{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:3X7MU2Z7OW2HTVQ6KKEGRU6H2X","short_pith_number":"pith:3X7MU2Z7","canonical_record":{"source":{"id":"math/9906186","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"1999-06-28T04:51:29Z","cross_cats_sorted":[],"title_canon_sha256":"c65eccb4291407089f425060730037ae3c54ccbc823e87a2bdb1df6d5fa57026","abstract_canon_sha256":"991d2a2860f345617e6b5533d4aa5ef0042b870888e869b7883802b7c2c6a33c"},"schema_version":"1.0"},"canonical_sha256":"ddfeca6b3f75b479d61e528868d3c7d5df1cbebe5a08833272313ea0bee2a7bb","source":{"kind":"arxiv","id":"math/9906186","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9906186","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/9906186v1","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9906186","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"pith_short_12","alias_value":"3X7MU2Z7OW2H","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"3X7MU2Z7OW2HTVQ6","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"3X7MU2Z7","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:3X7MU2Z7OW2HTVQ6KKEGRU6H2X","target":"record","payload":{"canonical_record":{"source":{"id":"math/9906186","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"1999-06-28T04:51:29Z","cross_cats_sorted":[],"title_canon_sha256":"c65eccb4291407089f425060730037ae3c54ccbc823e87a2bdb1df6d5fa57026","abstract_canon_sha256":"991d2a2860f345617e6b5533d4aa5ef0042b870888e869b7883802b7c2c6a33c"},"schema_version":"1.0"},"canonical_sha256":"ddfeca6b3f75b479d61e528868d3c7d5df1cbebe5a08833272313ea0bee2a7bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:32.899052Z","signature_b64":"8jZ24apDsn1I3WKU0qjZz88iagPA+hdWPa2xO6J/AiOOVcBBXFAz41WzTl25o2GkS8NMVXny1/+RKBRMi+leDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddfeca6b3f75b479d61e528868d3c7d5df1cbebe5a08833272313ea0bee2a7bb","last_reissued_at":"2026-05-18T01:05:32.898424Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:32.898424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9906186","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":"2026-05-18T01:05:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9/euBx1wM/O2zSyYMor1Fnv3T8Zt0HbtYA9XIuWk++eBOlK0063dpqTqXqiW/uk4E2FQlVkkhIE3+EnNLIZQBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:57:53.919090Z"},"content_sha256":"a7357f8d56c6c56ba5acecf4c6331600a9d64ed9187189c95574aa9b0ef7f130","schema_version":"1.0","event_id":"sha256:a7357f8d56c6c56ba5acecf4c6331600a9d64ed9187189c95574aa9b0ef7f130"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:3X7MU2Z7OW2HTVQ6KKEGRU6H2X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity of operators on essential extensions of the compacts","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Arupkumar Pal","submitted_at":"1999-06-28T04:51:29Z","abstract_excerpt":"A semiregular operator on a Hilbert C^*-module, or equivalently, on the C^*-algebra of `compact' operators on it, is a closable densely defined operator whose adjoint is also densely defined. It is shown that for operators on extensions of compacts by unital or abelian C^*-algebras, semiregularity leads to regularity. Two examples coming from quantum groups are discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9906186","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":"2026-05-18T01:05:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G47GLw9g3yYvNVz9EHO+FAt2Flv4fJgEf/BPtA8TR1e+stWvXdpC/bwpbU8BnQ726JgpNwg9igTdIbB+gYvtDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:57:53.919433Z"},"content_sha256":"ca11843810ffada0da1d12c759529b56168b6af0ffa9db5ddcd9aca38bbce853","schema_version":"1.0","event_id":"sha256:ca11843810ffada0da1d12c759529b56168b6af0ffa9db5ddcd9aca38bbce853"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3X7MU2Z7OW2HTVQ6KKEGRU6H2X/bundle.json","state_url":"https://pith.science/pith/3X7MU2Z7OW2HTVQ6KKEGRU6H2X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3X7MU2Z7OW2HTVQ6KKEGRU6H2X/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":"2026-06-09T09:57:53Z","links":{"resolver":"https://pith.science/pith/3X7MU2Z7OW2HTVQ6KKEGRU6H2X","bundle":"https://pith.science/pith/3X7MU2Z7OW2HTVQ6KKEGRU6H2X/bundle.json","state":"https://pith.science/pith/3X7MU2Z7OW2HTVQ6KKEGRU6H2X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3X7MU2Z7OW2HTVQ6KKEGRU6H2X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:3X7MU2Z7OW2HTVQ6KKEGRU6H2X","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":"991d2a2860f345617e6b5533d4aa5ef0042b870888e869b7883802b7c2c6a33c","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"1999-06-28T04:51:29Z","title_canon_sha256":"c65eccb4291407089f425060730037ae3c54ccbc823e87a2bdb1df6d5fa57026"},"schema_version":"1.0","source":{"id":"math/9906186","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9906186","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/9906186v1","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9906186","created_at":"2026-05-18T01:05:32Z"},{"alias_kind":"pith_short_12","alias_value":"3X7MU2Z7OW2H","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"3X7MU2Z7OW2HTVQ6","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"3X7MU2Z7","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:ca11843810ffada0da1d12c759529b56168b6af0ffa9db5ddcd9aca38bbce853","target":"graph","created_at":"2026-05-18T01:05:32Z","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 semiregular operator on a Hilbert C^*-module, or equivalently, on the C^*-algebra of `compact' operators on it, is a closable densely defined operator whose adjoint is also densely defined. It is shown that for operators on extensions of compacts by unital or abelian C^*-algebras, semiregularity leads to regularity. Two examples coming from quantum groups are discussed.","authors_text":"Arupkumar Pal","cross_cats":[],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"1999-06-28T04:51:29Z","title":"Regularity of operators on essential extensions of the compacts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9906186","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:a7357f8d56c6c56ba5acecf4c6331600a9d64ed9187189c95574aa9b0ef7f130","target":"record","created_at":"2026-05-18T01:05:32Z","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":"991d2a2860f345617e6b5533d4aa5ef0042b870888e869b7883802b7c2c6a33c","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"1999-06-28T04:51:29Z","title_canon_sha256":"c65eccb4291407089f425060730037ae3c54ccbc823e87a2bdb1df6d5fa57026"},"schema_version":"1.0","source":{"id":"math/9906186","kind":"arxiv","version":1}},"canonical_sha256":"ddfeca6b3f75b479d61e528868d3c7d5df1cbebe5a08833272313ea0bee2a7bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddfeca6b3f75b479d61e528868d3c7d5df1cbebe5a08833272313ea0bee2a7bb","first_computed_at":"2026-05-18T01:05:32.898424Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:32.898424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8jZ24apDsn1I3WKU0qjZz88iagPA+hdWPa2xO6J/AiOOVcBBXFAz41WzTl25o2GkS8NMVXny1/+RKBRMi+leDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:32.899052Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9906186","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7357f8d56c6c56ba5acecf4c6331600a9d64ed9187189c95574aa9b0ef7f130","sha256:ca11843810ffada0da1d12c759529b56168b6af0ffa9db5ddcd9aca38bbce853"],"state_sha256":"0ee8a9f5e2428b43c36d7eade07672ae4a79471b7815623f307acfe4a1f27934"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hr3jXeg7hAYxfRCzOoolJJFe34dnJJXs0JhxurZCqQvMVoHHqYXoUWwFHwDq3x+k6xdJaE3JuDrfi4K+joUpCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T09:57:53.921209Z","bundle_sha256":"7a63c2ca8cde053d9d1c58144aa0613daa608cdadf60a665dd23a9132f729314"}}