Prüft das behauptete rechte Kreweras-Komplement einer nichtkreuzenden Partition ...

{ "body": { "artifact": { "claimed_complement": [ [ 1, 2 ], [ 3, 4 ], [ 5 ] ], "claims": { "complement_blocks": 3, "complement_largest_block": 2, "complement_singletons": 1, "input_blocks": 3, "vertices": 5 }, "partition": [ [ 1, 3, 5 ], [ 2 ], [ 4 ] ], "vertices": 5 } }, "bodyType": "json", "method": "POST", "type": "http" }

{ "example": { "billable": true, "findings": [ { "confidence": 100, "evidence": [], "limits": [ "Novelli/Thibon arXiv2106.08257v2 §4.2.1: RIGHT Kreweras complement encoded by permutation p^−1 composed with long cycle(1..n), each original block read increasingly. Own cycle construction/inversion/composition/decomposition; no partition/permutation SDK. Right placement means circular order1,bar1,2,bar2,..,n,barn; no orientation choice silently swapped.", "Closed noncrossing partition of1..n with1<=n<=64. Input must cover each vertex once, nonempty blocks; crossing input outside NC premise=>whole unknown. Noncrossing checked by forbidden alternating same-block quadruples. Returned complement independently checked noncrossing and block-count rank identity.", "Caller complement is an unordered family of unordered blocks: member/block reordering is equivalent; within-profile nonpartition/duplicate/fractional/wrong-label claims give known observed mismatch rather than rounding or trusted coverage. Source malformed/incomplete partition unknown. One right-complement offer, no separate left/inverse/generalized/Coxeter/rotation variants.", "Formal coarsest barred noncrossing completion, not ordinary set complement, subgroup lattice, chosen graph layout, partition count or real circular-geometry measurement. No generic closure SDK or parameter-preset wrapper.", "Only bounded vertex/block-size counts and match boolean output. No original/complement vertex blocks, permutation, raw claim numbers or exception messages returned, including false phone-shaped claim labels/counters. No identity/contact/security/legal judgment." ], "module": "right-kreweras-noncrossing-partition-complement", "state": "not_observed", "value": { "claim_mismatches": 0, "claims_match": true, "complement_blocks": 3, "complement_claim_matches": true, "complement_largest_block": 2, "complement_singletons": 1, "input_blocks": 3, "vertices": 5 }, "warnings": [] } ], "known_count": 1, "scope": { "contact_values_returned": false, "network": false, "supplied_artifact_only": true }, "warnings": [] }, "type": "json" }