{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:54MDAEJN5RLHP366JF5JQV2GFJ","short_pith_number":"pith:54MDAEJN","canonical_record":{"source":{"id":"1012.5196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-23T13:29:17Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"701b8747c866d4ce9a0cbada5f32c02f92694aeee5ab7235bffe663ad31d4a81","abstract_canon_sha256":"2c2386ae866d2be5025a8609c90b49a65ed55002f1002bd6d1122a77e4582558"},"schema_version":"1.0"},"canonical_sha256":"ef1830112dec5677efde497a9857462a7bc9bb4abee81a8157e06851ee0f0ea9","source":{"kind":"arxiv","id":"1012.5196","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5196","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5196v1","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5196","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"54MDAEJN5RLH","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"54MDAEJN5RLHP366","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"54MDAEJN","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:54MDAEJN5RLHP366JF5JQV2GFJ","target":"record","payload":{"canonical_record":{"source":{"id":"1012.5196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-23T13:29:17Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"701b8747c866d4ce9a0cbada5f32c02f92694aeee5ab7235bffe663ad31d4a81","abstract_canon_sha256":"2c2386ae866d2be5025a8609c90b49a65ed55002f1002bd6d1122a77e4582558"},"schema_version":"1.0"},"canonical_sha256":"ef1830112dec5677efde497a9857462a7bc9bb4abee81a8157e06851ee0f0ea9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:35.626881Z","signature_b64":"31IfsUm9Vb+jkV2PE6hiEI/X/eFRpiD9jkf6PHumDS/0GdkdtHAitFk5ZfdMmBkKCMho5Y9tQFIECPwXNx7ZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef1830112dec5677efde497a9857462a7bc9bb4abee81a8157e06851ee0f0ea9","last_reissued_at":"2026-05-18T04:32:35.626483Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:35.626483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.5196","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":"2026-05-18T04:32:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XtsvoYUPU+hUDuiNdV6EJlbdfAPZXvn6KUgkuaOrGrn1BiptXyUJm+EAMEcLoS/x6lnPDGAqJj9dgntK1i0VDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-24T15:11:33.935554Z"},"content_sha256":"f4f0a6648f62a55bd02f71df30901adf06444de0cea1251cf5c0ed21b8c3f3db","schema_version":"1.0","event_id":"sha256:f4f0a6648f62a55bd02f71df30901adf06444de0cea1251cf5c0ed21b8c3f3db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:54MDAEJN5RLHP366JF5JQV2GFJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a Local Structure in Kaplansky Algebras. Definitions and Basic Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Alexander A. Katz","submitted_at":"2010-12-23T13:29:17Z","abstract_excerpt":"We introduce and study locally AW*-algebras (Baer locally C*-algebras) as a locally multiplicatively-convex generalization of AW*-algebras of Kaplansky. Among other basic properties of these algebras, it is established that: {\\bullet} A locally C*-algebra is a locally AW*-algebra iff there exists its Arens-Michael decomposition consisting entirely of AW*-algebras; {\\bullet} A bounded part of a locally AW*-algebra is an AW*-algebra; {\\bullet} The Spectral Theorem for locally AW*-algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5196","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":"2026-05-18T04:32:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5V3/9tC/xCjmIn61Z6tCWOMzrew9bAoRX6se1tWbX6IQg0W3hsbN1YwhdFKXBX0v7hoRkcjKBJ4m1PYU9WyzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-24T15:11:33.935894Z"},"content_sha256":"2e3464c75267adb27c64964478ad90cb11e03106cb78ff8ee063cd94b12860c4","schema_version":"1.0","event_id":"sha256:2e3464c75267adb27c64964478ad90cb11e03106cb78ff8ee063cd94b12860c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/54MDAEJN5RLHP366JF5JQV2GFJ/bundle.json","state_url":"https://pith.science/pith/54MDAEJN5RLHP366JF5JQV2GFJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/54MDAEJN5RLHP366JF5JQV2GFJ/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":"2026-07-24T15:11:33Z","links":{"resolver":"https://pith.science/pith/54MDAEJN5RLHP366JF5JQV2GFJ","bundle":"https://pith.science/pith/54MDAEJN5RLHP366JF5JQV2GFJ/bundle.json","state":"https://pith.science/pith/54MDAEJN5RLHP366JF5JQV2GFJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/54MDAEJN5RLHP366JF5JQV2GFJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:54MDAEJN5RLHP366JF5JQV2GFJ","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":"2c2386ae866d2be5025a8609c90b49a65ed55002f1002bd6d1122a77e4582558","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-23T13:29:17Z","title_canon_sha256":"701b8747c866d4ce9a0cbada5f32c02f92694aeee5ab7235bffe663ad31d4a81"},"schema_version":"1.0","source":{"id":"1012.5196","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5196","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5196v1","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5196","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"54MDAEJN5RLH","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"54MDAEJN5RLHP366","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"54MDAEJN","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:2e3464c75267adb27c64964478ad90cb11e03106cb78ff8ee063cd94b12860c4","target":"graph","created_at":"2026-05-18T04:32:35Z","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":"We introduce and study locally AW*-algebras (Baer locally C*-algebras) as a locally multiplicatively-convex generalization of AW*-algebras of Kaplansky. Among other basic properties of these algebras, it is established that: {\\bullet} A locally C*-algebra is a locally AW*-algebra iff there exists its Arens-Michael decomposition consisting entirely of AW*-algebras; {\\bullet} A bounded part of a locally AW*-algebra is an AW*-algebra; {\\bullet} The Spectral Theorem for locally AW*-algebras.","authors_text":"Alexander A. Katz","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-23T13:29:17Z","title":"On a Local Structure in Kaplansky Algebras. Definitions and Basic Properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5196","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:f4f0a6648f62a55bd02f71df30901adf06444de0cea1251cf5c0ed21b8c3f3db","target":"record","created_at":"2026-05-18T04:32:35Z","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":"2c2386ae866d2be5025a8609c90b49a65ed55002f1002bd6d1122a77e4582558","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-23T13:29:17Z","title_canon_sha256":"701b8747c866d4ce9a0cbada5f32c02f92694aeee5ab7235bffe663ad31d4a81"},"schema_version":"1.0","source":{"id":"1012.5196","kind":"arxiv","version":1}},"canonical_sha256":"ef1830112dec5677efde497a9857462a7bc9bb4abee81a8157e06851ee0f0ea9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef1830112dec5677efde497a9857462a7bc9bb4abee81a8157e06851ee0f0ea9","first_computed_at":"2026-05-18T04:32:35.626483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:35.626483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"31IfsUm9Vb+jkV2PE6hiEI/X/eFRpiD9jkf6PHumDS/0GdkdtHAitFk5ZfdMmBkKCMho5Y9tQFIECPwXNx7ZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:35.626881Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5196","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4f0a6648f62a55bd02f71df30901adf06444de0cea1251cf5c0ed21b8c3f3db","sha256:2e3464c75267adb27c64964478ad90cb11e03106cb78ff8ee063cd94b12860c4"],"state_sha256":"314c39bed320b9d5d0795005ffa19aadf76f76559f0fee6570ff13672b086c16"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8efEd7EzTYuaJGJOEBCShVa8LyK4VbKvkAQ50caTYBKgp6u1om6P93h8/KdJ+ybuV2NDePpQLyDGcRy8JgRnBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-24T15:11:33.937918Z","bundle_sha256":"6fb6a472e55b2ae08aa477930103b2d68748248355941292e9ad85d8581fea75"}}