{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:3OYSZMORMRLK5YSOSDZJJDOL2T","short_pith_number":"pith:3OYSZMOR","canonical_record":{"source":{"id":"1905.08334","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-05-20T20:26:39Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"1ceaec88fd29d8b32bc59a9789dc9330830bc493ddb0a9dacb85e250ae6f4043","abstract_canon_sha256":"f86101c75092a27b58d234b5d1a2e3cb88254b69d010ea0283acd03d4c4ed731"},"schema_version":"1.0"},"canonical_sha256":"dbb12cb1d16456aee24e90f2948dcbd4cf658da3ba85eba60be7ad93af9c078a","source":{"kind":"arxiv","id":"1905.08334","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.08334","created_at":"2026-05-17T23:45:43Z"},{"alias_kind":"arxiv_version","alias_value":"1905.08334v1","created_at":"2026-05-17T23:45:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.08334","created_at":"2026-05-17T23:45:43Z"},{"alias_kind":"pith_short_12","alias_value":"3OYSZMORMRLK","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"3OYSZMORMRLK5YSO","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"3OYSZMOR","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:3OYSZMORMRLK5YSOSDZJJDOL2T","target":"record","payload":{"canonical_record":{"source":{"id":"1905.08334","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-05-20T20:26:39Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"1ceaec88fd29d8b32bc59a9789dc9330830bc493ddb0a9dacb85e250ae6f4043","abstract_canon_sha256":"f86101c75092a27b58d234b5d1a2e3cb88254b69d010ea0283acd03d4c4ed731"},"schema_version":"1.0"},"canonical_sha256":"dbb12cb1d16456aee24e90f2948dcbd4cf658da3ba85eba60be7ad93af9c078a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:43.608964Z","signature_b64":"ZCCKdVKViU1jWTnZXZ+7jH9wluOxZodgxz0T40mECk9OHk14rDIBzMzohCE5mEUzMfZIRoSc2gEaVPnNcJG6AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dbb12cb1d16456aee24e90f2948dcbd4cf658da3ba85eba60be7ad93af9c078a","last_reissued_at":"2026-05-17T23:45:43.608461Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:43.608461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.08334","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":"2026-05-17T23:45:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9W+Z87fYj6ZvNsCAgnlGkEmYH1g2wHfNn70LPVzK5RjhGDpEIsj7ShznLn7/D8otEG1kf2fsyrJCFrEmeB5NCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:38:14.195390Z"},"content_sha256":"c141571c61dd6038e856f78bd0f788d8aa6509410903d35d7584dd20d5b1763e","schema_version":"1.0","event_id":"sha256:c141571c61dd6038e856f78bd0f788d8aa6509410903d35d7584dd20d5b1763e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:3OYSZMORMRLK5YSOSDZJJDOL2T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geodesic rays, the \"Lion-Man\" game, and the fixed point property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.MG","authors_text":"Adriana Nicolae, Bo\\.zena Pi\\k{a}tek, Genaro L\\'opez-Acedo","submitted_at":"2019-05-20T20:26:39Z","abstract_excerpt":"This paper focuses on the relation among the existence of different types of curves (such as directional ones, quasi-geodesic or geodesic rays), the (approximate) fixed point property for nonexpansive mappings, and a discrete lion and man game. Our main result holds in the setting of CAT(0) spaces that are additionally Gromov hyperbolic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08334","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":"2026-05-17T23:45:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J+DgSLR076ukgUd55ThoXu371FAN6frFyMjjQMW+hKNuGDrcD28+GNGTXz9+xVisyeqTczG1Qy3Q01UKGy4pAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:38:14.195780Z"},"content_sha256":"0051f4c974b66ea00dc9fb6422eaced669a9fd71864cc6f678c63ed1d3dd7100","schema_version":"1.0","event_id":"sha256:0051f4c974b66ea00dc9fb6422eaced669a9fd71864cc6f678c63ed1d3dd7100"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3OYSZMORMRLK5YSOSDZJJDOL2T/bundle.json","state_url":"https://pith.science/pith/3OYSZMORMRLK5YSOSDZJJDOL2T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3OYSZMORMRLK5YSOSDZJJDOL2T/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":"2026-05-31T08:38:14Z","links":{"resolver":"https://pith.science/pith/3OYSZMORMRLK5YSOSDZJJDOL2T","bundle":"https://pith.science/pith/3OYSZMORMRLK5YSOSDZJJDOL2T/bundle.json","state":"https://pith.science/pith/3OYSZMORMRLK5YSOSDZJJDOL2T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3OYSZMORMRLK5YSOSDZJJDOL2T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3OYSZMORMRLK5YSOSDZJJDOL2T","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":"f86101c75092a27b58d234b5d1a2e3cb88254b69d010ea0283acd03d4c4ed731","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-05-20T20:26:39Z","title_canon_sha256":"1ceaec88fd29d8b32bc59a9789dc9330830bc493ddb0a9dacb85e250ae6f4043"},"schema_version":"1.0","source":{"id":"1905.08334","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.08334","created_at":"2026-05-17T23:45:43Z"},{"alias_kind":"arxiv_version","alias_value":"1905.08334v1","created_at":"2026-05-17T23:45:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.08334","created_at":"2026-05-17T23:45:43Z"},{"alias_kind":"pith_short_12","alias_value":"3OYSZMORMRLK","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"3OYSZMORMRLK5YSO","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"3OYSZMOR","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:0051f4c974b66ea00dc9fb6422eaced669a9fd71864cc6f678c63ed1d3dd7100","target":"graph","created_at":"2026-05-17T23:45:43Z","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 focuses on the relation among the existence of different types of curves (such as directional ones, quasi-geodesic or geodesic rays), the (approximate) fixed point property for nonexpansive mappings, and a discrete lion and man game. Our main result holds in the setting of CAT(0) spaces that are additionally Gromov hyperbolic.","authors_text":"Adriana Nicolae, Bo\\.zena Pi\\k{a}tek, Genaro L\\'opez-Acedo","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-05-20T20:26:39Z","title":"Geodesic rays, the \"Lion-Man\" game, and the fixed point property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08334","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:c141571c61dd6038e856f78bd0f788d8aa6509410903d35d7584dd20d5b1763e","target":"record","created_at":"2026-05-17T23:45:43Z","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":"f86101c75092a27b58d234b5d1a2e3cb88254b69d010ea0283acd03d4c4ed731","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-05-20T20:26:39Z","title_canon_sha256":"1ceaec88fd29d8b32bc59a9789dc9330830bc493ddb0a9dacb85e250ae6f4043"},"schema_version":"1.0","source":{"id":"1905.08334","kind":"arxiv","version":1}},"canonical_sha256":"dbb12cb1d16456aee24e90f2948dcbd4cf658da3ba85eba60be7ad93af9c078a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbb12cb1d16456aee24e90f2948dcbd4cf658da3ba85eba60be7ad93af9c078a","first_computed_at":"2026-05-17T23:45:43.608461Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:43.608461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZCCKdVKViU1jWTnZXZ+7jH9wluOxZodgxz0T40mECk9OHk14rDIBzMzohCE5mEUzMfZIRoSc2gEaVPnNcJG6AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:43.608964Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.08334","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c141571c61dd6038e856f78bd0f788d8aa6509410903d35d7584dd20d5b1763e","sha256:0051f4c974b66ea00dc9fb6422eaced669a9fd71864cc6f678c63ed1d3dd7100"],"state_sha256":"a0dba6e374f562659f08b421c1e4f58c333112a110dedf0cafa515e042fe80c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uxIfdFoNSgVKTM5A6TRa7qMzEKQUny6lK9IPWDRUW6l1SMjKE0UTA5O4rM21zYAoI4vihlSYYwi6+W/xFEKyDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:38:14.200875Z","bundle_sha256":"7ed2506b42240ee0332cac45bbd6c0d10e294e8df0ba255870a048c06d86f57b"}}