{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RWNKC4NJS75V7OXRHHECQVFGF4","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":"44002ee3665bcb2926fb7c45602e5934628c08b0066fed0655ac28d6b19db5d4","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-18T01:32:39Z","title_canon_sha256":"496ff0009a1d5b1e04f9d96a182277af763c57cd1a24f7deb4eff13e7505067e"},"schema_version":"1.0","source":{"id":"1403.4311","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4311","created_at":"2026-05-18T02:56:06Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4311v1","created_at":"2026-05-18T02:56:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4311","created_at":"2026-05-18T02:56:06Z"},{"alias_kind":"pith_short_12","alias_value":"RWNKC4NJS75V","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RWNKC4NJS75V7OXR","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RWNKC4NJ","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:caee5a0df42b92eb2dad3baddd6e83a66ec3c9b3fbad7c1350736c157571f0de","target":"graph","created_at":"2026-05-18T02:56:06Z","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 note, we investigate the performance of the PCM scheme with linear quantization rule for quantizing unit-norm tight frame expansions for ${\\mathbb R}^d$ without the White Noise Hypothesis. In \\cite{WX}, Wang and Xu showed that for asymptotically equidistributed unit-norm tight frame the PCM quantization error has an upper bound ${\\mathcal O}(\\delta^{(d+1)/2})$ and they conjecture the upper bound is sharp. In this note, we confirm the conjecture with employing the asymptotic estimate of the Bessel functions.","authors_text":"Heng Zhou, Zhiqiang Xu","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-18T01:32:39Z","title":"The lower bound of the PCM quantization error in high dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4311","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":"sha256:9fddb1a0ec74e81727ea06d11e9e494f8ace8d7693da665e6491d7d5dc399e6e","target":"record","created_at":"2026-05-18T02:56:06Z","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":"44002ee3665bcb2926fb7c45602e5934628c08b0066fed0655ac28d6b19db5d4","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-18T01:32:39Z","title_canon_sha256":"496ff0009a1d5b1e04f9d96a182277af763c57cd1a24f7deb4eff13e7505067e"},"schema_version":"1.0","source":{"id":"1403.4311","kind":"arxiv","version":1}},"canonical_sha256":"8d9aa171a997fb5fbaf139c82854a62f316616080480a63b4d032946c2260715","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d9aa171a997fb5fbaf139c82854a62f316616080480a63b4d032946c2260715","first_computed_at":"2026-05-18T02:56:06.036431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:06.036431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c0uCQELKoCLxQ1mUfXEDgC2BOgWqrGlAukiE16GjZyjvA0mcW0bTPIVAmhM7WUei3Lwgu8SggfPIrvyb62jfAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:06.036880Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.4311","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fddb1a0ec74e81727ea06d11e9e494f8ace8d7693da665e6491d7d5dc399e6e","sha256:caee5a0df42b92eb2dad3baddd6e83a66ec3c9b3fbad7c1350736c157571f0de"],"state_sha256":"62ec50ba61b1cba07931b31cb7939549145483c39a4fcca8cb5d7a0ed611c871"}