{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KX5A2PONERMHQD6VFS6N3THKZL","short_pith_number":"pith:KX5A2PON","canonical_record":{"source":{"id":"1303.7146","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-03-28T15:07:10Z","cross_cats_sorted":[],"title_canon_sha256":"1add0f52822bceb474052e3e648251670cc8d34526f24f93b7dfb91698658e23","abstract_canon_sha256":"18954fd683edf3015371b900f52fad21e9bdd7cba57a0ec977c7bdf0be7ea556"},"schema_version":"1.0"},"canonical_sha256":"55fa0d3dcd2458780fd52cbcddcceacaff935a1d0a7d32e94836447969d01529","source":{"kind":"arxiv","id":"1303.7146","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.7146","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"1303.7146v1","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.7146","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"KX5A2PONERMH","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KX5A2PONERMHQD6V","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KX5A2PON","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KX5A2PONERMHQD6VFS6N3THKZL","target":"record","payload":{"canonical_record":{"source":{"id":"1303.7146","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-03-28T15:07:10Z","cross_cats_sorted":[],"title_canon_sha256":"1add0f52822bceb474052e3e648251670cc8d34526f24f93b7dfb91698658e23","abstract_canon_sha256":"18954fd683edf3015371b900f52fad21e9bdd7cba57a0ec977c7bdf0be7ea556"},"schema_version":"1.0"},"canonical_sha256":"55fa0d3dcd2458780fd52cbcddcceacaff935a1d0a7d32e94836447969d01529","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:24.472121Z","signature_b64":"8/94EwlfnpusDHLBv4PQF3aR0BoE3cMpC3JOsZTmr9Kq+oglyTMTLHb7hSqUd/SbxfW0lRRbP/aXgvhONM/aCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55fa0d3dcd2458780fd52cbcddcceacaff935a1d0a7d32e94836447969d01529","last_reissued_at":"2026-05-18T01:03:24.471618Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:24.471618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.7146","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":"2026-05-18T01:03:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jXMewHJdBu+81INZr/UzlyRmWxRP82pmkTNv08jiUZOaPXr3PCub/rTTYwnFwpzPyv8lkp98eyseuc9dIA++Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:33:51.864349Z"},"content_sha256":"c895ab8f7df63a64278e15571657ec32d0b703654cc61321e6c808fbeeedda24","schema_version":"1.0","event_id":"sha256:c895ab8f7df63a64278e15571657ec32d0b703654cc61321e6c808fbeeedda24"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KX5A2PONERMHQD6VFS6N3THKZL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diversities, hyperconvexity and fixed points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Bozena Piatek, Rafa Espinola","submitted_at":"2013-03-28T15:07:10Z","abstract_excerpt":"Diversities have been recently introduced as a generalization of metrics for which a rich tight span theory could be stated. In this work we take up a number of questions about hyperconvexity, diversities and fixed points of nonexpansive mappings. Most of these questions are motivated by the study of the connection between a hyperconvex diversity and its induced metric space for which we provide some answers. Examples are given, for instance, showing that such a metric space need not be hyperconvex but still we prove, as our main result, that they enjoy the fixed point property for nonexpansiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7146","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":"2026-05-18T01:03:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bqUg+ap5ca10j7bZJMfBpdIvVrrAmT22n78ett1D9E4HAuDxzFB+LF4BL2ci5u7/EJhe4dc24tOZn+Vl8FGGBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:33:51.864709Z"},"content_sha256":"28a85d82b51d4fedc278ba3b5db24c32b0a8131fd87fa8998b166e3c91e5f278","schema_version":"1.0","event_id":"sha256:28a85d82b51d4fedc278ba3b5db24c32b0a8131fd87fa8998b166e3c91e5f278"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KX5A2PONERMHQD6VFS6N3THKZL/bundle.json","state_url":"https://pith.science/pith/KX5A2PONERMHQD6VFS6N3THKZL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KX5A2PONERMHQD6VFS6N3THKZL/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":"2026-06-08T22:33:51Z","links":{"resolver":"https://pith.science/pith/KX5A2PONERMHQD6VFS6N3THKZL","bundle":"https://pith.science/pith/KX5A2PONERMHQD6VFS6N3THKZL/bundle.json","state":"https://pith.science/pith/KX5A2PONERMHQD6VFS6N3THKZL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KX5A2PONERMHQD6VFS6N3THKZL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KX5A2PONERMHQD6VFS6N3THKZL","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":"18954fd683edf3015371b900f52fad21e9bdd7cba57a0ec977c7bdf0be7ea556","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-03-28T15:07:10Z","title_canon_sha256":"1add0f52822bceb474052e3e648251670cc8d34526f24f93b7dfb91698658e23"},"schema_version":"1.0","source":{"id":"1303.7146","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.7146","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"1303.7146v1","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.7146","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"KX5A2PONERMH","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KX5A2PONERMHQD6V","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KX5A2PON","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:28a85d82b51d4fedc278ba3b5db24c32b0a8131fd87fa8998b166e3c91e5f278","target":"graph","created_at":"2026-05-18T01:03:24Z","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":"Diversities have been recently introduced as a generalization of metrics for which a rich tight span theory could be stated. In this work we take up a number of questions about hyperconvexity, diversities and fixed points of nonexpansive mappings. Most of these questions are motivated by the study of the connection between a hyperconvex diversity and its induced metric space for which we provide some answers. Examples are given, for instance, showing that such a metric space need not be hyperconvex but still we prove, as our main result, that they enjoy the fixed point property for nonexpansiv","authors_text":"Bozena Piatek, Rafa Espinola","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-03-28T15:07:10Z","title":"Diversities, hyperconvexity and fixed points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7146","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:c895ab8f7df63a64278e15571657ec32d0b703654cc61321e6c808fbeeedda24","target":"record","created_at":"2026-05-18T01:03:24Z","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":"18954fd683edf3015371b900f52fad21e9bdd7cba57a0ec977c7bdf0be7ea556","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-03-28T15:07:10Z","title_canon_sha256":"1add0f52822bceb474052e3e648251670cc8d34526f24f93b7dfb91698658e23"},"schema_version":"1.0","source":{"id":"1303.7146","kind":"arxiv","version":1}},"canonical_sha256":"55fa0d3dcd2458780fd52cbcddcceacaff935a1d0a7d32e94836447969d01529","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55fa0d3dcd2458780fd52cbcddcceacaff935a1d0a7d32e94836447969d01529","first_computed_at":"2026-05-18T01:03:24.471618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:24.471618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8/94EwlfnpusDHLBv4PQF3aR0BoE3cMpC3JOsZTmr9Kq+oglyTMTLHb7hSqUd/SbxfW0lRRbP/aXgvhONM/aCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:24.472121Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.7146","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c895ab8f7df63a64278e15571657ec32d0b703654cc61321e6c808fbeeedda24","sha256:28a85d82b51d4fedc278ba3b5db24c32b0a8131fd87fa8998b166e3c91e5f278"],"state_sha256":"aeabee50395f1f9899c48ebb12ed8b0d32a80cd43859215bff5d094739b35c88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RJPsT4KJFIiwTLYZweUdA9OF2bl+mhcXvq38RZFX3x7/0B/d40Te9iA9vukl37H+RJljTGfNKZNGiLbJeAtoAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T22:33:51.866910Z","bundle_sha256":"a3d8f0e02151b089a354aa188f2b338894b9ec03390efd449d68686f447f4b2b"}}