{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JPWA75VEUUNZ2KI5YJC4X6I26X","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":"f4d543098b06003f499e376f2bff5de67b709a97462b5e42b54f2abb7e8c6467","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-05T16:22:30Z","title_canon_sha256":"225cbc4f2417681e916dafc7d672904b5d300e08f92381a6c64d99b13d8f6609"},"schema_version":"1.0","source":{"id":"1508.01123","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01123","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01123v2","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01123","created_at":"2026-05-18T01:03:36Z"},{"alias_kind":"pith_short_12","alias_value":"JPWA75VEUUNZ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JPWA75VEUUNZ2KI5","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JPWA75VE","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:1dc37e4f6071a5715104d17b468551a26ae62587fa689a2ab0861cc4a348a9ae","target":"graph","created_at":"2026-05-18T01:03:36Z","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":"A tree is scattered if no subdivision of the complete binary tree is a subtree. Building on results of Halin, Polat and Sabidussi, we identify four types of subtrees of a scattered tree and a function of the tree into the integers at least one of which is preserved by every embedding.\n  With this result and a result of Tyomkyn, we prove that the tree alternative property conjecture of Bonato and Tardif holds for scattered trees and a conjecture of Tyomkin holds for locally finite scattered trees.","authors_text":"Claude Laflamme, Maurice Pouzet, Norbert Sauer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-05T16:22:30Z","title":"Invariant subsets of scattered trees. An application to the tree alternative property of Bonato and Tardif"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01123","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":"sha256:549666337b67790f8f55f7e5b93eaacd861cb31e673bbea63a8566b215d6d95c","target":"record","created_at":"2026-05-18T01:03:36Z","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":"f4d543098b06003f499e376f2bff5de67b709a97462b5e42b54f2abb7e8c6467","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-05T16:22:30Z","title_canon_sha256":"225cbc4f2417681e916dafc7d672904b5d300e08f92381a6c64d99b13d8f6609"},"schema_version":"1.0","source":{"id":"1508.01123","kind":"arxiv","version":2}},"canonical_sha256":"4bec0ff6a4a51b9d291dc245cbf91af5d07b0c5d90365323be623290ade8e3e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bec0ff6a4a51b9d291dc245cbf91af5d07b0c5d90365323be623290ade8e3e6","first_computed_at":"2026-05-18T01:03:36.887577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:36.887577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7IHkqnrcFxWVMlI6g6MCPceIftASxUcnoSUl8vBR/Ru0/7HlJmHNp2x5j4WlIHC6jggmgVMHTvuaKvg+cpFaBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:36.888376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01123","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:549666337b67790f8f55f7e5b93eaacd861cb31e673bbea63a8566b215d6d95c","sha256:1dc37e4f6071a5715104d17b468551a26ae62587fa689a2ab0861cc4a348a9ae"],"state_sha256":"051b3804f3d6b24d986f88d6cb05abefe43b94b56c9381f4a0d1bf7c2c103eda"}