{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:X4JYKL4VY5NXYAQWFM6VP7RMA5","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":"e870f0f2da8c0c2e413cdaef2da7d7992065f2dc48afce6c5c273a86051ae273","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-06T21:23:56Z","title_canon_sha256":"8491dfb4d3485f00b9d3f235de79cc68a5d0f78b2fb38cac01f028ef485a49be"},"schema_version":"1.0","source":{"id":"1303.1551","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1551","created_at":"2026-05-18T03:31:42Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1551v1","created_at":"2026-05-18T03:31:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1551","created_at":"2026-05-18T03:31:42Z"},{"alias_kind":"pith_short_12","alias_value":"X4JYKL4VY5NX","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"X4JYKL4VY5NXYAQW","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"X4JYKL4V","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:722a68d1c36e128f8fab19f846bf28b74851c458b49dc87438872d890daff8ac","target":"graph","created_at":"2026-05-18T03:31:42Z","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 finite tree $T$ with $|V(T)| \\geq 2$ is called {\\it automorphism-free} if there is no non-trivial automorphism of $T$. Let $\\mathcal{AFT}$ be the poset with the element set of all finite automorphism-free trees (up to graph isomorphism) ordered by $T_1 \\preceq T_2$ if $T_1$ can be obtained from $T_2$ by successively deleting one leaf at a time in such a way that each intermediate tree is also automorphism-free. In this paper, we prove that $\\mathcal{AFT}$ has a unique minimal element. This result gives an affirmative answer to the question asked by Rupinski.","authors_text":"Ilhee Kim, Paul Seymour, Ringi Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-06T21:23:56Z","title":"The Minimal Automorphism-Free Tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1551","kind":"arxiv","version":1},"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":"sha256:4484f2df276d39644c22ed1960a211dd9cf2235beb3c7ec814b5d3738e47d028","target":"record","created_at":"2026-05-18T03:31:42Z","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":"e870f0f2da8c0c2e413cdaef2da7d7992065f2dc48afce6c5c273a86051ae273","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-06T21:23:56Z","title_canon_sha256":"8491dfb4d3485f00b9d3f235de79cc68a5d0f78b2fb38cac01f028ef485a49be"},"schema_version":"1.0","source":{"id":"1303.1551","kind":"arxiv","version":1}},"canonical_sha256":"bf13852f95c75b7c02162b3d57fe2c07567faab06ff0549a1426c7f6d7e369c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf13852f95c75b7c02162b3d57fe2c07567faab06ff0549a1426c7f6d7e369c1","first_computed_at":"2026-05-18T03:31:42.292180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:42.292180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vAyfGDRs4raZv1dVSJsNnOBx0bH0H3pr+CDS37SGo0OtcX3kp+Muv9OVtpS46rReYMF25VL0tDLT7Z+358+SDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:42.292782Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1551","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4484f2df276d39644c22ed1960a211dd9cf2235beb3c7ec814b5d3738e47d028","sha256:722a68d1c36e128f8fab19f846bf28b74851c458b49dc87438872d890daff8ac"],"state_sha256":"24949a629f416ac5551525847f4c6fd47ac88717c16b9e7689d7b2e3ff959f91"}