{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:E2RSCL7K3BNFO3LJDXDKHDMCLL","short_pith_number":"pith:E2RSCL7K","canonical_record":{"source":{"id":"1805.06707","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-05-17T11:38:13Z","cross_cats_sorted":[],"title_canon_sha256":"9670bad80321dd42f3849733fad3debdc2f726a9518d584b10883dfe8e296ca6","abstract_canon_sha256":"64437fd45f1958be11e6c52e7bc655f6d4eee4089194f2fd83f27f6c92df5a63"},"schema_version":"1.0"},"canonical_sha256":"26a3212fead85a576d691dc6a38d825accd0f5ef761c66a5fc8c5323d0e6f77f","source":{"kind":"arxiv","id":"1805.06707","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06707","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06707v1","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06707","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"E2RSCL7K3BNF","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"E2RSCL7K3BNFO3LJ","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"E2RSCL7K","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:E2RSCL7K3BNFO3LJDXDKHDMCLL","target":"record","payload":{"canonical_record":{"source":{"id":"1805.06707","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-05-17T11:38:13Z","cross_cats_sorted":[],"title_canon_sha256":"9670bad80321dd42f3849733fad3debdc2f726a9518d584b10883dfe8e296ca6","abstract_canon_sha256":"64437fd45f1958be11e6c52e7bc655f6d4eee4089194f2fd83f27f6c92df5a63"},"schema_version":"1.0"},"canonical_sha256":"26a3212fead85a576d691dc6a38d825accd0f5ef761c66a5fc8c5323d0e6f77f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:43.558346Z","signature_b64":"8N4YjxTo1ZlNneH+b6UdN5fh/KDFZHpMUSKwDvkFXB5mqYcWz49eqz+HMZlgpS79CIVs1azFRe46aqS2i7Q9Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26a3212fead85a576d691dc6a38d825accd0f5ef761c66a5fc8c5323d0e6f77f","last_reissued_at":"2026-05-18T00:15:43.557617Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:43.557617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.06707","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":"2026-05-18T00:15:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WbxuLIXgUZFWTlhAgqFlHbgUuY68cA5VpKlLLg6dDzjjbOR2qjj/JnMN4U648OAnjy0vwhr8AdBQoscR/lGsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:03:28.206797Z"},"content_sha256":"b3d02210d9e20ed3dc66f41459961f5e43d2a0c5553d710b4f78bf2da2a16025","schema_version":"1.0","event_id":"sha256:b3d02210d9e20ed3dc66f41459961f5e43d2a0c5553d710b4f78bf2da2a16025"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:E2RSCL7K3BNFO3LJDXDKHDMCLL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diagonal realizability in the Nonnegative Inverse Eigenvalue Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Helena \\v{S}migoc, Thomas J. Laffey","submitted_at":"2018-05-17T11:38:13Z","abstract_excerpt":"We show that if a list of nonzero complex numbers $\\sigma=(\\lambda_1,\\lambda_2,\\ldots,\\lambda_k)$ is the nonzero spectrum of a diagonalizable nonnegative matrix, then $\\sigma$ is the nonzero spectrum of a diagonalizable nonnegative matrix of order $k+k^2.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06707","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":"2026-05-18T00:15:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aULvBRykxDGRI8IRjpRktKZf5OY+JJtg/G431ip324+1VEV4WT9/BW84m4imhVbI0DkroAGleITCf6mbeC5FAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:03:28.207142Z"},"content_sha256":"3852a57f07f966dfed41d8de40e270c8d56fd844fbe6029e2b4e0ee3c492a17c","schema_version":"1.0","event_id":"sha256:3852a57f07f966dfed41d8de40e270c8d56fd844fbe6029e2b4e0ee3c492a17c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E2RSCL7K3BNFO3LJDXDKHDMCLL/bundle.json","state_url":"https://pith.science/pith/E2RSCL7K3BNFO3LJDXDKHDMCLL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E2RSCL7K3BNFO3LJDXDKHDMCLL/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":"2026-06-03T07:03:28Z","links":{"resolver":"https://pith.science/pith/E2RSCL7K3BNFO3LJDXDKHDMCLL","bundle":"https://pith.science/pith/E2RSCL7K3BNFO3LJDXDKHDMCLL/bundle.json","state":"https://pith.science/pith/E2RSCL7K3BNFO3LJDXDKHDMCLL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E2RSCL7K3BNFO3LJDXDKHDMCLL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:E2RSCL7K3BNFO3LJDXDKHDMCLL","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":"64437fd45f1958be11e6c52e7bc655f6d4eee4089194f2fd83f27f6c92df5a63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-05-17T11:38:13Z","title_canon_sha256":"9670bad80321dd42f3849733fad3debdc2f726a9518d584b10883dfe8e296ca6"},"schema_version":"1.0","source":{"id":"1805.06707","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06707","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06707v1","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06707","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"E2RSCL7K3BNF","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"E2RSCL7K3BNFO3LJ","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"E2RSCL7K","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:3852a57f07f966dfed41d8de40e270c8d56fd844fbe6029e2b4e0ee3c492a17c","target":"graph","created_at":"2026-05-18T00:15:43Z","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 show that if a list of nonzero complex numbers $\\sigma=(\\lambda_1,\\lambda_2,\\ldots,\\lambda_k)$ is the nonzero spectrum of a diagonalizable nonnegative matrix, then $\\sigma$ is the nonzero spectrum of a diagonalizable nonnegative matrix of order $k+k^2.$","authors_text":"Helena \\v{S}migoc, Thomas J. Laffey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-05-17T11:38:13Z","title":"Diagonal realizability in the Nonnegative Inverse Eigenvalue Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06707","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:b3d02210d9e20ed3dc66f41459961f5e43d2a0c5553d710b4f78bf2da2a16025","target":"record","created_at":"2026-05-18T00:15:43Z","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":"64437fd45f1958be11e6c52e7bc655f6d4eee4089194f2fd83f27f6c92df5a63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-05-17T11:38:13Z","title_canon_sha256":"9670bad80321dd42f3849733fad3debdc2f726a9518d584b10883dfe8e296ca6"},"schema_version":"1.0","source":{"id":"1805.06707","kind":"arxiv","version":1}},"canonical_sha256":"26a3212fead85a576d691dc6a38d825accd0f5ef761c66a5fc8c5323d0e6f77f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26a3212fead85a576d691dc6a38d825accd0f5ef761c66a5fc8c5323d0e6f77f","first_computed_at":"2026-05-18T00:15:43.557617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:43.557617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8N4YjxTo1ZlNneH+b6UdN5fh/KDFZHpMUSKwDvkFXB5mqYcWz49eqz+HMZlgpS79CIVs1azFRe46aqS2i7Q9Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:43.558346Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.06707","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3d02210d9e20ed3dc66f41459961f5e43d2a0c5553d710b4f78bf2da2a16025","sha256:3852a57f07f966dfed41d8de40e270c8d56fd844fbe6029e2b4e0ee3c492a17c"],"state_sha256":"e2d2b0cd7863f6b66f421a985d5822bdae014d168e959c83bb5fb18fcda00b11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9LPgooO58HTO09QLzJirw4dNcXTft09h6NFiaTPJwfIs55jszrLhMcLoi0xTcgR102dDQrlG1rG5k+V/MSUUBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T07:03:28.209196Z","bundle_sha256":"97d5c4e3f0f118808b5227f78aeba6627705a33a3a5b41bb271459bc0dc3aec0"}}