{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZX53BTGO24VZL3QTDQ3ZXQ3J3X","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":"9f66789e55712a9e39730c8eea0595022fd75d89b25af5f6e0b0a00036673231","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-03-15T22:42:57Z","title_canon_sha256":"e4bb147def4c6fcf28d9b9f583a64ad5bbd53c8669f2a6f104822bb6bab12f49"},"schema_version":"1.0","source":{"id":"1003.3045","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.3045","created_at":"2026-05-18T04:42:03Z"},{"alias_kind":"arxiv_version","alias_value":"1003.3045v2","created_at":"2026-05-18T04:42:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3045","created_at":"2026-05-18T04:42:03Z"},{"alias_kind":"pith_short_12","alias_value":"ZX53BTGO24VZ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZX53BTGO24VZL3QT","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZX53BTGO","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:ca0ea80c2323b7b0115ff685ceb63410b1e269dc5fd8ddb3909dbdb8830830b5","target":"graph","created_at":"2026-05-18T04:42:03Z","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":"Graceful tree conjecture is a well-known open problem in graph theory. Here we present a computational approach to this conjecture. An algorithm for finding graceful labelling for trees is proposed. With this algorithm, we show that every tree with at most 35 vertices allows a graceful labelling, hence we verify that the graceful tree conjecture is correct for trees with at most 35 vertices.","authors_text":"Wenjie Fang","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-03-15T22:42:57Z","title":"A Computational Approach to the Graceful Tree Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3045","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:b6662424a73a8ceb254df3981542e909f993861f30c31bde4fa753840aa9aad1","target":"record","created_at":"2026-05-18T04:42:03Z","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":"9f66789e55712a9e39730c8eea0595022fd75d89b25af5f6e0b0a00036673231","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-03-15T22:42:57Z","title_canon_sha256":"e4bb147def4c6fcf28d9b9f583a64ad5bbd53c8669f2a6f104822bb6bab12f49"},"schema_version":"1.0","source":{"id":"1003.3045","kind":"arxiv","version":2}},"canonical_sha256":"cdfbb0ccced72b95ee131c379bc369ddd6d9fe122ef11b7dafda1664c438fd3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdfbb0ccced72b95ee131c379bc369ddd6d9fe122ef11b7dafda1664c438fd3e","first_computed_at":"2026-05-18T04:42:03.272411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:03.272411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7AcsfsasgandmCzFdeo3k33edIdSNTrezc12VQruVtOtCT5Bgxj57ObGTgdJqmiTGhajnTl57pPgbfMdMyk7Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:03.272864Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.3045","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6662424a73a8ceb254df3981542e909f993861f30c31bde4fa753840aa9aad1","sha256:ca0ea80c2323b7b0115ff685ceb63410b1e269dc5fd8ddb3909dbdb8830830b5"],"state_sha256":"1058f8354082e288cbda8149d7f5efcfc64fa1edc64bae89b071874082c96c19"}