{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DOV5H7UTJJXTU4I7BC7KCISUVZ","short_pith_number":"pith:DOV5H7UT","canonical_record":{"source":{"id":"1404.4991","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-04-19T22:03:45Z","cross_cats_sorted":[],"title_canon_sha256":"2305531f28e44f3a71c5b3afa989231088d5e3947514ce3d48f62ff6d6be3228","abstract_canon_sha256":"093d851a5b77029588874a2ad1c3caf43c4d92616f90f831679a4fd3afe39490"},"schema_version":"1.0"},"canonical_sha256":"1babd3fe934a6f3a711f08bea12254ae7f04fa861599e8c1e11e7128b1cddad1","source":{"kind":"arxiv","id":"1404.4991","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4991","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4991v2","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4991","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"pith_short_12","alias_value":"DOV5H7UTJJXT","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DOV5H7UTJJXTU4I7","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DOV5H7UT","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DOV5H7UTJJXTU4I7BC7KCISUVZ","target":"record","payload":{"canonical_record":{"source":{"id":"1404.4991","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-04-19T22:03:45Z","cross_cats_sorted":[],"title_canon_sha256":"2305531f28e44f3a71c5b3afa989231088d5e3947514ce3d48f62ff6d6be3228","abstract_canon_sha256":"093d851a5b77029588874a2ad1c3caf43c4d92616f90f831679a4fd3afe39490"},"schema_version":"1.0"},"canonical_sha256":"1babd3fe934a6f3a711f08bea12254ae7f04fa861599e8c1e11e7128b1cddad1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:54.414309Z","signature_b64":"F9fModk7TVOErA2saMadRKe415knr8lAeZ3gOyKIgkL7fA+Mbgioa7sgijvqEfYpZh6UiQwgsL0fWWiJD++RDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1babd3fe934a6f3a711f08bea12254ae7f04fa861599e8c1e11e7128b1cddad1","last_reissued_at":"2026-05-18T01:22:54.413850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:54.413850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.4991","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6+LDAkS4m6RlYlwXw19/hCU1yZXUlQ2PTiySzDYnEQ+b/sbLRRhPmqPUo2q4sZh0pURkCPo5orxM6/aWmBofBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:50:27.440192Z"},"content_sha256":"7cbaa3449e77515fa40c30b576d89160cf5012d799dda4e76b6df06167046cd3","schema_version":"1.0","event_id":"sha256:7cbaa3449e77515fa40c30b576d89160cf5012d799dda4e76b6df06167046cd3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DOV5H7UTJJXTU4I7BC7KCISUVZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral gap estimates for some block matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Ivan Veselic, Kresimir Veselic","submitted_at":"2014-04-19T22:03:45Z","abstract_excerpt":"We estimate the size of the spectral gap at zero for some Hermitian block matrices. Included are quasi-definite matrices, quasi-semidefinite matrices (the closure of the set of the quasi-definite matrices) and some related block matrices which need not belong to either of these classes. Matrices of such structure arise in quantum models of possibly disordered systems with supersymmetry or graphene like symmetry. Some of the results immediately extend to infinite dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4991","kind":"arxiv","version":2},"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":"2026-05-18T01:22:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DdpCm9Eh89VB+S2sSodCtIqCVtd7dN2XWmkLpR1maFjyUVVlBHk7A7KnWjRdUyO02Pkz4fl/tyJ83nzbMqr9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:50:27.440549Z"},"content_sha256":"5e9ad5de011be3de190ab3f4e867412013a7986dd3c3e434c33652b2cfc53560","schema_version":"1.0","event_id":"sha256:5e9ad5de011be3de190ab3f4e867412013a7986dd3c3e434c33652b2cfc53560"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DOV5H7UTJJXTU4I7BC7KCISUVZ/bundle.json","state_url":"https://pith.science/pith/DOV5H7UTJJXTU4I7BC7KCISUVZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DOV5H7UTJJXTU4I7BC7KCISUVZ/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":"2026-06-03T15:50:27Z","links":{"resolver":"https://pith.science/pith/DOV5H7UTJJXTU4I7BC7KCISUVZ","bundle":"https://pith.science/pith/DOV5H7UTJJXTU4I7BC7KCISUVZ/bundle.json","state":"https://pith.science/pith/DOV5H7UTJJXTU4I7BC7KCISUVZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DOV5H7UTJJXTU4I7BC7KCISUVZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DOV5H7UTJJXTU4I7BC7KCISUVZ","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":"093d851a5b77029588874a2ad1c3caf43c4d92616f90f831679a4fd3afe39490","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-04-19T22:03:45Z","title_canon_sha256":"2305531f28e44f3a71c5b3afa989231088d5e3947514ce3d48f62ff6d6be3228"},"schema_version":"1.0","source":{"id":"1404.4991","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4991","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4991v2","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4991","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"pith_short_12","alias_value":"DOV5H7UTJJXT","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DOV5H7UTJJXTU4I7","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DOV5H7UT","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:5e9ad5de011be3de190ab3f4e867412013a7986dd3c3e434c33652b2cfc53560","target":"graph","created_at":"2026-05-18T01:22:54Z","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 estimate the size of the spectral gap at zero for some Hermitian block matrices. Included are quasi-definite matrices, quasi-semidefinite matrices (the closure of the set of the quasi-definite matrices) and some related block matrices which need not belong to either of these classes. Matrices of such structure arise in quantum models of possibly disordered systems with supersymmetry or graphene like symmetry. Some of the results immediately extend to infinite dimension.","authors_text":"Ivan Veselic, Kresimir Veselic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-04-19T22:03:45Z","title":"Spectral gap estimates for some block matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4991","kind":"arxiv","version":2},"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":"sha256:7cbaa3449e77515fa40c30b576d89160cf5012d799dda4e76b6df06167046cd3","target":"record","created_at":"2026-05-18T01:22:54Z","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":"093d851a5b77029588874a2ad1c3caf43c4d92616f90f831679a4fd3afe39490","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-04-19T22:03:45Z","title_canon_sha256":"2305531f28e44f3a71c5b3afa989231088d5e3947514ce3d48f62ff6d6be3228"},"schema_version":"1.0","source":{"id":"1404.4991","kind":"arxiv","version":2}},"canonical_sha256":"1babd3fe934a6f3a711f08bea12254ae7f04fa861599e8c1e11e7128b1cddad1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1babd3fe934a6f3a711f08bea12254ae7f04fa861599e8c1e11e7128b1cddad1","first_computed_at":"2026-05-18T01:22:54.413850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:54.413850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F9fModk7TVOErA2saMadRKe415knr8lAeZ3gOyKIgkL7fA+Mbgioa7sgijvqEfYpZh6UiQwgsL0fWWiJD++RDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:54.414309Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4991","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cbaa3449e77515fa40c30b576d89160cf5012d799dda4e76b6df06167046cd3","sha256:5e9ad5de011be3de190ab3f4e867412013a7986dd3c3e434c33652b2cfc53560"],"state_sha256":"2887bbffce4981aa9f2592e6041b47757084bea068bd44a86126ccd6d9114096"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"03Pd1oosd6xaUC/vGP86qFVIRGVK21mOSouV8uQay8fRNF73dYvJIATAJVM5hhc5HpAeqTU1SEfPiwZgzdOpAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T15:50:27.443145Z","bundle_sha256":"d1d85780647abdb33d9026e283b2d048098016c26f31956e441c4063839998f7"}}