{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:J7IUTC5FRRBLCK462D6MEW5YTJ","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":"2d7c24c236e248565ae1a7d0f9d3bdc06a4501d65eafe0fb261f67458156783e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-02T14:41:18Z","title_canon_sha256":"8a4d74b075fdccf246e3096c97b188c4fdf332ea2f1e487ae53bbc180bebf033"},"schema_version":"1.0","source":{"id":"1409.0732","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0732","created_at":"2026-05-18T01:34:57Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0732v2","created_at":"2026-05-18T01:34:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0732","created_at":"2026-05-18T01:34:57Z"},{"alias_kind":"pith_short_12","alias_value":"J7IUTC5FRRBL","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J7IUTC5FRRBLCK46","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J7IUTC5F","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:f094ab34949e8455d9fcc9ebb351a23840252593fdbf8a76c77c263389e2a866","target":"graph","created_at":"2026-05-18T01:34:57Z","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":"We investigate the greedy version of the $L^p$-optimal vector quantization problem for an $\\mathbb{R}^d$-valued random vector $X\\!\\in L^p$. We show the existence of a sequence $(a_N)_{N\\ge 1}$ such that $a_N$ minimizes $a\\mapsto\\big \\|\\min_{1\\le i\\le N-1}|X-a_i|\\wedge |X-a|\\big\\|_{L^p}$ ($L^p$-mean quantization error at level $N$ induced by $(a_1,\\ldots,a_{N-1},a)$). We show that this sequence produces $L^p$-rate optimal $N$-tuples $a^{(N)}=(a_1,\\ldots,a_{_N})$ ($i.e.$ the $L^p$-mean quantization error at level $N$ induced by $a^{(N)}$ goes to $0$ at rate $N^{-\\frac 1d}$). Greedy optimal seque","authors_text":"Gilles Pag\\`es, Harald Luschgy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-02T14:41:18Z","title":"Greedy vector quantization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0732","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":"sha256:918249e38f38051703182707a82fb32f61ddf2478e5f33ecac0b670ae8459f74","target":"record","created_at":"2026-05-18T01:34:57Z","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":"2d7c24c236e248565ae1a7d0f9d3bdc06a4501d65eafe0fb261f67458156783e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-02T14:41:18Z","title_canon_sha256":"8a4d74b075fdccf246e3096c97b188c4fdf332ea2f1e487ae53bbc180bebf033"},"schema_version":"1.0","source":{"id":"1409.0732","kind":"arxiv","version":2}},"canonical_sha256":"4fd1498ba58c42b12b9ed0fcc25bb89a43425d8a2050dd788dc3d71928154f41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fd1498ba58c42b12b9ed0fcc25bb89a43425d8a2050dd788dc3d71928154f41","first_computed_at":"2026-05-18T01:34:57.437162Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:57.437162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sGa59T0ieVq6p/zePXrods23hgq51EOV8MhiJW3yt5i+D2X9sWzPhiIZr6HZT4J7ysd2YoRZZTDtvYcfZd2yAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:57.438002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0732","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:918249e38f38051703182707a82fb32f61ddf2478e5f33ecac0b670ae8459f74","sha256:f094ab34949e8455d9fcc9ebb351a23840252593fdbf8a76c77c263389e2a866"],"state_sha256":"53d1d7d924493c0025dd612e8bc3c1213d23cc771728b9b412a1f41b85f5bc88"}