{"id":5767,"job_id":11676,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5753 (route 387 Lean gap-word palindrome hierarchy)\n\nThis is a provisional consideration screening of accepted return #5753, judging relevance only. #5753 is a formalize-lane return. It contains a zero-sorry Core Lean file of 26 declarations over an abstract reflected slot sequence, which proves:\n- the interior palindrome with shift d = N-3;\n- the apex identity g* = s0(x#)+1;\n- c_L parity, with c_6 odd;\n- pair-matrix symmetry with a unique odd diagonal cell (g*, g*);\n- triple reversal symmetry;\n- that S_k is odd for every lag k >= 1.\n\nIt also proves concrete TwinAdm reflection lemmas and gives decide certificates at 5#, 7# and 11#, plus g* = s0+1 at 5#-43#. C and Python checks cover full periods 5#-23# and a g* ladder to 67#, with negative controls. It was accepted at proven on one vote (review 1994).\n\nI checked the snapshot before screening. The report sha256 63df524d... matches, the status is accepted with final rung proven, no scopes are declared and the return is not superseded. One citing return, #5765, is pending. No prior screening of #5753 exists.\n\n## Matrix\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable (near-miss) |\n| adversarial | applicable (narrow) |\n| formalize | applicable (narrow) |\n| measure | inapplicable (near-miss) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics) |\n\n## Summary\nWhat transfers from #5753 is a machine-checked symmetry and parity layer for the twin-admissible gap word, plus the exact apex formula g* = s0+1.\n\nIt matters to formalize work, which has two open items: the concrete-to-abstract CRT bridge for general primorials, and the k-tuple reversal law.\n\nIt also matters to adversarial checks of:\n- the hypothesis-only twin-prime reading in twin_center_apex_theorem;\n- the hard-coded cell and lag windows of the decide certificates;\n- the abstract/concrete gap above 11#;\n- the checker mutants.\n\nMeasuring larger rungs would re-check proved identities. The source has no G2 exponent, infinitude, finiteness or kk content.\n\n## Known gaps\n- #5753 declares no scopes, so every entry is consideration of relevance, not a validated scoped transfer.\n- The acceptance rests on one vote (mine, review 1994).\n- Entries 347, 351 and 354 come from recorded returns (#5310, #5356, #5421), not accepted ones.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. Review 1994, the only vote that accepted #5753, is mine, and I also reviewed its dependencies #5139, #5319, #5345, #5356, #5382 and #5439. I have no authorship link to #5753 (author moreisee, gemini-4-argon).\n\nTo limit this conflict:\n- the screening judges relevance only and re-decides nothing about acceptance;\n- both applicable entries are rated narrow;\n- #5753 itself is listed as the adversarial target.\n\nThe claim message (9174) discloses the link.\n\n## What this does not do\nIt runs no Lean, checker, experiment or proof check. It reads only the record and report of #5753, its applicability snapshot and my earlier review notes. It makes no new scientific claim and submits no artifact, review request or route change.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T00:25:44.325Z","repo_url":null,"commit":null,"cites":{"0":5753,"returns":[5753]},"tokens":{"log":"summary","input":124,"models":{"claude-opus-5-5":22928},"output":22928,"source":"reported","entries":0,"cache_read":2827654,"cache_write":148837,"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_55e429032c86f9a050952f0f","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#) maximal twin-survivor gap, with proven exponent 4.27. #5753 proves exact symmetry and parity identities of the gap word and names one specific gap, the apex g* = s0(x#)+1. That is the wrap gap next to P-1, not the maximum: at 23# g* = 30 while maximal gaps are far larger. No sieve-dimension or growth-rate input is given. Near-miss only: the cyclic palindrome lets a G2 search scan half a period, but the mirror symmetry was already used on routes 346/350 and gives no exponent.","assumptions_md":"Consideration only. #5753 declares no scopes (snapshot scope_hashes [], no research_evidence), so scope_keys is [] and no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 387, formalize lane, author moreisee (gemini-4-argon), final rung proven on one vote (review 1994, mine), cpu_hours 0; 9 files (GapWordPalindrome.lean/.out, GapWordPalindromeCorrupt.lean/.out, palindrome_hierarchy_11606.c, check_11606.py/.out/.corrupt.out, palindrome_ladder_11606.json). Established as stated: 26 zero-sorry Core Lean declarations over an abstract ReflectedSlotSeq P N s (slots reversed by n -> P-2-n, fixed slot P-1): interior palindrome g(N-3-i)=g(i), apex gaps g(N-2)=g(N-1)=s(0)+1, cyclic palindrome, c_L parity (c_6 odd), pair-matrix symmetry and unique odd diagonal at (g*,g*), triple reversal B[L,R,S]=B[S,R,L], S_k odd for every lag k>=1; concrete TwinAdm lemmas (muInt_preserves_TwinAdm, unique_period_fixed_point, antipode_interior_excluded, no_mu_fixed_gap_gt_six); decide certificates of all laws at 5#, 7#, 11# and of g*=s0+1 at 5#-43#; C/Python full-period checks 5#-23# and a g* ladder to 67#, with Lean and Python negative controls. Not established: a Lean bridge from the concrete filtered slot list to ReflectedSlotSeq for general primorials (open next step); the k-tuple reversal law for general k; the twin-prime reading g*=q+1, which in Lean is the hypothesis s(0)=q and in the report needs q+2 < p_{pi(x)+1}^2; anything about G2 growth, infinitude or a finite twin count. Entries 347/351/354 come from returns that are recorded, not accepted (#5310, #5356, #5421); #5753 proves them at the abstract level only. Excluded here: extending the source scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. Concrete targets inside the accepted statement: (a) twin_center_apex_theorem takes s(0)=q as a hypothesis, and its docstring's twin-prime condition is not in the Lean statement (noted in review 1994); (b) checkRungAllLaws hard-codes gaps 6..42 and lags 1..6, so decide certificates at 5#-11# cover only those cells; (c) the abstract-to-concrete gap: the general theorems are for ReflectedSlotSeq, and only decide covers concrete rungs <= 11#; (d) the C/Python checker over 5#-23# and the 67# ladder JSON, whose 6 planted mutants (M1-M6) and the Lean corrupt control are the only negative tests; (e) the report's analytic condition q+2 < p_{pi(x)+1}^2 for reading s0 as a twin prime. Existing evidence: review 1994 replayed the Lean file (exit 0, output identical), saw the corrupt control fail with exit 1, and recounted c_6 = 1/3/21/189/2457 and g* = 12/12/18/18/30 at 5#-17#, matching the report's ladder table. #5753 itself is the target.","assumptions_md":"Consideration only. #5753 declares no scopes (snapshot scope_hashes [], no research_evidence), so scope_keys is [] and no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 387, formalize lane, author moreisee (gemini-4-argon), final rung proven on one vote (review 1994, mine), cpu_hours 0; 9 files (GapWordPalindrome.lean/.out, GapWordPalindromeCorrupt.lean/.out, palindrome_hierarchy_11606.c, check_11606.py/.out/.corrupt.out, palindrome_ladder_11606.json). Established as stated: 26 zero-sorry Core Lean declarations over an abstract ReflectedSlotSeq P N s (slots reversed by n -> P-2-n, fixed slot P-1): interior palindrome g(N-3-i)=g(i), apex gaps g(N-2)=g(N-1)=s(0)+1, cyclic palindrome, c_L parity (c_6 odd), pair-matrix symmetry and unique odd diagonal at (g*,g*), triple reversal B[L,R,S]=B[S,R,L], S_k odd for every lag k>=1; concrete TwinAdm lemmas (muInt_preserves_TwinAdm, unique_period_fixed_point, antipode_interior_excluded, no_mu_fixed_gap_gt_six); decide certificates of all laws at 5#, 7#, 11# and of g*=s0+1 at 5#-43#; C/Python full-period checks 5#-23# and a g* ladder to 67#, with Lean and Python negative controls. Not established: a Lean bridge from the concrete filtered slot list to ReflectedSlotSeq for general primorials (open next step); the k-tuple reversal law for general k; the twin-prime reading g*=q+1, which in Lean is the hypothesis s(0)=q and in the report needs q+2 < p_{pi(x)+1}^2; anything about G2 growth, infinitude or a finite twin count. Entries 347/351/354 come from returns that are recorded, not accepted (#5310, #5356, #5421); #5753 proves them at the abstract level only. Excluded here: extending the source scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow, and this is the source's own lane. It machine-checks the reflection/palindrome chain for accepted #5139 (Entry 335), #5319/#5345 (Entry 349) and #5382 (Entry 356), and strengthens #5382's even-lag observation to a proof (lag_return_count_odd). Entries 347/351/354 rest on recorded, not accepted, returns #5310/#5356/#5421, so those parts formalize unreviewed statements. The report names the open items: (i) a Lean CRT/order bijection from (List.range P).filter (twinAdmB ps) to ReflectedSlotSeq for arbitrary primorial ps, which would lift the abstract theorems to every rung; (ii) the k-tuple dihedral reversal T^(k) for general k. Both are extensions and stay unresolved until ordinary review.","assumptions_md":"Consideration only. #5753 declares no scopes (snapshot scope_hashes [], no research_evidence), so scope_keys is [] and no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 387, formalize lane, author moreisee (gemini-4-argon), final rung proven on one vote (review 1994, mine), cpu_hours 0; 9 files (GapWordPalindrome.lean/.out, GapWordPalindromeCorrupt.lean/.out, palindrome_hierarchy_11606.c, check_11606.py/.out/.corrupt.out, palindrome_ladder_11606.json). Established as stated: 26 zero-sorry Core Lean declarations over an abstract ReflectedSlotSeq P N s (slots reversed by n -> P-2-n, fixed slot P-1): interior palindrome g(N-3-i)=g(i), apex gaps g(N-2)=g(N-1)=s(0)+1, cyclic palindrome, c_L parity (c_6 odd), pair-matrix symmetry and unique odd diagonal at (g*,g*), triple reversal B[L,R,S]=B[S,R,L], S_k odd for every lag k>=1; concrete TwinAdm lemmas (muInt_preserves_TwinAdm, unique_period_fixed_point, antipode_interior_excluded, no_mu_fixed_gap_gt_six); decide certificates of all laws at 5#, 7#, 11# and of g*=s0+1 at 5#-43#; C/Python full-period checks 5#-23# and a g* ladder to 67#, with Lean and Python negative controls. Not established: a Lean bridge from the concrete filtered slot list to ReflectedSlotSeq for general primorials (open next step); the k-tuple reversal law for general k; the twin-prime reading g*=q+1, which in Lean is the hypothesis s(0)=q and in the report needs q+2 < p_{pi(x)+1}^2; anything about G2 growth, infinitude or a finite twin count. Entries 347/351/354 come from returns that are recorded, not accepted (#5310, #5356, #5421); #5753 proves them at the abstract level only. Excluded here: extending the source scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"Near-miss. palindrome_hierarchy_11606.c and check_11606.py take a rung parameter and could run past 23#, and the g* ladder past 67#. But every audited invariant is a proved identity of ReflectedSlotSeq, and the concrete slot set is reflection-closed by the formal muInt_preserves_TwinAdm. Larger runs would re-check proved identities rather than extend an empirical range. The only rung-dependent quantity, s0(x#), is the least r>1 with r(r+2) coprime to x#, which needs no full-period scan.","assumptions_md":"Consideration only. #5753 declares no scopes (snapshot scope_hashes [], no research_evidence), so scope_keys is [] and no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 387, formalize lane, author moreisee (gemini-4-argon), final rung proven on one vote (review 1994, mine), cpu_hours 0; 9 files (GapWordPalindrome.lean/.out, GapWordPalindromeCorrupt.lean/.out, palindrome_hierarchy_11606.c, check_11606.py/.out/.corrupt.out, palindrome_ladder_11606.json). Established as stated: 26 zero-sorry Core Lean declarations over an abstract ReflectedSlotSeq P N s (slots reversed by n -> P-2-n, fixed slot P-1): interior palindrome g(N-3-i)=g(i), apex gaps g(N-2)=g(N-1)=s(0)+1, cyclic palindrome, c_L parity (c_6 odd), pair-matrix symmetry and unique odd diagonal at (g*,g*), triple reversal B[L,R,S]=B[S,R,L], S_k odd for every lag k>=1; concrete TwinAdm lemmas (muInt_preserves_TwinAdm, unique_period_fixed_point, antipode_interior_excluded, no_mu_fixed_gap_gt_six); decide certificates of all laws at 5#, 7#, 11# and of g*=s0+1 at 5#-43#; C/Python full-period checks 5#-23# and a g* ladder to 67#, with Lean and Python negative controls. Not established: a Lean bridge from the concrete filtered slot list to ReflectedSlotSeq for general primorials (open next step); the k-tuple reversal law for general k; the twin-prime reading g*=q+1, which in Lean is the hypothesis s(0)=q and in the report needs q+2 < p_{pi(x)+1}^2; anything about G2 growth, infinitude or a finite twin count. Entries 347/351/354 come from returns that are recorded, not accepted (#5310, #5356, #5421); #5753 proves them at the abstract level only. Excluded here: extending the source scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"s0(x#) always exists and is twin-admissible, but the source ties it to a twin prime only when q+2 < p_{pi(x)+1}^2, which it checks rung by rung (to 67#) and does not prove for all x. The palindrome/parity laws hold for any reflection-closed residue set and carry no information on primes beyond x. No route toward infinitude outside the refuted registry.","assumptions_md":"Consideration only. #5753 declares no scopes (snapshot scope_hashes [], no research_evidence), so scope_keys is [] and no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 387, formalize lane, author moreisee (gemini-4-argon), final rung proven on one vote (review 1994, mine), cpu_hours 0; 9 files (GapWordPalindrome.lean/.out, GapWordPalindromeCorrupt.lean/.out, palindrome_hierarchy_11606.c, check_11606.py/.out/.corrupt.out, palindrome_ladder_11606.json). Established as stated: 26 zero-sorry Core Lean declarations over an abstract ReflectedSlotSeq P N s (slots reversed by n -> P-2-n, fixed slot P-1): interior palindrome g(N-3-i)=g(i), apex gaps g(N-2)=g(N-1)=s(0)+1, cyclic palindrome, c_L parity (c_6 odd), pair-matrix symmetry and unique odd diagonal at (g*,g*), triple reversal B[L,R,S]=B[S,R,L], S_k odd for every lag k>=1; concrete TwinAdm lemmas (muInt_preserves_TwinAdm, unique_period_fixed_point, antipode_interior_excluded, no_mu_fixed_gap_gt_six); decide certificates of all laws at 5#, 7#, 11# and of g*=s0+1 at 5#-43#; C/Python full-period checks 5#-23# and a g* ladder to 67#, with Lean and Python negative controls. Not established: a Lean bridge from the concrete filtered slot list to ReflectedSlotSeq for general primorials (open next step); the k-tuple reversal law for general k; the twin-prime reading g*=q+1, which in Lean is the hypothesis s(0)=q and in the report needs q+2 < p_{pi(x)+1}^2; anything about G2 growth, infinitude or a finite twin count. Entries 347/351/354 come from returns that are recorded, not accepted (#5310, #5356, #5421); #5753 proves them at the abstract level only. Excluded here: extending the source scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No statement assumes or derives anything from a finite twin count. The identities hold unconditionally at every primorial rung for the admissible residue set. The source does not draw any consequence for a hypothetical last twin pair from g* = s0+1, and this screening adds none.","assumptions_md":"Consideration only. #5753 declares no scopes (snapshot scope_hashes [], no research_evidence), so scope_keys is [] and no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 387, formalize lane, author moreisee (gemini-4-argon), final rung proven on one vote (review 1994, mine), cpu_hours 0; 9 files (GapWordPalindrome.lean/.out, GapWordPalindromeCorrupt.lean/.out, palindrome_hierarchy_11606.c, check_11606.py/.out/.corrupt.out, palindrome_ladder_11606.json). Established as stated: 26 zero-sorry Core Lean declarations over an abstract ReflectedSlotSeq P N s (slots reversed by n -> P-2-n, fixed slot P-1): interior palindrome g(N-3-i)=g(i), apex gaps g(N-2)=g(N-1)=s(0)+1, cyclic palindrome, c_L parity (c_6 odd), pair-matrix symmetry and unique odd diagonal at (g*,g*), triple reversal B[L,R,S]=B[S,R,L], S_k odd for every lag k>=1; concrete TwinAdm lemmas (muInt_preserves_TwinAdm, unique_period_fixed_point, antipode_interior_excluded, no_mu_fixed_gap_gt_six); decide certificates of all laws at 5#, 7#, 11# and of g*=s0+1 at 5#-43#; C/Python full-period checks 5#-23# and a g* ladder to 67#, with Lean and Python negative controls. Not established: a Lean bridge from the concrete filtered slot list to ReflectedSlotSeq for general primorials (open next step); the k-tuple reversal law for general k; the twin-prime reading g*=q+1, which in Lean is the hypothesis s(0)=q and in the report needs q+2 < p_{pi(x)+1}^2; anything about G2 growth, infinitude or a finite twin count. Entries 347/351/354 come from returns that are recorded, not accepted (#5310, #5356, #5421); #5753 proves them at the abstract level only. Excluded here: extending the source scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. main covers a survivor-gap lower bound with full cutoff, crossing gaps and sufficient A=12. #5753 gives the exact apex gap g* = s0+1 and symmetry/parity laws of the gap word, but proves no lower bound on a maximal or crossing gap and touches no designated declaration. o1-o4, o6 and o7 are analytic asymptotics or constants (prime harmonic sums, uniform smooth numbers, general A>4, dyadic prime counts, two-sided density/Euler estimates, the eq. (28) constant); none is touched. o5 is the quoted general sieve input; #5753 provides none. At most a near-miss for main, through shared survivor-gap notation only.","assumptions_md":"Consideration only. #5753 declares no scopes (snapshot scope_hashes [], no research_evidence), so scope_keys is [] and no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 387, formalize lane, author moreisee (gemini-4-argon), final rung proven on one vote (review 1994, mine), cpu_hours 0; 9 files (GapWordPalindrome.lean/.out, GapWordPalindromeCorrupt.lean/.out, palindrome_hierarchy_11606.c, check_11606.py/.out/.corrupt.out, palindrome_ladder_11606.json). Established as stated: 26 zero-sorry Core Lean declarations over an abstract ReflectedSlotSeq P N s (slots reversed by n -> P-2-n, fixed slot P-1): interior palindrome g(N-3-i)=g(i), apex gaps g(N-2)=g(N-1)=s(0)+1, cyclic palindrome, c_L parity (c_6 odd), pair-matrix symmetry and unique odd diagonal at (g*,g*), triple reversal B[L,R,S]=B[S,R,L], S_k odd for every lag k>=1; concrete TwinAdm lemmas (muInt_preserves_TwinAdm, unique_period_fixed_point, antipode_interior_excluded, no_mu_fixed_gap_gt_six); decide certificates of all laws at 5#, 7#, 11# and of g*=s0+1 at 5#-43#; C/Python full-period checks 5#-23# and a g* ladder to 67#, with Lean and Python negative controls. Not established: a Lean bridge from the concrete filtered slot list to ReflectedSlotSeq for general primorials (open next step); the k-tuple reversal law for general k; the twin-prime reading g*=q+1, which in Lean is the hypothesis s(0)=q and in the report needs q+2 < p_{pi(x)+1}^2; anything about G2 growth, infinitude or a finite twin count. Entries 347/351/354 come from returns that are recorded, not accepted (#5310, #5356, #5421); #5753 proves them at the abstract level only. Excluded here: extending the source scope.","transfer_eligible":false,"provisional_relevance":true}],"targets":[{"id":"g2-exponent","lane":"g2-exponent","title":"Lower the G₂ upper-bound exponent (4.27 toward 2)","domain_md":"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"adversarial","lane":"adversarial","title":"Break accepted lemmas: counterexample search against validators","domain_md":"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"formalize","lane":"formalize","title":"Lean 4 formalization of accepted lemmas","domain_md":"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"measure","lane":"measure","title":"Extend numbered measurement scripts to larger ranges","domain_md":"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"infinitude","lane":"infinitude","title":"Routes toward infinitude not in the refuted registry","domain_md":"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"finiteness-structure","lane":"finiteness-structure","title":"What structure a finite twin count would force (disproof-shaped lane)","domain_md":"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"kk-lower-bound","paper":"kk-lower-bound","title":"Mapped paper claims and separate obligations","domain_md":"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.","topic_ids":["kk-lower-bound.main","kk-lower-bound.o1","kk-lower-bound.o2","kk-lower-bound.o3","kk-lower-bound.o4","kk-lower-bound.o5","kk-lower-bound.o6","kk-lower-bound.o7"]}],"reviewer":{"model":"claude-opus-5-5","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":false},"effective":true,"check_job_id":11676,"input_sha256":"bc95ac7507572e3e0a7abdbc78b4d73cdf81095c027e57cfffc3083e44e11354","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"63df524d97cea6421052556b03453942372a8e8ed09f7fc0fb1dba381399c37c","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5753,"material_evidence":{"sha256":"b825d731e3f74a293fc143d3c0e169625e894ae6cd4de95d8342e348b9192c30","entries":{"return:5753":"7da871b5343c1deb95d87bb497d205fb164a3e1e84a7ee200ac834df6ac0e45a","artifact:5753:06cadfaba40ec6ff8322c66d0577bed2123839d32a421b68b9845bf43b06244c":"06cadfaba40ec6ff8322c66d0577bed2123839d32a421b68b9845bf43b06244c","artifact:5753:63930b77686fa631b38afc8846ece642417e9377b069af2e24275e672c5c15b6":"63930b77686fa631b38afc8846ece642417e9377b069af2e24275e672c5c15b6","artifact:5753:64430c6e390bd6075d66de8a36213442e3d373219ab19be71fcdb5c8aac3f9ee":"64430c6e390bd6075d66de8a36213442e3d373219ab19be71fcdb5c8aac3f9ee","artifact:5753:740a5ae0c95b63516fc3e0e3a54c0f2dfeafcb5c594afc300ceec18cb3df6ca6":"740a5ae0c95b63516fc3e0e3a54c0f2dfeafcb5c594afc300ceec18cb3df6ca6","artifact:5753:8612e5b91b88672338c04d6d8b179d0d4a131a1d27be18ec756460092a76e4bd":"8612e5b91b88672338c04d6d8b179d0d4a131a1d27be18ec756460092a76e4bd","artifact:5753:970bf356b92b435f220c546ee239349c41e4a1d07347dc86b52a78371c006267":"970bf356b92b435f220c546ee239349c41e4a1d07347dc86b52a78371c006267","artifact:5753:b10cac85277db0104437976b9c46ac41612f4f7148abe4fd3b69d8d352ae7ec4":"b10cac85277db0104437976b9c46ac41612f4f7148abe4fd3b69d8d352ae7ec4","artifact:5753:c2bfc234e1c5a25cd24ac086b7621e762aa43cbee9a3357405e81efd23630e7c":"c2bfc234e1c5a25cd24ac086b7621e762aa43cbee9a3357405e81efd23630e7c","artifact:5753:de1c7bb4620a8603ebbb9f10008583d7c14a44be54b069392bb3925c8274a4f0":"de1c7bb4620a8603ebbb9f10008583d7c14a44be54b069392bb3925c8274a4f0"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5753,"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 #5753: 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\":5753,\"report_sha256\":\"63df524d97cea6421052556b03453942372a8e8ed09f7fc0fb1dba381399c37c\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5753\":\"7da871b5343c1deb95d87bb497d205fb164a3e1e84a7ee200ac834df6ac0e45a\",\"artifact:5753:06cadfaba40ec6ff8322c66d0577bed2123839d32a421b68b9845bf43b06244c\":\"06cadfaba40ec6ff8322c66d0577bed2123839d32a421b68b9845bf43b06244c\",\"artifact:5753:63930b77686fa631b38afc8846ece642417e9377b069af2e24275e672c5c15b6\":\"63930b77686fa631b38afc8846ece642417e9377b069af2e24275e672c5c15b6\",\"artifact:5753:64430c6e390bd6075d66de8a36213442e3d373219ab19be71fcdb5c8aac3f9ee\":\"64430c6e390bd6075d66de8a36213442e3d373219ab19be71fcdb5c8aac3f9ee\",\"artifact:5753:740a5ae0c95b63516fc3e0e3a54c0f2dfeafcb5c594afc300ceec18cb3df6ca6\":\"740a5ae0c95b63516fc3e0e3a54c0f2dfeafcb5c594afc300ceec18cb3df6ca6\",\"artifact:5753:8612e5b91b88672338c04d6d8b179d0d4a131a1d27be18ec756460092a76e4bd\":\"8612e5b91b88672338c04d6d8b179d0d4a131a1d27be18ec756460092a76e4bd\",\"artifact:5753:970bf356b92b435f220c546ee239349c41e4a1d07347dc86b52a78371c006267\":\"970bf356b92b435f220c546ee239349c41e4a1d07347dc86b52a78371c006267\",\"artifact:5753:b10cac85277db0104437976b9c46ac41612f4f7148abe4fd3b69d8d352ae7ec4\":\"b10cac85277db0104437976b9c46ac41612f4f7148abe4fd3b69d8d352ae7ec4\",\"artifact:5753:c2bfc234e1c5a25cd24ac086b7621e762aa43cbee9a3357405e81efd23630e7c\":\"c2bfc234e1c5a25cd24ac086b7621e762aa43cbee9a3357405e81efd23630e7c\",\"artifact:5753:de1c7bb4620a8603ebbb9f10008583d7c14a44be54b069392bb3925c8274a4f0\":\"de1c7bb4620a8603ebbb9f10008583d7c14a44be54b069392bb3925c8274a4f0\"},\"sha256\":\"b825d731e3f74a293fc143d3c0e169625e894ae6cd4de95d8342e348b9192c30\"},\"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:5753,input_sha256:\"bc95ac7507572e3e0a7abdbc78b4d73cdf81095c027e57cfffc3083e44e11354\",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. 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