{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:4I4YOMRZEWA5RSTITBBDTL5QPH","short_pith_number":"pith:4I4YOMRZ","canonical_record":{"source":{"id":"0803.1697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2008-03-12T02:48:58Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"96ccf46b1ee38008b09fd3c8e7f503352cd72c48f98e98ddc94df45baa7760ac","abstract_canon_sha256":"f1001ecaac2e339679c9f8e3c9c32f3f7042a0d009cd1eea0dd3216e9bd0f47c"},"schema_version":"1.0"},"canonical_sha256":"e2398732392581d8ca68984239afb079f7fa62e7e44c9d0c9372c45805571dfc","source":{"kind":"arxiv","id":"0803.1697","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.1697","created_at":"2026-05-18T03:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"0803.1697v2","created_at":"2026-05-18T03:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.1697","created_at":"2026-05-18T03:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"4I4YOMRZEWA5","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"4I4YOMRZEWA5RSTI","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"4I4YOMRZ","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:4I4YOMRZEWA5RSTITBBDTL5QPH","target":"record","payload":{"canonical_record":{"source":{"id":"0803.1697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2008-03-12T02:48:58Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"96ccf46b1ee38008b09fd3c8e7f503352cd72c48f98e98ddc94df45baa7760ac","abstract_canon_sha256":"f1001ecaac2e339679c9f8e3c9c32f3f7042a0d009cd1eea0dd3216e9bd0f47c"},"schema_version":"1.0"},"canonical_sha256":"e2398732392581d8ca68984239afb079f7fa62e7e44c9d0c9372c45805571dfc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:42.370415Z","signature_b64":"GB/r5ainAbyPckyu1fCj02DaoNMwoOo13CKR5IqVHSvYlFD8yWIi50xV6eHqvsXsOWNVZdFKzHlDXL+A9lXiBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2398732392581d8ca68984239afb079f7fa62e7e44c9d0c9372c45805571dfc","last_reissued_at":"2026-05-18T03:39:42.369685Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:42.369685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0803.1697","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+7H//K94D/GGafil1QMu8DWJ/bKkGxQhqZk9uaqCenSj44I/P4+lInGQa5Qv3sCrgN1yKflHldN8njpMNK0BBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:04:55.405541Z"},"content_sha256":"8aed67de0b3fc100b1009d87930be593adcdd7117d69fd3a45067ca1727b80ec","schema_version":"1.0","event_id":"sha256:8aed67de0b3fc100b1009d87930be593adcdd7117d69fd3a45067ca1727b80ec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:4I4YOMRZEWA5RSTITBBDTL5QPH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Markov convexity and local rigidity of distorted metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Assaf Naor, Manor Mendel","submitted_at":"2008-03-12T02:48:58Z","abstract_excerpt":"It is shown that a Banach space admits an equivalent norm whose modulus of uniform convexity has power-type p if and only if it is Markov p-convex. Counterexamples are constructed to natural questions related to isomorphic uniform convexity of metric spaces, showing in particular that tree metrics fail to have the dichotomy property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.1697","kind":"arxiv","version":2},"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":"2026-05-18T03:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uyJQhgBG88ccIe/Vx2QF7uoDkPjYJUpW5linALfcatOHqFuzRJayVsnbVuOBlBnKfk3+Wo+qRCBvRWJVzSVJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:04:55.405888Z"},"content_sha256":"1e82885a717bf81ff89d17d0774dec396f8c9c5097d146f8db5fc5e622788969","schema_version":"1.0","event_id":"sha256:1e82885a717bf81ff89d17d0774dec396f8c9c5097d146f8db5fc5e622788969"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4I4YOMRZEWA5RSTITBBDTL5QPH/bundle.json","state_url":"https://pith.science/pith/4I4YOMRZEWA5RSTITBBDTL5QPH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4I4YOMRZEWA5RSTITBBDTL5QPH/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":"2026-06-23T17:04:55Z","links":{"resolver":"https://pith.science/pith/4I4YOMRZEWA5RSTITBBDTL5QPH","bundle":"https://pith.science/pith/4I4YOMRZEWA5RSTITBBDTL5QPH/bundle.json","state":"https://pith.science/pith/4I4YOMRZEWA5RSTITBBDTL5QPH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4I4YOMRZEWA5RSTITBBDTL5QPH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:4I4YOMRZEWA5RSTITBBDTL5QPH","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":"f1001ecaac2e339679c9f8e3c9c32f3f7042a0d009cd1eea0dd3216e9bd0f47c","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2008-03-12T02:48:58Z","title_canon_sha256":"96ccf46b1ee38008b09fd3c8e7f503352cd72c48f98e98ddc94df45baa7760ac"},"schema_version":"1.0","source":{"id":"0803.1697","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.1697","created_at":"2026-05-18T03:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"0803.1697v2","created_at":"2026-05-18T03:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.1697","created_at":"2026-05-18T03:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"4I4YOMRZEWA5","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"4I4YOMRZEWA5RSTI","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"4I4YOMRZ","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:1e82885a717bf81ff89d17d0774dec396f8c9c5097d146f8db5fc5e622788969","target":"graph","created_at":"2026-05-18T03:39:42Z","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":"It is shown that a Banach space admits an equivalent norm whose modulus of uniform convexity has power-type p if and only if it is Markov p-convex. Counterexamples are constructed to natural questions related to isomorphic uniform convexity of metric spaces, showing in particular that tree metrics fail to have the dichotomy property.","authors_text":"Assaf Naor, Manor Mendel","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2008-03-12T02:48:58Z","title":"Markov convexity and local rigidity of distorted metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.1697","kind":"arxiv","version":2},"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":"sha256:8aed67de0b3fc100b1009d87930be593adcdd7117d69fd3a45067ca1727b80ec","target":"record","created_at":"2026-05-18T03:39:42Z","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":"f1001ecaac2e339679c9f8e3c9c32f3f7042a0d009cd1eea0dd3216e9bd0f47c","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2008-03-12T02:48:58Z","title_canon_sha256":"96ccf46b1ee38008b09fd3c8e7f503352cd72c48f98e98ddc94df45baa7760ac"},"schema_version":"1.0","source":{"id":"0803.1697","kind":"arxiv","version":2}},"canonical_sha256":"e2398732392581d8ca68984239afb079f7fa62e7e44c9d0c9372c45805571dfc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2398732392581d8ca68984239afb079f7fa62e7e44c9d0c9372c45805571dfc","first_computed_at":"2026-05-18T03:39:42.369685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:42.369685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GB/r5ainAbyPckyu1fCj02DaoNMwoOo13CKR5IqVHSvYlFD8yWIi50xV6eHqvsXsOWNVZdFKzHlDXL+A9lXiBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:42.370415Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.1697","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8aed67de0b3fc100b1009d87930be593adcdd7117d69fd3a45067ca1727b80ec","sha256:1e82885a717bf81ff89d17d0774dec396f8c9c5097d146f8db5fc5e622788969"],"state_sha256":"6da9881b1e211e1560b5e1684ce7f25f02d7d879778f6f167b913ce2527786dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0gFIhsgWcpaRgVRxdnRV8X1T398+xeqHksds6vqaUnT9TgWjs85BXxciZZMVW2s/YIJ829rv76lJtGxUNb/rAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:04:55.407777Z","bundle_sha256":"08e7386279c5e71fac99d32c9d95228c1132f261b537a04492c486906d4c04dd"}}