{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CMJCRMM324FAPTEQMXVSQW6NZ3","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":"fcb78ccce8b736ebd83ca479c983c951ed6a959f7fcca80f2ab13fba86415c22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-26T11:34:46Z","title_canon_sha256":"10e2525f7acdb6a1ed6621db4c949e726dfb39c92eb05969d1a031295381f3c5"},"schema_version":"1.0","source":{"id":"1706.08330","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08330","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08330v3","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08330","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"pith_short_12","alias_value":"CMJCRMM324FA","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CMJCRMM324FAPTEQ","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CMJCRMM3","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:0aebcf443e59586d1e0a7a2fc5bc5c0da1b70d298833c742246da856229a5adc","target":"graph","created_at":"2026-05-18T00:15:37Z","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 graph is one-ended if it contains a ray (a one way infinite path) and whenever we remove a finite number of vertices from the graph then what remains has only one component which contains rays. A vertex $v$ {\\em dominates} a ray in the end if there are infinitely many paths connecting $v$ to the ray such that any two of these paths have only the vertex $v$ in common. We prove that if a one-ended graph contains no ray which is dominated by a vertex and no infinite family of pairwise disjoint rays, then it has a tree-decomposition such that the decomposition tree is one-ended and the tree-deco","authors_text":"Florian Lehner, Johannes Carmesin, R\\\"ognvaldur G. M\\\"oller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-26T11:34:46Z","title":"On tree-decompositions of one-ended graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08330","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:de73d0a702aa6b3a3f529322052cedda555d78f422355c90200f49ef313117d5","target":"record","created_at":"2026-05-18T00:15:37Z","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":"fcb78ccce8b736ebd83ca479c983c951ed6a959f7fcca80f2ab13fba86415c22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-26T11:34:46Z","title_canon_sha256":"10e2525f7acdb6a1ed6621db4c949e726dfb39c92eb05969d1a031295381f3c5"},"schema_version":"1.0","source":{"id":"1706.08330","kind":"arxiv","version":3}},"canonical_sha256":"131228b19bd70a07cc9065eb285bcdcefd98f95e345a9c021917efe97f71dcbd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"131228b19bd70a07cc9065eb285bcdcefd98f95e345a9c021917efe97f71dcbd","first_computed_at":"2026-05-18T00:15:37.574421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:37.574421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZBA6B+6PnIBktaYfQg6n1Vh04thgSY+WPUfGNmyRYhAb2YQjjWzyWV73jnmeJy6ZqlEwozbUa8GXd1VzyGDlDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:37.574902Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.08330","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de73d0a702aa6b3a3f529322052cedda555d78f422355c90200f49ef313117d5","sha256:0aebcf443e59586d1e0a7a2fc5bc5c0da1b70d298833c742246da856229a5adc"],"state_sha256":"345c1179449f8e4f7ba08548247fdfc9698414f3d30072e5ad6364274ae2ff65"}