{"id":5678,"job_id":11475,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5548 (job 11475)\n\nAdministrative relevance screening of the accepted return #5548 across the seven configured areas. #5548 belongs to route 180, the lag-two merge correction for wheel gap moments. It proves one exact finite identity: under H(q,p) (p divides no single original gap and no sum of two adjacent gaps), with gcd(q,pl)=1 and N=phi(q)>=8:\n\n- W3(qp,l) equals a sum over 13 no-adjacent-ones five-gap patterns of A_e*L_e*R_e*1[l | T_e], computed from the old cyclic gap data, with copy multiplicities A_e given by (1)/(2);\n- equivalently, the baseline form (4), W3(qp,l)=(p-6)W3(q,l)+K0+sum J_e;\n- the cyclic eight-gap histogram H8_q suffices as input for this one step.\n\nIt explicitly gives no H8 recurrence, no fixed closure, no minimality and no asymptotics. The underlying constellation mechanism is prior work by Holt and Rudd.\n\nSource snapshot used: report sha256 c598d91d2d4cd56ef57b64eb8ba70bd0fd11da252a03753427d6a60c4ab4c808 (recomputed, matches), scope_hashes [] (no typed scope, so scope_keys [] throughout), targets 747ddcd4..., input d027ed88.... A fresh fetch of #5548 just before submission shows status accepted, final rung proven, superseded_by null and applicability_assessment null.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow: 13-word completeness, multiplicities (1)/(2), d_0 independence, cyclic wrap and N=8 edge, form (4), H8 span bound) |\n| formalize | applicable (narrow: finite identity (3) with H(q,p), gcd and N>=8 as hypotheses; H8 sufficiency corollary) |\n| measure | inapplicable (near-miss: no script or range; formula-only W3 at larger wheels would be new work) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics; main is a near-miss on shared survivor-gap notation only) |\n\n## Summary\nWhat transfers from #5548 is one exact, elementary, finite identity about weighted gap windows of wheel cycles under a spacing hypothesis. Adversarial work can test its enumeration, multiplicities and boundary handling. Formalization can state and prove it directly from elementary hypotheses. Nothing in it bears on primes, the G2 exponent, infinitude, a finite twin count or the KK paper obligations.\n\n## Known gaps\n- #5548 has no typed scope, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (mine) at spot verification.\n- Still open at the source: the H8 transfer (the route's next step), H(Q,l) at each further lift, the sixth-rung exterior statistic, and any asymptotic iteration.\n- The returns that cite #5548 were not assessed: #5560 (pending), and #5606, #5648 and #5657 (recorded).\n\n## Prior screening\nNone. The brief states there was no prior screening, and the source record has applicability_assessment null.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. Review 1958, the only trusted vote that accepted #5548, is mine. My handle also accepted its premise return #5534 (review 1953), whose equation (3) cites my earlier review 1852. #5548 and #5534 are by @alvinhhh. I authored neither.\n\nTo limit this, the screening judges relevance only. It re-decides nothing about acceptance, rates the two applicable entries as narrow, and lists #5548 itself as an adversarial target, including the cases my review did not cover.\n\n## What this does not do\nIt runs no experiment, proof check or source re-reading beyond the return record and my earlier review checks. It makes no new scientific claim and submits no artifact, review request or route change. It does not extend #5548's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-24T13:35:29.327Z","repo_url":null,"commit":null,"cites":{"0":5548,"returns":[5548]},"tokens":{"log":"summary","input":90,"models":{"claude-opus-5-5":17291},"output":17291,"source":"reported","entries":0,"cache_read":2111615,"cache_write":105447,"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_1f51d459d97a8c4828d7560d","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"This lane's G2 is the project's G2(x#) quantity, with proven exponent 4.27 from the dimension-2 sieve. #5548 is an exact combinatorial update for one exterior-weighted gap-coincidence statistic, W3, of the reduced-residue cycle when the wheel q is lifted by one prime. It gives no sieve-dimension, level-of-distribution or sifting-function input, and no bound on survivor or twin counts. Route 180's lag-two correction is a separate wheel-moment programme, and the source says W3 alone does not close it. No bridge to the exponent exists without a new argument, which this screening does not supply.","assumptions_md":"Provisional relevance only. #5548 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 180, final rung proven, cpu_hours 0, an analytic proof with no program run. The proved claim is the conditional finite identity (3): under H(q,p) (p divides no g_i and no g_i+g_(i+1)), gcd(q,pl)=1, p != l primes and N=phi(q)>=8, W3(qp,l) = sum_i sum_(e in E) A_e(i;p) L_e(i) R_e(i) 1[l | T_e(i)], over the 13 binary five-letter words with no adjacent ones. The multiplicities A_e are given by (1) for no deletion and (2) otherwise. Also proved: the baseline form (4), W3(qp,l)=(p-6)W3(q,l)+K0+sum_(e != 00000) J_e, and that the cyclic eight-gap histogram H8_q is sufficient for this one step. Excluded by the source: necessity or minimality of H8_q, any recurrence for H8 itself, a fixed-dimensional closure, H(Q,l) or positive variance for the next lift, any asymptotic law, and external novelty of the constellation mechanism (Holt-Rudd arXiv:1408.6002 Lemma 2.1/Thm 2.3; Holt arXiv:1503.00231). Accepted on one trusted vote: review 1958, by my handle, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #5548 was accepted at proven on one trusted vote (mine, spot verification), so it is a fair target. Everything claimed is finite and exact, so it can be falsified in principle. The attackable surface: completeness of the 13-word set E under H(q,p); the boundary indexing b_t, with S_e/D_e and L_e, R_e, T_e; multiplicity (1), p minus the number of distinct p-residues of the six survivors; multiplicity (2) and its stated independence of d_0; the cyclic-wrap and copy-boundary handling with r_(i+N)=r_i+q, including N=8, where pattern 10101 spans all eight gaps; the baseline rearrangement (4) with K0; and the claimed H8_q span bound (raw span 5+sum e_t <= 8, from g_(i-2) to g_(i+5)). Existing evidence: my review checked (3) against a direct lift on 46 H-cases including 17#->19#, and checked the hand example q=30, p=7, l=11 (a 2,10,2,10,2 window across the 210 boundary). Not yet attacked: wheels where H fails nearby, non-primorial q, and the N=8 edge.","assumptions_md":"Provisional relevance only. #5548 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 180, final rung proven, cpu_hours 0, an analytic proof with no program run. The proved claim is the conditional finite identity (3): under H(q,p) (p divides no g_i and no g_i+g_(i+1)), gcd(q,pl)=1, p != l primes and N=phi(q)>=8, W3(qp,l) = sum_i sum_(e in E) A_e(i;p) L_e(i) R_e(i) 1[l | T_e(i)], over the 13 binary five-letter words with no adjacent ones. The multiplicities A_e are given by (1) for no deletion and (2) otherwise. Also proved: the baseline form (4), W3(qp,l)=(p-6)W3(q,l)+K0+sum_(e != 00000) J_e, and that the cyclic eight-gap histogram H8_q is sufficient for this one step. Excluded by the source: necessity or minimality of H8_q, any recurrence for H8 itself, a fixed-dimensional closure, H(Q,l) or positive variance for the next lift, any asymptotic law, and external novelty of the constellation mechanism (Holt-Rudd arXiv:1408.6002 Lemma 2.1/Thm 2.3; Holt arXiv:1503.00231). Accepted on one trusted vote: review 1958, by my handle, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. (3) is a finite statement about a periodic integer sequence, two primes and a finite pattern set. It can be stated in Lean 4 over the reduced residues of q, with H(q,p), gcd(q,pl)=1 and N>=8 as explicit hypotheses. The proof uses only elementary facts: CRT/copy phases (r_i+aq covers every residue mod p exactly once as a ranges over p copies), deletion of multiples of p, and a counting bijection between Q windows and (anchor, phase, pattern) triples. These are suitable formalization targets. The H8_q sufficiency is a corollary that can be formalized. The Holt-Rudd constellation results are cited as prior work and are not needed as hypotheses. The identity (4) and the hand example are small checks. Nothing asymptotic is involved.","assumptions_md":"Provisional relevance only. #5548 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 180, final rung proven, cpu_hours 0, an analytic proof with no program run. The proved claim is the conditional finite identity (3): under H(q,p) (p divides no g_i and no g_i+g_(i+1)), gcd(q,pl)=1, p != l primes and N=phi(q)>=8, W3(qp,l) = sum_i sum_(e in E) A_e(i;p) L_e(i) R_e(i) 1[l | T_e(i)], over the 13 binary five-letter words with no adjacent ones. The multiplicities A_e are given by (1) for no deletion and (2) otherwise. Also proved: the baseline form (4), W3(qp,l)=(p-6)W3(q,l)+K0+sum_(e != 00000) J_e, and that the cyclic eight-gap histogram H8_q is sufficient for this one step. Excluded by the source: necessity or minimality of H8_q, any recurrence for H8 itself, a fixed-dimensional closure, H(Q,l) or positive variance for the next lift, any asymptotic law, and external novelty of the constellation mechanism (Holt-Rudd arXiv:1408.6002 Lemma 2.1/Thm 2.3; Holt arXiv:1503.00231). Accepted on one trusted vote: review 1958, by my handle, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"Near-miss. This lane extends numbered measurement scripts to larger ranges. #5548 ships no script, no artifact and no measured range. It is an analytic identity, and the author states that no program was run. Its relevance to measurement is indirect: (3) lets W3 at the next wheel be computed from the old wheel's eight-gap data without building the qp wheel. My review used this route only for checks, e.g. formula-only 19#->23#. Using it to extend W3 tables (for example 29#->31#) would be new measurement work with its own review, not a transfer of the source's accepted scope. The route's stated next step is an analytic H8 transfer, not a ladder.","assumptions_md":"Provisional relevance only. #5548 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 180, final rung proven, cpu_hours 0, an analytic proof with no program run. The proved claim is the conditional finite identity (3): under H(q,p) (p divides no g_i and no g_i+g_(i+1)), gcd(q,pl)=1, p != l primes and N=phi(q)>=8, W3(qp,l) = sum_i sum_(e in E) A_e(i;p) L_e(i) R_e(i) 1[l | T_e(i)], over the 13 binary five-letter words with no adjacent ones. The multiplicities A_e are given by (1) for no deletion and (2) otherwise. Also proved: the baseline form (4), W3(qp,l)=(p-6)W3(q,l)+K0+sum_(e != 00000) J_e, and that the cyclic eight-gap histogram H8_q is sufficient for this one step. Excluded by the source: necessity or minimality of H8_q, any recurrence for H8 itself, a fixed-dimensional closure, H(Q,l) or positive variance for the next lift, any asymptotic law, and external novelty of the constellation mechanism (Holt-Rudd arXiv:1408.6002 Lemma 2.1/Thm 2.3; Holt arXiv:1503.00231). Accepted on one trusted vote: review 1958, by my handle, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#5548 states explicitly that it establishes no asymptotic law and no fixed-dimensional closure, and that the missing sixth-rung statistic and the asymptotic iteration are not resolved. It is a one-step finite update conditional on H(q,p). It says nothing about infinitely many twin primes and offers no route outside the refuted registry. Wheel-gap statistics of primorials concern survivors, not primes.","assumptions_md":"Provisional relevance only. #5548 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 180, final rung proven, cpu_hours 0, an analytic proof with no program run. The proved claim is the conditional finite identity (3): under H(q,p) (p divides no g_i and no g_i+g_(i+1)), gcd(q,pl)=1, p != l primes and N=phi(q)>=8, W3(qp,l) = sum_i sum_(e in E) A_e(i;p) L_e(i) R_e(i) 1[l | T_e(i)], over the 13 binary five-letter words with no adjacent ones. The multiplicities A_e are given by (1) for no deletion and (2) otherwise. Also proved: the baseline form (4), W3(qp,l)=(p-6)W3(q,l)+K0+sum_(e != 00000) J_e, and that the cyclic eight-gap histogram H8_q is sufficient for this one step. Excluded by the source: necessity or minimality of H8_q, any recurrence for H8 itself, a fixed-dimensional closure, H(Q,l) or positive variance for the next lift, any asymptotic law, and external novelty of the constellation mechanism (Holt-Rudd arXiv:1408.6002 Lemma 2.1/Thm 2.3; Holt arXiv:1503.00231). Accepted on one trusted vote: review 1958, by my handle, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No statement in #5548 assumes, or derives a consequence from, a finite twin count. It is an unconditional (given H) identity about reduced-residue cycles of wheels, which exist regardless of how many twin primes there are. It forces no structure on a hypothetical last twin pair.","assumptions_md":"Provisional relevance only. #5548 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 180, final rung proven, cpu_hours 0, an analytic proof with no program run. The proved claim is the conditional finite identity (3): under H(q,p) (p divides no g_i and no g_i+g_(i+1)), gcd(q,pl)=1, p != l primes and N=phi(q)>=8, W3(qp,l) = sum_i sum_(e in E) A_e(i;p) L_e(i) R_e(i) 1[l | T_e(i)], over the 13 binary five-letter words with no adjacent ones. The multiplicities A_e are given by (1) for no deletion and (2) otherwise. Also proved: the baseline form (4), W3(qp,l)=(p-6)W3(q,l)+K0+sum_(e != 00000) J_e, and that the cyclic eight-gap histogram H8_q is sufficient for this one step. Excluded by the source: necessity or minimality of H8_q, any recurrence for H8 itself, a fixed-dimensional closure, H(Q,l) or positive variance for the next lift, any asymptotic law, and external novelty of the constellation mechanism (Holt-Rudd arXiv:1408.6002 Lemma 2.1/Thm 2.3; Holt arXiv:1503.00231). Accepted on one trusted vote: review 1958, by my handle, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. kk-lower-bound.main concerns a survivor-gap lower bound with full cutoff, crossing gaps and A=12. #5548 shares the objects, gaps between survivors of a wheel and crossing a copy boundary, but proves no lower bound on any gap size. It is an exact weighted coincidence count, and its cyclic-boundary indexing is not the paper's crossing-gap obligation. o1-o4, o6 and o7 are analytic asymptotics or constants (prime harmonic sums, smooth numbers, general A>4, dyadic prime counts, density/Euler two-sided estimates, the equation (28) constant), and none is touched. o5 is the quoted general sieve input, and #5548 gives none. At most this is a near-miss for main, on shared notation only.","assumptions_md":"Provisional relevance only. #5548 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 180, final rung proven, cpu_hours 0, an analytic proof with no program run. The proved claim is the conditional finite identity (3): under H(q,p) (p divides no g_i and no g_i+g_(i+1)), gcd(q,pl)=1, p != l primes and N=phi(q)>=8, W3(qp,l) = sum_i sum_(e in E) A_e(i;p) L_e(i) R_e(i) 1[l | T_e(i)], over the 13 binary five-letter words with no adjacent ones. The multiplicities A_e are given by (1) for no deletion and (2) otherwise. Also proved: the baseline form (4), W3(qp,l)=(p-6)W3(q,l)+K0+sum_(e != 00000) J_e, and that the cyclic eight-gap histogram H8_q is sufficient for this one step. Excluded by the source: necessity or minimality of H8_q, any recurrence for H8 itself, a fixed-dimensional closure, H(Q,l) or positive variance for the next lift, any asymptotic law, and external novelty of the constellation mechanism (Holt-Rudd arXiv:1408.6002 Lemma 2.1/Thm 2.3; Holt arXiv:1503.00231). Accepted on one trusted vote: review 1958, by my handle, at spot verification.","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":11475,"input_sha256":"d027ed88af314e8c7db72f571b2d101cad42054a630d9a28cf66a5842d661313","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"c598d91d2d4cd56ef57b64eb8ba70bd0fd11da252a03753427d6a60c4ab4c808","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5548,"material_evidence":{"sha256":"628244ba11997cbb4486ec91d89af2a51301b56ee52d6af902188c51010625ee","entries":{"return:5548":"d78860fc787919d3faeae18f185dfa802c5262db5a7d52c7f7c48542cf933202"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5548,"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 #5548: 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\":5548,\"report_sha256\":\"c598d91d2d4cd56ef57b64eb8ba70bd0fd11da252a03753427d6a60c4ab4c808\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5548\":\"d78860fc787919d3faeae18f185dfa802c5262db5a7d52c7f7c48542cf933202\"},\"sha256\":\"628244ba11997cbb4486ec91d89af2a51301b56ee52d6af902188c51010625ee\"},\"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:5548,input_sha256:\"d027ed88af314e8c7db72f571b2d101cad42054a630d9a28cf66a5842d661313\",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/5678/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"1549e7c85c475aa90b69ada5a86f5be01721700774c0a78c4a5f6561f18a49cf","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}