit CRT lemma that a formalization would naturally start from is #4859's, which is recorded but not accepted, so it does not transfer through #4886.","assumptions_md":"Provisional relevance only: #4886 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 336 (empty-window counting for the twin-slot maximal gap), outcome promising, rung measured by review 1746 (spot). Accepted content: the exact run-length histograms of the twin-slot set mod 29# and 31# (gaps29.csv, gaps31.csv; census 214,708,725 and 6,226,553,025 = prod(p-2); maxrun 257 = A144311(10) and 347 = A144311(11), so G2 = maxrun+1 = 258 and 348); the exact empty-window count E(H) = 0 at the pre-registered H_A = A p log^2 p, A in {1,2,4}, at all four levels 19#-31#; and the effective constant c_eff(H) = -ln(E(H)/P)/(H d) at matched depth, declining 1.6-3.0 % per step at 23#->29# (1/log p predicts 6.9 %) and 3.4-8.4 % cumulatively over 23#->31# (prediction 8.7 %), non-monotone at the deepest anchor; the frozen PREREG rule returns MIXED. Not claimed: any tail bound, G2 bound, exponent or statement about twin primes; the route's implication (uniform E(H) <= P exp(-cHd) => G2 <= A p log^2 p) stays open. Four levels and three matchings only; the deepest-anchor counts are single digits. The aligned-orbit lemma and class-structure gain belong to #4859 (recorded, not accepted) and are not part of this source's accepted scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Bridge (narrow, direct). #4886 is a numbered measurement extended to larger range, and its next_step is the next extension: the exact histogram at 37# (n = 12) as a fifth level, streaming the odd-sublattice marking in segments because the 464 GB bit array does not fit RAM, with A144311(12) = 527 as the served anchor (the g2-exponent summary records G2(37#) = 528 with an exhaustive maximality certificate), reusing gapdist_big.c's output convention and check_9760.py unchanged. The instrument chain (gapdist_big.c, evaluate.py, check_9760.py, PREREG.md) and its hashes are on the record. Related range work in the measure summary: the L-ladder T31 support {6,...,318} U {330,348} (#1473) and its proposed T37 tile; the 31# histogram here is the slot-gap census whose G2 = 348 matches that support's top value. The source's scope is the four levels 19#-31#; 37# is an unexecuted extension, not covered by this screening.","assumptions_md":"Provisional relevance only: #4886 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 336 (empty-window counting for the twin-slot maximal gap), outcome promising, rung measured by review 1746 (spot). Accepted content: the exact run-length histograms of the twin-slot set mod 29# and 31# (gaps29.csv, gaps31.csv; census 214,708,725 and 6,226,553,025 = prod(p-2); maxrun 257 = A144311(10) and 347 = A144311(11), so G2 = maxrun+1 = 258 and 348); the exact empty-window count E(H) = 0 at the pre-registered H_A = A p log^2 p, A in {1,2,4}, at all four levels 19#-31#; and the effective constant c_eff(H) = -ln(E(H)/P)/(H d) at matched depth, declining 1.6-3.0 % per step at 23#->29# (1/log p predicts 6.9 %) and 3.4-8.4 % cumulatively over 23#->31# (prediction 8.7 %), non-monotone at the deepest anchor; the frozen PREREG rule returns MIXED. Not claimed: any tail bound, G2 bound, exponent or statement about twin primes; the route's implication (uniform E(H) <= P exp(-cHd) => G2 <= A p log^2 p) stays open. Four levels and three matchings only; the deepest-anchor counts are single digits. The aligned-orbit lemma and class-structure gain belong to #4859 (recorded, not accepted) and are not part of this source's accepted scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. #4886 covers exactly four finite levels (19#-31#). The route's conditional chain (uniform empty-window bound => G2 <= A p log^2 p < p'^2 - 2 => a twin pair in (p, p'^2) infinitely often) is stated in the route record and in #4886 as open and untouched; the source supplies no uniform bound, no occupied zones on unbounded scales and no prime-detection estimate. Its relevance to the G2 route is recorded under g2-exponent, measure and adversarial; finite tail counts cannot discharge this target domain.","assumptions_md":"Provisional relevance only: #4886 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 336 (empty-window counting for the twin-slot maximal gap), outcome promising, rung measured by review 1746 (spot). Accepted content: the exact run-length histograms of the twin-slot set mod 29# and 31# (gaps29.csv, gaps31.csv; census 214,708,725 and 6,226,553,025 = prod(p-2); maxrun 257 = A144311(10) and 347 = A144311(11), so G2 = maxrun+1 = 258 and 348); the exact empty-window count E(H) = 0 at the pre-registered H_A = A p log^2 p, A in {1,2,4}, at all four levels 19#-31#; and the effective constant c_eff(H) = -ln(E(H)/P)/(H d) at matched depth, declining 1.6-3.0 % per step at 23#->29# (1/log p predicts 6.9 %) and 3.4-8.4 % cumulatively over 23#->31# (prediction 8.7 %), non-monotone at the deepest anchor; the frozen PREREG rule returns MIXED. Not claimed: any tail bound, G2 bound, exponent or statement about twin primes; the route's implication (uniform E(H) <= P exp(-cHd) => G2 <= A p log^2 p) stays open. Four levels and three matchings only; the deepest-anchor counts are single digits. The aligned-orbit lemma and class-structure gain belong to #4859 (recorded, not accepted) and are not part of this source's accepted scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. Nothing in #4886 is conditional on a finite twin count. The eventual consequence recorded in the finiteness-structure summary (G2(x#) >= x'^2 - 2) concerns G2 values; #4886's G2 values 258 and 348 are already on the verified ladder (A144311 b-file, #1816's D(T_31) and G2), so it adds no new finite margin. Its new content, the tail histograms and c_eff, measures how fast empty windows vanish below G2+2 and is not a structure forced under finiteness; the lane's PROVEN item that a finite calibration cannot identify the tail log exponent (#415) applies.","assumptions_md":"Provisional relevance only: #4886 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 336 (empty-window counting for the twin-slot maximal gap), outcome promising, rung measured by review 1746 (spot). Accepted content: the exact run-length histograms of the twin-slot set mod 29# and 31# (gaps29.csv, gaps31.csv; census 214,708,725 and 6,226,553,025 = prod(p-2); maxrun 257 = A144311(10) and 347 = A144311(11), so G2 = maxrun+1 = 258 and 348); the exact empty-window count E(H) = 0 at the pre-registered H_A = A p log^2 p, A in {1,2,4}, at all four levels 19#-31#; and the effective constant c_eff(H) = -ln(E(H)/P)/(H d) at matched depth, declining 1.6-3.0 % per step at 23#->29# (1/log p predicts 6.9 %) and 3.4-8.4 % cumulatively over 23#->31# (prediction 8.7 %), non-monotone at the deepest anchor; the frozen PREREG rule returns MIXED. Not claimed: any tail bound, G2 bound, exponent or statement about twin primes; the route's implication (uniform E(H) <= P exp(-cHd) => G2 <= A p log^2 p) stays open. Four levels and three matchings only; the deepest-anchor counts are single digits. The aligned-orbit lemma and class-structure gain belong to #4859 (recorded, not accepted) and are not part of this source's accepted scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Mismatch for main and O1-O7, each checked. main needs a quantified full-cutoff survivor-gap lower bound for all large y with the stated logarithmic shape at sufficient A = 12, and O3 every fixed A > 4: #4886 gives exact maxima at two finite levels and E(H) at upper-bound-shaped windows H_A = A p log^2 p (its A is the route's window parameter, not the paper's A), so it supplies no constant, onset or lower bound. O1 (prime harmonic asymptotic), O2 (uniform smooth-number asymptotic), O4 (dyadic prime count with coefficient 1/2), O6 (two-sided density/Euler estimates): no prime sums, smooth numbers or asymptotic density estimates; the census prod(p-2) is an exact finite product, not an Euler estimate. O5 (general sieve input; finite dimension-4, CRT, covering): the histograms are CRT computations of the dimension-2 twin-slot set, not a dimension-4 result, a sieve input or the one-class statement. O7 (eq. (28) constant): no such constant or parameter range. The shared survivor/CRT vocabulary is not a bridge, consistent with the screenings of the ladder sources #4727 and #4539.","assumptions_md":"Provisional relevance only: #4886 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 336 (empty-window counting for the twin-slot maximal gap), outcome promising, rung measured by review 1746 (spot). Accepted content: the exact run-length histograms of the twin-slot set mod 29# and 31# (gaps29.csv, gaps31.csv; census 214,708,725 and 6,226,553,025 = prod(p-2); maxrun 257 = A144311(10) and 347 = A144311(11), so G2 = maxrun+1 = 258 and 348); the exact empty-window count E(H) = 0 at the pre-registered H_A = A p log^2 p, A in {1,2,4}, at all four levels 19#-31#; and the effective constant c_eff(H) = -ln(E(H)/P)/(H d) at matched depth, declining 1.6-3.0 % per step at 23#->29# (1/log p predicts 6.9 %) and 3.4-8.4 % cumulatively over 23#->31# (prediction 8.7 %), non-monotone at the deepest anchor; the frozen PREREG rule returns MIXED. Not claimed: any tail bound, G2 bound, exponent or statement about twin primes; the route's implication (uniform E(H) <= P exp(-cHd) => G2 <= A p log^2 p) stays open. Four levels and three matchings only; the deepest-anchor counts are single digits. The aligned-orbit lemma and class-structure gain belong to #4859 (recorded, not accepted) and are not part of this source's accepted scope.","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":false},"effective":true,"check_job_id":9811,"input_sha256":"6847668e24b2d0b93a9db46bb2b8973390ea4892bf12033fa4e6f2e318a16b16","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"8f6bcc1c13361a61354afe804d6b24cdb434e046400102ba2dda13a12d7fcf6d","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4886,"material_evidence":{"sha256":"509e64261ab0665f51d6345e9ccbc9b18045906e0387632c5415fc874a775d89","entries":{"return:4886":"0c6b244436d9e73f003c414cf08ce9ec288f2d9ea9abd6be820283a3231b6fc5","artifact:4886:01ec2b642516e2261e345f55d35f5c930201cfbff2a6427f6f2f1c6e9deda08c":"01ec2b642516e2261e345f55d35f5c930201cfbff2a6427f6f2f1c6e9deda08c","artifact:4886:055a92f1def490608f899b251061d1c7ca17880c76e9481f9e02429e3e9a6c2e":"055a92f1def490608f899b251061d1c7ca17880c76e9481f9e02429e3e9a6c2e","artifact:4886:2cd011c674e2796ee3fb839b816c764a61e29d01279f73eec06f38e7e4592606":"2cd011c674e2796ee3fb839b816c764a61e29d01279f73eec06f38e7e4592606","artifact:4886:31ae1f35451d197772c309aa0e6950493bd34f9f0f925e4c6e01bd0663d31e42":"31ae1f35451d197772c309aa0e6950493bd34f9f0f925e4c6e01bd0663d31e42","artifact:4886:3c680c0f67717ca63426a8f7a515d2c3e7011ed4abf23908c17d2949c7fc2915":"3c680c0f67717ca63426a8f7a515d2c3e7011ed4abf23908c17d2949c7fc2915","artifact:4886:4e0bf1c688eeb80b0cd61eb07b12629eb03b6c124ebb090497d692928a2cf6dc":"4e0bf1c688eeb80b0cd61eb07b12629eb03b6c124ebb090497d692928a2cf6dc","artifact:4886:668d0423da051688a71a40d5f216d6e67a8451aa9d4f959d26e234bb2dcf7f3b":"668d0423da051688a71a40d5f216d6e67a8451aa9d4f959d26e234bb2dcf7f3b","artifact:4886:6a3a425611a5d73d8006613ac41b72ab895f654f10bfa48da692ca5be097076e":"6a3a425611a5d73d8006613ac41b72ab895f654f10bfa48da692ca5be097076e","artifact:4886:6c5fb4dc80918617cf155b84ee66a9016eeb484c75f911db79ec5f6686f60e41":"6c5fb4dc80918617cf155b84ee66a9016eeb484c75f911db79ec5f6686f60e41","artifact:4886:8f6bcc1c13361a61354afe804d6b24cdb434e046400102ba2dda13a12d7fcf6d":"8f6bcc1c13361a61354afe804d6b24cdb434e046400102ba2dda13a12d7fcf6d","artifact:4886:b3d41dea6e75ab2dbc17605c7bff1e73f7fe36703de39e74a71b5d49a33f67de":"b3d41dea6e75ab2dbc17605c7bff1e73f7fe36703de39e74a71b5d49a33f67de","artifact:4886:b61420beb0d39648db9781406c7df96caacbe22e901a54a636639ba3659a7b8e":"b61420beb0d39648db9781406c7df96caacbe22e901a54a636639ba3659a7b8e","artifact:4886:bf6893ce37bff6214825d66100d010f73211f93be231387f450d693dce2c1379":"bf6893ce37bff6214825d66100d010f73211f93be231387f450d693dce2c1379"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4886,"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 #4886: 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\":4886,\"report_sha256\":\"8f6bcc1c13361a61354afe804d6b24cdb434e046400102ba2dda13a12d7fcf6d\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4886\":\"0c6b244436d9e73f003c414cf08ce9ec288f2d9ea9abd6be820283a3231b6fc5\",\"artifact:4886:01ec2b642516e2261e345f55d35f5c930201cfbff2a6427f6f2f1c6e9deda08c\":\"01ec2b642516e2261e345f55d35f5c930201cfbff2a6427f6f2f1c6e9deda08c\",\"artifact:4886:055a92f1def490608f899b251061d1c7ca17880c76e9481f9e02429e3e9a6c2e\":\"055a92f1def490608f899b251061d1c7ca17880c76e9481f9e02429e3e9a6c2e\",\"artifact:4886:2cd011c674e2796ee3fb839b816c764a61e29d01279f73eec06f38e7e4592606\":\"2cd011c674e2796ee3fb839b816c764a61e29d01279f73eec06f38e7e4592606\",\"artifact:4886:31ae1f35451d197772c309aa0e6950493bd34f9f0f925e4c6e01bd0663d31e42\":\"31ae1f35451d197772c309aa0e6950493bd34f9f0f925e4c6e01bd0663d31e42\",\"artifact:4886:3c680c0f67717ca63426a8f7a515d2c3e7011ed4abf23908c17d2949c7fc2915\":\"3c680c0f67717ca63426a8f7a515d2c3e7011ed4abf23908c17d2949c7fc2915\",\"artifact:4886:4e0bf1c688eeb80b0cd61eb07b12629eb03b6c124ebb090497d692928a2cf6dc\":\"4e0bf1c688eeb80b0cd61eb07b12629eb03b6c124ebb090497d692928a2cf6dc\",\"artifact:4886:668d0423da051688a71a40d5f216d6e67a8451aa9d4f959d26e234bb2dcf7f3b\":\"668d0423da051688a71a40d5f216d6e67a8451aa9d4f959d26e234bb2dcf7f3b\",\"artifact:4886:6a3a425611a5d73d8006613ac41b72ab895f654f10bfa48da692ca5be097076e\":\"6a3a425611a5d73d8006613ac41b72ab895f654f10bfa48da692ca5be097076e\",\"artifact:4886:6c5fb4dc80918617cf155b84ee66a9016eeb484c75f911db79ec5f6686f60e41\":\"6c5fb4dc80918617cf155b84ee66a9016eeb484c75f911db79ec5f6686f60e41\",\"artifact:4886:8f6bcc1c13361a61354afe804d6b24cdb434e046400102ba2dda13a12d7fcf6d\":\"8f6bcc1c13361a61354afe804d6b24cdb434e046400102ba2dda13a12d7fcf6d\",\"artifact:4886:b3d41dea6e75ab2dbc17605c7bff1e73f7fe36703de39e74a71b5d49a33f67de\":\"b3d41dea6e75ab2dbc17605c7bff1e73f7fe36703de39e74a71b5d49a33f67de\",\"artifact:4886:b61420beb0d39648db9781406c7df96caacbe22e901a54a636639ba3659a7b8e\":\"b61420beb0d39648db9781406c7df96caacbe22e901a54a636639ba3659a7b8e\",\"artifact:4886:bf6893ce37bff6214825d66100d010f73211f93be231387f450d693dce2c1379\":\"bf6893ce37bff6214825d66100d010f73211f93be231387f450d693dce2c1379\"},\"sha256\":\"509e64261ab0665f51d6345e9ccbc9b18045906e0387632c5415fc874a775d89\"},\"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:4886,input_sha256:\"6847668e24b2d0b93a9db46bb2b8973390ea4892bf12033fa4e6f2e318a16b16\",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/4899/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"e4a153e5100e7de9b57597d89bbde955b2952ddc0cd4e1190b1f1baeb79428ba","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}