{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:I6C4A3FMXGRXXEBBC2NY42KRQS","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":"fbb457cc50152fb10ae918ad082e12f2142fe3996dd28f6b9663239456d882a1","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-12-07T11:32:20Z","title_canon_sha256":"f8aacc405b78fc1686247d5d6d6f60df9de1e4cec0b98027d084416658e6b469"},"schema_version":"1.0","source":{"id":"1012.1475","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.1475","created_at":"2026-05-18T04:31:21Z"},{"alias_kind":"arxiv_version","alias_value":"1012.1475v2","created_at":"2026-05-18T04:31:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1475","created_at":"2026-05-18T04:31:21Z"},{"alias_kind":"pith_short_12","alias_value":"I6C4A3FMXGRX","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"I6C4A3FMXGRXXEBB","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"I6C4A3FM","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:325ecf868c65c0abe6feab71803e9e9b7ba00d2fcce95b8bd77c41d3072dd804","target":"graph","created_at":"2026-05-18T04:31:21Z","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":"The idea of a line bundle in classical geometry is transferred to noncommutative geometry by the idea of a Morita context. From this we can construct Z and N graded algebras, the Z graded algebra being a Hopf-Galois extension. A non-degenerate Hermitian metric gives a star structure on this algebra, and an additional star operation on the line bundle gives a star operation on the N graded algebra. In this case, we can carry out the associated circle bundle and Thom constructions. Starting with a C* algebra as base, and with some positivity assumptions, the associated circle and Thom algebras a","authors_text":"E.J. Beggs, T. Brzezinski","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-12-07T11:32:20Z","title":"Line bundles and the Thom construction in noncommutative geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1475","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":"sha256:3d0255935f3aa4181fcf2d769ab7199cf77619b646135502cb1ca4a722e37e2f","target":"record","created_at":"2026-05-18T04:31:21Z","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":"fbb457cc50152fb10ae918ad082e12f2142fe3996dd28f6b9663239456d882a1","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-12-07T11:32:20Z","title_canon_sha256":"f8aacc405b78fc1686247d5d6d6f60df9de1e4cec0b98027d084416658e6b469"},"schema_version":"1.0","source":{"id":"1012.1475","kind":"arxiv","version":2}},"canonical_sha256":"4785c06cacb9a37b9021169b8e695184a785ad13867514d10a62d002b6999eef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4785c06cacb9a37b9021169b8e695184a785ad13867514d10a62d002b6999eef","first_computed_at":"2026-05-18T04:31:21.000850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:21.000850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mRane9uP64bWARwEcfm/BZ4yr05v4Am4/1xNhuzys/FMgrjT2yYjUQh4Qd1jzo6unNaB4XwFAvh0ieE4VGfVDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:21.001335Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.1475","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d0255935f3aa4181fcf2d769ab7199cf77619b646135502cb1ca4a722e37e2f","sha256:325ecf868c65c0abe6feab71803e9e9b7ba00d2fcce95b8bd77c41d3072dd804"],"state_sha256":"fb725aae6048541f061a4d2b34f5a56b7139afced446e9f4d5b120d05a0b4f68"}