{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TPXXWUVIFHVA7QWCPKSZVF2GNW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"39e9337f6f230dfb6e35334875f372a5e5fb06029841e22e4718564ba540ce8a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-16T17:07:10Z","title_canon_sha256":"d7c2b3811ac036da8eea85a0eb7ff7a8e6f4d16af99ea8f826d01909e81a5749"},"schema_version":"1.0","source":{"id":"1802.06030","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.06030","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"arxiv_version","alias_value":"1802.06030v2","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06030","created_at":"2026-05-18T00:21:01Z"},{"alias_kind":"pith_short_12","alias_value":"TPXXWUVIFHVA","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"TPXXWUVIFHVA7QWC","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"TPXXWUVI","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:34b8168148da28b58bf9725963cc82362539b33d62f1d549330f6bce863f7d0f","target":"graph","created_at":"2026-05-18T00:21:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We present random sampling procedures for Motzkin and Schr\\\"oder paths, following previous work on Dyck paths. Our algorithms follow the anticipated rejection method of the Florentine algorithms (Barcucci et al. 1994+), but introduce a recovery idea to greatly reduce the probability of rejection. They use an optimal amount of randomness and achieve a better time complexity than the Florentine algorithms.","authors_text":"Axel Bacher","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-16T17:07:10Z","title":"Improving the Florentine algorithms: recovering algorithms for Motzkin and Schr\\\"oder paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06030","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a0fa7e9eb6ad2bc1b8fbf45744b6b7399704006ff5d15439d917d24ecf28d7ce","target":"record","created_at":"2026-05-18T00:21:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"39e9337f6f230dfb6e35334875f372a5e5fb06029841e22e4718564ba540ce8a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-16T17:07:10Z","title_canon_sha256":"d7c2b3811ac036da8eea85a0eb7ff7a8e6f4d16af99ea8f826d01909e81a5749"},"schema_version":"1.0","source":{"id":"1802.06030","kind":"arxiv","version":2}},"canonical_sha256":"9bef7b52a829ea0fc2c27aa59a97466da7a138247a699f50d147f492d7d101b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bef7b52a829ea0fc2c27aa59a97466da7a138247a699f50d147f492d7d101b2","first_computed_at":"2026-05-18T00:21:01.430604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:01.430604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wfqva4F1AGTDZRE4clpbDVUr/Zjss7p81IbqSXoQMqFAqWx+0P96cbmbi6KLQcbpcWI8Vu7nbhB5I8c5s1uQDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:01.431019Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.06030","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0fa7e9eb6ad2bc1b8fbf45744b6b7399704006ff5d15439d917d24ecf28d7ce","sha256:34b8168148da28b58bf9725963cc82362539b33d62f1d549330f6bce863f7d0f"],"state_sha256":"552a0bea9d244ff18c9f7d15aa7f8eb1c7541e7f950cc8b39c80bd081f124717"}