{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:RZNDLP5EUOAELUFVVMIFVRRSX3","short_pith_number":"pith:RZNDLP5E","schema_version":"1.0","canonical_sha256":"8e5a35bfa4a38045d0b5ab105ac632bedac7ff79162bc993501a9e59cf0a35f3","source":{"kind":"arxiv","id":"1503.00754","version":2},"attestation_state":"computed","paper":{"title":"The One-Dimensional Line Scheme of a Certain Family of Quantum ${\\mathbb P}^3$s","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Michaela Vancliff, Richard G. Chandler","submitted_at":"2015-03-02T21:28:31Z","abstract_excerpt":"A quantum ${\\mathbb P}^3$ is a noncommutative analogue of a polynomial ring on four variables, and, herein, it is taken to be a regular algebra of global dimension four. It is well known that if a generic quadratic quantum ${\\mathbb P}^3$ exists, then it has a point scheme consisting of exactly twenty distinct points and a one-dimensional line scheme. In this article, we compute the line scheme of a family of algebras whose generic member is a candidate for a generic quadratic quantum ${\\mathbb P}^3$. We find that, as a closed subscheme of ${\\mathbb P}^5$, the line scheme of the generic member"},"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":"1503.00754","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-02T21:28:31Z","cross_cats_sorted":[],"title_canon_sha256":"3f99a55386d79d9fa35b8c831139afd84548b9215d769a3c12e4b050a17d66ce","abstract_canon_sha256":"8f8ed4d28ac27e457dec4231c9273b7d171d6be086d6482559c05fb93e6b21b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:59.626419Z","signature_b64":"z2PFK9MVP5KLxw9qZp+WJBgGMJODQHieSPt7kI8nxDf8d1nRcuS/rb22MJaqeInKU0yewLkUGznizz4RWM20Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e5a35bfa4a38045d0b5ab105ac632bedac7ff79162bc993501a9e59cf0a35f3","last_reissued_at":"2026-05-18T01:55:59.626010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:59.626010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The One-Dimensional Line Scheme of a Certain Family of Quantum ${\\mathbb P}^3$s","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Michaela Vancliff, Richard G. Chandler","submitted_at":"2015-03-02T21:28:31Z","abstract_excerpt":"A quantum ${\\mathbb P}^3$ is a noncommutative analogue of a polynomial ring on four variables, and, herein, it is taken to be a regular algebra of global dimension four. It is well known that if a generic quadratic quantum ${\\mathbb P}^3$ exists, then it has a point scheme consisting of exactly twenty distinct points and a one-dimensional line scheme. In this article, we compute the line scheme of a family of algebras whose generic member is a candidate for a generic quadratic quantum ${\\mathbb P}^3$. We find that, as a closed subscheme of ${\\mathbb P}^5$, the line scheme of the generic member"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00754","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":"1503.00754","created_at":"2026-05-18T01:55:59.626069+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.00754v2","created_at":"2026-05-18T01:55:59.626069+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00754","created_at":"2026-05-18T01:55:59.626069+00:00"},{"alias_kind":"pith_short_12","alias_value":"RZNDLP5EUOAE","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RZNDLP5EUOAELUFV","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RZNDLP5E","created_at":"2026-05-18T12:29:39.896362+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/RZNDLP5EUOAELUFVVMIFVRRSX3","json":"https://pith.science/pith/RZNDLP5EUOAELUFVVMIFVRRSX3.json","graph_json":"https://pith.science/api/pith-number/RZNDLP5EUOAELUFVVMIFVRRSX3/graph.json","events_json":"https://pith.science/api/pith-number/RZNDLP5EUOAELUFVVMIFVRRSX3/events.json","paper":"https://pith.science/paper/RZNDLP5E"},"agent_actions":{"view_html":"https://pith.science/pith/RZNDLP5EUOAELUFVVMIFVRRSX3","download_json":"https://pith.science/pith/RZNDLP5EUOAELUFVVMIFVRRSX3.json","view_paper":"https://pith.science/paper/RZNDLP5E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.00754&json=true","fetch_graph":"https://pith.science/api/pith-number/RZNDLP5EUOAELUFVVMIFVRRSX3/graph.json","fetch_events":"https://pith.science/api/pith-number/RZNDLP5EUOAELUFVVMIFVRRSX3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RZNDLP5EUOAELUFVVMIFVRRSX3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RZNDLP5EUOAELUFVVMIFVRRSX3/action/storage_attestation","attest_author":"https://pith.science/pith/RZNDLP5EUOAELUFVVMIFVRRSX3/action/author_attestation","sign_citation":"https://pith.science/pith/RZNDLP5EUOAELUFVVMIFVRRSX3/action/citation_signature","submit_replication":"https://pith.science/pith/RZNDLP5EUOAELUFVVMIFVRRSX3/action/replication_record"}},"created_at":"2026-05-18T01:55:59.626069+00:00","updated_at":"2026-05-18T01:55:59.626069+00:00"}