{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WSHAU2EYT4TYFCV2UYK6ZOEDTP","short_pith_number":"pith:WSHAU2EY","canonical_record":{"source":{"id":"1811.08658","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-21T10:06:54Z","cross_cats_sorted":[],"title_canon_sha256":"0676208da5e8fef7772ffdf17e7139540e0d84612e1e7daf3f49d716cd3c2ec1","abstract_canon_sha256":"f487c77ce681033f5c37701c01355643294c828ac6aa8b9bb430d27ab3941f51"},"schema_version":"1.0"},"canonical_sha256":"b48e0a68989f27828abaa615ecb8839bea967ede1835b0fc261ce602a91aa4cd","source":{"kind":"arxiv","id":"1811.08658","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.08658","created_at":"2026-05-18T00:00:11Z"},{"alias_kind":"arxiv_version","alias_value":"1811.08658v1","created_at":"2026-05-18T00:00:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08658","created_at":"2026-05-18T00:00:11Z"},{"alias_kind":"pith_short_12","alias_value":"WSHAU2EYT4TY","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WSHAU2EYT4TYFCV2","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WSHAU2EY","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WSHAU2EYT4TYFCV2UYK6ZOEDTP","target":"record","payload":{"canonical_record":{"source":{"id":"1811.08658","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-21T10:06:54Z","cross_cats_sorted":[],"title_canon_sha256":"0676208da5e8fef7772ffdf17e7139540e0d84612e1e7daf3f49d716cd3c2ec1","abstract_canon_sha256":"f487c77ce681033f5c37701c01355643294c828ac6aa8b9bb430d27ab3941f51"},"schema_version":"1.0"},"canonical_sha256":"b48e0a68989f27828abaa615ecb8839bea967ede1835b0fc261ce602a91aa4cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:11.966423Z","signature_b64":"4iuKts5xE/H1HhZjmlW5iPCDcaiZtP+qqORyBGqlg2hOEDdNjLQKmwTsTYWTBjzEL0ErkfaA8cOmzY8F5e/bCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b48e0a68989f27828abaa615ecb8839bea967ede1835b0fc261ce602a91aa4cd","last_reissued_at":"2026-05-18T00:00:11.966009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:11.966009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.08658","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":"2026-05-18T00:00:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SvMwijVJn+AXXusKQY1hZxmyEFHclI6bfyTkTMRF19OOb8JrYLMpxUDHMLoYfh+eOj4DiKsLLhXrn2Rguj+iBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T15:57:37.383931Z"},"content_sha256":"2a8467a07d8d73f2206a67d23e349cc4da2d1c8fa60558754dc0a510c09ac285","schema_version":"1.0","event_id":"sha256:2a8467a07d8d73f2206a67d23e349cc4da2d1c8fa60558754dc0a510c09ac285"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WSHAU2EYT4TYFCV2UYK6ZOEDTP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the complexity of detecting positive eigenvectors of nonlinear cone maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bas Lemmens, Lewis White","submitted_at":"2018-11-21T10:06:54Z","abstract_excerpt":"In recent work with Lins and Nussbaum the first author gave an algorithm that can detect the existence of a positive eigenvector for order-preserving homogeneous maps on the standard positive cone. The main goal of this paper is to determine the minimum number of iterations this algorithm requires. It is known that this number is equal to the illumination number of the unit ball of the variation norm. In this paper we determine its illumination number, and hence provide a sharp lower bound for the running time of the algorithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08658","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":"2026-05-18T00:00:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T8dV+0QVRsoaDZUYiKbU3/QIQSObhYqId+KpkvyJtq52dqGSC/4V5QLxMTGxDGuaSVgD2HSaTgn+U7ymz/EpBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T15:57:37.384658Z"},"content_sha256":"9ca5ae7bd9961be3da3784835540fec15b4fc907e0cbd52f23f36371c97e45f5","schema_version":"1.0","event_id":"sha256:9ca5ae7bd9961be3da3784835540fec15b4fc907e0cbd52f23f36371c97e45f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WSHAU2EYT4TYFCV2UYK6ZOEDTP/bundle.json","state_url":"https://pith.science/pith/WSHAU2EYT4TYFCV2UYK6ZOEDTP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WSHAU2EYT4TYFCV2UYK6ZOEDTP/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":"2026-06-08T15:57:37Z","links":{"resolver":"https://pith.science/pith/WSHAU2EYT4TYFCV2UYK6ZOEDTP","bundle":"https://pith.science/pith/WSHAU2EYT4TYFCV2UYK6ZOEDTP/bundle.json","state":"https://pith.science/pith/WSHAU2EYT4TYFCV2UYK6ZOEDTP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WSHAU2EYT4TYFCV2UYK6ZOEDTP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WSHAU2EYT4TYFCV2UYK6ZOEDTP","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":"f487c77ce681033f5c37701c01355643294c828ac6aa8b9bb430d27ab3941f51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-21T10:06:54Z","title_canon_sha256":"0676208da5e8fef7772ffdf17e7139540e0d84612e1e7daf3f49d716cd3c2ec1"},"schema_version":"1.0","source":{"id":"1811.08658","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.08658","created_at":"2026-05-18T00:00:11Z"},{"alias_kind":"arxiv_version","alias_value":"1811.08658v1","created_at":"2026-05-18T00:00:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08658","created_at":"2026-05-18T00:00:11Z"},{"alias_kind":"pith_short_12","alias_value":"WSHAU2EYT4TY","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WSHAU2EYT4TYFCV2","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WSHAU2EY","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:9ca5ae7bd9961be3da3784835540fec15b4fc907e0cbd52f23f36371c97e45f5","target":"graph","created_at":"2026-05-18T00:00:11Z","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 recent work with Lins and Nussbaum the first author gave an algorithm that can detect the existence of a positive eigenvector for order-preserving homogeneous maps on the standard positive cone. The main goal of this paper is to determine the minimum number of iterations this algorithm requires. It is known that this number is equal to the illumination number of the unit ball of the variation norm. In this paper we determine its illumination number, and hence provide a sharp lower bound for the running time of the algorithm.","authors_text":"Bas Lemmens, Lewis White","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-21T10:06:54Z","title":"On the complexity of detecting positive eigenvectors of nonlinear cone maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08658","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":"sha256:2a8467a07d8d73f2206a67d23e349cc4da2d1c8fa60558754dc0a510c09ac285","target":"record","created_at":"2026-05-18T00:00:11Z","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":"f487c77ce681033f5c37701c01355643294c828ac6aa8b9bb430d27ab3941f51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-11-21T10:06:54Z","title_canon_sha256":"0676208da5e8fef7772ffdf17e7139540e0d84612e1e7daf3f49d716cd3c2ec1"},"schema_version":"1.0","source":{"id":"1811.08658","kind":"arxiv","version":1}},"canonical_sha256":"b48e0a68989f27828abaa615ecb8839bea967ede1835b0fc261ce602a91aa4cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b48e0a68989f27828abaa615ecb8839bea967ede1835b0fc261ce602a91aa4cd","first_computed_at":"2026-05-18T00:00:11.966009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:11.966009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4iuKts5xE/H1HhZjmlW5iPCDcaiZtP+qqORyBGqlg2hOEDdNjLQKmwTsTYWTBjzEL0ErkfaA8cOmzY8F5e/bCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:11.966423Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.08658","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a8467a07d8d73f2206a67d23e349cc4da2d1c8fa60558754dc0a510c09ac285","sha256:9ca5ae7bd9961be3da3784835540fec15b4fc907e0cbd52f23f36371c97e45f5"],"state_sha256":"32c55901fd72d3e0908e8e7d35f0cd493bd0abf31fe977add40d7a6b7e4e3882"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q7yq8/cuJB6YgqNmNkF3rEWNQE4X9qSuho03yb0N3e7v3xQoVsIhnR48v1HlHd312RVok4z9VTcQ6Ysfwwc+DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T15:57:37.388441Z","bundle_sha256":"a5e5ddf5bab4859b145ebc3cc145ba2f91a2c644d671b202c966ec9885e1a45c"}}