{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LGP2VC4LTWRB75AOJQX2MHIHVS","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":"26a09f3c5dd3bf42c6be78312cb8dbc2f85bf79be4907c2ec8f032a33904f871","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-14T23:14:39Z","title_canon_sha256":"2b2c576a3b26fd69084bf1ee4aa46984c3762cc209e7bc8be829c24ca537c943"},"schema_version":"1.0","source":{"id":"1711.05353","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.05353","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"arxiv_version","alias_value":"1711.05353v3","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05353","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"pith_short_12","alias_value":"LGP2VC4LTWRB","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LGP2VC4LTWRB75AO","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LGP2VC4L","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:ee9e9cdab36b61ea2b9e129b9de0fc4cb879d2753070733bd9af965156007131","target":"graph","created_at":"2026-05-17T23:44:32Z","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":"For any lattice congruence of the weak order on $\\mathfrak{S}_n$, N. Reading proved that glueing together the cones of the braid fan that belong to the same congruence class defines a complete fan. We prove that this fan is the normal fan of a polytope.","authors_text":"Francisco Santos, Vincent Pilaud","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-14T23:14:39Z","title":"Quotientopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05353","kind":"arxiv","version":3},"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":"sha256:0aaace6203c99bcf25376d6933e103ebb4ee34b65dd25db7f9c520adb2fef8d2","target":"record","created_at":"2026-05-17T23:44:32Z","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":"26a09f3c5dd3bf42c6be78312cb8dbc2f85bf79be4907c2ec8f032a33904f871","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-14T23:14:39Z","title_canon_sha256":"2b2c576a3b26fd69084bf1ee4aa46984c3762cc209e7bc8be829c24ca537c943"},"schema_version":"1.0","source":{"id":"1711.05353","kind":"arxiv","version":3}},"canonical_sha256":"599faa8b8b9da21ff40e4c2fa61d07ac9596cd505f4e9543c2e11b378ab14ff7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"599faa8b8b9da21ff40e4c2fa61d07ac9596cd505f4e9543c2e11b378ab14ff7","first_computed_at":"2026-05-17T23:44:32.869250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:32.869250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yjVi7gUn2JJf3KZI8JY+HJrAZNP4xPM/8bRL3sV6n2f7JNwTnTqNudV77AciYtbWxGgUpzufmlxjJXXv2MUVAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:32.869897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.05353","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0aaace6203c99bcf25376d6933e103ebb4ee34b65dd25db7f9c520adb2fef8d2","sha256:ee9e9cdab36b61ea2b9e129b9de0fc4cb879d2753070733bd9af965156007131"],"state_sha256":"a0616f4b2870d3a2e5eb515a25c2491bea434c414d7c02d87538fa14c9bd369c"}