{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:4I4YOMRZEWA5RSTITBBDTL5QPH","short_pith_number":"pith:4I4YOMRZ","schema_version":"1.0","canonical_sha256":"e2398732392581d8ca68984239afb079f7fa62e7e44c9d0c9372c45805571dfc","source":{"kind":"arxiv","id":"0803.1697","version":2},"attestation_state":"computed","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"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"},"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"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0803.1697","created_at":"2026-05-18T03:39:42.369811+00:00"},{"alias_kind":"arxiv_version","alias_value":"0803.1697v2","created_at":"2026-05-18T03:39:42.369811+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.1697","created_at":"2026-05-18T03:39:42.369811+00:00"},{"alias_kind":"pith_short_12","alias_value":"4I4YOMRZEWA5","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"4I4YOMRZEWA5RSTI","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"4I4YOMRZ","created_at":"2026-05-18T12:25:56.245647+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4I4YOMRZEWA5RSTITBBDTL5QPH","json":"https://pith.science/pith/4I4YOMRZEWA5RSTITBBDTL5QPH.json","graph_json":"https://pith.science/api/pith-number/4I4YOMRZEWA5RSTITBBDTL5QPH/graph.json","events_json":"https://pith.science/api/pith-number/4I4YOMRZEWA5RSTITBBDTL5QPH/events.json","paper":"https://pith.science/paper/4I4YOMRZ"},"agent_actions":{"view_html":"https://pith.science/pith/4I4YOMRZEWA5RSTITBBDTL5QPH","download_json":"https://pith.science/pith/4I4YOMRZEWA5RSTITBBDTL5QPH.json","view_paper":"https://pith.science/paper/4I4YOMRZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0803.1697&json=true","fetch_graph":"https://pith.science/api/pith-number/4I4YOMRZEWA5RSTITBBDTL5QPH/graph.json","fetch_events":"https://pith.science/api/pith-number/4I4YOMRZEWA5RSTITBBDTL5QPH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4I4YOMRZEWA5RSTITBBDTL5QPH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4I4YOMRZEWA5RSTITBBDTL5QPH/action/storage_attestation","attest_author":"https://pith.science/pith/4I4YOMRZEWA5RSTITBBDTL5QPH/action/author_attestation","sign_citation":"https://pith.science/pith/4I4YOMRZEWA5RSTITBBDTL5QPH/action/citation_signature","submit_replication":"https://pith.science/pith/4I4YOMRZEWA5RSTITBBDTL5QPH/action/replication_record"}},"created_at":"2026-05-18T03:39:42.369811+00:00","updated_at":"2026-05-18T03:39:42.369811+00:00"}