{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KSQVWHKPBT5RHFYRLYEGC6QUXW","short_pith_number":"pith:KSQVWHKP","canonical_record":{"source":{"id":"1411.7757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-11-28T05:46:30Z","cross_cats_sorted":[],"title_canon_sha256":"bc649430af21a7f0bc3b449ef05f398f6035ef315a6df0a31406e5fd458e0d31","abstract_canon_sha256":"90ae799d7ba2bc134c5b8a53879ac4b17e945361be3e7c47534e9b5b6527a7af"},"schema_version":"1.0"},"canonical_sha256":"54a15b1d4f0cfb1397115e08617a14bd87a365eaeac82f2fdcca0f30de16e61a","source":{"kind":"arxiv","id":"1411.7757","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7757","created_at":"2026-05-18T01:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7757v1","created_at":"2026-05-18T01:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7757","created_at":"2026-05-18T01:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"KSQVWHKPBT5R","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KSQVWHKPBT5RHFYR","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KSQVWHKP","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KSQVWHKPBT5RHFYRLYEGC6QUXW","target":"record","payload":{"canonical_record":{"source":{"id":"1411.7757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-11-28T05:46:30Z","cross_cats_sorted":[],"title_canon_sha256":"bc649430af21a7f0bc3b449ef05f398f6035ef315a6df0a31406e5fd458e0d31","abstract_canon_sha256":"90ae799d7ba2bc134c5b8a53879ac4b17e945361be3e7c47534e9b5b6527a7af"},"schema_version":"1.0"},"canonical_sha256":"54a15b1d4f0cfb1397115e08617a14bd87a365eaeac82f2fdcca0f30de16e61a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:25.178756Z","signature_b64":"9nCywNaK75eA5G85omG9Bmmps7D22GmWQiCH713+0OSrPX1Hl31L0ypxglmDp6zzVE5xfpm+0+RoIRSoSTGUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54a15b1d4f0cfb1397115e08617a14bd87a365eaeac82f2fdcca0f30de16e61a","last_reissued_at":"2026-05-18T01:41:25.178138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:25.178138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.7757","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":"2026-05-18T01:41:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wDMz/5iSysI8CgJ+GsuIzYBtZMlLRfAKa3Ea0e4ASWVHGux0uedNctkvwJ/6OB6y87qvt38MJNFJECqi79JaDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:10:48.240153Z"},"content_sha256":"6be6125e310c51954b8861c179e72e43c7c67bc16249c02a8a6561f5b8aa786f","schema_version":"1.0","event_id":"sha256:6be6125e310c51954b8861c179e72e43c7c67bc16249c02a8a6561f5b8aa786f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KSQVWHKPBT5RHFYRLYEGC6QUXW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Perron-Frobenius theory for block matrices associated to a multiplex network","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"Alejandro Garc\\'ia del Amo, Esther Garc\\'ia, Julio Flores, Luis Sol\\'a, Miguel Romance, Regino Criado","submitted_at":"2014-11-28T05:46:30Z","abstract_excerpt":"The uniqueness of the Perron vector of a nonnegative block matrix associated to a multiplex network is discussed. The conclusions come from the relationships between the irreducibility of some nonnegative block matrix associated to a multiplex network and the irreducibility of the corresponding matrices to each layer as well as the irreducibility of the adjacency matrix of the projection network. In addition the computation of that Perron vector in terms of the Perron vectors of the blocks is also addressed. Finally we present the precise relations that allow to express the Perron eigenvector "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7757","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":"2026-05-18T01:41:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tm4tOjAsKOqRxgBpY2kotybHnvURKuYLk+XrbECVq8zaIYxIRH3rNPZEe4hkqpUM6lMuc/qBSmJefu0Bh/cfCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:10:48.240598Z"},"content_sha256":"a68e347d304588c391b5b9312dee19b72381791a8872bdf2bbac25ec0ffd398a","schema_version":"1.0","event_id":"sha256:a68e347d304588c391b5b9312dee19b72381791a8872bdf2bbac25ec0ffd398a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KSQVWHKPBT5RHFYRLYEGC6QUXW/bundle.json","state_url":"https://pith.science/pith/KSQVWHKPBT5RHFYRLYEGC6QUXW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KSQVWHKPBT5RHFYRLYEGC6QUXW/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":"2026-05-31T11:10:48Z","links":{"resolver":"https://pith.science/pith/KSQVWHKPBT5RHFYRLYEGC6QUXW","bundle":"https://pith.science/pith/KSQVWHKPBT5RHFYRLYEGC6QUXW/bundle.json","state":"https://pith.science/pith/KSQVWHKPBT5RHFYRLYEGC6QUXW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KSQVWHKPBT5RHFYRLYEGC6QUXW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KSQVWHKPBT5RHFYRLYEGC6QUXW","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":"90ae799d7ba2bc134c5b8a53879ac4b17e945361be3e7c47534e9b5b6527a7af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-11-28T05:46:30Z","title_canon_sha256":"bc649430af21a7f0bc3b449ef05f398f6035ef315a6df0a31406e5fd458e0d31"},"schema_version":"1.0","source":{"id":"1411.7757","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7757","created_at":"2026-05-18T01:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7757v1","created_at":"2026-05-18T01:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7757","created_at":"2026-05-18T01:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"KSQVWHKPBT5R","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KSQVWHKPBT5RHFYR","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KSQVWHKP","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:a68e347d304588c391b5b9312dee19b72381791a8872bdf2bbac25ec0ffd398a","target":"graph","created_at":"2026-05-18T01:41:25Z","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":"The uniqueness of the Perron vector of a nonnegative block matrix associated to a multiplex network is discussed. The conclusions come from the relationships between the irreducibility of some nonnegative block matrix associated to a multiplex network and the irreducibility of the corresponding matrices to each layer as well as the irreducibility of the adjacency matrix of the projection network. In addition the computation of that Perron vector in terms of the Perron vectors of the blocks is also addressed. Finally we present the precise relations that allow to express the Perron eigenvector ","authors_text":"Alejandro Garc\\'ia del Amo, Esther Garc\\'ia, Julio Flores, Luis Sol\\'a, Miguel Romance, Regino Criado","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-11-28T05:46:30Z","title":"A Perron-Frobenius theory for block matrices associated to a multiplex network"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7757","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":"sha256:6be6125e310c51954b8861c179e72e43c7c67bc16249c02a8a6561f5b8aa786f","target":"record","created_at":"2026-05-18T01:41:25Z","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":"90ae799d7ba2bc134c5b8a53879ac4b17e945361be3e7c47534e9b5b6527a7af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-11-28T05:46:30Z","title_canon_sha256":"bc649430af21a7f0bc3b449ef05f398f6035ef315a6df0a31406e5fd458e0d31"},"schema_version":"1.0","source":{"id":"1411.7757","kind":"arxiv","version":1}},"canonical_sha256":"54a15b1d4f0cfb1397115e08617a14bd87a365eaeac82f2fdcca0f30de16e61a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54a15b1d4f0cfb1397115e08617a14bd87a365eaeac82f2fdcca0f30de16e61a","first_computed_at":"2026-05-18T01:41:25.178138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:25.178138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9nCywNaK75eA5G85omG9Bmmps7D22GmWQiCH713+0OSrPX1Hl31L0ypxglmDp6zzVE5xfpm+0+RoIRSoSTGUBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:25.178756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.7757","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6be6125e310c51954b8861c179e72e43c7c67bc16249c02a8a6561f5b8aa786f","sha256:a68e347d304588c391b5b9312dee19b72381791a8872bdf2bbac25ec0ffd398a"],"state_sha256":"46f04087e521bfbd32cb0c5caaa7ec08e7c345f71564f542ee432758ebc225e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KVR28GJP23/cD4Y4aCIH8wNXwCXiWVS379nMPZKPbA2km9SSfUpyxFEifdKGb2NhMj7s6cgej9ETXO5Kj1n2Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T11:10:48.243359Z","bundle_sha256":"2aabd10083cb227e79f78dc3068ec7a102e1a1e1ceab58d52d2c46f10bf38460"}}