{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:W2JIUKWZFKS42QDFGJHBONW3CH","short_pith_number":"pith:W2JIUKWZ","canonical_record":{"source":{"id":"1405.5551","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-21T20:31:16Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"aec7bd621158aa599a3160a39ec4362e710be1a65cb16b1a7096ee87fa4f6122","abstract_canon_sha256":"97083a16e58bbcc1dd3a87b6f7c180a1c96fd6ec7983adabe3945e38affb43ef"},"schema_version":"1.0"},"canonical_sha256":"b6928a2ad92aa5cd4065324e1736db11edaf729bbc4d72a1c14f40e2d40cdb4c","source":{"kind":"arxiv","id":"1405.5551","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5551","created_at":"2026-05-18T01:22:22Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5551v4","created_at":"2026-05-18T01:22:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5551","created_at":"2026-05-18T01:22:22Z"},{"alias_kind":"pith_short_12","alias_value":"W2JIUKWZFKS4","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W2JIUKWZFKS42QDF","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W2JIUKWZ","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:W2JIUKWZFKS42QDFGJHBONW3CH","target":"record","payload":{"canonical_record":{"source":{"id":"1405.5551","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-21T20:31:16Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"aec7bd621158aa599a3160a39ec4362e710be1a65cb16b1a7096ee87fa4f6122","abstract_canon_sha256":"97083a16e58bbcc1dd3a87b6f7c180a1c96fd6ec7983adabe3945e38affb43ef"},"schema_version":"1.0"},"canonical_sha256":"b6928a2ad92aa5cd4065324e1736db11edaf729bbc4d72a1c14f40e2d40cdb4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:22.180414Z","signature_b64":"yvHVaSK5wWO+6AbhJZ9ZpKRP+gOrcK47tGFm9qmZl/KudkhDtpSVms8S6u8oyZrXDpwzyr2NwDh0tFa4S37iCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6928a2ad92aa5cd4065324e1736db11edaf729bbc4d72a1c14f40e2d40cdb4c","last_reissued_at":"2026-05-18T01:22:22.179649Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:22.179649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.5551","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AXWPjwCNZbYNiRRjVSlu2e4FtlTnUjxw8rA1THxjhv2GTtyMM+2oPTdQVVJMPDQVv6XCl5sLBDPJ0Nx5QF+TBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:39:16.624134Z"},"content_sha256":"82f0f888b778dd40ca710c811d9be463e210b4339f1d1f66f2993787ea2e4501","schema_version":"1.0","event_id":"sha256:82f0f888b778dd40ca710c811d9be463e210b4339f1d1f66f2993787ea2e4501"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:W2JIUKWZFKS42QDFGJHBONW3CH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Real positivity and approximate identities in Banach algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"David P. Blecher, Narutaka Ozawa","submitted_at":"2014-05-21T20:31:16Z","abstract_excerpt":"Blecher and Read have recently introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain $C^*$-algebraic results and theories to more general algebras. In the present paper we generalize some part of this, and some other facts, to larger classes of Banach algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5551","kind":"arxiv","version":4},"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":"2026-05-18T01:22:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6xNEHQIym6cEPpqQQT0GzZ1E/M4q7r7ZWDhj/7ZmP1NGISd1QlLOsmnKj/zpA7pk32fF6pJA6x8CP2zGckdrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:39:16.624754Z"},"content_sha256":"bed9717d7e9d3571cae138979ae17d5960550b6a95c4795d1d929dbaba4945f0","schema_version":"1.0","event_id":"sha256:bed9717d7e9d3571cae138979ae17d5960550b6a95c4795d1d929dbaba4945f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W2JIUKWZFKS42QDFGJHBONW3CH/bundle.json","state_url":"https://pith.science/pith/W2JIUKWZFKS42QDFGJHBONW3CH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W2JIUKWZFKS42QDFGJHBONW3CH/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":"2026-06-06T18:39:16Z","links":{"resolver":"https://pith.science/pith/W2JIUKWZFKS42QDFGJHBONW3CH","bundle":"https://pith.science/pith/W2JIUKWZFKS42QDFGJHBONW3CH/bundle.json","state":"https://pith.science/pith/W2JIUKWZFKS42QDFGJHBONW3CH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W2JIUKWZFKS42QDFGJHBONW3CH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:W2JIUKWZFKS42QDFGJHBONW3CH","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":"97083a16e58bbcc1dd3a87b6f7c180a1c96fd6ec7983adabe3945e38affb43ef","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-21T20:31:16Z","title_canon_sha256":"aec7bd621158aa599a3160a39ec4362e710be1a65cb16b1a7096ee87fa4f6122"},"schema_version":"1.0","source":{"id":"1405.5551","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5551","created_at":"2026-05-18T01:22:22Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5551v4","created_at":"2026-05-18T01:22:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5551","created_at":"2026-05-18T01:22:22Z"},{"alias_kind":"pith_short_12","alias_value":"W2JIUKWZFKS4","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W2JIUKWZFKS42QDF","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W2JIUKWZ","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:bed9717d7e9d3571cae138979ae17d5960550b6a95c4795d1d929dbaba4945f0","target":"graph","created_at":"2026-05-18T01:22:22Z","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":"Blecher and Read have recently introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain $C^*$-algebraic results and theories to more general algebras. In the present paper we generalize some part of this, and some other facts, to larger classes of Banach algebras.","authors_text":"David P. Blecher, Narutaka Ozawa","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-21T20:31:16Z","title":"Real positivity and approximate identities in Banach algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5551","kind":"arxiv","version":4},"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":"sha256:82f0f888b778dd40ca710c811d9be463e210b4339f1d1f66f2993787ea2e4501","target":"record","created_at":"2026-05-18T01:22:22Z","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":"97083a16e58bbcc1dd3a87b6f7c180a1c96fd6ec7983adabe3945e38affb43ef","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-21T20:31:16Z","title_canon_sha256":"aec7bd621158aa599a3160a39ec4362e710be1a65cb16b1a7096ee87fa4f6122"},"schema_version":"1.0","source":{"id":"1405.5551","kind":"arxiv","version":4}},"canonical_sha256":"b6928a2ad92aa5cd4065324e1736db11edaf729bbc4d72a1c14f40e2d40cdb4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6928a2ad92aa5cd4065324e1736db11edaf729bbc4d72a1c14f40e2d40cdb4c","first_computed_at":"2026-05-18T01:22:22.179649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:22.179649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yvHVaSK5wWO+6AbhJZ9ZpKRP+gOrcK47tGFm9qmZl/KudkhDtpSVms8S6u8oyZrXDpwzyr2NwDh0tFa4S37iCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:22.180414Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.5551","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82f0f888b778dd40ca710c811d9be463e210b4339f1d1f66f2993787ea2e4501","sha256:bed9717d7e9d3571cae138979ae17d5960550b6a95c4795d1d929dbaba4945f0"],"state_sha256":"24192134d5c662549d92942d32af29664506249bfaac3b04477a36a0e4c891c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BW22Fw6dj/moejIu3ygf2xxlicCc29CSMHU3X0rUpyQo/JH/jq3YjlwFPYD5nh0O0ItSadp23mvxc66n+ZUxAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T18:39:16.627929Z","bundle_sha256":"35ae322c5459ee52ddd55133ae3552c36ce5123993480b953cc0ad2fa3038733"}}