{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UCW6NHOV7Y4FKZWAZVR22A6QVN","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":"05b4fc474edf6ca2882926d6eed1d19ec41eb9e976a39a0195baa28bb80c070e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-01-23T04:33:52Z","title_canon_sha256":"aef84a7a438efb43ec76d7a541008b6befffa53f6ff7cc8a5838120e84a175cf"},"schema_version":"1.0","source":{"id":"2501.13374","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.13374","created_at":"2026-07-05T10:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"2501.13374v1","created_at":"2026-07-05T10:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.13374","created_at":"2026-07-05T10:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"UCW6NHOV7Y4F","created_at":"2026-07-05T10:04:27Z"},{"alias_kind":"pith_short_16","alias_value":"UCW6NHOV7Y4FKZWA","created_at":"2026-07-05T10:04:27Z"},{"alias_kind":"pith_short_8","alias_value":"UCW6NHOV","created_at":"2026-07-05T10:04:27Z"}],"graph_snapshots":[{"event_id":"sha256:76a1e7aca244a97e85e2a813c2d508a6607ca2d9d25228c3ab8d88c35f8a7fe8","target":"graph","created_at":"2026-07-05T10:04:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.13374/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that Loday's polytopal realisation of the nth Tamari lattice T_n, called associahedron, has 2^{n-1} common points with the permutohedron, which form a maximal never-middle (symmetric) Condorcet domain.","authors_text":"Arkadii Slinko","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-01-23T04:33:52Z","title":"A hidden Condorcet domain in Loday's realisation of the associahedron"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.13374","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:c7b365d4f0c8421fb0f53958a19edbc51fd937baf3bb959ea83f6e7ae9198b6d","target":"record","created_at":"2026-07-05T10:04:27Z","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":"05b4fc474edf6ca2882926d6eed1d19ec41eb9e976a39a0195baa28bb80c070e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-01-23T04:33:52Z","title_canon_sha256":"aef84a7a438efb43ec76d7a541008b6befffa53f6ff7cc8a5838120e84a175cf"},"schema_version":"1.0","source":{"id":"2501.13374","kind":"arxiv","version":1}},"canonical_sha256":"a0ade69dd5fe385566c0cd63ad03d0ab717ac53fcd868c97df500e8155e6e999","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0ade69dd5fe385566c0cd63ad03d0ab717ac53fcd868c97df500e8155e6e999","first_computed_at":"2026-07-05T10:04:27.511277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:04:27.511277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GdvhXG0lLjShOeZofHgR/PqnduO1sAgiPHZP2vXntZAx6uwhqxY/Uze8A+raKdiErLuhxiIXDOxRTfnP8v6aCA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:04:27.511761Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.13374","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7b365d4f0c8421fb0f53958a19edbc51fd937baf3bb959ea83f6e7ae9198b6d","sha256:76a1e7aca244a97e85e2a813c2d508a6607ca2d9d25228c3ab8d88c35f8a7fe8"],"state_sha256":"1b2462092af853a25f5644e6ec53dd700349eaf6900e2cf3732a11379b681bb6"}