{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HBP3YN77WQFIJHYO24EIIP4WJ4","short_pith_number":"pith:HBP3YN77","canonical_record":{"source":{"id":"1304.7921","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-04-30T09:00:09Z","cross_cats_sorted":[],"title_canon_sha256":"4cbe7d94dbcbe9c4b07b149164ad0b86ec401df52026dbeacdf4c00831f29a9f","abstract_canon_sha256":"302f268b70065a3f20d0aed921f6b3f4846c5796c9f2d18c473ccc28872550e4"},"schema_version":"1.0"},"canonical_sha256":"385fbc37ffb40a849f0ed708843f964f2c5646ce9e1473f5adb7ee3a4d709dc5","source":{"kind":"arxiv","id":"1304.7921","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7921","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7921v1","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7921","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"pith_short_12","alias_value":"HBP3YN77WQFI","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HBP3YN77WQFIJHYO","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HBP3YN77","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HBP3YN77WQFIJHYO24EIIP4WJ4","target":"record","payload":{"canonical_record":{"source":{"id":"1304.7921","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-04-30T09:00:09Z","cross_cats_sorted":[],"title_canon_sha256":"4cbe7d94dbcbe9c4b07b149164ad0b86ec401df52026dbeacdf4c00831f29a9f","abstract_canon_sha256":"302f268b70065a3f20d0aed921f6b3f4846c5796c9f2d18c473ccc28872550e4"},"schema_version":"1.0"},"canonical_sha256":"385fbc37ffb40a849f0ed708843f964f2c5646ce9e1473f5adb7ee3a4d709dc5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:51.387573Z","signature_b64":"NipHm77t9R7KxwvSYoey6uKrIrdxa4SuxuTFuz5YdHYbaB0fhfC8G2yrjeAKcEQkUKe4D58sVnfUUdnmHSP6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"385fbc37ffb40a849f0ed708843f964f2c5646ce9e1473f5adb7ee3a4d709dc5","last_reissued_at":"2026-05-18T03:26:51.387075Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:51.387075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.7921","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":"2026-05-18T03:26:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rm6JnjRYeDSt7AgLthFlxHoBlINdwjYmAY3A5pyagsZNNF/CfO3EdFlEXfNIku0y1svMAS3vA10+x06yhcioCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:33:47.009739Z"},"content_sha256":"f45574b7ea9307dd9e9d797754b191a09d74d3ac9ab9ecc34f2e8548a56488bd","schema_version":"1.0","event_id":"sha256:f45574b7ea9307dd9e9d797754b191a09d74d3ac9ab9ecc34f2e8548a56488bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HBP3YN77WQFIJHYO24EIIP4WJ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Birkhoff's version of Hilbert's metric and its applications in analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Bas Lemmens, Roger Nussbaum","submitted_at":"2013-04-30T09:00:09Z","abstract_excerpt":"This is a survey article concerning applications of Hilbert's metric in the analysis and dynamics of linear and nonlinear mappings on cones. It will appear as a chapter in the \"Handbook of Hilbert geometry\", ed. G. Besson, A. Papadopoulos and M. Troyanov, European Mathematical Society Publishing House, Z\\\"urich."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7921","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":"2026-05-18T03:26:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iOz8j9kMT+/VV4jxaXhPDrdc8iuZtwbUpnnXdGyDgBqYLYL3NAjsRXL4S2bKH/EwoPH9B10L9gLiE/4qIqQ3DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:33:47.010458Z"},"content_sha256":"ce4e65a53b8710292c0f55edad9aebca4bc46155c44f9653bd9c1efb875f79e1","schema_version":"1.0","event_id":"sha256:ce4e65a53b8710292c0f55edad9aebca4bc46155c44f9653bd9c1efb875f79e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HBP3YN77WQFIJHYO24EIIP4WJ4/bundle.json","state_url":"https://pith.science/pith/HBP3YN77WQFIJHYO24EIIP4WJ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HBP3YN77WQFIJHYO24EIIP4WJ4/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":"2026-06-08T20:33:47Z","links":{"resolver":"https://pith.science/pith/HBP3YN77WQFIJHYO24EIIP4WJ4","bundle":"https://pith.science/pith/HBP3YN77WQFIJHYO24EIIP4WJ4/bundle.json","state":"https://pith.science/pith/HBP3YN77WQFIJHYO24EIIP4WJ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HBP3YN77WQFIJHYO24EIIP4WJ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HBP3YN77WQFIJHYO24EIIP4WJ4","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":"302f268b70065a3f20d0aed921f6b3f4846c5796c9f2d18c473ccc28872550e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-04-30T09:00:09Z","title_canon_sha256":"4cbe7d94dbcbe9c4b07b149164ad0b86ec401df52026dbeacdf4c00831f29a9f"},"schema_version":"1.0","source":{"id":"1304.7921","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7921","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7921v1","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7921","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"pith_short_12","alias_value":"HBP3YN77WQFI","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HBP3YN77WQFIJHYO","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HBP3YN77","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:ce4e65a53b8710292c0f55edad9aebca4bc46155c44f9653bd9c1efb875f79e1","target":"graph","created_at":"2026-05-18T03:26:51Z","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 is a survey article concerning applications of Hilbert's metric in the analysis and dynamics of linear and nonlinear mappings on cones. It will appear as a chapter in the \"Handbook of Hilbert geometry\", ed. G. Besson, A. Papadopoulos and M. Troyanov, European Mathematical Society Publishing House, Z\\\"urich.","authors_text":"Bas Lemmens, Roger Nussbaum","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-04-30T09:00:09Z","title":"Birkhoff's version of Hilbert's metric and its applications in analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7921","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:f45574b7ea9307dd9e9d797754b191a09d74d3ac9ab9ecc34f2e8548a56488bd","target":"record","created_at":"2026-05-18T03:26:51Z","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":"302f268b70065a3f20d0aed921f6b3f4846c5796c9f2d18c473ccc28872550e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-04-30T09:00:09Z","title_canon_sha256":"4cbe7d94dbcbe9c4b07b149164ad0b86ec401df52026dbeacdf4c00831f29a9f"},"schema_version":"1.0","source":{"id":"1304.7921","kind":"arxiv","version":1}},"canonical_sha256":"385fbc37ffb40a849f0ed708843f964f2c5646ce9e1473f5adb7ee3a4d709dc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"385fbc37ffb40a849f0ed708843f964f2c5646ce9e1473f5adb7ee3a4d709dc5","first_computed_at":"2026-05-18T03:26:51.387075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:51.387075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NipHm77t9R7KxwvSYoey6uKrIrdxa4SuxuTFuz5YdHYbaB0fhfC8G2yrjeAKcEQkUKe4D58sVnfUUdnmHSP6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:51.387573Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.7921","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f45574b7ea9307dd9e9d797754b191a09d74d3ac9ab9ecc34f2e8548a56488bd","sha256:ce4e65a53b8710292c0f55edad9aebca4bc46155c44f9653bd9c1efb875f79e1"],"state_sha256":"349a14cbc217a2bef5cf6dcdac62364490e13a5334ccf776c85a3e360bc7306b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I83SlgGcZ2U9Rpdr/WeI3gEDwhbGS7aNXzQXbBbSbizYqIjukI8FDJ7TWG8tOv6stS+AyB7XfrlD1Syt3Sv+DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T20:33:47.014140Z","bundle_sha256":"608de03d29061acab8d6088d6b7e6b55179aa893744e5b4ac8d4163303bb8991"}}