{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:MECKGLYFF572QPIHFSWCMJZNE3","short_pith_number":"pith:MECKGLYF","canonical_record":{"source":{"id":"1107.1218","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-07-06T18:42:04Z","cross_cats_sorted":["math.FA","math.PR"],"title_canon_sha256":"2a97fb220f830c711f6aeb070f56e264f34e78d18d604de97ab9ce4292dac69f","abstract_canon_sha256":"07fc4bad2c602f59b74577bb1fdf21765d14d81ac39c13505a284b4e8b002258"},"schema_version":"1.0"},"canonical_sha256":"6104a32f052f7fa83d072cac26272d26ebce10ed9d68470d0d03232efc11f145","source":{"kind":"arxiv","id":"1107.1218","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1218","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1218v1","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1218","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"pith_short_12","alias_value":"MECKGLYFF572","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MECKGLYFF572QPIH","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MECKGLYF","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:MECKGLYFF572QPIHFSWCMJZNE3","target":"record","payload":{"canonical_record":{"source":{"id":"1107.1218","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-07-06T18:42:04Z","cross_cats_sorted":["math.FA","math.PR"],"title_canon_sha256":"2a97fb220f830c711f6aeb070f56e264f34e78d18d604de97ab9ce4292dac69f","abstract_canon_sha256":"07fc4bad2c602f59b74577bb1fdf21765d14d81ac39c13505a284b4e8b002258"},"schema_version":"1.0"},"canonical_sha256":"6104a32f052f7fa83d072cac26272d26ebce10ed9d68470d0d03232efc11f145","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:45.307225Z","signature_b64":"qfA2GgY1qgRjFlt+OjgkpHcxIXlYgz9ELEv3HZPLXxXqxCyYlx0IWaO2yKdH29EWNwtWoHAaN5F/yv9ixW72CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6104a32f052f7fa83d072cac26272d26ebce10ed9d68470d0d03232efc11f145","last_reissued_at":"2026-05-18T04:18:45.306787Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:45.306787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.1218","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":"2026-05-18T04:18:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EOC/6LyQBKciOsbrEvtLJFaQtlEsxwl+rej2WgZKFW8JOo252RTbBuadObhLU2dp+h2cLThilfx8zzwb1BPPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:33:38.226055Z"},"content_sha256":"940404e2b21596b5b9f5f5ae14a17ac2b139b0a75b66145d6cffde4046a30a62","schema_version":"1.0","event_id":"sha256:940404e2b21596b5b9f5f5ae14a17ac2b139b0a75b66145d6cffde4046a30a62"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:MECKGLYFF572QPIHFSWCMJZNE3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convex hyperspaces of probability measures and extensors in the asymptotic category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.GN","authors_text":"Du\\v{s}an Repov\\v{s}, Mykhailo Zarichnyi","submitted_at":"2011-07-06T18:42:04Z","abstract_excerpt":"The objects of the Dranishnikov asymptotic category are proper metric spaces and the morphisms are asymptotically Lipschitz maps. In this paper we provide an example of an asymptotically zero-dimensional space (in the sense of Gromov) whose space of compact convex subsets of probability measures is not an absolute extensor in the asymptotic category in the sense of Dranishnikov."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1218","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":"2026-05-18T04:18:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uke+xiiO3xc1YWilSNHpuA6oZuWoL8BB3woEJWQ2yBL/8QvKsko5oUBv7MNfDelzY+gmaSHw3b8HaBYqitFyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:33:38.226796Z"},"content_sha256":"aba3e64274fd5ef7b812b0b769a4f7acf475ecfb0ec2897974d888930ed710a3","schema_version":"1.0","event_id":"sha256:aba3e64274fd5ef7b812b0b769a4f7acf475ecfb0ec2897974d888930ed710a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MECKGLYFF572QPIHFSWCMJZNE3/bundle.json","state_url":"https://pith.science/pith/MECKGLYFF572QPIHFSWCMJZNE3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MECKGLYFF572QPIHFSWCMJZNE3/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":"2026-06-09T06:33:38Z","links":{"resolver":"https://pith.science/pith/MECKGLYFF572QPIHFSWCMJZNE3","bundle":"https://pith.science/pith/MECKGLYFF572QPIHFSWCMJZNE3/bundle.json","state":"https://pith.science/pith/MECKGLYFF572QPIHFSWCMJZNE3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MECKGLYFF572QPIHFSWCMJZNE3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MECKGLYFF572QPIHFSWCMJZNE3","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":"07fc4bad2c602f59b74577bb1fdf21765d14d81ac39c13505a284b4e8b002258","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-07-06T18:42:04Z","title_canon_sha256":"2a97fb220f830c711f6aeb070f56e264f34e78d18d604de97ab9ce4292dac69f"},"schema_version":"1.0","source":{"id":"1107.1218","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1218","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1218v1","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1218","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"pith_short_12","alias_value":"MECKGLYFF572","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MECKGLYFF572QPIH","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MECKGLYF","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:aba3e64274fd5ef7b812b0b769a4f7acf475ecfb0ec2897974d888930ed710a3","target":"graph","created_at":"2026-05-18T04:18:45Z","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":"The objects of the Dranishnikov asymptotic category are proper metric spaces and the morphisms are asymptotically Lipschitz maps. In this paper we provide an example of an asymptotically zero-dimensional space (in the sense of Gromov) whose space of compact convex subsets of probability measures is not an absolute extensor in the asymptotic category in the sense of Dranishnikov.","authors_text":"Du\\v{s}an Repov\\v{s}, Mykhailo Zarichnyi","cross_cats":["math.FA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-07-06T18:42:04Z","title":"Convex hyperspaces of probability measures and extensors in the asymptotic category"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1218","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":"sha256:940404e2b21596b5b9f5f5ae14a17ac2b139b0a75b66145d6cffde4046a30a62","target":"record","created_at":"2026-05-18T04:18:45Z","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":"07fc4bad2c602f59b74577bb1fdf21765d14d81ac39c13505a284b4e8b002258","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-07-06T18:42:04Z","title_canon_sha256":"2a97fb220f830c711f6aeb070f56e264f34e78d18d604de97ab9ce4292dac69f"},"schema_version":"1.0","source":{"id":"1107.1218","kind":"arxiv","version":1}},"canonical_sha256":"6104a32f052f7fa83d072cac26272d26ebce10ed9d68470d0d03232efc11f145","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6104a32f052f7fa83d072cac26272d26ebce10ed9d68470d0d03232efc11f145","first_computed_at":"2026-05-18T04:18:45.306787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:45.306787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qfA2GgY1qgRjFlt+OjgkpHcxIXlYgz9ELEv3HZPLXxXqxCyYlx0IWaO2yKdH29EWNwtWoHAaN5F/yv9ixW72CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:45.307225Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1218","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:940404e2b21596b5b9f5f5ae14a17ac2b139b0a75b66145d6cffde4046a30a62","sha256:aba3e64274fd5ef7b812b0b769a4f7acf475ecfb0ec2897974d888930ed710a3"],"state_sha256":"763736b176ba7bc5af2036f117a62a2e912d4e7c8edb0bfb1d0ca1343585c3e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ni9kc2Qk9DruS/L//V/BriRhE+29IwI4pDiHNZ4VC+BGFw+n6os/syO2QsSWcGYpvxOyH5Dv7EvKYmL/79cSBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:33:38.230717Z","bundle_sha256":"dd89c8c1bc090ddfc7b6410913b1e43abf5182be12028c4e2a6c00ca776ed8b8"}}