{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:K7OODMKRKUV746FMZA2KRLQSWX","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":"1eedd463378bcb8dc4f9237b4f0dce7850a047ee576daae395730a200fd78d10","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-12-24T14:32:44Z","title_canon_sha256":"a338ff146b600647ea49559a4b75df0e1e61c7e5edce60c55a92763730ad6383"},"schema_version":"1.0","source":{"id":"1412.7670","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7670","created_at":"2026-05-18T01:09:37Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7670v2","created_at":"2026-05-18T01:09:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7670","created_at":"2026-05-18T01:09:37Z"},{"alias_kind":"pith_short_12","alias_value":"K7OODMKRKUV7","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"K7OODMKRKUV746FM","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"K7OODMKR","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:c53a3908a7fa8c71368161fa8d237c03c033fadcd7197e718200128af050a50f","target":"graph","created_at":"2026-05-18T01:09:37Z","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":"For a fixed $K\\gg 1$ and $n\\in\\mathbb{N}$, $n\\gg 1$, we study metric spaces which admit embeddings with distortion $\\le K$ into each $n$-dimensional Banach space. Classical examples include spaces embeddable into $\\log n$-dimensional Euclidean spaces, and equilateral spaces.\n  We prove that good embeddability properties are preserved under the operation of metric composition of metric spaces. In particular, we prove that any $n$-point ultrametric can be embedded with uniformly bounded distortion into any Banach space of dimension $\\log n$.\n  The main result of the paper is a new example of a f","authors_text":"Beata Randrianantoanina, Mikhail I. Ostrovskii","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-12-24T14:32:44Z","title":"Metric spaces admitting low-distortion embeddings into all $n$-dimensional Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7670","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:b48acc6e26834fcc394b7f602dcf2acfcbeb06293031577ce0cc542994da6aef","target":"record","created_at":"2026-05-18T01:09:37Z","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":"1eedd463378bcb8dc4f9237b4f0dce7850a047ee576daae395730a200fd78d10","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-12-24T14:32:44Z","title_canon_sha256":"a338ff146b600647ea49559a4b75df0e1e61c7e5edce60c55a92763730ad6383"},"schema_version":"1.0","source":{"id":"1412.7670","kind":"arxiv","version":2}},"canonical_sha256":"57dce1b151552bfe78acc834a8ae12b5fc89b2c3154468e900bd5576c3ac09a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57dce1b151552bfe78acc834a8ae12b5fc89b2c3154468e900bd5576c3ac09a6","first_computed_at":"2026-05-18T01:09:37.025575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:37.025575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uFZcn05l5s3sGM8DAFECjKSx6D6A23PMaIo/BbSyzS9RwT8zd7KpwS4IQvVr5ZOP9ITwgb8lulAlaneXg2qoDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:37.026467Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7670","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b48acc6e26834fcc394b7f602dcf2acfcbeb06293031577ce0cc542994da6aef","sha256:c53a3908a7fa8c71368161fa8d237c03c033fadcd7197e718200128af050a50f"],"state_sha256":"ef8d128f8d091b4b32476c410d741ed969f16f942ac93ffdc84f6a083a5bdf94"}