{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RZNDLP5EUOAELUFVVMIFVRRSX3","short_pith_number":"pith:RZNDLP5E","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"},"canonical_sha256":"8e5a35bfa4a38045d0b5ab105ac632bedac7ff79162bc993501a9e59cf0a35f3","source":{"kind":"arxiv","id":"1503.00754","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00754","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00754v2","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00754","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"RZNDLP5EUOAE","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RZNDLP5EUOAELUFV","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RZNDLP5E","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RZNDLP5EUOAELUFVVMIFVRRSX3","target":"record","payload":{"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"},"canonical_sha256":"8e5a35bfa4a38045d0b5ab105ac632bedac7ff79162bc993501a9e59cf0a35f3","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"},"source_kind":"arxiv","source_id":"1503.00754","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:55:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pyj6lwketZoC8qqdSiOdWIEkStFZ2eznJSLGxOJGbhwceNZEEiUH8Jy+7gKzpJeEjbnyqfBeAYHg3PuNzdqoBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:54:15.997881Z"},"content_sha256":"4f525dc1428e1ea248a1d1573a613d597bc38a6ccb6aa487abed413e0ebcc521","schema_version":"1.0","event_id":"sha256:4f525dc1428e1ea248a1d1573a613d597bc38a6ccb6aa487abed413e0ebcc521"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RZNDLP5EUOAELUFVVMIFVRRSX3","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:55:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3S7sbGPnwyF2Ndtw82xwJqnz7ayyIqXqG/wC6y34rWZ8EwW8FaD1SYv1koKe89khrFwNCqx0yAvVQNKcn/3jDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:54:15.998544Z"},"content_sha256":"6523795e21fff1dcd0d6387bbc9aa38977a36fce4dc524400fbce5fc1d448554","schema_version":"1.0","event_id":"sha256:6523795e21fff1dcd0d6387bbc9aa38977a36fce4dc524400fbce5fc1d448554"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RZNDLP5EUOAELUFVVMIFVRRSX3/bundle.json","state_url":"https://pith.science/pith/RZNDLP5EUOAELUFVVMIFVRRSX3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RZNDLP5EUOAELUFVVMIFVRRSX3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T04:54:16Z","links":{"resolver":"https://pith.science/pith/RZNDLP5EUOAELUFVVMIFVRRSX3","bundle":"https://pith.science/pith/RZNDLP5EUOAELUFVVMIFVRRSX3/bundle.json","state":"https://pith.science/pith/RZNDLP5EUOAELUFVVMIFVRRSX3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RZNDLP5EUOAELUFVVMIFVRRSX3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RZNDLP5EUOAELUFVVMIFVRRSX3","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":"8f8ed4d28ac27e457dec4231c9273b7d171d6be086d6482559c05fb93e6b21b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-02T21:28:31Z","title_canon_sha256":"3f99a55386d79d9fa35b8c831139afd84548b9215d769a3c12e4b050a17d66ce"},"schema_version":"1.0","source":{"id":"1503.00754","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00754","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00754v2","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00754","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"RZNDLP5EUOAE","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RZNDLP5EUOAELUFV","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RZNDLP5E","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:6523795e21fff1dcd0d6387bbc9aa38977a36fce4dc524400fbce5fc1d448554","target":"graph","created_at":"2026-05-18T01:55:59Z","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":"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","authors_text":"Michaela Vancliff, Richard G. Chandler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-02T21:28:31Z","title":"The One-Dimensional Line Scheme of a Certain Family of Quantum ${\\mathbb P}^3$s"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00754","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":"sha256:4f525dc1428e1ea248a1d1573a613d597bc38a6ccb6aa487abed413e0ebcc521","target":"record","created_at":"2026-05-18T01:55:59Z","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":"8f8ed4d28ac27e457dec4231c9273b7d171d6be086d6482559c05fb93e6b21b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-02T21:28:31Z","title_canon_sha256":"3f99a55386d79d9fa35b8c831139afd84548b9215d769a3c12e4b050a17d66ce"},"schema_version":"1.0","source":{"id":"1503.00754","kind":"arxiv","version":2}},"canonical_sha256":"8e5a35bfa4a38045d0b5ab105ac632bedac7ff79162bc993501a9e59cf0a35f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e5a35bfa4a38045d0b5ab105ac632bedac7ff79162bc993501a9e59cf0a35f3","first_computed_at":"2026-05-18T01:55:59.626010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:59.626010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z2PFK9MVP5KLxw9qZp+WJBgGMJODQHieSPt7kI8nxDf8d1nRcuS/rb22MJaqeInKU0yewLkUGznizz4RWM20Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:59.626419Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00754","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f525dc1428e1ea248a1d1573a613d597bc38a6ccb6aa487abed413e0ebcc521","sha256:6523795e21fff1dcd0d6387bbc9aa38977a36fce4dc524400fbce5fc1d448554"],"state_sha256":"7f4f0858a3820e33b50d89eb0d59d4a611eaf36860860af2f34363454b72e858"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pw5Ms1qsQR7hDFHDrpmdhcbx1BEfxMMoyfFCCu0wbbQfZKrk+y8pLLC0zsfg56yISLcWgd+4RJ6VvHr1QXkNAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T04:54:16.002201Z","bundle_sha256":"1398b47c6ed3c15b4e7872091fdf31b73e9e5b834a966b63cdacfd2552072e01"}}