{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:TQQRNZU4F6DZKAPCBITCQMCULZ","short_pith_number":"pith:TQQRNZU4","canonical_record":{"source":{"id":"2002.00138","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-02-01T04:47:15Z","cross_cats_sorted":[],"title_canon_sha256":"2643516e016212a760507a821eec3ac8b8503658acf910272e7957c7be46eac0","abstract_canon_sha256":"76ccd9132e9ac845cc1ca924ca1dba9913fdb5a443b7e23da88251b9184542a8"},"schema_version":"1.0"},"canonical_sha256":"9c2116e69c2f879501e20a262830545e6680565c9e74593aefce305dfe0e6a77","source":{"kind":"arxiv","id":"2002.00138","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.00138","created_at":"2026-07-05T00:37:52Z"},{"alias_kind":"arxiv_version","alias_value":"2002.00138v1","created_at":"2026-07-05T00:37:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.00138","created_at":"2026-07-05T00:37:52Z"},{"alias_kind":"pith_short_12","alias_value":"TQQRNZU4F6DZ","created_at":"2026-07-05T00:37:52Z"},{"alias_kind":"pith_short_16","alias_value":"TQQRNZU4F6DZKAPC","created_at":"2026-07-05T00:37:52Z"},{"alias_kind":"pith_short_8","alias_value":"TQQRNZU4","created_at":"2026-07-05T00:37:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:TQQRNZU4F6DZKAPCBITCQMCULZ","target":"record","payload":{"canonical_record":{"source":{"id":"2002.00138","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-02-01T04:47:15Z","cross_cats_sorted":[],"title_canon_sha256":"2643516e016212a760507a821eec3ac8b8503658acf910272e7957c7be46eac0","abstract_canon_sha256":"76ccd9132e9ac845cc1ca924ca1dba9913fdb5a443b7e23da88251b9184542a8"},"schema_version":"1.0"},"canonical_sha256":"9c2116e69c2f879501e20a262830545e6680565c9e74593aefce305dfe0e6a77","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:37:52.053952Z","signature_b64":"zeKP0WH6XtavddoW9VBoy7iEjrD50MxKNfNapNTw98ia6oqqkqKmnLkW7Mt0+oQtFXRna3kqfuHtqQMUPefSDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c2116e69c2f879501e20a262830545e6680565c9e74593aefce305dfe0e6a77","last_reissued_at":"2026-07-05T00:37:52.053568Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:37:52.053568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2002.00138","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":"2026-07-05T00:37:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FCdW36m6ozFa8gp741ub9ACMH8MYebtBPPkgFBhdIXbsswoix0MvYiCuMgh28p6jfzgUhn0CrcVSWw4Qk3akBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-19T20:31:04.451453Z"},"content_sha256":"94ddb014fc156b9a178752a05c9ecc4514fec4a807915f76bd0ee1512cb5ece1","schema_version":"1.0","event_id":"sha256:94ddb014fc156b9a178752a05c9ecc4514fec4a807915f76bd0ee1512cb5ece1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:TQQRNZU4F6DZKAPCBITCQMCULZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive linear maps and eigenvalue estimates for nonnegative matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Sharma, M. Pal, R. Sharma","submitted_at":"2020-02-01T04:47:15Z","abstract_excerpt":"We show how positive unital linear maps can be used to obtain some bounds for the eigenvalues of nonnegative matrices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.00138","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.00138/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:37:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gZHiQUiHXvSQG64p6M8dFcsHUddv3pCAjAKWC99O19FeetfHBCsDKl2YWsKt2vBAe3OV/8Ewolgej42ZAXS7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-19T20:31:04.451819Z"},"content_sha256":"94a9a964a7d44ab475b09c36b04738477c783ba34681ce6e4e35265c16a4f3d1","schema_version":"1.0","event_id":"sha256:94a9a964a7d44ab475b09c36b04738477c783ba34681ce6e4e35265c16a4f3d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TQQRNZU4F6DZKAPCBITCQMCULZ/bundle.json","state_url":"https://pith.science/pith/TQQRNZU4F6DZKAPCBITCQMCULZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TQQRNZU4F6DZKAPCBITCQMCULZ/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":"2026-07-19T20:31:04Z","links":{"resolver":"https://pith.science/pith/TQQRNZU4F6DZKAPCBITCQMCULZ","bundle":"https://pith.science/pith/TQQRNZU4F6DZKAPCBITCQMCULZ/bundle.json","state":"https://pith.science/pith/TQQRNZU4F6DZKAPCBITCQMCULZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TQQRNZU4F6DZKAPCBITCQMCULZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:TQQRNZU4F6DZKAPCBITCQMCULZ","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":"76ccd9132e9ac845cc1ca924ca1dba9913fdb5a443b7e23da88251b9184542a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-02-01T04:47:15Z","title_canon_sha256":"2643516e016212a760507a821eec3ac8b8503658acf910272e7957c7be46eac0"},"schema_version":"1.0","source":{"id":"2002.00138","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.00138","created_at":"2026-07-05T00:37:52Z"},{"alias_kind":"arxiv_version","alias_value":"2002.00138v1","created_at":"2026-07-05T00:37:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.00138","created_at":"2026-07-05T00:37:52Z"},{"alias_kind":"pith_short_12","alias_value":"TQQRNZU4F6DZ","created_at":"2026-07-05T00:37:52Z"},{"alias_kind":"pith_short_16","alias_value":"TQQRNZU4F6DZKAPC","created_at":"2026-07-05T00:37:52Z"},{"alias_kind":"pith_short_8","alias_value":"TQQRNZU4","created_at":"2026-07-05T00:37:52Z"}],"graph_snapshots":[{"event_id":"sha256:94a9a964a7d44ab475b09c36b04738477c783ba34681ce6e4e35265c16a4f3d1","target":"graph","created_at":"2026-07-05T00:37:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2002.00138/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show how positive unital linear maps can be used to obtain some bounds for the eigenvalues of nonnegative matrices.","authors_text":"A. Sharma, M. Pal, R. Sharma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-02-01T04:47:15Z","title":"Positive linear maps and eigenvalue estimates for nonnegative matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.00138","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":"sha256:94ddb014fc156b9a178752a05c9ecc4514fec4a807915f76bd0ee1512cb5ece1","target":"record","created_at":"2026-07-05T00:37:52Z","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":"76ccd9132e9ac845cc1ca924ca1dba9913fdb5a443b7e23da88251b9184542a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-02-01T04:47:15Z","title_canon_sha256":"2643516e016212a760507a821eec3ac8b8503658acf910272e7957c7be46eac0"},"schema_version":"1.0","source":{"id":"2002.00138","kind":"arxiv","version":1}},"canonical_sha256":"9c2116e69c2f879501e20a262830545e6680565c9e74593aefce305dfe0e6a77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c2116e69c2f879501e20a262830545e6680565c9e74593aefce305dfe0e6a77","first_computed_at":"2026-07-05T00:37:52.053568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:37:52.053568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zeKP0WH6XtavddoW9VBoy7iEjrD50MxKNfNapNTw98ia6oqqkqKmnLkW7Mt0+oQtFXRna3kqfuHtqQMUPefSDw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:37:52.053952Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.00138","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94ddb014fc156b9a178752a05c9ecc4514fec4a807915f76bd0ee1512cb5ece1","sha256:94a9a964a7d44ab475b09c36b04738477c783ba34681ce6e4e35265c16a4f3d1"],"state_sha256":"d89b53a04e273bda92deaef02d7733a7651b77f3e3bcaffb899ea4a13d16c3c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0QNM5YLFKvSxu8YJQDJCg4DvVs+LBhuGVBYZKfJvxx1tMe0XZ0QyBjxPZrHahH+KzofFVTprds5KGgqjC7OjDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-19T20:31:04.454356Z","bundle_sha256":"4cd24736276d244ff53eb76fe0565cedddb89d4e6739940f84818751443f48b6"}}