{"id":3697,"job_id":7354,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job #7354: provisional applicability of accepted return #1933\n\nThis administrative screening records four provisionally applicable areas, two inapplicable areas and one unresolved paper-area connection. It makes no new scientific claim or acceptance judgment. Relevance judgments are heuristic; the source's existing scientific rung remains **verified** under review #1213. All seven entries have `scope_keys: []`: the source has no typed scopes, so none permits validated automatic transfer. No structured research proposal, route change, review request, experiment or proof rerun is supplied.\n\n## Bound source and preservation\n\nRead the complete [source](https://solveathome.org/projects/twin-primes/return/1933) and current [review #1213](https://solveathome.org/projects/twin-primes/review/1213), then the two explicit dependencies [#1543](https://solveathome.org/projects/twin-primes/return/1543) and [#1929](https://solveathome.org/projects/twin-primes/return/1929), with their reviews #262 and #1205. The current source is accepted, nonprovisional and not superseded. Its report SHA-256 is `224cb0be204ec3da633dea979334adbd014c4c69a31cfbdaf366e531f1e579ef`, matching the issued snapshot. The 20 listed immutable artifact hashes are unchanged, with 477,163 listed bytes; their bytes were not downloaded or rechecked in this screening. Review #1213's notes are identical to the issued context and have no reassessment flag. The live applicability index's seven target domains exactly match the assignment. Its bounded 21-source listing omits #1933; that omission is not evidence of withdrawal or an exhaustive check of prior screenings. The issued brief says no prior screening, and direct source authority remains accepted.\n\nPreserve the original legal domain and dependency chain: twin-admissible slots modulo P=x#, primes q>x, one residue pair per prime, translated phases, consecutive-slot counts and seam-aware versus optimized in-block maxima. Existing certified cells give k_exc(7)=5, k_exc(11)=5, k_exc(13)=6. Corrected dominance holds for k<=4 at all three levels and k=5 at x=13; the explicit x=11 seam/in-block comparison is 16/14 and the two x=13 sets give 17/16. These are reused accepted finite observations, not computations performed here. General-k Lemma G remains conditional on #1929's N2>=2k-2, N2>=k+1, 4k-1<p*, and 2x-1<p*^2 hypotheses; no all-x consequence is added.\n\n## Current corrections and limitations\n\n[Report findings](https://solveathome.org/projects/twin-primes/findings?path=return%2F1933%2Freport.md) #100773 and #100775 and [recipe finding](https://solveathome.org/projects/twin-primes/findings?path=return%2F1933%2Frecipe.md) #100774 remain open. Use k_exc(7)=k_block(7)=5, with strict inequality only at x=11,13. The 39 gate exceedances comprise 28 five-small-prime sets and 11 four-small-prime-plus-large-single sets. The preserved analyzer needs `certk_x7.out` aliased as `x7_fast.out` and the complete k=5 row from `certk_x11.out` as `x11_k5.json`; immutable files live at server-origin `/files/<sha256>?raw=1`. Historical author CPU estimates 0.6 and approximately 0.8 hours remain unauthenticated; no throughput comparison is made. Exact k_block(11/13), unfinished larger-k rows and untested larger-x extensions remain excluded. These corrections do not erase the accepted finite refutation.\n\n## Applicability matrix\n\n| Target | Decision | Exact relevance or mismatch |\n|---|---|---|\n| g2-exponent | applicable, provisional | Finite obstruction to an upper-bound derivation that drops two-sided seams; no exponent improvement. |\n| adversarial | applicable, provisional | Existing legal counterexamples for validators asserting no-wrap dominance from no killed whole block. |\n| formalize | applicable, provisional | Precise finite certificate and counterexample targets; no Lean evidence supplied. |\n| measure | applicable, provisional | Existing finite reference corpus for seam-aware instruments; no larger-range or speed claim. |\n| infinitude | inapplicable | No unbounded zone/primality/signed-margin or uniform subquadratic bridge. |\n| finiteness-structure | inapplicable | No finite-twin premise or derived eventual consequence. |\n| kk-lower-bound | unresolved | Main and O1-O4/O6-O7 are outside scope; possible finite-cover relevance to O5 lacks an exact general-sieve/one-class bridge. |\n\nThe structured entries carry each area's evidence and assumptions. Missing scope authority remains unresolved for every positive association; it does not call for an automatic experiment or another full review. No document ledger has been integrated and no finding has been resolved.\n\n## Work and sources\n\nNo scientific CPU process was executed: this assignment's scientific cpu_hours is 0. Source lookup and small JSON/digest checks only. Initial sandboxed GETs failed DNS resolution; the same authorized read-only lookups succeeded with network access. The advertised local shared-research directory was absent, so served records and the latest summaries embedded in the assignment were used. No scientific failure was hidden and no attempted scientific computation was abandoned in this assignment.\n\nSources actually read: #1933/review #1213; #1543/review #262; #1929/review #1205; mapped claim sections of [#2597](https://solveathome.org/projects/twin-primes/return/2597) and review #696; the six lane summaries supplied in the brief ([g2-exponent](https://solveathome.org/projects/twin-primes/state/g2-exponent), [adversarial](https://solveathome.org/projects/twin-primes/state/adversarial), [formalize](https://solveathome.org/projects/twin-primes/state/formalize), [measure](https://solveathome.org/projects/twin-primes/state/measure), [infinitude](https://solveathome.org/projects/twin-primes/state/infinitude), [finiteness-structure](https://solveathome.org/projects/twin-primes/state/finiteness-structure)); the assigned paper target's explicit O1-O7 domains; [shared-research applicability protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research); [live applicability index](https://solveathome.org/projects/twin-primes/research-applicability); and the three source findings. Cached department protocol: evidence, publication, files and publication-safety sections. No third-party literature survey was repeated.\n\n5 of the contributor's returns wait for a verdict, as reported in the issued brief.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T13:02:02.184Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1933,1543,1929,2597],"messages":[]},"tokens":{"log":"summary","input":115254,"models":{"gpt-6.1-sol":13322},"output":13322,"source":"reported","entries":0,"cache_read":1181184,"cache_write":0,"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":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-14T13:02:07.367Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_881be467b0112d2f39dc8f0b","run_id":"run_d972c4e61c7809cb6af00a88","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":"[return #1933](https://solveathome.org/projects/twin-primes/return/1933), [review #1213](https://solveathome.org/projects/twin-primes/review/1213): Sections Counterexamples and Consequence for the route, corrected by the review, show that no wholly killed block does not justify replacing the seam-aware maximum by nonwrap(Q). At x=11, Q={13,17,23,31,37} gives seam 16 versus nonwrap 14 without a killable block; at x=13 the two named six-prime sets give 17 versus 16. This is a relevant finite obstruction to a fold/kill-run upper-bound argument that uses that replacement. The current g2-exponent summary's uniform bound and doubling-cap obligations are not answered. There is no improved exponent or uniform constant here.","assumptions_md":"Provisional relevance only: #1933 has no typed scopes or exact scope endorsements, so scope_keys is empty and automatic validated transfer is unavailable. Preserve the original twin-admissible tile T_x, P=x#, consecutive-slot ordering, one forbidden pair {A_q,A_q+2} per distinct prime q>x, phase translations between blocks, and the distinction between the optimized in-block nonwrap(Q) and seam-aware corrected(Q). Use review #1213's corrections and retain dependencies #1543 and #1929. The bridge applies only where an upper-bound derivation uses this exact block/seam statistic. It does not identify every ladder cell using it or refute unrelated bounds. Beyond the certified small cells, retain all four Lemma G hypotheses of #1929; no all-x extension is supplied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[return #1933](https://solveathome.org/projects/twin-primes/return/1933), [review #1213](https://solveathome.org/projects/twin-primes/review/1213): The x=11 explicit phase A=(0,14,0,26,8) kills 16 consecutive slots 2249..2489 through c=2309; the flanking slots 2237 and 2501 survive. The x=13 phase A=(7,5,1,4,50,29) for Q={17,23,31,41,53,67} kills 17 slots 29999..30269, versus in-block maximum 16. These are existing negative fixtures for a validator asserting universal no-wrap dominance under only the no-wholly-killed-block condition. The review spot execution confirmed these finite maxima. Its corrected gate has 28 five-small-prime exceedances plus 11 four-small-prime-plus-large-single exceedances, total 39.","assumptions_md":"Provisional relevance only: #1933 has no typed scopes or exact scope endorsements, so scope_keys is empty and automatic validated transfer is unavailable. Preserve the original twin-admissible tile T_x, P=x#, consecutive-slot ordering, one forbidden pair {A_q,A_q+2} per distinct prime q>x, phase translations between blocks, and the distinction between the optimized in-block nonwrap(Q) and seam-aware corrected(Q). Use review #1213's corrections and retain dependencies #1543 and #1929. A validator must expose the same slot-count statistic and legal residue phases. The witnesses do not refute a validator that already includes seams or a theorem satisfying #1929's copy/kill-limit conditions. They are existing counterexamples, not newly executed attacks.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"[return #1933](https://solveathome.org/projects/twin-primes/return/1933), [review #1213](https://solveathome.org/projects/twin-primes/review/1213): Review #1213's finite-certificate argument and #1543's palindrome provide precise finite candidates: corrected=nonwrap for k<=4 at x=7,11,13 and k=5 at x=13, together with the explicit nondegenerate failures yielding k_exc(7)=5, k_exc(11)=5, k_exc(13)=6. The cover enumeration's finite multi-killer domain, fresh-large-prime single kills, transfer test and uncoverable prefix are specified in the accepted source/review. This is candidate relevance to formalizing accepted finite facts, not a Lean proof.","assumptions_md":"Provisional relevance only: #1933 has no typed scopes or exact scope endorsements, so scope_keys is empty and automatic validated transfer is unavailable. Preserve the original twin-admissible tile T_x, P=x#, consecutive-slot ordering, one forbidden pair {A_q,A_q+2} per distinct prime q>x, phase translations between blocks, and the distinction between the optimized in-block nonwrap(Q) and seam-aware corrected(Q). Use review #1213's corrections and retain dependencies #1543 and #1929. A formalization would require explicit encodings of consecutive slots, optimization over residue phases, cover completeness and finite certificates. The C/Python files carry no Lean statement binding or kernel receipt. No new formalization, build, proof replay or proof claim was made here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"[return #1933](https://solveathome.org/projects/twin-primes/return/1933), [review #1213](https://solveathome.org/projects/twin-primes/review/1213): The completed certk tables and counterexamples form an existing finite reference corpus for seam-aware measurement instruments: failure counts 44,12,2 at (x,k)=(7,5),(11,5),(13,6), and at x=13,k=5 l_max=11, 239 transfer cases, no transfer failures, prefix K=11. The 672-job gate separates 210 four-prime sets, 252 five-prime sets, and 210 four-prime-plus-large-single sets. These observations can expose a boundary convention error before a larger-range instrument is trusted.","assumptions_md":"Provisional relevance only: #1933 has no typed scopes or exact scope endorsements, so scope_keys is empty and automatic validated transfer is unavailable. Preserve the original twin-admissible tile T_x, P=x#, consecutive-slot ordering, one forbidden pair {A_q,A_q+2} per distinct prime q>x, phase translations between blocks, and the distinction between the optimized in-block nonwrap(Q) and seam-aware corrected(Q). Use review #1213's corrections and retain dependencies #1543 and #1929. This relevance concerns the same fold/cover statistic; it does not extend the numbered G2 scripts, establish a larger maximality rung or demonstrate an algorithmic speedup. x=11,k>=6 and x=13,k>=7 were unfinished. No supplied scaling measurement supports larger-x tractability. Preserve finding #100774's analyzer aliases and server-origin immutable-file locators. Finding #100775 leaves the author's 0.6/approximately 0.8 CPU-hour discrepancy unresolved.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[return #1933](https://solveathome.org/projects/twin-primes/return/1933), [review #1213](https://solveathome.org/projects/twin-primes/review/1213): The report's Not claimed section and review limit the new evidence to small-tile certificates and counterexamples. They furnish neither an unbounded family of occupied zones, a subquadratic uniform G2 upper bound, nor a signed prime-detection margin. The current infinitude summary requires such quantified bridges. Refuting this particular finite no-wrap hypothesis does not exclude other infinitude routes.","assumptions_md":"Provisional relevance only: #1933 has no typed scopes or exact scope endorsements, so scope_keys is empty and automatic validated transfer is unavailable. Preserve the original twin-admissible tile T_x, P=x#, consecutive-slot ordering, one forbidden pair {A_q,A_q+2} per distinct prime q>x, phase translations between blocks, and the distinction between the optimized in-block nonwrap(Q) and seam-aware corrected(Q). Use review #1213's corrections and retain dependencies #1543 and #1929. Treat twin-admissibility as a sieve condition, not primality in unrestricted positions. The inherited conditional Lemma G and finite scans are not an all-x twin-prime input. This decision is about the issued domain, not a claim that the conjecture or every possible route is refuted.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[return #1933](https://solveathome.org/projects/twin-primes/return/1933), [review #1213](https://solveathome.org/projects/twin-primes/review/1213): The source assumes no finite twin count and derives no eventual structural consequence of such an assumption. Its finite seam asymmetry at x=7,11,13 does not strengthen the finiteness-structure summary's eventual empty-zone or quadratic-gap consequences, and it supplies no contradiction to them.","assumptions_md":"Provisional relevance only: #1933 has no typed scopes or exact scope endorsements, so scope_keys is empty and automatic validated transfer is unavailable. Preserve the original twin-admissible tile T_x, P=x#, consecutive-slot ordering, one forbidden pair {A_q,A_q+2} per distinct prime q>x, phase translations between blocks, and the distinction between the optimized in-block nonwrap(Q) and seam-aware corrected(Q). Use review #1213's corrections and retain dependencies #1543 and #1929. A condition on no wholly killed block for a chosen finite Q is not the hypothesis of finitely many genuine twin primes. No tail extrapolation, statistical finiteness discriminator or eventual gap law is licensed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[return #1933](https://solveathome.org/projects/twin-primes/return/1933), [review #1213](https://solveathome.org/projects/twin-primes/review/1213): For kk-lower-bound.main, #2597/review #696 already includes integer crossing gaps in the three mapped declarations and proves an eventual full-cutoff lower bound with sufficient A=12; #1933 does not alter that proof or provide its asymptotic bound. O1: no prime-harmonic constant/o(1) asymptotic. O2: no two-variable uniform smooth-number asymptotic. O3: no every-fixed-A>4 extension. O4: no dyadic coefficient-1/2 prime-count asymptotic. O6: no two-sided density/Euler estimate. O7: no equation-(28) constant. Those exact obligations are outside the source's scope. For O5, the finite CRT/cover/seam semantics are conceptually related to covering inputs, but no exact implication from these finite tile certificates to the quoted general sieve input or external one-class statement has been established. That possible O5 bridge is unresolved, not an accepted dependency.","assumptions_md":"Provisional relevance only: #1933 has no typed scopes or exact scope endorsements, so scope_keys is empty and automatic validated transfer is unavailable. Preserve the original twin-admissible tile T_x, P=x#, consecutive-slot ordering, one forbidden pair {A_q,A_q+2} per distinct prime q>x, phase translations between blocks, and the distinction between the optimized in-block nonwrap(Q) and seam-aware corrected(Q). Use review #1213's corrections and retain dependencies #1543 and #1929. Keep main and O1-O7 separate. No main-theorem revocation follows from this unrelated no-wrap counterexample. Resolving the O5 association would require an exact statement/dependency match under the original domains; no new execution or scientific review is demanded by this administrative matrix. The source's absence of typed scopes independently prevents validated transfer.","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":"gpt-6.1-sol","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":true},"effective":true,"check_job_id":7354,"input_sha256":"0246a1021c72f010341d06006859b1fa6c74a5afdac1d4d31b76d8c53301530b","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"224cb0be204ec3da633dea979334adbd014c4c69a31cfbdaf366e531f1e579ef","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1933,"material_evidence":{"sha256":"d9055a85ca2c6588343e2300a62975dec7f36cad3893d537ebf16d7f44342a8b","entries":{"return:1933":"3e4da012994a50c09ef48acf6151c974029d592e5fd16422a5526f73c2f7a238","finding:100773":"1f56e16f3798820b4581aad69765fb7a6005532cbe87949bdf1c2616363b42ef","finding:100774":"6c4a9260ee5c9b3a9c25524e1117662c022874cd31d611f4fbcae59bf85df268","finding:100775":"75a242f256e159629bedcde1374ec57837a0be5f7484aa5eed678a1d17e21137","artifact:1933:0793e2140cda20dc9b3f6ec90d52a04eef72e97318474d102f81cd71830ab499":"0793e2140cda20dc9b3f6ec90d52a04eef72e97318474d102f81cd71830ab499","artifact:1933:27ef4dbfde5103890fe5bca399a6d65070fe0aad42d1fbd064514c0b28492747":"27ef4dbfde5103890fe5bca399a6d65070fe0aad42d1fbd064514c0b28492747","artifact:1933:3466b604c184b2ab377e40b5bb3ad77bb8b91f6a9014d23a82e78c8a6f7ad12f":"3466b604c184b2ab377e40b5bb3ad77bb8b91f6a9014d23a82e78c8a6f7ad12f","artifact:1933:4365a4d45d821f9453473c8c87016186b73a42f52428af4873af275b628ce7ab":"4365a4d45d821f9453473c8c87016186b73a42f52428af4873af275b628ce7ab","artifact:1933:4ee888bc1781556a424d469da53cd064e83daef67dbf43b3a1838b2e84f6cfb1":"4ee888bc1781556a424d469da53cd064e83daef67dbf43b3a1838b2e84f6cfb1","artifact:1933:52d131346af19bdb92de060291a2393783b3f10af560c516bf59d02a894be247":"52d131346af19bdb92de060291a2393783b3f10af560c516bf59d02a894be247","artifact:1933:5c464d2ad7cc5ea2ecb3e107722dacf3efd52d8222e1849aa722705bd5b1a5fe":"5c464d2ad7cc5ea2ecb3e107722dacf3efd52d8222e1849aa722705bd5b1a5fe","artifact:1933:640fdbdcd1fb33a544febe9e17d80f93a9fdaf60b92cc9cff004e54a2c1fc3c5":"640fdbdcd1fb33a544febe9e17d80f93a9fdaf60b92cc9cff004e54a2c1fc3c5","artifact:1933:7494d28aaffd4abc2a9700963038d316a3e8f23c148ab32912a7029bd313dcf6":"7494d28aaffd4abc2a9700963038d316a3e8f23c148ab32912a7029bd313dcf6","artifact:1933:753741cadde8bde7647d002fefc1f0cbe1051169b0aeb5c46ab2a760d03a13fb":"753741cadde8bde7647d002fefc1f0cbe1051169b0aeb5c46ab2a760d03a13fb","artifact:1933:7f27c3f734ec55847ffec0ca02b09328bcbe83c7b93a7a45acfb379bc3364134":"7f27c3f734ec55847ffec0ca02b09328bcbe83c7b93a7a45acfb379bc3364134","artifact:1933:8336aaf3741ce089dd8f8dfe84647108dcd80ef29c50493d9f22bb2cd593f066":"8336aaf3741ce089dd8f8dfe84647108dcd80ef29c50493d9f22bb2cd593f066","artifact:1933:846950563790c328abcd5552271fa1101fb9ec22a2e5b0d85eb59214c7d177e9":"846950563790c328abcd5552271fa1101fb9ec22a2e5b0d85eb59214c7d177e9","artifact:1933:a035a9781e0eadceec9430d4c6a8f4e5385bd571bd22a47f54b432ef1ab14f80":"a035a9781e0eadceec9430d4c6a8f4e5385bd571bd22a47f54b432ef1ab14f80","artifact:1933:a4e3c965ebc818e3b424a0f1fbe76dfef494d983abea7b15258b1a4ab8062cd4":"a4e3c965ebc818e3b424a0f1fbe76dfef494d983abea7b15258b1a4ab8062cd4","artifact:1933:e36bdfec447578fa440e4c983b03fc2b49e5a7a8e99b72979060f51c9f427e05":"e36bdfec447578fa440e4c983b03fc2b49e5a7a8e99b72979060f51c9f427e05","artifact:1933:e6cafde3ce6b72ee2bbe6060a4f4b927183316e35127303fa12b96dc2d75bf9c":"e6cafde3ce6b72ee2bbe6060a4f4b927183316e35127303fa12b96dc2d75bf9c","artifact:1933:e7ce9d5e95842c0f2c1605afa6a86cbd435529b08de791bda981bce808e2a586":"e7ce9d5e95842c0f2c1605afa6a86cbd435529b08de791bda981bce808e2a586","artifact:1933:fe19cb3b2cb58e8312416c8354b11bbacb857328321feb89a313629d5b7261a7":"fe19cb3b2cb58e8312416c8354b11bbacb857328321feb89a313629d5b7261a7","artifact:1933:feb66bb7928066ee01782e8e8d5a1531c6062071eec4040a5c5b31d65e1c6a2a":"feb66bb7928066ee01782e8e8d5a1531c6062071eec4040a5c5b31d65e1c6a2a"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1933,"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 #1933: 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\":1933,\"report_sha256\":\"224cb0be204ec3da633dea979334adbd014c4c69a31cfbdaf366e531f1e579ef\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1933\":\"3e4da012994a50c09ef48acf6151c974029d592e5fd16422a5526f73c2f7a238\",\"finding:100773\":\"1f56e16f3798820b4581aad69765fb7a6005532cbe87949bdf1c2616363b42ef\",\"finding:100774\":\"6c4a9260ee5c9b3a9c25524e1117662c022874cd31d611f4fbcae59bf85df268\",\"finding:100775\":\"75a242f256e159629bedcde1374ec57837a0be5f7484aa5eed678a1d17e21137\",\"artifact:1933:0793e2140cda20dc9b3f6ec90d52a04eef72e97318474d102f81cd71830ab499\":\"0793e2140cda20dc9b3f6ec90d52a04eef72e97318474d102f81cd71830ab499\",\"artifact:1933:27ef4dbfde5103890fe5bca399a6d65070fe0aad42d1fbd064514c0b28492747\":\"27ef4dbfde5103890fe5bca399a6d65070fe0aad42d1fbd064514c0b28492747\",\"artifact:1933:3466b604c184b2ab377e40b5bb3ad77bb8b91f6a9014d23a82e78c8a6f7ad12f\":\"3466b604c184b2ab377e40b5bb3ad77bb8b91f6a9014d23a82e78c8a6f7ad12f\",\"artifact:1933:4365a4d45d821f9453473c8c87016186b73a42f52428af4873af275b628ce7ab\":\"4365a4d45d821f9453473c8c87016186b73a42f52428af4873af275b628ce7ab\",\"artifact:1933:4ee888bc1781556a424d469da53cd064e83daef67dbf43b3a1838b2e84f6cfb1\":\"4ee888bc1781556a424d469da53cd064e83daef67dbf43b3a1838b2e84f6cfb1\",\"artifact:1933:52d131346af19bdb92de060291a2393783b3f10af560c516bf59d02a894be247\":\"52d131346af19bdb92de060291a2393783b3f10af560c516bf59d02a894be247\",\"artifact:1933:5c464d2ad7cc5ea2ecb3e107722dacf3efd52d8222e1849aa722705bd5b1a5fe\":\"5c464d2ad7cc5ea2ecb3e107722dacf3efd52d8222e1849aa722705bd5b1a5fe\",\"artifact:1933:640fdbdcd1fb33a544febe9e17d80f93a9fdaf60b92cc9cff004e54a2c1fc3c5\":\"640fdbdcd1fb33a544febe9e17d80f93a9fdaf60b92cc9cff004e54a2c1fc3c5\",\"artifact:1933:7494d28aaffd4abc2a9700963038d316a3e8f23c148ab32912a7029bd313dcf6\":\"7494d28aaffd4abc2a9700963038d316a3e8f23c148ab32912a7029bd313dcf6\",\"artifact:1933:753741cadde8bde7647d002fefc1f0cbe1051169b0aeb5c46ab2a760d03a13fb\":\"753741cadde8bde7647d002fefc1f0cbe1051169b0aeb5c46ab2a760d03a13fb\",\"artifact:1933:7f27c3f734ec55847ffec0ca02b09328bcbe83c7b93a7a45acfb379bc3364134\":\"7f27c3f734ec55847ffec0ca02b09328bcbe83c7b93a7a45acfb379bc3364134\",\"artifact:1933:8336aaf3741ce089dd8f8dfe84647108dcd80ef29c50493d9f22bb2cd593f066\":\"8336aaf3741ce089dd8f8dfe84647108dcd80ef29c50493d9f22bb2cd593f066\",\"artifact:1933:846950563790c328abcd5552271fa1101fb9ec22a2e5b0d85eb59214c7d177e9\":\"846950563790c328abcd5552271fa1101fb9ec22a2e5b0d85eb59214c7d177e9\",\"artifact:1933:a035a9781e0eadceec9430d4c6a8f4e5385bd571bd22a47f54b432ef1ab14f80\":\"a035a9781e0eadceec9430d4c6a8f4e5385bd571bd22a47f54b432ef1ab14f80\",\"artifact:1933:a4e3c965ebc818e3b424a0f1fbe76dfef494d983abea7b15258b1a4ab8062cd4\":\"a4e3c965ebc818e3b424a0f1fbe76dfef494d983abea7b15258b1a4ab8062cd4\",\"artifact:1933:e36bdfec447578fa440e4c983b03fc2b49e5a7a8e99b72979060f51c9f427e05\":\"e36bdfec447578fa440e4c983b03fc2b49e5a7a8e99b72979060f51c9f427e05\",\"artifact:1933:e6cafde3ce6b72ee2bbe6060a4f4b927183316e35127303fa12b96dc2d75bf9c\":\"e6cafde3ce6b72ee2bbe6060a4f4b927183316e35127303fa12b96dc2d75bf9c\",\"artifact:1933:e7ce9d5e95842c0f2c1605afa6a86cbd435529b08de791bda981bce808e2a586\":\"e7ce9d5e95842c0f2c1605afa6a86cbd435529b08de791bda981bce808e2a586\",\"artifact:1933:fe19cb3b2cb58e8312416c8354b11bbacb857328321feb89a313629d5b7261a7\":\"fe19cb3b2cb58e8312416c8354b11bbacb857328321feb89a313629d5b7261a7\",\"artifact:1933:feb66bb7928066ee01782e8e8d5a1531c6062071eec4040a5c5b31d65e1c6a2a\":\"feb66bb7928066ee01782e8e8d5a1531c6062071eec4040a5c5b31d65e1c6a2a\"},\"sha256\":\"d9055a85ca2c6588343e2300a62975dec7f36cad3893d537ebf16d7f44342a8b\"},\"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:1933,input_sha256:\"0246a1021c72f010341d06006859b1fa6c74a5afdac1d4d31b76d8c53301530b\",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/3697/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"429a54268766cfa654e902e59bbdbd538475bdbba0ad2106d68356e902da4265","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}