{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:II4K3UCRE2CS56AI447RXEIHTH","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":"33ec8b13d44a3f5a95e92011a4ff37f9aa81824da0b2c988f9b7afc652fef4e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-18T15:35:31Z","title_canon_sha256":"b61f396071eb8e5d1eb4916ce75b07804c582b31db48ccb6c3bf3906de7dbb2e"},"schema_version":"1.0","source":{"id":"1512.05993","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05993","created_at":"2026-05-17T23:46:32Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05993v4","created_at":"2026-05-17T23:46:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05993","created_at":"2026-05-17T23:46:32Z"},{"alias_kind":"pith_short_12","alias_value":"II4K3UCRE2CS","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"II4K3UCRE2CS56AI","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"II4K3UCR","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:e7db883ba55cd518437bbf365de2d4a74d5789c4213555749e1881096c01fea4","target":"graph","created_at":"2026-05-17T23:46:32Z","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":"Balogh, Bollobas and Weinreich showed that a parameter that has since been termed the distinguishing number can be used to identify a jump in the possible speeds of hereditary classes of graphs at the sequence of Bell numbers.\n  We prove that every hereditary class that lies above the Bell numbers and has finite distinguishing number contains a boundary class for well-quasi-ordering. This means that any such hereditary class which in addition is defined by finitely many minimal forbidden induced subgraphs must contain an infinite antichain. As all hereditary classes below the Bell numbers are ","authors_text":"Aistis Atminas, Robert Brignall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-18T15:35:31Z","title":"Well-quasi-ordering and finite distinguishing number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05993","kind":"arxiv","version":4},"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:b8954d14cade6938750fe0812e006b6f678fdaed0c978aa68abb9ec2214dd882","target":"record","created_at":"2026-05-17T23:46:32Z","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":"33ec8b13d44a3f5a95e92011a4ff37f9aa81824da0b2c988f9b7afc652fef4e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-18T15:35:31Z","title_canon_sha256":"b61f396071eb8e5d1eb4916ce75b07804c582b31db48ccb6c3bf3906de7dbb2e"},"schema_version":"1.0","source":{"id":"1512.05993","kind":"arxiv","version":4}},"canonical_sha256":"4238add05126852ef808e73f1b910799d044e980c9526d38804f4550621f92eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4238add05126852ef808e73f1b910799d044e980c9526d38804f4550621f92eb","first_computed_at":"2026-05-17T23:46:32.206933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:32.206933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y1FeqT6CKXISw4cyTVxC3alVKcAWKKZtt1bsWBZ6GpGlK6SB4MCCS2KbTgWTeWpdewcNzSFIXp6KuQ335vB1CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:32.207561Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.05993","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8954d14cade6938750fe0812e006b6f678fdaed0c978aa68abb9ec2214dd882","sha256:e7db883ba55cd518437bbf365de2d4a74d5789c4213555749e1881096c01fea4"],"state_sha256":"ef539727a08b46f9ac9ce786be25fb49a439b6e9c2258c1b4e792d959116648f"}