{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QXCL7Y7EWDFH47XIZUPMX56FH4","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":"d56f2b70cdf877727c66b9fd9d397304252733e04e54dfd4a3b6c842e2c6c31a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-08-01T13:47:39Z","title_canon_sha256":"0448aa25a5e98f7e5cdb8fb2d2a55efc62c03e035f0ae4d7bd0cbe36ffab9a4c"},"schema_version":"1.0","source":{"id":"1708.00316","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00316","created_at":"2026-05-18T00:39:05Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00316v1","created_at":"2026-05-18T00:39:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00316","created_at":"2026-05-18T00:39:05Z"},{"alias_kind":"pith_short_12","alias_value":"QXCL7Y7EWDFH","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QXCL7Y7EWDFH47XI","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QXCL7Y7E","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:36f7a5cee3f71152c3caba5491bbbdbd0110c3c1dff1c54b7bc23d1f55fbf512","target":"graph","created_at":"2026-05-18T00:39:05Z","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 this paper, we propose a unified framework for sampling, clustering and embedding data points in semi-metric spaces. For a set of data points $\\Omega=\\{x_1, x_2, \\ldots, x_n\\}$ in a semi-metric space, we consider a complete graph with $n$ nodes and $n$ self edges and then map each data point in $\\Omega$ to a node in the graph with the edge weight between two nodes being the distance between the corresponding two points in $\\Omega$. By doing so, several well-known sampling techniques can be applied for clustering data points in a semi-metric space. One particularly interesting sampling techn","authors_text":"Cheng-Shang Chang, Chia-Tai Chang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-08-01T13:47:39Z","title":"A Unified Framework for Sampling, Clustering and Embedding Data Points in Semi-Metric Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00316","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:eaa979980a5cd1e848365e54ad0f8a96ebb4ba579e97272b52d3d20c060ccea2","target":"record","created_at":"2026-05-18T00:39:05Z","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":"d56f2b70cdf877727c66b9fd9d397304252733e04e54dfd4a3b6c842e2c6c31a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-08-01T13:47:39Z","title_canon_sha256":"0448aa25a5e98f7e5cdb8fb2d2a55efc62c03e035f0ae4d7bd0cbe36ffab9a4c"},"schema_version":"1.0","source":{"id":"1708.00316","kind":"arxiv","version":1}},"canonical_sha256":"85c4bfe3e4b0ca7e7ee8cd1ecbf7c53f2a0a1c0004a1119444e04e439628f6e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85c4bfe3e4b0ca7e7ee8cd1ecbf7c53f2a0a1c0004a1119444e04e439628f6e6","first_computed_at":"2026-05-18T00:39:05.505435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:05.505435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"au9ntKXy0OH4LivS4w2F4qIp0kotU6cYwRe8t6MyQu3vJFMt+9IhCrGOGmwW8ZpaxcUb9kWH+YXsiYvWMDBrDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:05.506117Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.00316","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eaa979980a5cd1e848365e54ad0f8a96ebb4ba579e97272b52d3d20c060ccea2","sha256:36f7a5cee3f71152c3caba5491bbbdbd0110c3c1dff1c54b7bc23d1f55fbf512"],"state_sha256":"95177cbb8e04f6c3f85fbeaf35e53c0d90a938abe4eceb0bdff6f8ead20f32ac"}