{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XIBK7BHAKMUIZXSN4OJQF3VS2X","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":"1ce8076f02af58002eacfdfda44550b018a287f1a0658a7bbe158460ffa10d3e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.LO","submitted_at":"2014-08-11T20:42:28Z","title_canon_sha256":"4a30eb68b84fc71606b6415f26f4645eefb6fc3ac4460e20feb6ad310cf4608f"},"schema_version":"1.0","source":{"id":"1408.2554","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2554","created_at":"2026-05-18T01:20:01Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2554v2","created_at":"2026-05-18T01:20:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2554","created_at":"2026-05-18T01:20:01Z"},{"alias_kind":"pith_short_12","alias_value":"XIBK7BHAKMUI","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XIBK7BHAKMUIZXSN","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XIBK7BHA","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:4e97bb41a78d2af749a90998d1ebd2c846af29ba97f92cef07950bcababed4a7","target":"graph","created_at":"2026-05-18T01:20:01Z","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":"Let (L;C) be the (up to isomorphism unique) countable homogeneous structure carrying a binary branching C-relation. We study the reducts of (L;C), i.e., the structures with domain L that are first-order definable in (L;C). We show that up to existential interdefinability, there are finitely many such reducts. This implies that there are finitely many reducts up to first-order interdefinability, thus confirming a conjecture of Simon Thomas for the special case of (L;C). We also study the endomorphism monoids of such reducts and show that they fall into four categories.","authors_text":"Manuel Bodirsky, Peter Jonsson, Trung Van Pham","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.LO","submitted_at":"2014-08-11T20:42:28Z","title":"The Reducts of the Homogeneous Binary Branching C-relation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2554","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:b3a30a5e88341fc3dc672b76fffe6e07fc044aebcbead842e88a90d6b604bb7a","target":"record","created_at":"2026-05-18T01:20:01Z","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":"1ce8076f02af58002eacfdfda44550b018a287f1a0658a7bbe158460ffa10d3e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.LO","submitted_at":"2014-08-11T20:42:28Z","title_canon_sha256":"4a30eb68b84fc71606b6415f26f4645eefb6fc3ac4460e20feb6ad310cf4608f"},"schema_version":"1.0","source":{"id":"1408.2554","kind":"arxiv","version":2}},"canonical_sha256":"ba02af84e053288cde4de39302eeb2d5d90b97a729b8a4049b5e2c6f055ddf96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba02af84e053288cde4de39302eeb2d5d90b97a729b8a4049b5e2c6f055ddf96","first_computed_at":"2026-05-18T01:20:01.962737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:01.962737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MkEIhkmx3+XoTNaOKlEEFdPxdI/wAij5HQktUB4NpZGBoNhxKyeP0hQUpxS2lzn/NBx7BgglVAQI+dznLJyTAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:01.963302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.2554","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3a30a5e88341fc3dc672b76fffe6e07fc044aebcbead842e88a90d6b604bb7a","sha256:4e97bb41a78d2af749a90998d1ebd2c846af29ba97f92cef07950bcababed4a7"],"state_sha256":"da01aa78e539942613e6855b35f4fb4266c4e5176b331936f0c74176c471365c"}