{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PWQOOC3T3KPHTXZVXPEHLK2Y36","short_pith_number":"pith:PWQOOC3T","canonical_record":{"source":{"id":"1611.04623","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-14T21:09:48Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"a1a2175996132bb335cb4b10ac2267ac5f2c32dce2c4f23416ff1e6dff440718","abstract_canon_sha256":"505f87a47dd856812a9904bb16778822af0c1a75cb20a5d2e786e0c4e2312b6c"},"schema_version":"1.0"},"canonical_sha256":"7da0e70b73da9e79df35bbc875ab58dfaded52d21a3769104fd3a93299078861","source":{"kind":"arxiv","id":"1611.04623","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04623","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04623v2","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04623","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"pith_short_12","alias_value":"PWQOOC3T3KPH","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PWQOOC3T3KPHTXZV","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PWQOOC3T","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PWQOOC3T3KPHTXZVXPEHLK2Y36","target":"record","payload":{"canonical_record":{"source":{"id":"1611.04623","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-14T21:09:48Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"a1a2175996132bb335cb4b10ac2267ac5f2c32dce2c4f23416ff1e6dff440718","abstract_canon_sha256":"505f87a47dd856812a9904bb16778822af0c1a75cb20a5d2e786e0c4e2312b6c"},"schema_version":"1.0"},"canonical_sha256":"7da0e70b73da9e79df35bbc875ab58dfaded52d21a3769104fd3a93299078861","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:14.403571Z","signature_b64":"CmRvt2sOQtXGetTywaJY4tRCODnlALsXwWP8DLv/CA3fsR6kldznZ0RD3bI4NfY0YNJ1dtHnLwNPNLCbfA98CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7da0e70b73da9e79df35bbc875ab58dfaded52d21a3769104fd3a93299078861","last_reissued_at":"2026-05-18T00:32:14.402974Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:14.402974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.04623","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6CqmRJYtlwvjD/hhkg0qgsdP5E2hQt6v2tDaBLqBh6q5DDHYzDqm2KAyg4SMARnyxOLJqh7UD9RUoOuyWoQmBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:41:58.256959Z"},"content_sha256":"7ab63dc3c8c65d4749e539b376325285af262fb7b3a350b05d79bb5ae29a9946","schema_version":"1.0","event_id":"sha256:7ab63dc3c8c65d4749e539b376325285af262fb7b3a350b05d79bb5ae29a9946"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PWQOOC3T3KPHTXZVXPEHLK2Y36","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On coarse Lipschitz embeddability into $c_0(\\kappa)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Andrew Swift","submitted_at":"2016-11-14T21:09:48Z","abstract_excerpt":"In 1994, Jan Pelant proved that a metric property related to the notion of paracompactness called the uniform Stone property characterizes a metric space's uniform embeddability into $c_0(\\kappa)$ for some cardinality $\\kappa$. In this paper it is shown that coarse Lipschitz embeddability of a metric space into $c_0(\\kappa)$ can be characterized in a similar manner. It is also shown that coarse, uniform, and bi-Lipschitz embeddability into $c_0(\\kappa)$ are equivalent notions for normed linear spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04623","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dl8DpwdMs6W1Ytkk9pqMgOs0pvaa+Mcag8zsuF8befnXIhoc3HuPi8PunPTZBSW58Enp7p+qWIuhk7mnhxLKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:41:58.257556Z"},"content_sha256":"4abe4e3bfca501467fb47bccfa24da41b89efd213cc194875d393a6eed4ae338","schema_version":"1.0","event_id":"sha256:4abe4e3bfca501467fb47bccfa24da41b89efd213cc194875d393a6eed4ae338"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PWQOOC3T3KPHTXZVXPEHLK2Y36/bundle.json","state_url":"https://pith.science/pith/PWQOOC3T3KPHTXZVXPEHLK2Y36/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PWQOOC3T3KPHTXZVXPEHLK2Y36/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T02:41:58Z","links":{"resolver":"https://pith.science/pith/PWQOOC3T3KPHTXZVXPEHLK2Y36","bundle":"https://pith.science/pith/PWQOOC3T3KPHTXZVXPEHLK2Y36/bundle.json","state":"https://pith.science/pith/PWQOOC3T3KPHTXZVXPEHLK2Y36/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PWQOOC3T3KPHTXZVXPEHLK2Y36/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PWQOOC3T3KPHTXZVXPEHLK2Y36","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":"505f87a47dd856812a9904bb16778822af0c1a75cb20a5d2e786e0c4e2312b6c","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-14T21:09:48Z","title_canon_sha256":"a1a2175996132bb335cb4b10ac2267ac5f2c32dce2c4f23416ff1e6dff440718"},"schema_version":"1.0","source":{"id":"1611.04623","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04623","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04623v2","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04623","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"pith_short_12","alias_value":"PWQOOC3T3KPH","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PWQOOC3T3KPHTXZV","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PWQOOC3T","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:4abe4e3bfca501467fb47bccfa24da41b89efd213cc194875d393a6eed4ae338","target":"graph","created_at":"2026-05-18T00:32:14Z","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":"In 1994, Jan Pelant proved that a metric property related to the notion of paracompactness called the uniform Stone property characterizes a metric space's uniform embeddability into $c_0(\\kappa)$ for some cardinality $\\kappa$. In this paper it is shown that coarse Lipschitz embeddability of a metric space into $c_0(\\kappa)$ can be characterized in a similar manner. It is also shown that coarse, uniform, and bi-Lipschitz embeddability into $c_0(\\kappa)$ are equivalent notions for normed linear spaces.","authors_text":"Andrew Swift","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-14T21:09:48Z","title":"On coarse Lipschitz embeddability into $c_0(\\kappa)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04623","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":"sha256:7ab63dc3c8c65d4749e539b376325285af262fb7b3a350b05d79bb5ae29a9946","target":"record","created_at":"2026-05-18T00:32:14Z","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":"505f87a47dd856812a9904bb16778822af0c1a75cb20a5d2e786e0c4e2312b6c","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-14T21:09:48Z","title_canon_sha256":"a1a2175996132bb335cb4b10ac2267ac5f2c32dce2c4f23416ff1e6dff440718"},"schema_version":"1.0","source":{"id":"1611.04623","kind":"arxiv","version":2}},"canonical_sha256":"7da0e70b73da9e79df35bbc875ab58dfaded52d21a3769104fd3a93299078861","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7da0e70b73da9e79df35bbc875ab58dfaded52d21a3769104fd3a93299078861","first_computed_at":"2026-05-18T00:32:14.402974Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:14.402974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CmRvt2sOQtXGetTywaJY4tRCODnlALsXwWP8DLv/CA3fsR6kldznZ0RD3bI4NfY0YNJ1dtHnLwNPNLCbfA98CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:14.403571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04623","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ab63dc3c8c65d4749e539b376325285af262fb7b3a350b05d79bb5ae29a9946","sha256:4abe4e3bfca501467fb47bccfa24da41b89efd213cc194875d393a6eed4ae338"],"state_sha256":"9d843195202e54fc8d5cb98e6140afa4057e0faa046bd55cce7b935ff69eb494"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PpzaYZgD6MXsPJagv/P/tqRYrQPyuoqC7eZ6tCh3shlR27fvBWakew9G1wGzhtpLu5dmP216v43Mei+NW+WsAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:41:58.260209Z","bundle_sha256":"54f6e45fc3df341f4393454d217d7311823b95a625d5781742030c8d8c7d22a9"}}