{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LJ3CF6IUYUOZKKSLZUT7HIWFTT","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":"9f6e169c493f0a5d2697f92ca28194514f958df5091eb92b3f1cd8b9cf834293","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-05T15:45:46Z","title_canon_sha256":"3b4de38caa3034e00c854fdd19d9e6f8ef20f92269a8e185d0ea6f980da24ec5"},"schema_version":"1.0","source":{"id":"1405.0935","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0935","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0935v2","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0935","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"pith_short_12","alias_value":"LJ3CF6IUYUOZ","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LJ3CF6IUYUOZKKSL","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LJ3CF6IU","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:7eef2fdcb14dd8a0a563e57d8cc2b7c1761c606e2459ae10d6fbe5bfe0c6f7c8","target":"graph","created_at":"2026-05-18T01:20:56Z","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 characterize conservative median algebras and semilattices by means of forbidden substructures and by providing their representation as chains. Moreover, using a dual equivalence between median algebras and certain topological structures, we obtain descriptions of the median-preserving mappings between products of finitely many chains.","authors_text":"Bruno Teheux, Jean-Luc Marichal, Miguel Couceiro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-05T15:45:46Z","title":"Conservative median algebras and semilattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0935","kind":"arxiv","version":2},"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":"sha256:650bcd9a60ab4d5bd76928c559bce5e2c14eba1fe67854540f997fa09770163b","target":"record","created_at":"2026-05-18T01:20:56Z","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":"9f6e169c493f0a5d2697f92ca28194514f958df5091eb92b3f1cd8b9cf834293","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-05T15:45:46Z","title_canon_sha256":"3b4de38caa3034e00c854fdd19d9e6f8ef20f92269a8e185d0ea6f980da24ec5"},"schema_version":"1.0","source":{"id":"1405.0935","kind":"arxiv","version":2}},"canonical_sha256":"5a7622f914c51d952a4bcd27f3a2c59cdf508075d631a901b5cb3160a49025e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a7622f914c51d952a4bcd27f3a2c59cdf508075d631a901b5cb3160a49025e2","first_computed_at":"2026-05-18T01:20:56.211334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:56.211334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XwRuHMz4c4ZqX6d91ipC1qHiPMA6yeyKGGCLlGmzA03nmKmJi5MhagxIO+X5Lnkz/ieQsTNQQyaPK4RlLzPvAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:56.211847Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0935","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:650bcd9a60ab4d5bd76928c559bce5e2c14eba1fe67854540f997fa09770163b","sha256:7eef2fdcb14dd8a0a563e57d8cc2b7c1761c606e2459ae10d6fbe5bfe0c6f7c8"],"state_sha256":"42abb22460c0588ab8d12312f439c616643820824dd2a5b3a98b6baa84028da8"}