{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KF5GAGBTWDRZHQ4LYW4FRDNIPK","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":"fce54d2f63819c1ac5e36641209571a0ea464627d7fd8bf3c940683e797cab4d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.SP","submitted_at":"2011-01-13T03:11:25Z","title_canon_sha256":"20ac2d597582249a87cac4e53aff582189493f181ff7a72c060f0736962ab742"},"schema_version":"1.0","source":{"id":"1101.2479","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2479","created_at":"2026-05-18T04:00:16Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2479v2","created_at":"2026-05-18T04:00:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2479","created_at":"2026-05-18T04:00:16Z"},{"alias_kind":"pith_short_12","alias_value":"KF5GAGBTWDRZ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KF5GAGBTWDRZHQ4L","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KF5GAGBT","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:867bd725ce92a378e2c4fc9574603404a7f1c27dc1145702111bb42b893065dd","target":"graph","created_at":"2026-05-18T04:00:16Z","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 prove that the spectral radius of even order nonnegative irreducible tensors is real geometrically simple. In the case when the order of the tensor is odd, or in the complex field, some conditions are given to guarantee the geometric simplicity of the spectral radius.","authors_text":"Qingzhi Yang, Yuning Yang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.SP","submitted_at":"2011-01-13T03:11:25Z","title":"A note on the geometric simplicity of the spectral radius of nonnegative irreducible tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2479","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:ebbb1fc482b938c7b2ee408961a22a40d376f9844070a4f999a2ebe3eebce691","target":"record","created_at":"2026-05-18T04:00:16Z","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":"fce54d2f63819c1ac5e36641209571a0ea464627d7fd8bf3c940683e797cab4d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.SP","submitted_at":"2011-01-13T03:11:25Z","title_canon_sha256":"20ac2d597582249a87cac4e53aff582189493f181ff7a72c060f0736962ab742"},"schema_version":"1.0","source":{"id":"1101.2479","kind":"arxiv","version":2}},"canonical_sha256":"517a601833b0e393c38bc5b8588da87a9f10b0233328e52fcff1c324f6f9307a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"517a601833b0e393c38bc5b8588da87a9f10b0233328e52fcff1c324f6f9307a","first_computed_at":"2026-05-18T04:00:16.037994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:16.037994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"30ttSSbYNsvdyeyO363rJudKDy5Ey+hXwsDQewoB0FfyoTlM4/+IhNWJYM0M4Vc5MrmR8QjLEx3jtkNT/43cAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:16.038787Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2479","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebbb1fc482b938c7b2ee408961a22a40d376f9844070a4f999a2ebe3eebce691","sha256:867bd725ce92a378e2c4fc9574603404a7f1c27dc1145702111bb42b893065dd"],"state_sha256":"2a40d6e1e1a767622ce2d95b25c2090757a505b541199fb02cd2b9f74bcd034b"}