{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GKL5D3HY7DYS4NMOYYIKFI2RQO","short_pith_number":"pith:GKL5D3HY","canonical_record":{"source":{"id":"1302.3905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-15T22:24:40Z","cross_cats_sorted":[],"title_canon_sha256":"4e6235a82bb6eb23b9ee414c05074a1c7e6eb6c42fe5172c2d135e6d99f9bb44","abstract_canon_sha256":"fc6ff72fc3d7c82b56b0bfcafbdc6ebb98a0e0b882e4e83ebba7c7da2bd50cff"},"schema_version":"1.0"},"canonical_sha256":"3297d1ecf8f8f12e358ec610a2a3518397468f078ba02ca73221ab05292db01e","source":{"kind":"arxiv","id":"1302.3905","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3905","created_at":"2026-05-18T03:33:24Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3905v1","created_at":"2026-05-18T03:33:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3905","created_at":"2026-05-18T03:33:24Z"},{"alias_kind":"pith_short_12","alias_value":"GKL5D3HY7DYS","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GKL5D3HY7DYS4NMO","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GKL5D3HY","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GKL5D3HY7DYS4NMOYYIKFI2RQO","target":"record","payload":{"canonical_record":{"source":{"id":"1302.3905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-15T22:24:40Z","cross_cats_sorted":[],"title_canon_sha256":"4e6235a82bb6eb23b9ee414c05074a1c7e6eb6c42fe5172c2d135e6d99f9bb44","abstract_canon_sha256":"fc6ff72fc3d7c82b56b0bfcafbdc6ebb98a0e0b882e4e83ebba7c7da2bd50cff"},"schema_version":"1.0"},"canonical_sha256":"3297d1ecf8f8f12e358ec610a2a3518397468f078ba02ca73221ab05292db01e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:24.916393Z","signature_b64":"lTM2Je7BF7PeWmgBKISBjJvjof7cWZb+w8Yi1uOdjK8uCjn1LJTiRJtfjjBQZ1jg8tM1h7BDAHp68AYj3HmRBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3297d1ecf8f8f12e358ec610a2a3518397468f078ba02ca73221ab05292db01e","last_reissued_at":"2026-05-18T03:33:24.915766Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:24.915766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.3905","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":"2026-05-18T03:33:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+s1pbXK1TsnOfy2M5o7f0OkGOH21F1yvEjpyO20O2KihkVOu7dUZL/jM68fNDvnXBFDQrob/RUAPSjDJYHZ9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T10:05:52.462703Z"},"content_sha256":"0d3bbae0979f7757055a6ffdf8fbc33b4b09bb6829f6a08e9f3f0ba7a1026f79","schema_version":"1.0","event_id":"sha256:0d3bbae0979f7757055a6ffdf8fbc33b4b09bb6829f6a08e9f3f0ba7a1026f79"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GKL5D3HY7DYS4NMOYYIKFI2RQO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenvectors and eigenfunctionals of homogeneous order-preserving maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Horst R. Thieme","submitted_at":"2013-02-15T22:24:40Z","abstract_excerpt":"This paper considers homogeneous order preserving continuous maps on the normal cone of an ordered normed vector space. It is shown that certain operators of that kind which are not necessarily compact themselves but have a compact power have a positive eigenvector that is associated with the cone spectral radius. We also derive conditions for the existence of homogeneous order preserving eigenfunctionals. Our results are illustrated in a model for spatially distributed two-sex populations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3905","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":"2026-05-18T03:33:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ekF2GCfcju4NoHwFH2/PoNFKddxVpSuuTCa5ClQqDpcsFlG0I86cWEpYvyjMfsw2bDC2iOGWemQYCoXNEyYMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T10:05:52.463041Z"},"content_sha256":"fc399568e38c7f667b8deffa3fd4645f684d89cca948e0b40df7dcb3123b29c3","schema_version":"1.0","event_id":"sha256:fc399568e38c7f667b8deffa3fd4645f684d89cca948e0b40df7dcb3123b29c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GKL5D3HY7DYS4NMOYYIKFI2RQO/bundle.json","state_url":"https://pith.science/pith/GKL5D3HY7DYS4NMOYYIKFI2RQO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GKL5D3HY7DYS4NMOYYIKFI2RQO/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":"2026-07-04T10:05:52Z","links":{"resolver":"https://pith.science/pith/GKL5D3HY7DYS4NMOYYIKFI2RQO","bundle":"https://pith.science/pith/GKL5D3HY7DYS4NMOYYIKFI2RQO/bundle.json","state":"https://pith.science/pith/GKL5D3HY7DYS4NMOYYIKFI2RQO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GKL5D3HY7DYS4NMOYYIKFI2RQO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GKL5D3HY7DYS4NMOYYIKFI2RQO","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":"fc6ff72fc3d7c82b56b0bfcafbdc6ebb98a0e0b882e4e83ebba7c7da2bd50cff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-15T22:24:40Z","title_canon_sha256":"4e6235a82bb6eb23b9ee414c05074a1c7e6eb6c42fe5172c2d135e6d99f9bb44"},"schema_version":"1.0","source":{"id":"1302.3905","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3905","created_at":"2026-05-18T03:33:24Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3905v1","created_at":"2026-05-18T03:33:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3905","created_at":"2026-05-18T03:33:24Z"},{"alias_kind":"pith_short_12","alias_value":"GKL5D3HY7DYS","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GKL5D3HY7DYS4NMO","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GKL5D3HY","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:fc399568e38c7f667b8deffa3fd4645f684d89cca948e0b40df7dcb3123b29c3","target":"graph","created_at":"2026-05-18T03:33:24Z","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":"This paper considers homogeneous order preserving continuous maps on the normal cone of an ordered normed vector space. It is shown that certain operators of that kind which are not necessarily compact themselves but have a compact power have a positive eigenvector that is associated with the cone spectral radius. We also derive conditions for the existence of homogeneous order preserving eigenfunctionals. Our results are illustrated in a model for spatially distributed two-sex populations.","authors_text":"Horst R. Thieme","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-15T22:24:40Z","title":"Eigenvectors and eigenfunctionals of homogeneous order-preserving maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3905","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":"sha256:0d3bbae0979f7757055a6ffdf8fbc33b4b09bb6829f6a08e9f3f0ba7a1026f79","target":"record","created_at":"2026-05-18T03:33:24Z","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":"fc6ff72fc3d7c82b56b0bfcafbdc6ebb98a0e0b882e4e83ebba7c7da2bd50cff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-15T22:24:40Z","title_canon_sha256":"4e6235a82bb6eb23b9ee414c05074a1c7e6eb6c42fe5172c2d135e6d99f9bb44"},"schema_version":"1.0","source":{"id":"1302.3905","kind":"arxiv","version":1}},"canonical_sha256":"3297d1ecf8f8f12e358ec610a2a3518397468f078ba02ca73221ab05292db01e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3297d1ecf8f8f12e358ec610a2a3518397468f078ba02ca73221ab05292db01e","first_computed_at":"2026-05-18T03:33:24.915766Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:24.915766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lTM2Je7BF7PeWmgBKISBjJvjof7cWZb+w8Yi1uOdjK8uCjn1LJTiRJtfjjBQZ1jg8tM1h7BDAHp68AYj3HmRBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:24.916393Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3905","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d3bbae0979f7757055a6ffdf8fbc33b4b09bb6829f6a08e9f3f0ba7a1026f79","sha256:fc399568e38c7f667b8deffa3fd4645f684d89cca948e0b40df7dcb3123b29c3"],"state_sha256":"d61e4ee7da953de936bde25748e624bacd51ddd0acd9ebd9dc1bdc03c8ce888f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"10zJ1FnCwgg7r+B/EHe3TykaOrKao1WXWZoV0On7XzP2ZiTDuWpD+5VoTUx9uNGzNXok/ctgmj3uOKxn2mvXCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T10:05:52.464954Z","bundle_sha256":"a0598bce09410bddec9b9ad3f3ee35be7356d8c44c00b85a6802db0502f941af"}}