{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ME24QAR5U5KXCSTCZNOHXDCRPO","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":"ee817b2bf29476b0f0d6819ad861f59379324f96ee138609caf27508fcf0918f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-28T12:09:53Z","title_canon_sha256":"b757fbd620f614ea2185e65dc9123bc445a2e48ddbc98dc643a1e6445ab3f472"},"schema_version":"1.0","source":{"id":"1809.10981","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10981","created_at":"2026-05-18T00:04:33Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10981v1","created_at":"2026-05-18T00:04:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10981","created_at":"2026-05-18T00:04:33Z"},{"alias_kind":"pith_short_12","alias_value":"ME24QAR5U5KX","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"ME24QAR5U5KXCSTC","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"ME24QAR5","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:2566a1621f91438f2bb3c3c2880281f4ea78ca9eed5ad507dff9f8ab8765d1e2","target":"graph","created_at":"2026-05-18T00:04:33Z","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 introduce and study a new partial order on Dyck paths. We prove that these posets are meet-semilattices. We show that their numbers of intervals are the same as the number of bicubic planar maps. We describe an unexpected connection with the Hochschild polytopes of Saneblidze.","authors_text":"Fr\\'ed\\'eric Chapoton (IRMA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-28T12:09:53Z","title":"Some properties of a new partial order on Dyck paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10981","kind":"arxiv","version":1},"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":"sha256:1c0baf780144f7a7a7dea5d6dd12a7457dfba5b4366f3102a057dffee7f48024","target":"record","created_at":"2026-05-18T00:04:33Z","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":"ee817b2bf29476b0f0d6819ad861f59379324f96ee138609caf27508fcf0918f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-28T12:09:53Z","title_canon_sha256":"b757fbd620f614ea2185e65dc9123bc445a2e48ddbc98dc643a1e6445ab3f472"},"schema_version":"1.0","source":{"id":"1809.10981","kind":"arxiv","version":1}},"canonical_sha256":"6135c8023da755714a62cb5c7b8c517b95816d960d09f33d91c040e43a697810","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6135c8023da755714a62cb5c7b8c517b95816d960d09f33d91c040e43a697810","first_computed_at":"2026-05-18T00:04:33.721024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:33.721024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HIy3p6xvWE1T+hS76B+f61WVl8i7tX9v06PKCz6juu2sozsz6dBKspHFSIHU0KGltRFtPVFgypRPpaEXI9FWCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:33.721750Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.10981","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c0baf780144f7a7a7dea5d6dd12a7457dfba5b4366f3102a057dffee7f48024","sha256:2566a1621f91438f2bb3c3c2880281f4ea78ca9eed5ad507dff9f8ab8765d1e2"],"state_sha256":"8b85c4ba696009c3ff3c6eb0ad249b6748a91e4309f75afce7b98a3377a6490d"}