{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZENBNVIL5GZSWIMKPOAI2J2LSY","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":"fe3a43c47dc2b8c56a43db0ae3524932c839273ff7defb96e1e443606ef782b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-12T16:40:19Z","title_canon_sha256":"5432de81451fb5e8b61e3b0f7aba152e899ffccba7de2bdddb8a22f00d4cdd5d"},"schema_version":"1.0","source":{"id":"1212.2876","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2876","created_at":"2026-05-18T03:38:35Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2876v1","created_at":"2026-05-18T03:38:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2876","created_at":"2026-05-18T03:38:35Z"},{"alias_kind":"pith_short_12","alias_value":"ZENBNVIL5GZS","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZENBNVIL5GZSWIMK","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZENBNVIL","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:5d0106c5b62698ecd8cbacff088ecbf0e2f6748b02f2403efa79e8c51c040005","target":"graph","created_at":"2026-05-18T03:38:35Z","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":"We discuss properties of root posets for finite crystallographic root systems, and show that these properties uniquely determine root posets for the noncrystallographic dihedral types and type $H_3$, while proving that there does not exist a poset satisfying all of the properties in type $H_4$. We do this by exhaustive computer searches for posets having these properties. We further give a realization of the poset of type $H_3$ as restricted roots of type $D_6$, and conjecture a Hilbert polynomial for the $q,t$-Catalan numbers for type $H_4$.","authors_text":"Christian Stump, Michael Cuntz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-12T16:40:19Z","title":"On root posets for noncrystallographic root systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2876","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":"sha256:8f461cdec28fa097888a88f29c6f3d171377155d99d1da9704d6921c2a686318","target":"record","created_at":"2026-05-18T03:38:35Z","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":"fe3a43c47dc2b8c56a43db0ae3524932c839273ff7defb96e1e443606ef782b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-12T16:40:19Z","title_canon_sha256":"5432de81451fb5e8b61e3b0f7aba152e899ffccba7de2bdddb8a22f00d4cdd5d"},"schema_version":"1.0","source":{"id":"1212.2876","kind":"arxiv","version":1}},"canonical_sha256":"c91a16d50be9b32b218a7b808d274b963d84e8f4cd37e099a5ac3e9465e946c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c91a16d50be9b32b218a7b808d274b963d84e8f4cd37e099a5ac3e9465e946c9","first_computed_at":"2026-05-18T03:38:35.064961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:35.064961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dZa69A0F/A/10w2XM1541+1FDK11QXioaAbBHNQXM7whsnB+VDXTP4askb64H10d22qIH6yV7guAXPv1osILDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:35.065468Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.2876","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f461cdec28fa097888a88f29c6f3d171377155d99d1da9704d6921c2a686318","sha256:5d0106c5b62698ecd8cbacff088ecbf0e2f6748b02f2403efa79e8c51c040005"],"state_sha256":"709763cd28f9a63d55939d84f1fead6bca931515f8736cdc17d0bb011b9873bf"}