{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:45DAXUQZSGR4T5YNNVINDARMRL","short_pith_number":"pith:45DAXUQZ","canonical_record":{"source":{"id":"1408.4634","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-08-20T12:53:59Z","cross_cats_sorted":[],"title_canon_sha256":"15a68d678d5df35b0196ac9f999113554888bf1a2258c87474e53b6a53063091","abstract_canon_sha256":"d6e9fd4964c86dfc2dfd66ee4335ca7d6b4c0aaebf65b7be00cb0f9b44041c7e"},"schema_version":"1.0"},"canonical_sha256":"e7460bd21991a3c9f70d6d50d1822c8aee44d55246815dbd0058a57b488e8d46","source":{"kind":"arxiv","id":"1408.4634","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4634","created_at":"2026-05-18T01:16:07Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4634v3","created_at":"2026-05-18T01:16:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4634","created_at":"2026-05-18T01:16:07Z"},{"alias_kind":"pith_short_12","alias_value":"45DAXUQZSGR4","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"45DAXUQZSGR4T5YN","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"45DAXUQZ","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:45DAXUQZSGR4T5YNNVINDARMRL","target":"record","payload":{"canonical_record":{"source":{"id":"1408.4634","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-08-20T12:53:59Z","cross_cats_sorted":[],"title_canon_sha256":"15a68d678d5df35b0196ac9f999113554888bf1a2258c87474e53b6a53063091","abstract_canon_sha256":"d6e9fd4964c86dfc2dfd66ee4335ca7d6b4c0aaebf65b7be00cb0f9b44041c7e"},"schema_version":"1.0"},"canonical_sha256":"e7460bd21991a3c9f70d6d50d1822c8aee44d55246815dbd0058a57b488e8d46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:07.439211Z","signature_b64":"ZJifqSb56S3TmaxgvNFR1jKeaI1el+oUjeKjpQvN9V7ZhYS62xMOAcnkjXB4hVTg/pPePbzIpc/WvfcB1uYKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7460bd21991a3c9f70d6d50d1822c8aee44d55246815dbd0058a57b488e8d46","last_reissued_at":"2026-05-18T01:16:07.438644Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:07.438644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.4634","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0/B5geak9lLREIeM+uGqg2i7jOx71rrLYJcLwZQ5kZId2LIsfUkW8paXn8dHlb82WYEB0Tn56fSA92L6tccJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:15:50.153021Z"},"content_sha256":"3988f946dfc71d06a6a6aa5a8774a4f4257ebfd623ac28fcf76aca0f13da6f7a","schema_version":"1.0","event_id":"sha256:3988f946dfc71d06a6a6aa5a8774a4f4257ebfd623ac28fcf76aca0f13da6f7a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:45DAXUQZSGR4T5YNNVINDARMRL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Further results on $B$-tensors with application to the location of real eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Lu Ye, Zhongming Chen","submitted_at":"2014-08-20T12:53:59Z","abstract_excerpt":"In this paper, we give a further study on $B$-tensors and introduce doubly $B$-tensors that contain $B$-tensors. We show that they have similar properties, including their decompositions and strong relationship with strictly (doubly) diagonally dominated tensors. As an application, the properties of $B$-tensors are used to localize real eigenvalues of some tensors, which would be very useful in verifying the positive semi-definiteness of a tensor."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4634","kind":"arxiv","version":3},"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":"2026-05-18T01:16:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jMqhButnRPyQoNh9R1gSBeBh4xVdDKQjfhPjDkaQvYPNrA6eQ8dNPNQhfI1WHaRxcjoARSvlfvs/iOb3U17wBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:15:50.153381Z"},"content_sha256":"c04a0f6ed6deaec95f04eb0abf347d7b2e07b5a8b9d61f0f1852656e0009d4b1","schema_version":"1.0","event_id":"sha256:c04a0f6ed6deaec95f04eb0abf347d7b2e07b5a8b9d61f0f1852656e0009d4b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/45DAXUQZSGR4T5YNNVINDARMRL/bundle.json","state_url":"https://pith.science/pith/45DAXUQZSGR4T5YNNVINDARMRL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/45DAXUQZSGR4T5YNNVINDARMRL/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":"2026-05-28T02:15:50Z","links":{"resolver":"https://pith.science/pith/45DAXUQZSGR4T5YNNVINDARMRL","bundle":"https://pith.science/pith/45DAXUQZSGR4T5YNNVINDARMRL/bundle.json","state":"https://pith.science/pith/45DAXUQZSGR4T5YNNVINDARMRL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/45DAXUQZSGR4T5YNNVINDARMRL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:45DAXUQZSGR4T5YNNVINDARMRL","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":"d6e9fd4964c86dfc2dfd66ee4335ca7d6b4c0aaebf65b7be00cb0f9b44041c7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-08-20T12:53:59Z","title_canon_sha256":"15a68d678d5df35b0196ac9f999113554888bf1a2258c87474e53b6a53063091"},"schema_version":"1.0","source":{"id":"1408.4634","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4634","created_at":"2026-05-18T01:16:07Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4634v3","created_at":"2026-05-18T01:16:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4634","created_at":"2026-05-18T01:16:07Z"},{"alias_kind":"pith_short_12","alias_value":"45DAXUQZSGR4","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"45DAXUQZSGR4T5YN","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"45DAXUQZ","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:c04a0f6ed6deaec95f04eb0abf347d7b2e07b5a8b9d61f0f1852656e0009d4b1","target":"graph","created_at":"2026-05-18T01:16:07Z","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":"In this paper, we give a further study on $B$-tensors and introduce doubly $B$-tensors that contain $B$-tensors. We show that they have similar properties, including their decompositions and strong relationship with strictly (doubly) diagonally dominated tensors. As an application, the properties of $B$-tensors are used to localize real eigenvalues of some tensors, which would be very useful in verifying the positive semi-definiteness of a tensor.","authors_text":"Lu Ye, Zhongming Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-08-20T12:53:59Z","title":"Further results on $B$-tensors with application to the location of real eigenvalues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4634","kind":"arxiv","version":3},"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":"sha256:3988f946dfc71d06a6a6aa5a8774a4f4257ebfd623ac28fcf76aca0f13da6f7a","target":"record","created_at":"2026-05-18T01:16:07Z","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":"d6e9fd4964c86dfc2dfd66ee4335ca7d6b4c0aaebf65b7be00cb0f9b44041c7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-08-20T12:53:59Z","title_canon_sha256":"15a68d678d5df35b0196ac9f999113554888bf1a2258c87474e53b6a53063091"},"schema_version":"1.0","source":{"id":"1408.4634","kind":"arxiv","version":3}},"canonical_sha256":"e7460bd21991a3c9f70d6d50d1822c8aee44d55246815dbd0058a57b488e8d46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7460bd21991a3c9f70d6d50d1822c8aee44d55246815dbd0058a57b488e8d46","first_computed_at":"2026-05-18T01:16:07.438644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:07.438644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZJifqSb56S3TmaxgvNFR1jKeaI1el+oUjeKjpQvN9V7ZhYS62xMOAcnkjXB4hVTg/pPePbzIpc/WvfcB1uYKCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:07.439211Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4634","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3988f946dfc71d06a6a6aa5a8774a4f4257ebfd623ac28fcf76aca0f13da6f7a","sha256:c04a0f6ed6deaec95f04eb0abf347d7b2e07b5a8b9d61f0f1852656e0009d4b1"],"state_sha256":"6b0798c994663bf521cb499fd0e1316c9c1eda46f606274fce19ef9ebe14e2b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8/RymZtOjCyPXEMayVZoORerUc16FWCuGj0kwU1EebUnXVuHQooRfxEfl03M/qX6U6k8F9egtCR6Gne+eDrUAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:15:50.155428Z","bundle_sha256":"42eb35cd35e005bc01e41e8ab86c85f8d4849b662f907d3b7c79792bf69cb950"}}