{"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"}