{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BCH4TL5S57NUY5Z2GN47MS5MX2","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":"7193788bb1ea6e4c930d5129aed7d55cb241cc6ec8d3823df58cdb11917c2315","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-03-20T14:18:11Z","title_canon_sha256":"8319696ae62515df4e76ec4ad034d2d3cce27ca426420d10801ddb501a2d72bc"},"schema_version":"1.0","source":{"id":"2503.16176","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.16176","created_at":"2026-07-05T10:40:18Z"},{"alias_kind":"arxiv_version","alias_value":"2503.16176v2","created_at":"2026-07-05T10:40:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.16176","created_at":"2026-07-05T10:40:18Z"},{"alias_kind":"pith_short_12","alias_value":"BCH4TL5S57NU","created_at":"2026-07-05T10:40:18Z"},{"alias_kind":"pith_short_16","alias_value":"BCH4TL5S57NUY5Z2","created_at":"2026-07-05T10:40:18Z"},{"alias_kind":"pith_short_8","alias_value":"BCH4TL5S","created_at":"2026-07-05T10:40:18Z"}],"graph_snapshots":[{"event_id":"sha256:5cbdff8204d5d7da8e794ff7b6dac8ad8e731969fcef54670dddf43729dacdfe","target":"graph","created_at":"2026-07-05T10:40:18Z","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/2503.16176/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An M-eigenvalue of a nonnegative biquadratic tensor is referred to as an M$^+$-eigenvalue if it has a pair of nonnegative M-eigenvectors. If furthermore that pair of M-eigenvectors is positive, then that M$^+$-eigenvalue is called an M$^{++}$-eigenvalue. A nonnegative biquadratic tensor has at least one M$^+$ eigenvalue, and the largest M$^+$-eigenvalue is both the largest M-eigenvalue and the M-spectral radius. For irreducible nonnegative biquadratic tensors, all the M$^+$-eigenvalues are M$^{++}$-eigenvalues. Although the M$^+$-eigenvalues of irreducible nonnegative biquadratic tensors are n","authors_text":"Chunfeng Cui, Liqun Qi","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-03-20T14:18:11Z","title":"Nonnegative Biquadratic Tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.16176","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:f8c1e22d309034c3892cfc5947d7cc1979f197dc11281485ac1691d6e7a2612e","target":"record","created_at":"2026-07-05T10:40:18Z","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":"7193788bb1ea6e4c930d5129aed7d55cb241cc6ec8d3823df58cdb11917c2315","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-03-20T14:18:11Z","title_canon_sha256":"8319696ae62515df4e76ec4ad034d2d3cce27ca426420d10801ddb501a2d72bc"},"schema_version":"1.0","source":{"id":"2503.16176","kind":"arxiv","version":2}},"canonical_sha256":"088fc9afb2efdb4c773a3379f64bacbe94c7c9e9b5bcbdfb901fdd98e1bbbe2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"088fc9afb2efdb4c773a3379f64bacbe94c7c9e9b5bcbdfb901fdd98e1bbbe2b","first_computed_at":"2026-07-05T10:40:18.431640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:40:18.431640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RUOM7hi7GCIe+/9dvEsmVSmwnAWImCCj/LhT5JSi7/bIX4hwmNh7hJpmfQDXdQ9Q6LUEkFFbVgc517zm5suACw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:40:18.432097Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.16176","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8c1e22d309034c3892cfc5947d7cc1979f197dc11281485ac1691d6e7a2612e","sha256:5cbdff8204d5d7da8e794ff7b6dac8ad8e731969fcef54670dddf43729dacdfe"],"state_sha256":"6e989ef851c094f41644249e5c39f86ddaad0b0a174142efd34ac5feb0fcea3e"}