{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:7Q5M7BS4HFVPOS76PHEMZY45NF","short_pith_number":"pith:7Q5M7BS4","canonical_record":{"source":{"id":"2407.03164","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-07-03T14:37:44Z","cross_cats_sorted":[],"title_canon_sha256":"c7e00a4e58ac7560294070cace71f9a92f857ecc8d97fa072dd6ee1012adf605","abstract_canon_sha256":"578ddb95fe498e47bcfac16c9575bc8c872e16090b76914f16e4593475509353"},"schema_version":"1.0"},"canonical_sha256":"fc3acf865c396af74bfe79c8cce39d694dafb18a1fa3cec1262a082f7930d249","source":{"kind":"arxiv","id":"2407.03164","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.03164","created_at":"2026-07-05T08:40:20Z"},{"alias_kind":"arxiv_version","alias_value":"2407.03164v2","created_at":"2026-07-05T08:40:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.03164","created_at":"2026-07-05T08:40:20Z"},{"alias_kind":"pith_short_12","alias_value":"7Q5M7BS4HFVP","created_at":"2026-07-05T08:40:20Z"},{"alias_kind":"pith_short_16","alias_value":"7Q5M7BS4HFVPOS76","created_at":"2026-07-05T08:40:20Z"},{"alias_kind":"pith_short_8","alias_value":"7Q5M7BS4","created_at":"2026-07-05T08:40:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:7Q5M7BS4HFVPOS76PHEMZY45NF","target":"record","payload":{"canonical_record":{"source":{"id":"2407.03164","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-07-03T14:37:44Z","cross_cats_sorted":[],"title_canon_sha256":"c7e00a4e58ac7560294070cace71f9a92f857ecc8d97fa072dd6ee1012adf605","abstract_canon_sha256":"578ddb95fe498e47bcfac16c9575bc8c872e16090b76914f16e4593475509353"},"schema_version":"1.0"},"canonical_sha256":"fc3acf865c396af74bfe79c8cce39d694dafb18a1fa3cec1262a082f7930d249","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:40:20.707700Z","signature_b64":"wRl1Wapw1zAJ6lQnz4EZhbo2ytkekYEuj8KBz9VPqzFSsBA0WX9rzImZK20CbYP6L26G0vZN4eTyn/qdbPWeCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc3acf865c396af74bfe79c8cce39d694dafb18a1fa3cec1262a082f7930d249","last_reissued_at":"2026-07-05T08:40:20.707229Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:40:20.707229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.03164","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":"2026-07-05T08:40:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WWFzL+FRF+oMf9tjDKxSB/G0VqpjJb39Ds1xIasDtGtQEj8vUzuooK6yjrXgE3kHPVA68fFA+2pb/ZW7NxVOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T15:05:55.237692Z"},"content_sha256":"797007fa81181a6ba563a86780b03b85f988ac7cb72db5a1310cc51d7c1481a9","schema_version":"1.0","event_id":"sha256:797007fa81181a6ba563a86780b03b85f988ac7cb72db5a1310cc51d7c1481a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:7Q5M7BS4HFVPOS76PHEMZY45NF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matrices with Hyperbolical Krein Space Numerical Range","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"G. Soares, N. Bebiano, R. Lemos","submitted_at":"2024-07-03T14:37:44Z","abstract_excerpt":"This paper is devoted to matrices with hyperbolical Krein space numerical range. This shape characterizes the 2-by-2 case and persists for certain classes of matrices, independently of their size. Ne\\-cessary and sufficient conditions for low dimensional tridiagonal matrices to have this shape are obtained only involving the matrix entries"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.03164","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.03164/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":"2026-07-05T08:40:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+o2IPBVtejy3NMWq/hUsacDkA+J4W3c8DeS2gmYmJhO6Rlqze7DmHdDxuB7o1hkxknHlOJYmd57+lvjL/pK+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T15:05:55.238637Z"},"content_sha256":"84d952282a8a4cc07202fa6c7b77955fd17f3f76314da086d362b87945069b02","schema_version":"1.0","event_id":"sha256:84d952282a8a4cc07202fa6c7b77955fd17f3f76314da086d362b87945069b02"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7Q5M7BS4HFVPOS76PHEMZY45NF/bundle.json","state_url":"https://pith.science/pith/7Q5M7BS4HFVPOS76PHEMZY45NF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7Q5M7BS4HFVPOS76PHEMZY45NF/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":"2026-08-06T15:05:55Z","links":{"resolver":"https://pith.science/pith/7Q5M7BS4HFVPOS76PHEMZY45NF","bundle":"https://pith.science/pith/7Q5M7BS4HFVPOS76PHEMZY45NF/bundle.json","state":"https://pith.science/pith/7Q5M7BS4HFVPOS76PHEMZY45NF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7Q5M7BS4HFVPOS76PHEMZY45NF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7Q5M7BS4HFVPOS76PHEMZY45NF","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":"578ddb95fe498e47bcfac16c9575bc8c872e16090b76914f16e4593475509353","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-07-03T14:37:44Z","title_canon_sha256":"c7e00a4e58ac7560294070cace71f9a92f857ecc8d97fa072dd6ee1012adf605"},"schema_version":"1.0","source":{"id":"2407.03164","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.03164","created_at":"2026-07-05T08:40:20Z"},{"alias_kind":"arxiv_version","alias_value":"2407.03164v2","created_at":"2026-07-05T08:40:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.03164","created_at":"2026-07-05T08:40:20Z"},{"alias_kind":"pith_short_12","alias_value":"7Q5M7BS4HFVP","created_at":"2026-07-05T08:40:20Z"},{"alias_kind":"pith_short_16","alias_value":"7Q5M7BS4HFVPOS76","created_at":"2026-07-05T08:40:20Z"},{"alias_kind":"pith_short_8","alias_value":"7Q5M7BS4","created_at":"2026-07-05T08:40:20Z"}],"graph_snapshots":[{"event_id":"sha256:84d952282a8a4cc07202fa6c7b77955fd17f3f76314da086d362b87945069b02","target":"graph","created_at":"2026-07-05T08:40:20Z","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/2407.03164/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is devoted to matrices with hyperbolical Krein space numerical range. This shape characterizes the 2-by-2 case and persists for certain classes of matrices, independently of their size. Ne\\-cessary and sufficient conditions for low dimensional tridiagonal matrices to have this shape are obtained only involving the matrix entries","authors_text":"G. Soares, N. Bebiano, R. Lemos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-07-03T14:37:44Z","title":"Matrices with Hyperbolical Krein Space Numerical Range"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.03164","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":"sha256:797007fa81181a6ba563a86780b03b85f988ac7cb72db5a1310cc51d7c1481a9","target":"record","created_at":"2026-07-05T08:40:20Z","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":"578ddb95fe498e47bcfac16c9575bc8c872e16090b76914f16e4593475509353","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-07-03T14:37:44Z","title_canon_sha256":"c7e00a4e58ac7560294070cace71f9a92f857ecc8d97fa072dd6ee1012adf605"},"schema_version":"1.0","source":{"id":"2407.03164","kind":"arxiv","version":2}},"canonical_sha256":"fc3acf865c396af74bfe79c8cce39d694dafb18a1fa3cec1262a082f7930d249","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc3acf865c396af74bfe79c8cce39d694dafb18a1fa3cec1262a082f7930d249","first_computed_at":"2026-07-05T08:40:20.707229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:40:20.707229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wRl1Wapw1zAJ6lQnz4EZhbo2ytkekYEuj8KBz9VPqzFSsBA0WX9rzImZK20CbYP6L26G0vZN4eTyn/qdbPWeCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:40:20.707700Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.03164","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:797007fa81181a6ba563a86780b03b85f988ac7cb72db5a1310cc51d7c1481a9","sha256:84d952282a8a4cc07202fa6c7b77955fd17f3f76314da086d362b87945069b02"],"state_sha256":"bb9b6b39708fb0053de01405ae9e979a73d08729bb48d530d0ced659db15f9c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FFYqzN3waeQUes108sKcORdKdFKNWXzyN0DhmoTAN+ZNQYFgx+sL5z+XL0bBQZMTWEuaUbF0IB+X4ohqwA38DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T15:05:55.251148Z","bundle_sha256":"7c41e436f98e4f1070e7524ccf1793ad314431f6f668c932d892ebdf5375748f"}}