{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:WVYIAH45WL4OY7ADECI54TPCDF","short_pith_number":"pith:WVYIAH45","canonical_record":{"source":{"id":"1208.3498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-16T21:31:09Z","cross_cats_sorted":[],"title_canon_sha256":"9b041397d91b9f19d75b013cff8f20699f1dc77a26178eacacb20c48cf314192","abstract_canon_sha256":"0d09145c9e975ab777874c6f7b3b353a626691768f9578ab5d7a3dbcdca750bd"},"schema_version":"1.0"},"canonical_sha256":"b570801f9db2f8ec7c032091de4de21940af116f20e1f5b8298946b50cb96f82","source":{"kind":"arxiv","id":"1208.3498","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3498","created_at":"2026-05-18T03:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3498v1","created_at":"2026-05-18T03:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3498","created_at":"2026-05-18T03:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"WVYIAH45WL4O","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WVYIAH45WL4OY7AD","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WVYIAH45","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:WVYIAH45WL4OY7ADECI54TPCDF","target":"record","payload":{"canonical_record":{"source":{"id":"1208.3498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-16T21:31:09Z","cross_cats_sorted":[],"title_canon_sha256":"9b041397d91b9f19d75b013cff8f20699f1dc77a26178eacacb20c48cf314192","abstract_canon_sha256":"0d09145c9e975ab777874c6f7b3b353a626691768f9578ab5d7a3dbcdca750bd"},"schema_version":"1.0"},"canonical_sha256":"b570801f9db2f8ec7c032091de4de21940af116f20e1f5b8298946b50cb96f82","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:35.055370Z","signature_b64":"9++QMj5YIeIxVTVozrO9n1d6hGuQnz0oSDAybE0FRDU4d3Vjwc2xfm3a4oJU6cpoC/UGqhjJJ5Fhc+l3uudjAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b570801f9db2f8ec7c032091de4de21940af116f20e1f5b8298946b50cb96f82","last_reissued_at":"2026-05-18T03:48:35.054760Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:35.054760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.3498","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":"2026-05-18T03:48:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FXlRy0G4E6mBgziOMQmT2LhgS6cVpH1Mif4b1xL4zXVj4Zjlyb709Pi0Wc3snC6Y9HQD+WlZduE3N1vrdOvdDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:34:41.261338Z"},"content_sha256":"9eb7b1ff5982a98671e81d50df64ad0920d81037b15d159649806ada10d6372a","schema_version":"1.0","event_id":"sha256:9eb7b1ff5982a98671e81d50df64ad0920d81037b15d159649806ada10d6372a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:WVYIAH45WL4OY7ADECI54TPCDF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Irreducible Semigroups of Positive Operators on Banach Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Niushan Gao, Vladimir G. Troitsky","submitted_at":"2012-08-16T21:31:09Z","abstract_excerpt":"The classical Perron-Frobenius theory asserts that an irreducible matrix $A$ has cyclic peripheral spectrum and its spectral radius $r(A)$ is an eigenvalue corresponding to a positive eigenvector. In Radjavi (1999) and Radjavi and Rosenthal (2000), this was extended to semigroups of matrices and of compact operators on $L_p$-spaces. We extend this approach to operators on an arbitrary Banach lattice $X$. We prove, in particular, that if $\\iS$ is a commutative irreducible semigroup of positive operators on $X$ containing a compact operator $T$ then there exist positive disjoint vectors $x_1,..."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3498","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":"2026-05-18T03:48:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"93Yrz+v0LcZ0s2PxRQqcpGRGDJV52Czek+NMRTvtKS9Druc9K8OYypjoovBl0O9GliWgY9VtWOajKXD58KtRAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:34:41.261691Z"},"content_sha256":"f54c3c68f31c148b42c2def37c254f082f1ec0340412b76a18fd9d6f357bb4af","schema_version":"1.0","event_id":"sha256:f54c3c68f31c148b42c2def37c254f082f1ec0340412b76a18fd9d6f357bb4af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WVYIAH45WL4OY7ADECI54TPCDF/bundle.json","state_url":"https://pith.science/pith/WVYIAH45WL4OY7ADECI54TPCDF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WVYIAH45WL4OY7ADECI54TPCDF/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":"2026-05-31T09:34:41Z","links":{"resolver":"https://pith.science/pith/WVYIAH45WL4OY7ADECI54TPCDF","bundle":"https://pith.science/pith/WVYIAH45WL4OY7ADECI54TPCDF/bundle.json","state":"https://pith.science/pith/WVYIAH45WL4OY7ADECI54TPCDF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WVYIAH45WL4OY7ADECI54TPCDF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WVYIAH45WL4OY7ADECI54TPCDF","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":"0d09145c9e975ab777874c6f7b3b353a626691768f9578ab5d7a3dbcdca750bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-16T21:31:09Z","title_canon_sha256":"9b041397d91b9f19d75b013cff8f20699f1dc77a26178eacacb20c48cf314192"},"schema_version":"1.0","source":{"id":"1208.3498","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3498","created_at":"2026-05-18T03:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3498v1","created_at":"2026-05-18T03:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3498","created_at":"2026-05-18T03:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"WVYIAH45WL4O","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WVYIAH45WL4OY7AD","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WVYIAH45","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:f54c3c68f31c148b42c2def37c254f082f1ec0340412b76a18fd9d6f357bb4af","target":"graph","created_at":"2026-05-18T03:48:35Z","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 classical Perron-Frobenius theory asserts that an irreducible matrix $A$ has cyclic peripheral spectrum and its spectral radius $r(A)$ is an eigenvalue corresponding to a positive eigenvector. In Radjavi (1999) and Radjavi and Rosenthal (2000), this was extended to semigroups of matrices and of compact operators on $L_p$-spaces. We extend this approach to operators on an arbitrary Banach lattice $X$. We prove, in particular, that if $\\iS$ is a commutative irreducible semigroup of positive operators on $X$ containing a compact operator $T$ then there exist positive disjoint vectors $x_1,...","authors_text":"Niushan Gao, Vladimir G. Troitsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-16T21:31:09Z","title":"Irreducible Semigroups of Positive Operators on Banach Lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3498","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":"sha256:9eb7b1ff5982a98671e81d50df64ad0920d81037b15d159649806ada10d6372a","target":"record","created_at":"2026-05-18T03:48:35Z","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":"0d09145c9e975ab777874c6f7b3b353a626691768f9578ab5d7a3dbcdca750bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-16T21:31:09Z","title_canon_sha256":"9b041397d91b9f19d75b013cff8f20699f1dc77a26178eacacb20c48cf314192"},"schema_version":"1.0","source":{"id":"1208.3498","kind":"arxiv","version":1}},"canonical_sha256":"b570801f9db2f8ec7c032091de4de21940af116f20e1f5b8298946b50cb96f82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b570801f9db2f8ec7c032091de4de21940af116f20e1f5b8298946b50cb96f82","first_computed_at":"2026-05-18T03:48:35.054760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:35.054760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9++QMj5YIeIxVTVozrO9n1d6hGuQnz0oSDAybE0FRDU4d3Vjwc2xfm3a4oJU6cpoC/UGqhjJJ5Fhc+l3uudjAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:35.055370Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3498","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9eb7b1ff5982a98671e81d50df64ad0920d81037b15d159649806ada10d6372a","sha256:f54c3c68f31c148b42c2def37c254f082f1ec0340412b76a18fd9d6f357bb4af"],"state_sha256":"4c4d95cd2e82e66c303b7e00b5504ba9b710b0454ac7ef89a4bce9a3613e07b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RVTKSnFnR40j/Hyrf7Izfre5BUkXPVfkuoKK8nrXCIgupNFUgWL/1u/sIiXUSAp4w29HvfzO38ZJ8QxAouV1Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T09:34:41.264051Z","bundle_sha256":"2a5adfac98251d1c9c73457db80a72e60c66a3d64714aa9fc5b06a75d6494bd0"}}