{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OXO6FBM6445BRRZYAYQHMU2XCR","short_pith_number":"pith:OXO6FBM6","canonical_record":{"source":{"id":"1307.7119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-26T18:24:16Z","cross_cats_sorted":[],"title_canon_sha256":"6a80fef321779232e88c3d918520bd59ba5ae65ca587dc5018279621e5c179b4","abstract_canon_sha256":"f90890a5eb98af7114b21fc439f996a0b819a5321ffb2e434a4d92724a142315"},"schema_version":"1.0"},"canonical_sha256":"75dde2859ee73a18c73806207653571475ae6d242e186766a7f8a3e11e70a1fa","source":{"kind":"arxiv","id":"1307.7119","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7119","created_at":"2026-05-18T03:17:25Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7119v1","created_at":"2026-05-18T03:17:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7119","created_at":"2026-05-18T03:17:25Z"},{"alias_kind":"pith_short_12","alias_value":"OXO6FBM6445B","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OXO6FBM6445BRRZY","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OXO6FBM6","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OXO6FBM6445BRRZYAYQHMU2XCR","target":"record","payload":{"canonical_record":{"source":{"id":"1307.7119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-26T18:24:16Z","cross_cats_sorted":[],"title_canon_sha256":"6a80fef321779232e88c3d918520bd59ba5ae65ca587dc5018279621e5c179b4","abstract_canon_sha256":"f90890a5eb98af7114b21fc439f996a0b819a5321ffb2e434a4d92724a142315"},"schema_version":"1.0"},"canonical_sha256":"75dde2859ee73a18c73806207653571475ae6d242e186766a7f8a3e11e70a1fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:25.307029Z","signature_b64":"V7rvHXVhNFs+I/RiCWQyhGTa1CXXr7NDOdG2TvoI4SVhk/+MD3J75CcSathesl3UEXgY+Puu10owO2H4+MBBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75dde2859ee73a18c73806207653571475ae6d242e186766a7f8a3e11e70a1fa","last_reissued_at":"2026-05-18T03:17:25.306541Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:25.306541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.7119","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":"2026-05-18T03:17:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wl56Ak1Bw7LN5ouVGW6u9L2rOXo6Kyiz3KuHz/ZM0epF98KoMUefg0pyknciD82mANnGJ3/mcGba8+n+Eti2Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:35:13.930230Z"},"content_sha256":"dc5257b61a73d334e9c1a347288a9ffced256d46133a2678b8e08782bafa7c82","schema_version":"1.0","event_id":"sha256:dc5257b61a73d334e9c1a347288a9ffced256d46133a2678b8e08782bafa7c82"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OXO6FBM6445BRRZYAYQHMU2XCR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decay properties for functions of matrices over $C^*$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Michele Benzi, Paola Boito","submitted_at":"2013-07-26T18:24:16Z","abstract_excerpt":"We extend previous results on the exponential off-diagonal decay of the entries of analytic functions of banded and sparse matrices to the case where the matrix entries are elements of a $C^*$-algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7119","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":"2026-05-18T03:17:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"krmBZVLgnJ9Tw6bY+5vvBLJ23LZjcm3sDvpPN+CkDUOLypYA0cJHL+7W7pOTD0j8AMr9ECHl6tk4irm1GhDyCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:35:13.930598Z"},"content_sha256":"accbdea4fb7f99f0904c7c0a84d23f6d339818ca4f76ac554524e8d959d6a05b","schema_version":"1.0","event_id":"sha256:accbdea4fb7f99f0904c7c0a84d23f6d339818ca4f76ac554524e8d959d6a05b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OXO6FBM6445BRRZYAYQHMU2XCR/bundle.json","state_url":"https://pith.science/pith/OXO6FBM6445BRRZYAYQHMU2XCR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OXO6FBM6445BRRZYAYQHMU2XCR/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":"2026-06-23T00:35:13Z","links":{"resolver":"https://pith.science/pith/OXO6FBM6445BRRZYAYQHMU2XCR","bundle":"https://pith.science/pith/OXO6FBM6445BRRZYAYQHMU2XCR/bundle.json","state":"https://pith.science/pith/OXO6FBM6445BRRZYAYQHMU2XCR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OXO6FBM6445BRRZYAYQHMU2XCR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OXO6FBM6445BRRZYAYQHMU2XCR","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":"f90890a5eb98af7114b21fc439f996a0b819a5321ffb2e434a4d92724a142315","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-26T18:24:16Z","title_canon_sha256":"6a80fef321779232e88c3d918520bd59ba5ae65ca587dc5018279621e5c179b4"},"schema_version":"1.0","source":{"id":"1307.7119","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7119","created_at":"2026-05-18T03:17:25Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7119v1","created_at":"2026-05-18T03:17:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7119","created_at":"2026-05-18T03:17:25Z"},{"alias_kind":"pith_short_12","alias_value":"OXO6FBM6445B","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OXO6FBM6445BRRZY","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OXO6FBM6","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:accbdea4fb7f99f0904c7c0a84d23f6d339818ca4f76ac554524e8d959d6a05b","target":"graph","created_at":"2026-05-18T03:17:25Z","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 extend previous results on the exponential off-diagonal decay of the entries of analytic functions of banded and sparse matrices to the case where the matrix entries are elements of a $C^*$-algebra.","authors_text":"Michele Benzi, Paola Boito","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-26T18:24:16Z","title":"Decay properties for functions of matrices over $C^*$-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7119","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:dc5257b61a73d334e9c1a347288a9ffced256d46133a2678b8e08782bafa7c82","target":"record","created_at":"2026-05-18T03:17:25Z","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":"f90890a5eb98af7114b21fc439f996a0b819a5321ffb2e434a4d92724a142315","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-26T18:24:16Z","title_canon_sha256":"6a80fef321779232e88c3d918520bd59ba5ae65ca587dc5018279621e5c179b4"},"schema_version":"1.0","source":{"id":"1307.7119","kind":"arxiv","version":1}},"canonical_sha256":"75dde2859ee73a18c73806207653571475ae6d242e186766a7f8a3e11e70a1fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75dde2859ee73a18c73806207653571475ae6d242e186766a7f8a3e11e70a1fa","first_computed_at":"2026-05-18T03:17:25.306541Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:25.306541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V7rvHXVhNFs+I/RiCWQyhGTa1CXXr7NDOdG2TvoI4SVhk/+MD3J75CcSathesl3UEXgY+Puu10owO2H4+MBBAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:25.307029Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.7119","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc5257b61a73d334e9c1a347288a9ffced256d46133a2678b8e08782bafa7c82","sha256:accbdea4fb7f99f0904c7c0a84d23f6d339818ca4f76ac554524e8d959d6a05b"],"state_sha256":"85d2efa765ed6a2c5bb1a25de310725deba0fe863b8cd735f342f592a2298cf9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dY3DdOqcapLYrWfvgsMyAzEOgJrFBDy+rN3uYIt2hFa+hoCUC+bPQy/GJbI/23jiejJumUPYuLZVM2j0c5WDDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T00:35:13.932578Z","bundle_sha256":"e2a3c05ae049e68a0945a30107de152be88bc58357eba6dfed0df7c9d4cb88a6"}}