{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:I4R24UOESL7X7A32KGE7E5CG6K","short_pith_number":"pith:I4R24UOE","schema_version":"1.0","canonical_sha256":"4723ae51c492ff7f837a5189f27446f297aff71c3894caef217cb5ed67931e94","source":{"kind":"arxiv","id":"1203.1761","version":1},"attestation_state":"computed","paper":{"title":"Embedding proper ultrametric spaces into $\\ell_p$ and its application to nonlinear Dvoretzky's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Kei Funano","submitted_at":"2012-03-08T11:54:16Z","abstract_excerpt":"We prove that every proper ultrametric space isometrically embeds into $\\ell_p$ for any $p\\geq 1$. As an application we discuss an $\\ell_p$-version of nonlinear Dvoretzky's theorem."},"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":"1203.1761","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-03-08T11:54:16Z","cross_cats_sorted":[],"title_canon_sha256":"428d12bfaa15eee116d80d087a88faca5bda3588adf06c5faabaeadef2f4f687","abstract_canon_sha256":"b48215a5575eef385912c3138568b208302833a3b1ac1452fc8f83254ec37352"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:37.075288Z","signature_b64":"u+6W95XtDtAVVqOyrfh6cNlBUcLi3y34XsK2Nd0kfo2SjMBEimG0+RJV95SSQBZ1s24A7A9Qtru0DIoYOTQKBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4723ae51c492ff7f837a5189f27446f297aff71c3894caef217cb5ed67931e94","last_reissued_at":"2026-05-18T04:00:37.074734Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:37.074734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Embedding proper ultrametric spaces into $\\ell_p$ and its application to nonlinear Dvoretzky's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Kei Funano","submitted_at":"2012-03-08T11:54:16Z","abstract_excerpt":"We prove that every proper ultrametric space isometrically embeds into $\\ell_p$ for any $p\\geq 1$. As an application we discuss an $\\ell_p$-version of nonlinear Dvoretzky's theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1761","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1203.1761","created_at":"2026-05-18T04:00:37.074823+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.1761v1","created_at":"2026-05-18T04:00:37.074823+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1761","created_at":"2026-05-18T04:00:37.074823+00:00"},{"alias_kind":"pith_short_12","alias_value":"I4R24UOESL7X","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"I4R24UOESL7X7A32","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"I4R24UOE","created_at":"2026-05-18T12:27:09.501522+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/I4R24UOESL7X7A32KGE7E5CG6K","json":"https://pith.science/pith/I4R24UOESL7X7A32KGE7E5CG6K.json","graph_json":"https://pith.science/api/pith-number/I4R24UOESL7X7A32KGE7E5CG6K/graph.json","events_json":"https://pith.science/api/pith-number/I4R24UOESL7X7A32KGE7E5CG6K/events.json","paper":"https://pith.science/paper/I4R24UOE"},"agent_actions":{"view_html":"https://pith.science/pith/I4R24UOESL7X7A32KGE7E5CG6K","download_json":"https://pith.science/pith/I4R24UOESL7X7A32KGE7E5CG6K.json","view_paper":"https://pith.science/paper/I4R24UOE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.1761&json=true","fetch_graph":"https://pith.science/api/pith-number/I4R24UOESL7X7A32KGE7E5CG6K/graph.json","fetch_events":"https://pith.science/api/pith-number/I4R24UOESL7X7A32KGE7E5CG6K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I4R24UOESL7X7A32KGE7E5CG6K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I4R24UOESL7X7A32KGE7E5CG6K/action/storage_attestation","attest_author":"https://pith.science/pith/I4R24UOESL7X7A32KGE7E5CG6K/action/author_attestation","sign_citation":"https://pith.science/pith/I4R24UOESL7X7A32KGE7E5CG6K/action/citation_signature","submit_replication":"https://pith.science/pith/I4R24UOESL7X7A32KGE7E5CG6K/action/replication_record"}},"created_at":"2026-05-18T04:00:37.074823+00:00","updated_at":"2026-05-18T04:00:37.074823+00:00"}