{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JEWF7CJQUTPG2DIFZ46AUDZCE4","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":"28de06d62e932fb113feb46159cb572440a9c0fb69051dd8a9fac1b990c71425","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-06T15:18:02Z","title_canon_sha256":"b6bda9a2173f7f05741c2712fce30c8bdb429ce110478c32602a9ade2dd1b005"},"schema_version":"1.0","source":{"id":"1809.02039","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02039","created_at":"2026-05-17T23:50:24Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02039v1","created_at":"2026-05-17T23:50:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02039","created_at":"2026-05-17T23:50:24Z"},{"alias_kind":"pith_short_12","alias_value":"JEWF7CJQUTPG","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JEWF7CJQUTPG2DIF","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JEWF7CJQ","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:f12a4daba8929cc4f618712c418d7a9a99b15549cc6f5d7a79bdc0d583f02828","target":"graph","created_at":"2026-05-17T23:50:24Z","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 prove that an $\\mathbb{R}$-action on a compact metric space embeds equivariantly in the space of one-Lipschitz functions $\\mathbb{R}\\to[0,1]$ if its fixed point set can be topologically embedded in the unit interval. This is a refinement of the classical Bebutov--Kakutani theorem (1968).","authors_text":"Lei Jin, Masaki Tsukamoto, Yonatan Gutman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-06T15:18:02Z","title":"A Lipschitz refinement of the Bebutov--Kakutani dynamical embedding theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02039","kind":"arxiv","version":1},"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":"sha256:455c4c692786345a4526fc45cec4cdb84aefeb0d67e87d20660a0a33ff451d30","target":"record","created_at":"2026-05-17T23:50:24Z","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":"28de06d62e932fb113feb46159cb572440a9c0fb69051dd8a9fac1b990c71425","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-06T15:18:02Z","title_canon_sha256":"b6bda9a2173f7f05741c2712fce30c8bdb429ce110478c32602a9ade2dd1b005"},"schema_version":"1.0","source":{"id":"1809.02039","kind":"arxiv","version":1}},"canonical_sha256":"492c5f8930a4de6d0d05cf3c0a0f22272ff79834048cbc248dd1984d5a04e5d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"492c5f8930a4de6d0d05cf3c0a0f22272ff79834048cbc248dd1984d5a04e5d3","first_computed_at":"2026-05-17T23:50:24.068285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:24.068285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bXloUj99Wfdc1Bygh1c+rGxfJ/00E3QeZEIjY5mWD4pFVOtdy/yoBG70f+3iuOgX5drMbup36+9zJ0seIyk1Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:24.068761Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02039","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:455c4c692786345a4526fc45cec4cdb84aefeb0d67e87d20660a0a33ff451d30","sha256:f12a4daba8929cc4f618712c418d7a9a99b15549cc6f5d7a79bdc0d583f02828"],"state_sha256":"bcba2d8c5f3485f7f5e30166337ec5625d70771be12a0d303f6058e7dda69695"}