{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:M22BSWUXA252TF6T552EXN2U4C","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":"40fc6bc5f9d5c7f93c0a69aa2decf8484c15c38a325fa3a977c9c7bbf4d58b26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2020-11-08T08:48:51Z","title_canon_sha256":"d1a9aa68bef3ce89d851873c0c50711a01a01ac0513fe794646072d12a040245"},"schema_version":"1.0","source":{"id":"2011.03925","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.03925","created_at":"2026-07-05T07:44:38Z"},{"alias_kind":"arxiv_version","alias_value":"2011.03925v3","created_at":"2026-07-05T07:44:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.03925","created_at":"2026-07-05T07:44:38Z"},{"alias_kind":"pith_short_12","alias_value":"M22BSWUXA252","created_at":"2026-07-05T07:44:38Z"},{"alias_kind":"pith_short_16","alias_value":"M22BSWUXA252TF6T","created_at":"2026-07-05T07:44:38Z"},{"alias_kind":"pith_short_8","alias_value":"M22BSWUX","created_at":"2026-07-05T07:44:38Z"}],"graph_snapshots":[{"event_id":"sha256:ad1cb8f238b0a5bd828d4e2f86ce95f76b91ee73621f7de29d1bde1200c82e04","target":"graph","created_at":"2026-07-05T07:44:38Z","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/2011.03925/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. We show that on the algebra of binary trees whose leaves are labeled by letters of an alphabet containing at least three letters, a function is congruence preserving if and only if it is polynomial.","authors_text":"Andre Arnold, Irene Guessarian, Patrick Cegielski, Serge Grigorieff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2020-11-08T08:48:51Z","title":"The algebra of binary trees is affine complete"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.03925","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:b87cdaa19fa2fd9709561759de20da6863a3ef7aaec3ce36e190ed7444cca81f","target":"record","created_at":"2026-07-05T07:44:38Z","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":"40fc6bc5f9d5c7f93c0a69aa2decf8484c15c38a325fa3a977c9c7bbf4d58b26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2020-11-08T08:48:51Z","title_canon_sha256":"d1a9aa68bef3ce89d851873c0c50711a01a01ac0513fe794646072d12a040245"},"schema_version":"1.0","source":{"id":"2011.03925","kind":"arxiv","version":3}},"canonical_sha256":"66b4195a9706bba997d3ef744bb754e09f75205c6649bbb78b0f19d349ba0434","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66b4195a9706bba997d3ef744bb754e09f75205c6649bbb78b0f19d349ba0434","first_computed_at":"2026-07-05T07:44:38.291739Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:44:38.291739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RxTWW69ntgBeV9Dkh76mCOxARCtQaHcsHiBIwfRCln9S+v158nGp2eOr1x0z742waUO2zYgi6QIkjHbUI1CbAA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:44:38.292156Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.03925","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b87cdaa19fa2fd9709561759de20da6863a3ef7aaec3ce36e190ed7444cca81f","sha256:ad1cb8f238b0a5bd828d4e2f86ce95f76b91ee73621f7de29d1bde1200c82e04"],"state_sha256":"87a73a21199a2318b2a1b776023c3669b9a259a82fffa4f52e5146b0c70e7c12"}