{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZNNUHB7UBOLVJSPQCMCZL3WNOS","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":"be9476b4b6e4a9a543d1c594ceeedbe75557461c851f6544c21c4bd06edbd122","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-14T09:48:16Z","title_canon_sha256":"44dce744ac6dc5f83611994b5d235ac27d4dacbd711af4411cbd19992915b671"},"schema_version":"1.0","source":{"id":"1711.05027","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.05027","created_at":"2026-05-18T00:30:35Z"},{"alias_kind":"arxiv_version","alias_value":"1711.05027v1","created_at":"2026-05-18T00:30:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05027","created_at":"2026-05-18T00:30:35Z"},{"alias_kind":"pith_short_12","alias_value":"ZNNUHB7UBOLV","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZNNUHB7UBOLVJSPQ","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZNNUHB7U","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:7135246495430da98b9586f0ee7b74cd42a1aeb1137de1ae2e8030d493198779","target":"graph","created_at":"2026-05-18T00:30:35Z","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":"To every partial order P, one associates a polynomial $\\mathbb{D}_P$ in 4 variables that enumerates the intervals of P according to 4 parameters. Some symmetry properties of this polynomial are obtained for a specific family of posets, the Tamari lattices. A ternary symmetry is proved for the polynomial in 3 variables obtained by setting one variable to 1. Another global symmetry is conjectured. The set of synchronized intervals is described using a facet of the Newton polytope. A relation to the statistics of the canopy of binary planar trees is described.","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":"2017-11-14T09:48:16Z","title":"A note on Tamari intervals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05027","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:e8eaf32109a8f75918725c74129ff8b714d33735368491ea3a2daf6c4ea3f7e2","target":"record","created_at":"2026-05-18T00:30:35Z","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":"be9476b4b6e4a9a543d1c594ceeedbe75557461c851f6544c21c4bd06edbd122","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-14T09:48:16Z","title_canon_sha256":"44dce744ac6dc5f83611994b5d235ac27d4dacbd711af4411cbd19992915b671"},"schema_version":"1.0","source":{"id":"1711.05027","kind":"arxiv","version":1}},"canonical_sha256":"cb5b4387f40b9754c9f0130595eecd74abc78277d075bab12ba171def17db663","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb5b4387f40b9754c9f0130595eecd74abc78277d075bab12ba171def17db663","first_computed_at":"2026-05-18T00:30:35.132131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:35.132131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xDukgIUrhNBAxSbobqfjfqBv0uYomI8EyuIVuTWLFHeOMzOqQShtTDKUcCOgNnzlLzpyBmBAWEe35dGIOlLRAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:35.132856Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.05027","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8eaf32109a8f75918725c74129ff8b714d33735368491ea3a2daf6c4ea3f7e2","sha256:7135246495430da98b9586f0ee7b74cd42a1aeb1137de1ae2e8030d493198779"],"state_sha256":"ffaf17b475a14715342083edc861010935fae799f60ca42fff876e19f2c0ffa6"}