{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:KJZ34VSVKS5ED7PUJ73GFEYY7W","short_pith_number":"pith:KJZ34VSV","canonical_record":{"source":{"id":"2606.08713","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-06-07T16:09:04Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"04c8562a6dde3e974e85d8daff8c63064dc6babb894e1b4004712495b5dfd52a","abstract_canon_sha256":"2c617f010babf576e2b3e4b31e7bbcf96477838dbb6385d81d1818a373e21ab0"},"schema_version":"1.0"},"canonical_sha256":"5273be565554ba41fdf44ff6629318fdbd9ed3444c6d9b5688a3bfae1e53ee40","source":{"kind":"arxiv","id":"2606.08713","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08713","created_at":"2026-06-09T01:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08713v1","created_at":"2026-06-09T01:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08713","created_at":"2026-06-09T01:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"KJZ34VSVKS5E","created_at":"2026-06-09T01:05:48Z"},{"alias_kind":"pith_short_16","alias_value":"KJZ34VSVKS5ED7PU","created_at":"2026-06-09T01:05:48Z"},{"alias_kind":"pith_short_8","alias_value":"KJZ34VSV","created_at":"2026-06-09T01:05:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:KJZ34VSVKS5ED7PUJ73GFEYY7W","target":"record","payload":{"canonical_record":{"source":{"id":"2606.08713","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-06-07T16:09:04Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"04c8562a6dde3e974e85d8daff8c63064dc6babb894e1b4004712495b5dfd52a","abstract_canon_sha256":"2c617f010babf576e2b3e4b31e7bbcf96477838dbb6385d81d1818a373e21ab0"},"schema_version":"1.0"},"canonical_sha256":"5273be565554ba41fdf44ff6629318fdbd9ed3444c6d9b5688a3bfae1e53ee40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:48.037533Z","signature_b64":"TQFfOqDM+/YwC/hC26qMfNgOxcX7OqRxljvcY99sqG6tS0ITuTh8VH6X+Dgi2Cbz/YWsKCu20vvfGTm2j5qGCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5273be565554ba41fdf44ff6629318fdbd9ed3444c6d9b5688a3bfae1e53ee40","last_reissued_at":"2026-06-09T01:05:48.037121Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:48.037121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.08713","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-09T01:05:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FLi35u6GFLgYmNYnbfDs0vCk9IUFmXLH4tBDMSMKhR6lnxB7Lrv5+XaN0I4BBQOgNha1wVzZzY/M31NTJFJpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T13:46:19.579804Z"},"content_sha256":"c8f77e5464881be353bc5d281d6b894688a52796b30762db4013226da4653d12","schema_version":"1.0","event_id":"sha256:c8f77e5464881be353bc5d281d6b894688a52796b30762db4013226da4653d12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:KJZ34VSVKS5ED7PUJ73GFEYY7W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The price of incrementality in k-center clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"L\\'aszl\\'o Kozma","submitted_at":"2026-06-07T16:09:04Z","abstract_excerpt":"The $k$-center problem is one of the best-studied and most intuitive clustering formulations. It asks, given a set of $n$ points in a metric space, for $k$ of the points to be designated as cluster centers, so that the maximum distance of an input point to its nearest center is minimized. Gonzalez's greedy algorithm from 1985 is a simple and efficient way to find a $2$-approximate solution. The algorithm has the attractive feature of \\emph{incrementality}: it outputs the centers one by one, with a guaranteed $2$-approximation for every prefix of the obtained sequence of centers.\n  Incrementali"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08713","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.08713/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-09T01:05:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mxrs22mAVfDbipqkxppUapFXQyKmFKXV+0YOMHejIPWWUrSxosDtpstv5Hxc4EX7zzXPmCOMF7usC5dWh8V4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T13:46:19.580167Z"},"content_sha256":"c58dcc82df6aa69b391b525664ac965d4f3e8ceca8bae11b23879c1f1384a095","schema_version":"1.0","event_id":"sha256:c58dcc82df6aa69b391b525664ac965d4f3e8ceca8bae11b23879c1f1384a095"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KJZ34VSVKS5ED7PUJ73GFEYY7W/bundle.json","state_url":"https://pith.science/pith/KJZ34VSVKS5ED7PUJ73GFEYY7W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KJZ34VSVKS5ED7PUJ73GFEYY7W/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":"2026-06-29T13:46:19Z","links":{"resolver":"https://pith.science/pith/KJZ34VSVKS5ED7PUJ73GFEYY7W","bundle":"https://pith.science/pith/KJZ34VSVKS5ED7PUJ73GFEYY7W/bundle.json","state":"https://pith.science/pith/KJZ34VSVKS5ED7PUJ73GFEYY7W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KJZ34VSVKS5ED7PUJ73GFEYY7W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KJZ34VSVKS5ED7PUJ73GFEYY7W","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":"2c617f010babf576e2b3e4b31e7bbcf96477838dbb6385d81d1818a373e21ab0","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-06-07T16:09:04Z","title_canon_sha256":"04c8562a6dde3e974e85d8daff8c63064dc6babb894e1b4004712495b5dfd52a"},"schema_version":"1.0","source":{"id":"2606.08713","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08713","created_at":"2026-06-09T01:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08713v1","created_at":"2026-06-09T01:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08713","created_at":"2026-06-09T01:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"KJZ34VSVKS5E","created_at":"2026-06-09T01:05:48Z"},{"alias_kind":"pith_short_16","alias_value":"KJZ34VSVKS5ED7PU","created_at":"2026-06-09T01:05:48Z"},{"alias_kind":"pith_short_8","alias_value":"KJZ34VSV","created_at":"2026-06-09T01:05:48Z"}],"graph_snapshots":[{"event_id":"sha256:c58dcc82df6aa69b391b525664ac965d4f3e8ceca8bae11b23879c1f1384a095","target":"graph","created_at":"2026-06-09T01:05:48Z","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/2606.08713/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The $k$-center problem is one of the best-studied and most intuitive clustering formulations. It asks, given a set of $n$ points in a metric space, for $k$ of the points to be designated as cluster centers, so that the maximum distance of an input point to its nearest center is minimized. Gonzalez's greedy algorithm from 1985 is a simple and efficient way to find a $2$-approximate solution. The algorithm has the attractive feature of \\emph{incrementality}: it outputs the centers one by one, with a guaranteed $2$-approximation for every prefix of the obtained sequence of centers.\n  Incrementali","authors_text":"L\\'aszl\\'o Kozma","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-06-07T16:09:04Z","title":"The price of incrementality in k-center clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08713","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:c8f77e5464881be353bc5d281d6b894688a52796b30762db4013226da4653d12","target":"record","created_at":"2026-06-09T01:05:48Z","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":"2c617f010babf576e2b3e4b31e7bbcf96477838dbb6385d81d1818a373e21ab0","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-06-07T16:09:04Z","title_canon_sha256":"04c8562a6dde3e974e85d8daff8c63064dc6babb894e1b4004712495b5dfd52a"},"schema_version":"1.0","source":{"id":"2606.08713","kind":"arxiv","version":1}},"canonical_sha256":"5273be565554ba41fdf44ff6629318fdbd9ed3444c6d9b5688a3bfae1e53ee40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5273be565554ba41fdf44ff6629318fdbd9ed3444c6d9b5688a3bfae1e53ee40","first_computed_at":"2026-06-09T01:05:48.037121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:48.037121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TQFfOqDM+/YwC/hC26qMfNgOxcX7OqRxljvcY99sqG6tS0ITuTh8VH6X+Dgi2Cbz/YWsKCu20vvfGTm2j5qGCg==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:48.037533Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.08713","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8f77e5464881be353bc5d281d6b894688a52796b30762db4013226da4653d12","sha256:c58dcc82df6aa69b391b525664ac965d4f3e8ceca8bae11b23879c1f1384a095"],"state_sha256":"ea506c10ff3e40faf7157508612708acf71942808ab2e3e1d480e35523ac9968"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1I0SYdh/vqBxJkjjrmxGaEmTiJ43Byz4RYZRMKZ7jduFyBdte8M8R22MbxahzxCYFAeFTY2XxYWae0+Y813ICg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T13:46:19.582108Z","bundle_sha256":"37e70fec19fa17b3b325647b8b5a47b77f4c36ea8d9cef17dc11f3a5b1fd9d9a"}}