{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YL25VPLWTMJCNR3VPCRBZSTP6Q","short_pith_number":"pith:YL25VPLW","canonical_record":{"source":{"id":"1104.0316","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-04-02T14:14:25Z","cross_cats_sorted":[],"title_canon_sha256":"02e3de1aac4409d212ea67c1762b1f6e22ac1015c1daa67476252b8542e3bc02","abstract_canon_sha256":"59fd18d6b1f871c2f2b0f59d7b7fc2784ab934781fd305b69a65dfd2f09b857e"},"schema_version":"1.0"},"canonical_sha256":"c2f5dabd769b1226c77578a21cca6ff405e9ce85565bb60b6aba389476b49308","source":{"kind":"arxiv","id":"1104.0316","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0316","created_at":"2026-05-18T03:40:25Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0316v4","created_at":"2026-05-18T03:40:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0316","created_at":"2026-05-18T03:40:25Z"},{"alias_kind":"pith_short_12","alias_value":"YL25VPLWTMJC","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YL25VPLWTMJCNR3V","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YL25VPLW","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YL25VPLWTMJCNR3VPCRBZSTP6Q","target":"record","payload":{"canonical_record":{"source":{"id":"1104.0316","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-04-02T14:14:25Z","cross_cats_sorted":[],"title_canon_sha256":"02e3de1aac4409d212ea67c1762b1f6e22ac1015c1daa67476252b8542e3bc02","abstract_canon_sha256":"59fd18d6b1f871c2f2b0f59d7b7fc2784ab934781fd305b69a65dfd2f09b857e"},"schema_version":"1.0"},"canonical_sha256":"c2f5dabd769b1226c77578a21cca6ff405e9ce85565bb60b6aba389476b49308","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:25.856905Z","signature_b64":"VgOEAq//1179XmQwl2Mkk0GRVCRpOxqXcgd+uWAq6cGdA9xP4ehvv6pOMwbwDIVotiDgvppZcQGaIzUKKvlkBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2f5dabd769b1226c77578a21cca6ff405e9ce85565bb60b6aba389476b49308","last_reissued_at":"2026-05-18T03:40:25.855855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:25.855855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.0316","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:40:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Aife9GvlO7vB9/pOIQzzvuLv8vCDpRVxTNtBhWWvdfk80FOT57DvNoLMq6HeVq48mM+ysxF6+FPjYMwFPLIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:08:42.298207Z"},"content_sha256":"a2e42f31f4fd61a0bc152a098ac2ef53b0efff92abbfdadf6c40412ff4660248","schema_version":"1.0","event_id":"sha256:a2e42f31f4fd61a0bc152a098ac2ef53b0efff92abbfdadf6c40412ff4660248"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YL25VPLWTMJCNR3VPCRBZSTP6Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Further Results for Perron-Frobenius Theorem for Nonnegative Tensors II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Qingzhi Yang, Yuning Yang","submitted_at":"2011-04-02T14:14:25Z","abstract_excerpt":"In this paper, we generalize some conclusions from the nonnegative irreducible tensor to the nonnegative weakly irreducible tensor and give more properties of eigenvalue problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0316","kind":"arxiv","version":4},"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":"2026-05-18T03:40:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TJZ0cvLISrP8VP5cYH/AnsMEatjajR294JJVW4g7VfNGkCZNlVSbDXH7cYxII2O1sGLaIwXbBFSOnNAdx5TsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:08:42.298883Z"},"content_sha256":"029ee0d76d41764cb366e02a9250408575456a1a3415ec5c8314995ded788340","schema_version":"1.0","event_id":"sha256:029ee0d76d41764cb366e02a9250408575456a1a3415ec5c8314995ded788340"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YL25VPLWTMJCNR3VPCRBZSTP6Q/bundle.json","state_url":"https://pith.science/pith/YL25VPLWTMJCNR3VPCRBZSTP6Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YL25VPLWTMJCNR3VPCRBZSTP6Q/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":"2026-05-31T02:08:42Z","links":{"resolver":"https://pith.science/pith/YL25VPLWTMJCNR3VPCRBZSTP6Q","bundle":"https://pith.science/pith/YL25VPLWTMJCNR3VPCRBZSTP6Q/bundle.json","state":"https://pith.science/pith/YL25VPLWTMJCNR3VPCRBZSTP6Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YL25VPLWTMJCNR3VPCRBZSTP6Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YL25VPLWTMJCNR3VPCRBZSTP6Q","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":"59fd18d6b1f871c2f2b0f59d7b7fc2784ab934781fd305b69a65dfd2f09b857e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-04-02T14:14:25Z","title_canon_sha256":"02e3de1aac4409d212ea67c1762b1f6e22ac1015c1daa67476252b8542e3bc02"},"schema_version":"1.0","source":{"id":"1104.0316","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0316","created_at":"2026-05-18T03:40:25Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0316v4","created_at":"2026-05-18T03:40:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0316","created_at":"2026-05-18T03:40:25Z"},{"alias_kind":"pith_short_12","alias_value":"YL25VPLWTMJC","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YL25VPLWTMJCNR3V","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YL25VPLW","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:029ee0d76d41764cb366e02a9250408575456a1a3415ec5c8314995ded788340","target":"graph","created_at":"2026-05-18T03:40:25Z","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":"In this paper, we generalize some conclusions from the nonnegative irreducible tensor to the nonnegative weakly irreducible tensor and give more properties of eigenvalue problems.","authors_text":"Qingzhi Yang, Yuning Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-04-02T14:14:25Z","title":"Further Results for Perron-Frobenius Theorem for Nonnegative Tensors II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0316","kind":"arxiv","version":4},"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:a2e42f31f4fd61a0bc152a098ac2ef53b0efff92abbfdadf6c40412ff4660248","target":"record","created_at":"2026-05-18T03:40:25Z","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":"59fd18d6b1f871c2f2b0f59d7b7fc2784ab934781fd305b69a65dfd2f09b857e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-04-02T14:14:25Z","title_canon_sha256":"02e3de1aac4409d212ea67c1762b1f6e22ac1015c1daa67476252b8542e3bc02"},"schema_version":"1.0","source":{"id":"1104.0316","kind":"arxiv","version":4}},"canonical_sha256":"c2f5dabd769b1226c77578a21cca6ff405e9ce85565bb60b6aba389476b49308","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2f5dabd769b1226c77578a21cca6ff405e9ce85565bb60b6aba389476b49308","first_computed_at":"2026-05-18T03:40:25.855855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:25.855855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VgOEAq//1179XmQwl2Mkk0GRVCRpOxqXcgd+uWAq6cGdA9xP4ehvv6pOMwbwDIVotiDgvppZcQGaIzUKKvlkBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:25.856905Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0316","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2e42f31f4fd61a0bc152a098ac2ef53b0efff92abbfdadf6c40412ff4660248","sha256:029ee0d76d41764cb366e02a9250408575456a1a3415ec5c8314995ded788340"],"state_sha256":"89c7de95eb3383824db20c4b2b1c3a03284e96551772290ceea5487ef7fa0e0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LVimHXy/Vi59KzrCHmvU1SqiB5BqA02M1EHRk9znTDTDGF3l0H6jXzDznco1Mugqg1e6lopMYT1tFdqHpVO6CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:08:42.301623Z","bundle_sha256":"63b28dc8901a06e1ea4ffcee4d7005db4fafc2b664466ac78c7bc8d4e90079c8"}}