{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BFSUZ3X2BRRSK6WEJBIFEB2KI5","short_pith_number":"pith:BFSUZ3X2","canonical_record":{"source":{"id":"1711.01171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-11-03T14:05:48Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"84cd33fdf0a07a53899b0ea3d362520f4888c1ff89fb0010c3d7b992d9a2db64","abstract_canon_sha256":"c39f3f255c1a1ded0d38cd3542ea532f29218f9f581ca39479b2829586f54440"},"schema_version":"1.0"},"canonical_sha256":"09654ceefa0c63257ac4485052074a47787ed2c2e96fdaedb950814f70e343b8","source":{"kind":"arxiv","id":"1711.01171","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.01171","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"arxiv_version","alias_value":"1711.01171v1","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01171","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"pith_short_12","alias_value":"BFSUZ3X2BRRS","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BFSUZ3X2BRRSK6WE","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BFSUZ3X2","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BFSUZ3X2BRRSK6WEJBIFEB2KI5","target":"record","payload":{"canonical_record":{"source":{"id":"1711.01171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-11-03T14:05:48Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"84cd33fdf0a07a53899b0ea3d362520f4888c1ff89fb0010c3d7b992d9a2db64","abstract_canon_sha256":"c39f3f255c1a1ded0d38cd3542ea532f29218f9f581ca39479b2829586f54440"},"schema_version":"1.0"},"canonical_sha256":"09654ceefa0c63257ac4485052074a47787ed2c2e96fdaedb950814f70e343b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:23.246476Z","signature_b64":"cdToMAcmdkdZpu/QIceTbNaI+5WSLBhAYU84ejgbK6OXdKVxvfUbU6xur6HWj2wsgl1dezXlxzX02tGvXz5fAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09654ceefa0c63257ac4485052074a47787ed2c2e96fdaedb950814f70e343b8","last_reissued_at":"2026-05-18T00:31:23.245933Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:23.245933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.01171","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":"2026-05-18T00:31:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o3EIjNecyK+9TmbSdYMGyDBspAcLqn9iU+KB/x5NaFKzbzitxR+Tr661g4fWl0ysei42g/c3fTGX2HoU+XKqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:26:30.553655Z"},"content_sha256":"2a99e795cc7b1667e969431498a06386d966c7560a8ee7ce5d68d54d15c54a3a","schema_version":"1.0","event_id":"sha256:2a99e795cc7b1667e969431498a06386d966c7560a8ee7ce5d68d54d15c54a3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BFSUZ3X2BRRSK6WEJBIFEB2KI5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Bane of Low-Dimensionality Clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Alan Roytman, Arnaud de Mesmay, Eva Rotenberg, Vincent Cohen-Addad","submitted_at":"2017-11-03T14:05:48Z","abstract_excerpt":"In this paper, we give a conditional lower bound of $n^{\\Omega(k)}$ on running time for the classic k-median and k-means clustering objectives (where n is the size of the input), even in low-dimensional Euclidean space of dimension four, assuming the Exponential Time Hypothesis (ETH). We also consider k-median (and k-means) with penalties where each point need not be assigned to a center, in which case it must pay a penalty, and extend our lower bound to at least three-dimensional Euclidean space.\n  This stands in stark contrast to many other geometric problems such as the traveling salesman p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01171","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":""},"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":"2026-05-18T00:31:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fcrCL5p3K2y9PP0KcePLI2eNbj7W+Sf26M79MPlzVIg27+cykhxlK339cEoKsvaCsn/sZdXM0bIv8vovgllCAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:26:30.554401Z"},"content_sha256":"07f4fd477d1c4b96e223f0689ee2b77d7438ea082e2ce34ff08ebcc9905dc99b","schema_version":"1.0","event_id":"sha256:07f4fd477d1c4b96e223f0689ee2b77d7438ea082e2ce34ff08ebcc9905dc99b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BFSUZ3X2BRRSK6WEJBIFEB2KI5/bundle.json","state_url":"https://pith.science/pith/BFSUZ3X2BRRSK6WEJBIFEB2KI5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BFSUZ3X2BRRSK6WEJBIFEB2KI5/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":"2026-05-31T04:26:30Z","links":{"resolver":"https://pith.science/pith/BFSUZ3X2BRRSK6WEJBIFEB2KI5","bundle":"https://pith.science/pith/BFSUZ3X2BRRSK6WEJBIFEB2KI5/bundle.json","state":"https://pith.science/pith/BFSUZ3X2BRRSK6WEJBIFEB2KI5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BFSUZ3X2BRRSK6WEJBIFEB2KI5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BFSUZ3X2BRRSK6WEJBIFEB2KI5","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":"c39f3f255c1a1ded0d38cd3542ea532f29218f9f581ca39479b2829586f54440","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-11-03T14:05:48Z","title_canon_sha256":"84cd33fdf0a07a53899b0ea3d362520f4888c1ff89fb0010c3d7b992d9a2db64"},"schema_version":"1.0","source":{"id":"1711.01171","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.01171","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"arxiv_version","alias_value":"1711.01171v1","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01171","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"pith_short_12","alias_value":"BFSUZ3X2BRRS","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BFSUZ3X2BRRSK6WE","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BFSUZ3X2","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:07f4fd477d1c4b96e223f0689ee2b77d7438ea082e2ce34ff08ebcc9905dc99b","target":"graph","created_at":"2026-05-18T00:31:23Z","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 give a conditional lower bound of $n^{\\Omega(k)}$ on running time for the classic k-median and k-means clustering objectives (where n is the size of the input), even in low-dimensional Euclidean space of dimension four, assuming the Exponential Time Hypothesis (ETH). We also consider k-median (and k-means) with penalties where each point need not be assigned to a center, in which case it must pay a penalty, and extend our lower bound to at least three-dimensional Euclidean space.\n  This stands in stark contrast to many other geometric problems such as the traveling salesman p","authors_text":"Alan Roytman, Arnaud de Mesmay, Eva Rotenberg, Vincent Cohen-Addad","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-11-03T14:05:48Z","title":"The Bane of Low-Dimensionality Clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01171","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":"sha256:2a99e795cc7b1667e969431498a06386d966c7560a8ee7ce5d68d54d15c54a3a","target":"record","created_at":"2026-05-18T00:31:23Z","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":"c39f3f255c1a1ded0d38cd3542ea532f29218f9f581ca39479b2829586f54440","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-11-03T14:05:48Z","title_canon_sha256":"84cd33fdf0a07a53899b0ea3d362520f4888c1ff89fb0010c3d7b992d9a2db64"},"schema_version":"1.0","source":{"id":"1711.01171","kind":"arxiv","version":1}},"canonical_sha256":"09654ceefa0c63257ac4485052074a47787ed2c2e96fdaedb950814f70e343b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09654ceefa0c63257ac4485052074a47787ed2c2e96fdaedb950814f70e343b8","first_computed_at":"2026-05-18T00:31:23.245933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:23.245933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cdToMAcmdkdZpu/QIceTbNaI+5WSLBhAYU84ejgbK6OXdKVxvfUbU6xur6HWj2wsgl1dezXlxzX02tGvXz5fAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:23.246476Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.01171","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a99e795cc7b1667e969431498a06386d966c7560a8ee7ce5d68d54d15c54a3a","sha256:07f4fd477d1c4b96e223f0689ee2b77d7438ea082e2ce34ff08ebcc9905dc99b"],"state_sha256":"83ac7bb4a0853ac4b5731a59c4cea9ca8e8dfe178de2c554512dad7e9b8196f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rlgezmemgJI4pRb1cbc8EQdLWF3NDE6lv0cF/s38FtftMK8O0SVo/ZCIN/AhV6UezUIihiWZj5jlLZ0xUFq/Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:26:30.557941Z","bundle_sha256":"04b00ca0055401992c66b30baff5b9f092ab27722500da3b8e5966073605e9c1"}}