{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WELO32SK2R3A6LAFGDAH5UHWMM","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":"9143fdde3eb0de9594fcd55e6663523e42dbfc78f15cefbb3fa2dc2895c4792d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-06-15T21:48:03Z","title_canon_sha256":"5ef4d6754bf80e8b9c32911302fee62b5914bb8ae77dc38e2d24a55b8a68d097"},"schema_version":"1.0","source":{"id":"2606.17316","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17316","created_at":"2026-06-19T16:10:08Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17316v1","created_at":"2026-06-19T16:10:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17316","created_at":"2026-06-19T16:10:08Z"},{"alias_kind":"pith_short_12","alias_value":"WELO32SK2R3A","created_at":"2026-06-19T16:10:08Z"},{"alias_kind":"pith_short_16","alias_value":"WELO32SK2R3A6LAF","created_at":"2026-06-19T16:10:08Z"},{"alias_kind":"pith_short_8","alias_value":"WELO32SK","created_at":"2026-06-19T16:10:08Z"}],"graph_snapshots":[{"event_id":"sha256:8978d87cf9a6bb509a630c897f1e68b15ea4e3f2a78faeaf73d8e135259e9b5b","target":"graph","created_at":"2026-06-19T16:10:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.17316/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Clustering in a big data setting is an intensively studied problem, with coresets emerging as one of the important paradigms in this line of work. Given a cost function $\\text{cost}(P,S)$ mapping input points $P$ and a solution $S$ to an objective value, a coreset is a typically weighted sketch $\\Omega\\subseteq P$ such that $\\text{cost}(\\Omega,S)\\approx \\text{cost}(P,S)$. In practice, coreset sizes much smaller than those suggested by theoretical guarantees are often found to be sufficient.\n  In this paper, we offer an explanation for this phenomenon. Smaller coreset sizes suffice if we only w","authors_text":"Chris Schwiegelshohn, Milind Prabhu, Sudarshan Shyam","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-06-15T21:48:03Z","title":"Approximation Preserving Coresets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17316","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:ed44625112ffd254b9609612ede77c507c922d8b020bce8e2c89ddd8fb4d3ac6","target":"record","created_at":"2026-06-19T16:10:08Z","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":"9143fdde3eb0de9594fcd55e6663523e42dbfc78f15cefbb3fa2dc2895c4792d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-06-15T21:48:03Z","title_canon_sha256":"5ef4d6754bf80e8b9c32911302fee62b5914bb8ae77dc38e2d24a55b8a68d097"},"schema_version":"1.0","source":{"id":"2606.17316","kind":"arxiv","version":1}},"canonical_sha256":"b116edea4ad4760f2c0530c07ed0f6630a28f32e0fcdc0e220171073f9bd3ed4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b116edea4ad4760f2c0530c07ed0f6630a28f32e0fcdc0e220171073f9bd3ed4","first_computed_at":"2026-06-19T16:10:08.830736Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:08.830736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lyWFzi8d3TcY6X3RToFVDNmg/EmXxwQEhYTm8ZxiMDjuyS2mbHj3JvsWe6QbRdNtXvZhPWD35xRy67W+eTjsDg==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:08.831080Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.17316","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed44625112ffd254b9609612ede77c507c922d8b020bce8e2c89ddd8fb4d3ac6","sha256:8978d87cf9a6bb509a630c897f1e68b15ea4e3f2a78faeaf73d8e135259e9b5b"],"state_sha256":"c570ba7ec5194d6a83c800df4a4210b52dfc9600eb1a38b26079e9dd8c1e6a4b"}