{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:FB4WT3J3Y6RZT7234DELXLWW7N","short_pith_number":"pith:FB4WT3J3","canonical_record":{"source":{"id":"1902.09354","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.RA","submitted_at":"2019-02-25T15:16:21Z","cross_cats_sorted":[],"title_canon_sha256":"94446f5c7b436c836441ad289b7b1e8d08a5b21563770cf6aed4c8db3ab919cb","abstract_canon_sha256":"ab23049995b3262b0d24782e92b5451e1f9f921a546adb618dbd80af1a92febb"},"schema_version":"1.0"},"canonical_sha256":"287969ed3bc7a399ff5be0c8bbaed6fb53cf4460b31f2db02b4449308faaf2d1","source":{"kind":"arxiv","id":"1902.09354","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.09354","created_at":"2026-05-17T23:52:45Z"},{"alias_kind":"arxiv_version","alias_value":"1902.09354v1","created_at":"2026-05-17T23:52:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09354","created_at":"2026-05-17T23:52:45Z"},{"alias_kind":"pith_short_12","alias_value":"FB4WT3J3Y6RZ","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FB4WT3J3Y6RZT723","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FB4WT3J3","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:FB4WT3J3Y6RZT7234DELXLWW7N","target":"record","payload":{"canonical_record":{"source":{"id":"1902.09354","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.RA","submitted_at":"2019-02-25T15:16:21Z","cross_cats_sorted":[],"title_canon_sha256":"94446f5c7b436c836441ad289b7b1e8d08a5b21563770cf6aed4c8db3ab919cb","abstract_canon_sha256":"ab23049995b3262b0d24782e92b5451e1f9f921a546adb618dbd80af1a92febb"},"schema_version":"1.0"},"canonical_sha256":"287969ed3bc7a399ff5be0c8bbaed6fb53cf4460b31f2db02b4449308faaf2d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:45.990826Z","signature_b64":"kj8uI8JR9aOB91Zd0XNDBtB4s2g+l4p4aUhiNK2XPUWRcwgvgWO+IJntxYV6VT92tss3DnIWL8epTwgSxYipBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"287969ed3bc7a399ff5be0c8bbaed6fb53cf4460b31f2db02b4449308faaf2d1","last_reissued_at":"2026-05-17T23:52:45.990286Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:45.990286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.09354","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":"2026-05-17T23:52:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vgjarbqqo0sPMFsIFwjCtEglFJTojPmziBUueOab0mcPH3t64xoG7i8PxzhtF6Nmg0GUPLeJY51PORWgWfqmAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:35:57.811378Z"},"content_sha256":"6cf861a4ad9dce8a612bbed876f5df083e48b2c15d7cffa7705bb4bb878b62d2","schema_version":"1.0","event_id":"sha256:6cf861a4ad9dce8a612bbed876f5df083e48b2c15d7cffa7705bb4bb878b62d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:FB4WT3J3Y6RZT7234DELXLWW7N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Centrosymmetric nonnegative realization of spectra","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ana I. Julio, Oscar Rojo, Ricardo L. Soto","submitted_at":"2019-02-25T15:16:21Z","abstract_excerpt":"A list $\\Lambda =\\{\\lambda _{1},\\lambda _{2},\\ldots ,\\lambda _{n}\\}$ of complex numbers is said to be realizable if it is the spectrum of an entrywise nonnegative matrix. In this paper we intent to characterize those lists of complex numbers, which are realizable by a centrosymmetric nonnegative matrix. In particular, we show that lists of nonnegative real numbers, and lists of complex numbers of Suleimanova type (except in one particular case), are always the spectrum of some centrosymmetric nonnegative matrix. For the general lists we give sufficient conditions via a perturbation result. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09354","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":"2026-05-17T23:52:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oqkc1KsCdVWeQ39X8Btwj3ORSbmkBUNtTJweoF+23CMa5U2JtxhavbarK+mAK1YUa2EgSh8w5mliyhGSgsLhDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:35:57.811726Z"},"content_sha256":"d4970ea105c15859e09689506f4852e90e9dc3cf9e1f602c2e0cf52d208640b9","schema_version":"1.0","event_id":"sha256:d4970ea105c15859e09689506f4852e90e9dc3cf9e1f602c2e0cf52d208640b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FB4WT3J3Y6RZT7234DELXLWW7N/bundle.json","state_url":"https://pith.science/pith/FB4WT3J3Y6RZT7234DELXLWW7N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FB4WT3J3Y6RZT7234DELXLWW7N/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":"2026-06-01T16:35:57Z","links":{"resolver":"https://pith.science/pith/FB4WT3J3Y6RZT7234DELXLWW7N","bundle":"https://pith.science/pith/FB4WT3J3Y6RZT7234DELXLWW7N/bundle.json","state":"https://pith.science/pith/FB4WT3J3Y6RZT7234DELXLWW7N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FB4WT3J3Y6RZT7234DELXLWW7N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FB4WT3J3Y6RZT7234DELXLWW7N","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":"ab23049995b3262b0d24782e92b5451e1f9f921a546adb618dbd80af1a92febb","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.RA","submitted_at":"2019-02-25T15:16:21Z","title_canon_sha256":"94446f5c7b436c836441ad289b7b1e8d08a5b21563770cf6aed4c8db3ab919cb"},"schema_version":"1.0","source":{"id":"1902.09354","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.09354","created_at":"2026-05-17T23:52:45Z"},{"alias_kind":"arxiv_version","alias_value":"1902.09354v1","created_at":"2026-05-17T23:52:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09354","created_at":"2026-05-17T23:52:45Z"},{"alias_kind":"pith_short_12","alias_value":"FB4WT3J3Y6RZ","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FB4WT3J3Y6RZT723","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FB4WT3J3","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:d4970ea105c15859e09689506f4852e90e9dc3cf9e1f602c2e0cf52d208640b9","target":"graph","created_at":"2026-05-17T23:52:45Z","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":"A list $\\Lambda =\\{\\lambda _{1},\\lambda _{2},\\ldots ,\\lambda _{n}\\}$ of complex numbers is said to be realizable if it is the spectrum of an entrywise nonnegative matrix. In this paper we intent to characterize those lists of complex numbers, which are realizable by a centrosymmetric nonnegative matrix. In particular, we show that lists of nonnegative real numbers, and lists of complex numbers of Suleimanova type (except in one particular case), are always the spectrum of some centrosymmetric nonnegative matrix. For the general lists we give sufficient conditions via a perturbation result. We ","authors_text":"Ana I. Julio, Oscar Rojo, Ricardo L. Soto","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.RA","submitted_at":"2019-02-25T15:16:21Z","title":"Centrosymmetric nonnegative realization of spectra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09354","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":"sha256:6cf861a4ad9dce8a612bbed876f5df083e48b2c15d7cffa7705bb4bb878b62d2","target":"record","created_at":"2026-05-17T23:52:45Z","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":"ab23049995b3262b0d24782e92b5451e1f9f921a546adb618dbd80af1a92febb","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.RA","submitted_at":"2019-02-25T15:16:21Z","title_canon_sha256":"94446f5c7b436c836441ad289b7b1e8d08a5b21563770cf6aed4c8db3ab919cb"},"schema_version":"1.0","source":{"id":"1902.09354","kind":"arxiv","version":1}},"canonical_sha256":"287969ed3bc7a399ff5be0c8bbaed6fb53cf4460b31f2db02b4449308faaf2d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"287969ed3bc7a399ff5be0c8bbaed6fb53cf4460b31f2db02b4449308faaf2d1","first_computed_at":"2026-05-17T23:52:45.990286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:45.990286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kj8uI8JR9aOB91Zd0XNDBtB4s2g+l4p4aUhiNK2XPUWRcwgvgWO+IJntxYV6VT92tss3DnIWL8epTwgSxYipBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:45.990826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.09354","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cf861a4ad9dce8a612bbed876f5df083e48b2c15d7cffa7705bb4bb878b62d2","sha256:d4970ea105c15859e09689506f4852e90e9dc3cf9e1f602c2e0cf52d208640b9"],"state_sha256":"d1f73c4048cafbb263aa9e7ce995f186686b51a0cea15664516e483a13f1b1c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X6gA2x5oPaEAFtgPVFDeson4CXZj0T5PO0QGGH1dbRICfhV6jYHa4Ar5Yhv2CLa2EVPfF07syLCVx764zThaAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:35:57.813654Z","bundle_sha256":"e538b9bb0a25936845fd512ac71a1eec88c853e8475fea7b2e9c360285cc76a5"}}