{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:PR7HVLFYUASUHQW7MKUX2XRZWG","short_pith_number":"pith:PR7HVLFY","schema_version":"1.0","canonical_sha256":"7c7e7aacb8a02543c2df62a97d5e39b1a12007407e65689ae6f489fc6121a3bb","source":{"kind":"arxiv","id":"1204.3048","version":1},"attestation_state":"computed","paper":{"title":"The Rank of Tree-Automatic Linear Orderings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Martin Huschenbett","submitted_at":"2012-04-13T16:48:30Z","abstract_excerpt":"We generalise Delhomm\\'e's result that each tree-automatic ordinal is strictly below \\omega^\\omega^\\omega{} by showing that any tree-automatic linear ordering has FC-rank strictly below \\omega^\\omega. We further investigate a restricted form of tree-automaticity and prove that every linear ordering which admits a tree-automatic presentation of branching complexity at most k has FC-rank strictly below \\omega^k."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1204.3048","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-04-13T16:48:30Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"e2d4d63aced860ae280814fdff09e3f73286058a03dd048682aa4e326d6eb93c","abstract_canon_sha256":"5c9eeacd8241aa7defa619f1fc4091dd315f40354a1ed0b80128a87b21707c5b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:54.081868Z","signature_b64":"nPw6rmTNuzOcbLM/HXVtWjUc8/06osYTwCe+fECE3wSEKpyzzHRbtlwLUdDHj1TuYCQSjPE4Ok1T4F2SFA4tAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c7e7aacb8a02543c2df62a97d5e39b1a12007407e65689ae6f489fc6121a3bb","last_reissued_at":"2026-05-18T03:57:54.081045Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:54.081045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Rank of Tree-Automatic Linear Orderings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Martin Huschenbett","submitted_at":"2012-04-13T16:48:30Z","abstract_excerpt":"We generalise Delhomm\\'e's result that each tree-automatic ordinal is strictly below \\omega^\\omega^\\omega{} by showing that any tree-automatic linear ordering has FC-rank strictly below \\omega^\\omega. We further investigate a restricted form of tree-automaticity and prove that every linear ordering which admits a tree-automatic presentation of branching complexity at most k has FC-rank strictly below \\omega^k."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3048","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1204.3048","created_at":"2026-05-18T03:57:54.081159+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.3048v1","created_at":"2026-05-18T03:57:54.081159+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3048","created_at":"2026-05-18T03:57:54.081159+00:00"},{"alias_kind":"pith_short_12","alias_value":"PR7HVLFYUASU","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"PR7HVLFYUASUHQW7","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"PR7HVLFY","created_at":"2026-05-18T12:27:18.751474+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PR7HVLFYUASUHQW7MKUX2XRZWG","json":"https://pith.science/pith/PR7HVLFYUASUHQW7MKUX2XRZWG.json","graph_json":"https://pith.science/api/pith-number/PR7HVLFYUASUHQW7MKUX2XRZWG/graph.json","events_json":"https://pith.science/api/pith-number/PR7HVLFYUASUHQW7MKUX2XRZWG/events.json","paper":"https://pith.science/paper/PR7HVLFY"},"agent_actions":{"view_html":"https://pith.science/pith/PR7HVLFYUASUHQW7MKUX2XRZWG","download_json":"https://pith.science/pith/PR7HVLFYUASUHQW7MKUX2XRZWG.json","view_paper":"https://pith.science/paper/PR7HVLFY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.3048&json=true","fetch_graph":"https://pith.science/api/pith-number/PR7HVLFYUASUHQW7MKUX2XRZWG/graph.json","fetch_events":"https://pith.science/api/pith-number/PR7HVLFYUASUHQW7MKUX2XRZWG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PR7HVLFYUASUHQW7MKUX2XRZWG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PR7HVLFYUASUHQW7MKUX2XRZWG/action/storage_attestation","attest_author":"https://pith.science/pith/PR7HVLFYUASUHQW7MKUX2XRZWG/action/author_attestation","sign_citation":"https://pith.science/pith/PR7HVLFYUASUHQW7MKUX2XRZWG/action/citation_signature","submit_replication":"https://pith.science/pith/PR7HVLFYUASUHQW7MKUX2XRZWG/action/replication_record"}},"created_at":"2026-05-18T03:57:54.081159+00:00","updated_at":"2026-05-18T03:57:54.081159+00:00"}