{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:K46G3EYZIO75I5EMPZNBW5L4HE","short_pith_number":"pith:K46G3EYZ","canonical_record":{"source":{"id":"math/9807052","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"1998-07-10T19:15:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d9389bb8b6a8c1fd4f313228310c19db42e41278da1235322bd102f3e4e808ba","abstract_canon_sha256":"019600dc9b79fa394b69794172dbbd9269719dd61f110786a778759255793253"},"schema_version":"1.0"},"canonical_sha256":"573c6d931943bfd4748c7e5a1b757c3912c014efe053cc5dae9b992aba56bd65","source":{"kind":"arxiv","id":"math/9807052","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9807052","created_at":"2026-05-18T04:33:36Z"},{"alias_kind":"arxiv_version","alias_value":"math/9807052v1","created_at":"2026-05-18T04:33:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9807052","created_at":"2026-05-18T04:33:36Z"},{"alias_kind":"pith_short_12","alias_value":"K46G3EYZIO75","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"K46G3EYZIO75I5EM","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"K46G3EYZ","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:K46G3EYZIO75I5EMPZNBW5L4HE","target":"record","payload":{"canonical_record":{"source":{"id":"math/9807052","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"1998-07-10T19:15:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d9389bb8b6a8c1fd4f313228310c19db42e41278da1235322bd102f3e4e808ba","abstract_canon_sha256":"019600dc9b79fa394b69794172dbbd9269719dd61f110786a778759255793253"},"schema_version":"1.0"},"canonical_sha256":"573c6d931943bfd4748c7e5a1b757c3912c014efe053cc5dae9b992aba56bd65","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:36.835800Z","signature_b64":"5zjxZhbmQKMYiPxYGJz4KaeetWYBYZ8OHU6Fe+nUdpJvrHnFldPBIy+HtEE3Vj9wKAntNicZCxs59pa4XzSZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"573c6d931943bfd4748c7e5a1b757c3912c014efe053cc5dae9b992aba56bd65","last_reissued_at":"2026-05-18T04:33:36.835255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:36.835255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9807052","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:33:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z91hx6wFnZliJl58QvxuSvNdcvyRtkeyLu2vb+Q0f92uniAuryoQyqMTl/WSWVLK8EPW0o1OqgzSsxIT7c4sCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:32:14.637190Z"},"content_sha256":"6c522f897cc393603354aa38a9c30553d0af735b7c97e77c91f122a942e091fd","schema_version":"1.0","event_id":"sha256:6c522f897cc393603354aa38a9c30553d0af735b7c97e77c91f122a942e091fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:K46G3EYZIO75I5EMPZNBW5L4HE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Line bundles on quantum spheres","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Shahn Majid, Tomasz Brzezinski","submitted_at":"1998-07-10T19:15:29Z","abstract_excerpt":"The (left coalgebra) line bundle associated to the quantum Hopf fibration of any quantum two-sphere is shown to be a finitely generated projective module. The corresponding projector is constructed and its monopole charge is computed. It is shown that the Dirac $q$-monopole connection on any quantum two-sphere induces the Grassmannian connection built with this projector."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9807052","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:33:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kc/6slNphED112oObTHwghHjyM7aQ5k4sQYPJaCQC8oT+ZlILzzS6CsGKHV5eEfi2Z3zgEOlSudHBlgGKHO5Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:32:14.637885Z"},"content_sha256":"7a045ff4324a6d48d9187483d78bdebe8299b3ecb51d64a8dda9ed5e7c56575c","schema_version":"1.0","event_id":"sha256:7a045ff4324a6d48d9187483d78bdebe8299b3ecb51d64a8dda9ed5e7c56575c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K46G3EYZIO75I5EMPZNBW5L4HE/bundle.json","state_url":"https://pith.science/pith/K46G3EYZIO75I5EMPZNBW5L4HE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K46G3EYZIO75I5EMPZNBW5L4HE/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":"2026-06-07T21:32:14Z","links":{"resolver":"https://pith.science/pith/K46G3EYZIO75I5EMPZNBW5L4HE","bundle":"https://pith.science/pith/K46G3EYZIO75I5EMPZNBW5L4HE/bundle.json","state":"https://pith.science/pith/K46G3EYZIO75I5EMPZNBW5L4HE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K46G3EYZIO75I5EMPZNBW5L4HE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:K46G3EYZIO75I5EMPZNBW5L4HE","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":"019600dc9b79fa394b69794172dbbd9269719dd61f110786a778759255793253","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"1998-07-10T19:15:29Z","title_canon_sha256":"d9389bb8b6a8c1fd4f313228310c19db42e41278da1235322bd102f3e4e808ba"},"schema_version":"1.0","source":{"id":"math/9807052","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9807052","created_at":"2026-05-18T04:33:36Z"},{"alias_kind":"arxiv_version","alias_value":"math/9807052v1","created_at":"2026-05-18T04:33:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9807052","created_at":"2026-05-18T04:33:36Z"},{"alias_kind":"pith_short_12","alias_value":"K46G3EYZIO75","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"K46G3EYZIO75I5EM","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"K46G3EYZ","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:7a045ff4324a6d48d9187483d78bdebe8299b3ecb51d64a8dda9ed5e7c56575c","target":"graph","created_at":"2026-05-18T04:33:36Z","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 (left coalgebra) line bundle associated to the quantum Hopf fibration of any quantum two-sphere is shown to be a finitely generated projective module. The corresponding projector is constructed and its monopole charge is computed. It is shown that the Dirac $q$-monopole connection on any quantum two-sphere induces the Grassmannian connection built with this projector.","authors_text":"Shahn Majid, Tomasz Brzezinski","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"1998-07-10T19:15:29Z","title":"Line bundles on quantum spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9807052","kind":"arxiv","version":1},"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":"sha256:6c522f897cc393603354aa38a9c30553d0af735b7c97e77c91f122a942e091fd","target":"record","created_at":"2026-05-18T04:33:36Z","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":"019600dc9b79fa394b69794172dbbd9269719dd61f110786a778759255793253","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"1998-07-10T19:15:29Z","title_canon_sha256":"d9389bb8b6a8c1fd4f313228310c19db42e41278da1235322bd102f3e4e808ba"},"schema_version":"1.0","source":{"id":"math/9807052","kind":"arxiv","version":1}},"canonical_sha256":"573c6d931943bfd4748c7e5a1b757c3912c014efe053cc5dae9b992aba56bd65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"573c6d931943bfd4748c7e5a1b757c3912c014efe053cc5dae9b992aba56bd65","first_computed_at":"2026-05-18T04:33:36.835255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:36.835255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5zjxZhbmQKMYiPxYGJz4KaeetWYBYZ8OHU6Fe+nUdpJvrHnFldPBIy+HtEE3Vj9wKAntNicZCxs59pa4XzSZCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:36.835800Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9807052","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c522f897cc393603354aa38a9c30553d0af735b7c97e77c91f122a942e091fd","sha256:7a045ff4324a6d48d9187483d78bdebe8299b3ecb51d64a8dda9ed5e7c56575c"],"state_sha256":"45ee6c8fdeacdb5b6f6bc5e4ab5c2d9c69d4738048e9c61beff06839d0a321b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HhIMTNZ1aZAVtOCQNlib5w9r815wowbncoS28H6btWFZZKaqFbceqSAPZp+Lo6BL2RQMCh/Yi1Ljv2nv2Qz/Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T21:32:14.641608Z","bundle_sha256":"e659cfff5c00a44ce4f6b49db12dfddb7e06eddd93eef22f1c063420e4e1cff6"}}