{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:OH7OIEBKPZTEPZOIZI5PYVSN5X","short_pith_number":"pith:OH7OIEBK","schema_version":"1.0","canonical_sha256":"71fee4102a7e6647e5c8ca3afc564dedd41976a7df0e7434f15a1f7b3f865bd2","source":{"kind":"arxiv","id":"1307.4113","version":2},"attestation_state":"computed","paper":{"title":"On a common generalization of Shelah's 2-rank, dp-rank, and o-minimal dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Cameron Donnay Hill, Vincent Guingona","submitted_at":"2013-07-15T22:01:45Z","abstract_excerpt":"In this paper, we build a dimension theory related to Shelah's 2-rank, dp-rank, and o-minimal dimension. We call this dimension op-dimension. We exhibit the notion of the n-multi-order property, generalizing the order property, and use this to create op-rank, which generalizes 2-rank. From this we build op-dimension. We show that op-dimension bounds dp-rank, that op-dimension is sub-additive, and op-dimension generalizes o-minimal dimension in o-minimal theories."},"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":"1307.4113","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-07-15T22:01:45Z","cross_cats_sorted":[],"title_canon_sha256":"21ac59decc8f4260dd3e337e8025fc6db6c4c1e7fabdba3e23046756771a9341","abstract_canon_sha256":"b48a37926850c14b5070e6fc88bcadc3bf7d700aff8f8377c3b0f69533fcc367"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:35.112501Z","signature_b64":"u8yaZnEP2Zw/uOt2V08n41yJ1sAWTrZgqrdnljnkLrbmYFI+1xfy4/yQ1S37QJHl0FhYxj8yuEoisvAiS+3ZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71fee4102a7e6647e5c8ca3afc564dedd41976a7df0e7434f15a1f7b3f865bd2","last_reissued_at":"2026-05-18T03:17:35.111879Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:35.111879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a common generalization of Shelah's 2-rank, dp-rank, and o-minimal dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Cameron Donnay Hill, Vincent Guingona","submitted_at":"2013-07-15T22:01:45Z","abstract_excerpt":"In this paper, we build a dimension theory related to Shelah's 2-rank, dp-rank, and o-minimal dimension. We call this dimension op-dimension. We exhibit the notion of the n-multi-order property, generalizing the order property, and use this to create op-rank, which generalizes 2-rank. From this we build op-dimension. We show that op-dimension bounds dp-rank, that op-dimension is sub-additive, and op-dimension generalizes o-minimal dimension in o-minimal theories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4113","kind":"arxiv","version":2},"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":"1307.4113","created_at":"2026-05-18T03:17:35.112002+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.4113v2","created_at":"2026-05-18T03:17:35.112002+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4113","created_at":"2026-05-18T03:17:35.112002+00:00"},{"alias_kind":"pith_short_12","alias_value":"OH7OIEBKPZTE","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OH7OIEBKPZTEPZOI","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OH7OIEBK","created_at":"2026-05-18T12:27:54.935989+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/OH7OIEBKPZTEPZOIZI5PYVSN5X","json":"https://pith.science/pith/OH7OIEBKPZTEPZOIZI5PYVSN5X.json","graph_json":"https://pith.science/api/pith-number/OH7OIEBKPZTEPZOIZI5PYVSN5X/graph.json","events_json":"https://pith.science/api/pith-number/OH7OIEBKPZTEPZOIZI5PYVSN5X/events.json","paper":"https://pith.science/paper/OH7OIEBK"},"agent_actions":{"view_html":"https://pith.science/pith/OH7OIEBKPZTEPZOIZI5PYVSN5X","download_json":"https://pith.science/pith/OH7OIEBKPZTEPZOIZI5PYVSN5X.json","view_paper":"https://pith.science/paper/OH7OIEBK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.4113&json=true","fetch_graph":"https://pith.science/api/pith-number/OH7OIEBKPZTEPZOIZI5PYVSN5X/graph.json","fetch_events":"https://pith.science/api/pith-number/OH7OIEBKPZTEPZOIZI5PYVSN5X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OH7OIEBKPZTEPZOIZI5PYVSN5X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OH7OIEBKPZTEPZOIZI5PYVSN5X/action/storage_attestation","attest_author":"https://pith.science/pith/OH7OIEBKPZTEPZOIZI5PYVSN5X/action/author_attestation","sign_citation":"https://pith.science/pith/OH7OIEBKPZTEPZOIZI5PYVSN5X/action/citation_signature","submit_replication":"https://pith.science/pith/OH7OIEBKPZTEPZOIZI5PYVSN5X/action/replication_record"}},"created_at":"2026-05-18T03:17:35.112002+00:00","updated_at":"2026-05-18T03:17:35.112002+00:00"}