{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LZDQHJEBF7U5LCL5QCOR67YUJW","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":"15cbe16da4ea42c12eed159d23c63dec7710add5fe801271daa3522283a83a95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-08-25T15:12:31Z","title_canon_sha256":"9fbe29bb25ea3995804c955d55d0c6330cc6c99603770381478b371cdb1cb95f"},"schema_version":"1.0","source":{"id":"1408.5793","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5793","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5793v2","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5793","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"LZDQHJEBF7U5","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LZDQHJEBF7U5LCL5","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LZDQHJEB","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:e930a6adc59850a0be45c435ddc41603aa308d5fbb201b1c886f604ad6e407ab","target":"graph","created_at":"2026-05-18T02:41:25Z","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":"We give a metric characterization of snowflakes of Euclidean spaces. Namely, a metric space is isometric to $\\mathbb R^n$ equipped with a distance $(d_{\\rm E})^\\epsilon$, for some $n\\in \\mathbb N_0$ and $\\epsilon\\in (0,1]$, where $d_{\\rm E}$ is the Euclidean distance, if and only if it is locally compact, $2$-point isometrically homogeneous, and admits dilations of any factor.","authors_text":"Enrico Le Donne, Kyle Kinneberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-08-25T15:12:31Z","title":"A metric characterization of snowflakes of Euclidean spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5793","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":"sha256:6dffb2ce98c97a21fa07daf22330088090bf708c34f1a2effdec7e0fe6912e28","target":"record","created_at":"2026-05-18T02:41:25Z","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":"15cbe16da4ea42c12eed159d23c63dec7710add5fe801271daa3522283a83a95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-08-25T15:12:31Z","title_canon_sha256":"9fbe29bb25ea3995804c955d55d0c6330cc6c99603770381478b371cdb1cb95f"},"schema_version":"1.0","source":{"id":"1408.5793","kind":"arxiv","version":2}},"canonical_sha256":"5e4703a4812fe9d5897d809d1f7f144daf83f4ea832724cb7d643144132e500a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e4703a4812fe9d5897d809d1f7f144daf83f4ea832724cb7d643144132e500a","first_computed_at":"2026-05-18T02:41:25.809814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:25.809814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iF8pWtk4WGmSeQXp095R01kiYM2KPDeNb42wWZHHCf6RMSaV/GtkX6lxjdIs/MQko3a9VcawB507H8dAK4ARBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:25.810333Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5793","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dffb2ce98c97a21fa07daf22330088090bf708c34f1a2effdec7e0fe6912e28","sha256:e930a6adc59850a0be45c435ddc41603aa308d5fbb201b1c886f604ad6e407ab"],"state_sha256":"fc4642fed4b314090b9c6afb2c178df8345d5d7f3961c825be5e3967396b6a5a"}