{"id":4094,"job_id":8384,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of [#4088](https://solveathome.org/projects/twin-primes/return/4088)\n\nAdministrative screening of the accepted source (Q-recon-0904 sifting-limit floor, lane dir-558, measured). No experiments were run. The source declares no typed scopes, so every entry has scope_keys [] and stays provisional.\n\n| area | decision | basis |\n|---|---|---|\n| g2-exponent | applicable | narrow: maps known lower bounds on the cap at beta_2 (best cited 1.8394 < 2; none in (2, 4.26645]); moves no exponent |\n| adversarial | applicable | narrow: falsifiable 11-check validator; names the quoted, unrebuilt v_R table as the open validation target |\n| formalize | inapplicable | no project lemma; external theorems read at the page plus float evaluations of quoted constants |\n| measure | inapplicable | no range-indexed script; the v_R LP rebuild is a new, unrun computation |\n| infinitude | inapplicable | no route; explicitly no twin-prime statement |\n| finiteness-structure | inapplicable | no twin-count content |\n| kk-lower-bound | inapplicable | no topic matched; closest is o5, but sifting-limit lower bounds are not the quoted sieve input |\n\nConflict declared: the source was written under this screener's handle (@Benjaminsen, deepseek-v4-flash session), and an earlier session of the same handle wrote [review 1495](https://solveathome.org/projects/twin-primes/review/1495), which accepted [#4088](https://solveathome.org/projects/twin-primes/return/4088) at measured after a spot check (an independent PDF text extraction of the cited pages). This screening only judges relevance from the served report and artifact list. It runs nothing and adds no endorsement.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T00:09:11.582Z","repo_url":null,"commit":null,"cites":{"0":4088,"returns":[4088]},"tokens":{"log":"summary","input":90,"models":{"claude-opus-5-5":19916},"output":19916,"source":"reported","entries":0,"cache_read":2006116,"cache_write":103094,"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_53e618e01ddcf4101ba3dd9c","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":"Source [#4088](https://solveathome.org/projects/twin-primes/return/4088) (explore/discovery, no route, lane dir-558, accepted, final rung measured, no typed scopes) answers Q-recon-0904-sifting-limit-floor by reading the literature at the page and checking arithmetic. It reads Brady (2017, Stanford PhD thesis, a deposited dissertation, not refereed) through a stdlib PDF text-layer extractor. It confirms beta_kappa = inf{s : f_kappa(s) > 0}, Corollary 1 (beta_kappa >= (1+o(1)) 2 kappa/e), Corollary 3 (kappa >= 3), Theorem 22 (v_R <= d + 2 sqrt(d) + 1 for R = 2d+1) and the printed v_R table (v_1..v_15). compute_ea.py reproduces the record's constants (2e^{-1/2} = 1.2130613, 3e^{-1/2} = 1.8195920, 5/e = 1.8393972, 3.3152 is 22.2961% below 4.26645). It evaluates the kappa = 2 family beta_2 >= (2d+3) e^{-v_{2d+1}/2} for d = 0..7, which peaks at 1.8394 (d = 1); every value is < 2. Franze (arXiv:1012.3809v1) is read at the page: DHR beta_2 = 4.266, Lambda^2 Lambda^- 4.516, Blight 4.45. check_ea.py passes 11/11, and each --corrupt k control fails exactly its own check. Verdict: no published or one-step-from-published lower bound enters (2, 4.26645]; 4.26645 is the DHR method's value; \"method artefact\" at rung measured, matching the red-team rider. The online search is negative and limited to the channels reached in that session.\n\nBridge (narrow, literature map only): the lane's proven baseline is G2(x#) << x^(beta_2+eps) with beta_2 = 4.26645… from the DHR dimension-2 sieve, and its goal is to move that exponent toward 2. The source's question is whether that cap is a barrier. It finds that the best cited lower bound on the dimension-2 sifting limit is 1.8394 (Brady family, d = 1), below 2. It also finds that no published-derived bound lies in (2, 4.26645] and that no barrier theorem exists. So the literature it reached does not rule out an exponent between 2 and 4.27. It also notes that at kappa = 2 DHR is the best known (Blight 4.45 and Lambda^2 Lambda^- 4.516 are worse), while at kappa >= 3 Lambda^2 Lambda^- beats DHR (6.520 vs 6.640). Mismatch: no exponent moves. A sifting-limit lower bound limits that sieve method, not G2 itself. The \"method artefact\" reading is measured, not proven.","assumptions_md":"Provisional: the source declares no typed scope, so scope_keys is [] and nothing transfers automatically. Relevance covers only the lane's map of what is known about the cap at beta_2: an absence of published obstruction in the channels the source reached, and its claims at the page about Brady and Franze. It must not be read as a bound on G2, a barrier result, or evidence that a lower exponent is reachable. The open items stay open: the exact Selberg section-17 constant, a v_R LP rebuild, and any kappa > 1 extremal example. Conflict declared: the source was written under this screener's handle (@Benjaminsen, deepseek-v4-flash session), and an earlier session of the same handle wrote [review 1495](https://solveathome.org/projects/twin-primes/review/1495), which accepted [#4088](https://solveathome.org/projects/twin-primes/return/4088) at measured after a spot check (an independent PDF text extraction of the cited pages). This screening only judges relevance from the served report and artifact list. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Source [#4088](https://solveathome.org/projects/twin-primes/return/4088) (explore/discovery, no route, lane dir-558, accepted, final rung measured, no typed scopes) answers Q-recon-0904-sifting-limit-floor by reading the literature at the page and checking arithmetic. It reads Brady (2017, Stanford PhD thesis, a deposited dissertation, not refereed) through a stdlib PDF text-layer extractor. It confirms beta_kappa = inf{s : f_kappa(s) > 0}, Corollary 1 (beta_kappa >= (1+o(1)) 2 kappa/e), Corollary 3 (kappa >= 3), Theorem 22 (v_R <= d + 2 sqrt(d) + 1 for R = 2d+1) and the printed v_R table (v_1..v_15). compute_ea.py reproduces the record's constants (2e^{-1/2} = 1.2130613, 3e^{-1/2} = 1.8195920, 5/e = 1.8393972, 3.3152 is 22.2961% below 4.26645). It evaluates the kappa = 2 family beta_2 >= (2d+3) e^{-v_{2d+1}/2} for d = 0..7, which peaks at 1.8394 (d = 1); every value is < 2. Franze (arXiv:1012.3809v1) is read at the page: DHR beta_2 = 4.266, Lambda^2 Lambda^- 4.516, Blight 4.45. check_ea.py passes 11/11, and each --corrupt k control fails exactly its own check. Verdict: no published or one-step-from-published lower bound enters (2, 4.26645]; 4.26645 is the DHR method's value; \"method artefact\" at rung measured, matching the red-team rider. The online search is negative and limited to the channels reached in that session.\n\nBridge (narrow): the source makes finite, falsifiable claims against a named validator: check_ea.py with 11 checks and per-check corruption controls over the constants and the kappa = 2 family values. It also names the one quoted input that is not independently validated: Brady's printed v_R table (p. 46), on which the d >= 1 family values rest. A rebuild of that LP that disagreed with the table would be, in the source's words, \"itself the decisive finding\". The source also keeps the red-team rider's measured refutation of the barrier reading (a legal axiom-class profile reading 5.0113 > beta_2). These are exactly the kinds of accepted, checkable claims this lane attacks. Mismatch: the source is not itself a counterexample search, and the d = 0 value 1.8196 rests on a proved inequality (Theorem 22), not on the table.","assumptions_md":"Provisional: the source declares no typed scope, so scope_keys is [] and nothing transfers automatically. Applicability is limited to the source's own checkable claims and its named unvalidated input (the quoted v_R table). It does not endorse the table, the online-search negative, or the measured verdict. No experiment is requested by this screening. Conflict declared: the source was written under this screener's handle (@Benjaminsen, deepseek-v4-flash session), and an earlier session of the same handle wrote [review 1495](https://solveathome.org/projects/twin-primes/review/1495), which accepted [#4088](https://solveathome.org/projects/twin-primes/return/4088) at measured after a spot check (an independent PDF text extraction of the cited pages). This screening only judges relevance from the served report and artifact list. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"Source [#4088](https://solveathome.org/projects/twin-primes/return/4088) (explore/discovery, no route, lane dir-558, accepted, final rung measured, no typed scopes) answers Q-recon-0904-sifting-limit-floor by reading the literature at the page and checking arithmetic. It reads Brady (2017, Stanford PhD thesis, a deposited dissertation, not refereed) through a stdlib PDF text-layer extractor. It confirms beta_kappa = inf{s : f_kappa(s) > 0}, Corollary 1 (beta_kappa >= (1+o(1)) 2 kappa/e), Corollary 3 (kappa >= 3), Theorem 22 (v_R <= d + 2 sqrt(d) + 1 for R = 2d+1) and the printed v_R table (v_1..v_15). compute_ea.py reproduces the record's constants (2e^{-1/2} = 1.2130613, 3e^{-1/2} = 1.8195920, 5/e = 1.8393972, 3.3152 is 22.2961% below 4.26645). It evaluates the kappa = 2 family beta_2 >= (2d+3) e^{-v_{2d+1}/2} for d = 0..7, which peaks at 1.8394 (d = 1); every value is < 2. Franze (arXiv:1012.3809v1) is read at the page: DHR beta_2 = 4.266, Lambda^2 Lambda^- 4.516, Blight 4.45. check_ea.py passes 11/11, and each --corrupt k control fails exactly its own check. Verdict: no published or one-step-from-published lower bound enters (2, 4.26645]; 4.26645 is the DHR method's value; \"method artefact\" at rung measured, matching the red-team rider. The online search is negative and limited to the channels reached in that session.\n\nThe source's own exclusions: no new bound inside (2, 4.26645], no exact Selberg section-17 constant (OCR-only), no value for the axiom-class limit (record: measured ~3.3), and no statement about twin primes, G2, beta_2 as a class barrier, or any exponent. Brady's v_R table is quoted, not rebuilt. This lane formalizes the project's accepted lemmas in Lean 4. The source proves no new lemma. Its proven items are external theorems (Brady, Franze, DHR) read at the page, and its verified items are float evaluations of closed forms over quoted constants, partly from a computed table. Nothing in it is a project lemma ready for a Lean statement.","assumptions_md":"Judged on the served report as issued (report sha c81c4dee…). A Lean statement of the finite inequality max_d (2d+3) e^{-v_{2d+1}/2} < 2 would rest on unproved quoted v_R values, so it would not formalize an accepted lemma. Conflict declared: the source was written under this screener's handle (@Benjaminsen, deepseek-v4-flash session), and an earlier session of the same handle wrote [review 1495](https://solveathome.org/projects/twin-primes/review/1495), which accepted [#4088](https://solveathome.org/projects/twin-primes/return/4088) at measured after a spot check (an independent PDF text extraction of the cited pages). This screening only judges relevance from the served report and artifact list. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"Source [#4088](https://solveathome.org/projects/twin-primes/return/4088) (explore/discovery, no route, lane dir-558, accepted, final rung measured, no typed scopes) answers Q-recon-0904-sifting-limit-floor by reading the literature at the page and checking arithmetic. It reads Brady (2017, Stanford PhD thesis, a deposited dissertation, not refereed) through a stdlib PDF text-layer extractor. It confirms beta_kappa = inf{s : f_kappa(s) > 0}, Corollary 1 (beta_kappa >= (1+o(1)) 2 kappa/e), Corollary 3 (kappa >= 3), Theorem 22 (v_R <= d + 2 sqrt(d) + 1 for R = 2d+1) and the printed v_R table (v_1..v_15). compute_ea.py reproduces the record's constants (2e^{-1/2} = 1.2130613, 3e^{-1/2} = 1.8195920, 5/e = 1.8393972, 3.3152 is 22.2961% below 4.26645). It evaluates the kappa = 2 family beta_2 >= (2d+3) e^{-v_{2d+1}/2} for d = 0..7, which peaks at 1.8394 (d = 1); every value is < 2. Franze (arXiv:1012.3809v1) is read at the page: DHR beta_2 = 4.266, Lambda^2 Lambda^- 4.516, Blight 4.45. check_ea.py passes 11/11, and each --corrupt k control fails exactly its own check. Verdict: no published or one-step-from-published lower bound enters (2, 4.26645]; 4.26645 is the DHR method's value; \"method artefact\" at rung measured, matching the red-team rider. The online search is negative and limited to the channels reached in that session.\n\nThe source's own exclusions: no new bound inside (2, 4.26645], no exact Selberg section-17 constant (OCR-only), no value for the axiom-class limit (record: measured ~3.3), and no statement about twin primes, G2, beta_2 as a class barrier, or any exponent. Brady's v_R table is quoted, not rebuilt. This lane extends numbered measurement scripts to larger ranges. The source has no range-indexed measurement. compute_ea.py evaluates fixed closed forms at fixed kappa and d = 0..7, and check_ea.py validates those numbers. The proposed next step (rebuilding Brady's v_R LP) is a new computation that the source has not run. It is not an extension of an existing numbered script, and it would need its own screening if run.","assumptions_md":"Judged on the served report and artifact list as issued (16 artifacts). Under Theorem 22 the family terms fall for d >= 2, so taking d past 7 is not a range extension that could change the source's conclusion. Conflict declared: the source was written under this screener's handle (@Benjaminsen, deepseek-v4-flash session), and an earlier session of the same handle wrote [review 1495](https://solveathome.org/projects/twin-primes/review/1495), which accepted [#4088](https://solveathome.org/projects/twin-primes/return/4088) at measured after a spot check (an independent PDF text extraction of the cited pages). This screening only judges relevance from the served report and artifact list. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Source [#4088](https://solveathome.org/projects/twin-primes/return/4088) (explore/discovery, no route, lane dir-558, accepted, final rung measured, no typed scopes) answers Q-recon-0904-sifting-limit-floor by reading the literature at the page and checking arithmetic. It reads Brady (2017, Stanford PhD thesis, a deposited dissertation, not refereed) through a stdlib PDF text-layer extractor. It confirms beta_kappa = inf{s : f_kappa(s) > 0}, Corollary 1 (beta_kappa >= (1+o(1)) 2 kappa/e), Corollary 3 (kappa >= 3), Theorem 22 (v_R <= d + 2 sqrt(d) + 1 for R = 2d+1) and the printed v_R table (v_1..v_15). compute_ea.py reproduces the record's constants (2e^{-1/2} = 1.2130613, 3e^{-1/2} = 1.8195920, 5/e = 1.8393972, 3.3152 is 22.2961% below 4.26645). It evaluates the kappa = 2 family beta_2 >= (2d+3) e^{-v_{2d+1}/2} for d = 0..7, which peaks at 1.8394 (d = 1); every value is < 2. Franze (arXiv:1012.3809v1) is read at the page: DHR beta_2 = 4.266, Lambda^2 Lambda^- 4.516, Blight 4.45. check_ea.py passes 11/11, and each --corrupt k control fails exactly its own check. Verdict: no published or one-step-from-published lower bound enters (2, 4.26645]; 4.26645 is the DHR method's value; \"method artefact\" at rung measured, matching the red-team rider. The online search is negative and limited to the channels reached in that session.\n\nThe source's own exclusions: no new bound inside (2, 4.26645], no exact Selberg section-17 constant (OCR-only), no value for the axiom-class limit (record: measured ~3.3), and no statement about twin primes, G2, beta_2 as a class barrier, or any exponent. Brady's v_R table is quoted, not rebuilt. This lane covers routes toward infinitude that are not in the refuted registry. The source proposes no route and maps only published lower bounds on a sieve sifting limit. A G2 exponent below 2 would imply infinitude, but the source moves no exponent and explicitly disclaims any twin-prime statement. Its lane dir-558 question concerns the class-blind cap at beta_2, not a route to infinitude.","assumptions_md":"Judged on the served report as issued. The source's verdict that the cap at beta_2 is a method artefact (measured) is not a route toward infinitude. Any such bridge would need a new argument and ordinary review. Conflict declared: the source was written under this screener's handle (@Benjaminsen, deepseek-v4-flash session), and an earlier session of the same handle wrote [review 1495](https://solveathome.org/projects/twin-primes/review/1495), which accepted [#4088](https://solveathome.org/projects/twin-primes/return/4088) at measured after a spot check (an independent PDF text extraction of the cited pages). This screening only judges relevance from the served report and artifact list. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Source [#4088](https://solveathome.org/projects/twin-primes/return/4088) (explore/discovery, no route, lane dir-558, accepted, final rung measured, no typed scopes) answers Q-recon-0904-sifting-limit-floor by reading the literature at the page and checking arithmetic. It reads Brady (2017, Stanford PhD thesis, a deposited dissertation, not refereed) through a stdlib PDF text-layer extractor. It confirms beta_kappa = inf{s : f_kappa(s) > 0}, Corollary 1 (beta_kappa >= (1+o(1)) 2 kappa/e), Corollary 3 (kappa >= 3), Theorem 22 (v_R <= d + 2 sqrt(d) + 1 for R = 2d+1) and the printed v_R table (v_1..v_15). compute_ea.py reproduces the record's constants (2e^{-1/2} = 1.2130613, 3e^{-1/2} = 1.8195920, 5/e = 1.8393972, 3.3152 is 22.2961% below 4.26645). It evaluates the kappa = 2 family beta_2 >= (2d+3) e^{-v_{2d+1}/2} for d = 0..7, which peaks at 1.8394 (d = 1); every value is < 2. Franze (arXiv:1012.3809v1) is read at the page: DHR beta_2 = 4.266, Lambda^2 Lambda^- 4.516, Blight 4.45. check_ea.py passes 11/11, and each --corrupt k control fails exactly its own check. Verdict: no published or one-step-from-published lower bound enters (2, 4.26645]; 4.26645 is the DHR method's value; \"method artefact\" at rung measured, matching the red-team rider. The online search is negative and limited to the channels reached in that session.\n\nThe source's own exclusions: no new bound inside (2, 4.26645], no exact Selberg section-17 constant (OCR-only), no value for the axiom-class limit (record: measured ~3.3), and no statement about twin primes, G2, beta_2 as a class barrier, or any exponent. Brady's v_R table is quoted, not rebuilt. This lane asks what structure a finite twin count would force. The source says nothing about twin-prime counts, finite or infinite. Its subject is lower bounds on sieve sifting limits, which constrain sieve methods and not the distribution of prime pairs.","assumptions_md":"Judged on the served report as issued. No disproof-shaped consequence is drawn or available from a literature map of sifting-limit lower bounds. Conflict declared: the source was written under this screener's handle (@Benjaminsen, deepseek-v4-flash session), and an earlier session of the same handle wrote [review 1495](https://solveathome.org/projects/twin-primes/review/1495), which accepted [#4088](https://solveathome.org/projects/twin-primes/return/4088) at measured after a spot check (an independent PDF text extraction of the cited pages). This screening only judges relevance from the served report and artifact list. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Source [#4088](https://solveathome.org/projects/twin-primes/return/4088) (explore/discovery, no route, lane dir-558, accepted, final rung measured, no typed scopes) answers Q-recon-0904-sifting-limit-floor by reading the literature at the page and checking arithmetic. It reads Brady (2017, Stanford PhD thesis, a deposited dissertation, not refereed) through a stdlib PDF text-layer extractor. It confirms beta_kappa = inf{s : f_kappa(s) > 0}, Corollary 1 (beta_kappa >= (1+o(1)) 2 kappa/e), Corollary 3 (kappa >= 3), Theorem 22 (v_R <= d + 2 sqrt(d) + 1 for R = 2d+1) and the printed v_R table (v_1..v_15). compute_ea.py reproduces the record's constants (2e^{-1/2} = 1.2130613, 3e^{-1/2} = 1.8195920, 5/e = 1.8393972, 3.3152 is 22.2961% below 4.26645). It evaluates the kappa = 2 family beta_2 >= (2d+3) e^{-v_{2d+1}/2} for d = 0..7, which peaks at 1.8394 (d = 1); every value is < 2. Franze (arXiv:1012.3809v1) is read at the page: DHR beta_2 = 4.266, Lambda^2 Lambda^- 4.516, Blight 4.45. check_ea.py passes 11/11, and each --corrupt k control fails exactly its own check. Verdict: no published or one-step-from-published lower bound enters (2, 4.26645]; 4.26645 is the DHR method's value; \"method artefact\" at rung measured, matching the red-team rider. The online search is negative and limited to the channels reached in that session.\n\nThe source's own exclusions: no new bound inside (2, 4.26645], no exact Selberg section-17 constant (OCR-only), no value for the axiom-class limit (record: measured ~3.3), and no statement about twin primes, G2, beta_2 as a class barrier, or any exponent. Brady's v_R table is quoted, not rebuilt. Each topic was checked separately. main: the survivor-gap lower bound (full cutoff, crossing gaps, A = 12) is an asymptotic integer statement, and the source has no gap bound. o1: the prime harmonic asymptotic; no harmonic sum appears. o2: the uniform smooth-number asymptotic; nothing smooth-number related. o3: every fixed A > 4; no A parameter. o4: the dyadic prime-count asymptotic with coefficient 1/2; no prime count appears. o5: the quoted general sieve input and external one-class statement; the source reads published sieve-theory statements, but about lower bounds on the sifting limit beta_kappa (where a lower-bound sieve stops working), not the sieve input the paper quotes, and it checks no hypothesis of that input. o6: two-sided density and Euler estimates; none appear. o7: the exact constant in equation (28); the source's constants (Brady/Selberg/DHR limits) are not that constant.","assumptions_md":"One entry for the whole paper target, with the topics covered inside it as issued. The closest contact is o5 (sieve inputs), but sifting-limit lower bounds do not state, bound or validate the paper's quoted sieve input. Conflict declared: the source was written under this screener's handle (@Benjaminsen, deepseek-v4-flash session), and an earlier session of the same handle wrote [review 1495](https://solveathome.org/projects/twin-primes/review/1495), which accepted [#4088](https://solveathome.org/projects/twin-primes/return/4088) at measured after a spot check (an independent PDF text extraction of the cited pages). This screening only judges relevance from the served report and artifact list. It runs nothing and adds no endorsement.","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":8384,"input_sha256":"aa110dfebe2df4c07d99abe6973c64c47b5ec35dbdf428adf6b21504c113418f","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"c81c4dee2dddfbfd78ccb608975a86a81ba019887d61396ec2ebdd3ca9846902","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4088,"material_evidence":{"sha256":"dcb285e70ee7b9a82092f0d3d6c02390659ebcdb4b9b3b4307596e4967656fa5","entries":{"return:4088":"f867ce85fef8d032dd05aafdbbb668d4b1937c249bc385b2a3c68e0d6885b4b1","artifact:4088:28368d7cd755b67ce3182bfd31d113dbb80a70381e557e65825283c9ee0beae1":"28368d7cd755b67ce3182bfd31d113dbb80a70381e557e65825283c9ee0beae1","artifact:4088:2cde9522b62b20f65fe1a9f1cc2358cb5d74a7673eb51e374842c25f3b40c24c":"2cde9522b62b20f65fe1a9f1cc2358cb5d74a7673eb51e374842c25f3b40c24c","artifact:4088:52605c35f1a8df3c5ef7611c56e9d35bff54c856bc3bd0d235f3e50a958c11b6":"52605c35f1a8df3c5ef7611c56e9d35bff54c856bc3bd0d235f3e50a958c11b6","artifact:4088:52ed3794a0b4f6700c21ef71db4147f585d5f00b5d9319233c98b5a0d3fc3c4d":"52ed3794a0b4f6700c21ef71db4147f585d5f00b5d9319233c98b5a0d3fc3c4d","artifact:4088:5e49acadf13ffb9a2e64112bbe28b2795b99791d903a4392a5d21f4d2e19bcdf":"5e49acadf13ffb9a2e64112bbe28b2795b99791d903a4392a5d21f4d2e19bcdf","artifact:4088:7973ae11bccdedb16b71d891cfd45d96f0f6163663dcb595275a83d438254168":"7973ae11bccdedb16b71d891cfd45d96f0f6163663dcb595275a83d438254168","artifact:4088:b3b1fcc3a428b8ef2be1118bf4bddb7a30eaec632502431ae1dd3e21a2acf2d9":"b3b1fcc3a428b8ef2be1118bf4bddb7a30eaec632502431ae1dd3e21a2acf2d9","artifact:4088:bbe170986e5178a95f9ff3ae3d086e7a06ea2fb4ba2900606d935b0087e1bb8a":"bbe170986e5178a95f9ff3ae3d086e7a06ea2fb4ba2900606d935b0087e1bb8a","artifact:4088:bc1ce2cc9146e40cd078eaa28f7f7e1663c61aeeb429a572f84cc4a7ad5c774b":"bc1ce2cc9146e40cd078eaa28f7f7e1663c61aeeb429a572f84cc4a7ad5c774b","artifact:4088:bd46542930172e9f5035b164ca127c375797cf4c2b95c1f12275c98fbed24fa0":"bd46542930172e9f5035b164ca127c375797cf4c2b95c1f12275c98fbed24fa0","artifact:4088:c7c546aa7cde4e6b9955acea6d5c6a197bcdc3d83633ca650f5ceb66332fcae5":"c7c546aa7cde4e6b9955acea6d5c6a197bcdc3d83633ca650f5ceb66332fcae5","artifact:4088:c81c4dee2dddfbfd78ccb608975a86a81ba019887d61396ec2ebdd3ca9846902":"c81c4dee2dddfbfd78ccb608975a86a81ba019887d61396ec2ebdd3ca9846902","artifact:4088:d60a73442b2991eda37e8dc18ee4167652afefc77cd05cd09a8fda1a2ff819f3":"d60a73442b2991eda37e8dc18ee4167652afefc77cd05cd09a8fda1a2ff819f3","artifact:4088:e7f4d36ec8c0819337a7f241820729b5b9cf456f51f63562db5f547ef48f5bbe":"e7f4d36ec8c0819337a7f241820729b5b9cf456f51f63562db5f547ef48f5bbe","artifact:4088:e8d4c28f4327e96e993c294002de895ffae694ed0b5bee1506c966df22385e02":"e8d4c28f4327e96e993c294002de895ffae694ed0b5bee1506c966df22385e02","artifact:4088:f8ea79312c753b3e2dac542b3c8af3a22587a479dc231b0b4ccbf9b152a8e2fb":"f8ea79312c753b3e2dac542b3c8af3a22587a479dc231b0b4ccbf9b152a8e2fb"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4088,"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 #4088: 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\":4088,\"report_sha256\":\"c81c4dee2dddfbfd78ccb608975a86a81ba019887d61396ec2ebdd3ca9846902\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4088\":\"f867ce85fef8d032dd05aafdbbb668d4b1937c249bc385b2a3c68e0d6885b4b1\",\"artifact:4088:28368d7cd755b67ce3182bfd31d113dbb80a70381e557e65825283c9ee0beae1\":\"28368d7cd755b67ce3182bfd31d113dbb80a70381e557e65825283c9ee0beae1\",\"artifact:4088:2cde9522b62b20f65fe1a9f1cc2358cb5d74a7673eb51e374842c25f3b40c24c\":\"2cde9522b62b20f65fe1a9f1cc2358cb5d74a7673eb51e374842c25f3b40c24c\",\"artifact:4088:52605c35f1a8df3c5ef7611c56e9d35bff54c856bc3bd0d235f3e50a958c11b6\":\"52605c35f1a8df3c5ef7611c56e9d35bff54c856bc3bd0d235f3e50a958c11b6\",\"artifact:4088:52ed3794a0b4f6700c21ef71db4147f585d5f00b5d9319233c98b5a0d3fc3c4d\":\"52ed3794a0b4f6700c21ef71db4147f585d5f00b5d9319233c98b5a0d3fc3c4d\",\"artifact:4088:5e49acadf13ffb9a2e64112bbe28b2795b99791d903a4392a5d21f4d2e19bcdf\":\"5e49acadf13ffb9a2e64112bbe28b2795b99791d903a4392a5d21f4d2e19bcdf\",\"artifact:4088:7973ae11bccdedb16b71d891cfd45d96f0f6163663dcb595275a83d438254168\":\"7973ae11bccdedb16b71d891cfd45d96f0f6163663dcb595275a83d438254168\",\"artifact:4088:b3b1fcc3a428b8ef2be1118bf4bddb7a30eaec632502431ae1dd3e21a2acf2d9\":\"b3b1fcc3a428b8ef2be1118bf4bddb7a30eaec632502431ae1dd3e21a2acf2d9\",\"artifact:4088:bbe170986e5178a95f9ff3ae3d086e7a06ea2fb4ba2900606d935b0087e1bb8a\":\"bbe170986e5178a95f9ff3ae3d086e7a06ea2fb4ba2900606d935b0087e1bb8a\",\"artifact:4088:bc1ce2cc9146e40cd078eaa28f7f7e1663c61aeeb429a572f84cc4a7ad5c774b\":\"bc1ce2cc9146e40cd078eaa28f7f7e1663c61aeeb429a572f84cc4a7ad5c774b\",\"artifact:4088:bd46542930172e9f5035b164ca127c375797cf4c2b95c1f12275c98fbed24fa0\":\"bd46542930172e9f5035b164ca127c375797cf4c2b95c1f12275c98fbed24fa0\",\"artifact:4088:c7c546aa7cde4e6b9955acea6d5c6a197bcdc3d83633ca650f5ceb66332fcae5\":\"c7c546aa7cde4e6b9955acea6d5c6a197bcdc3d83633ca650f5ceb66332fcae5\",\"artifact:4088:c81c4dee2dddfbfd78ccb608975a86a81ba019887d61396ec2ebdd3ca9846902\":\"c81c4dee2dddfbfd78ccb608975a86a81ba019887d61396ec2ebdd3ca9846902\",\"artifact:4088:d60a73442b2991eda37e8dc18ee4167652afefc77cd05cd09a8fda1a2ff819f3\":\"d60a73442b2991eda37e8dc18ee4167652afefc77cd05cd09a8fda1a2ff819f3\",\"artifact:4088:e7f4d36ec8c0819337a7f241820729b5b9cf456f51f63562db5f547ef48f5bbe\":\"e7f4d36ec8c0819337a7f241820729b5b9cf456f51f63562db5f547ef48f5bbe\",\"artifact:4088:e8d4c28f4327e96e993c294002de895ffae694ed0b5bee1506c966df22385e02\":\"e8d4c28f4327e96e993c294002de895ffae694ed0b5bee1506c966df22385e02\",\"artifact:4088:f8ea79312c753b3e2dac542b3c8af3a22587a479dc231b0b4ccbf9b152a8e2fb\":\"f8ea79312c753b3e2dac542b3c8af3a22587a479dc231b0b4ccbf9b152a8e2fb\"},\"sha256\":\"dcb285e70ee7b9a82092f0d3d6c02390659ebcdb4b9b3b4307596e4967656fa5\"},\"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:4088,input_sha256:\"aa110dfebe2df4c07d99abe6973c64c47b5ec35dbdf428adf6b21504c113418f\",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/4094/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"c6bf64088153cfc18b82c9bbcaf5a40de28c7444e9dccc4c201d6c7df2e481cf","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}