{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:TRIY635U2SDTQTETJDOMZG2TQ7","short_pith_number":"pith:TRIY635U","canonical_record":{"source":{"id":"1009.3145","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-09-16T11:14:09Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"f0af689ee0c2abca3306584e81d89a6f7e91f32e50e2faaf79239fbd1493b541","abstract_canon_sha256":"46a6eeb3c1ec5ea6b91c4d1c8b93dc08c4e26eccf3183e99c352497b0b1310d2"},"schema_version":"1.0"},"canonical_sha256":"9c518f6fb4d487384c9348dccc9b5387c3d8fcb1b3fd3e7f6b1a38c4974dc34d","source":{"kind":"arxiv","id":"1009.3145","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3145","created_at":"2026-05-18T04:18:15Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3145v3","created_at":"2026-05-18T04:18:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3145","created_at":"2026-05-18T04:18:15Z"},{"alias_kind":"pith_short_12","alias_value":"TRIY635U2SDT","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"TRIY635U2SDTQTET","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"TRIY635U","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:TRIY635U2SDTQTETJDOMZG2TQ7","target":"record","payload":{"canonical_record":{"source":{"id":"1009.3145","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-09-16T11:14:09Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"f0af689ee0c2abca3306584e81d89a6f7e91f32e50e2faaf79239fbd1493b541","abstract_canon_sha256":"46a6eeb3c1ec5ea6b91c4d1c8b93dc08c4e26eccf3183e99c352497b0b1310d2"},"schema_version":"1.0"},"canonical_sha256":"9c518f6fb4d487384c9348dccc9b5387c3d8fcb1b3fd3e7f6b1a38c4974dc34d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:15.293929Z","signature_b64":"aSBv57ZuHr3GiRt+aMhMSUXgTdnQEX9bhf7gyui3xXX0Rw2sF9oHe2z+UesJSol0fsowzoE7yIycWvXr3nAeBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c518f6fb4d487384c9348dccc9b5387c3d8fcb1b3fd3e7f6b1a38c4974dc34d","last_reissued_at":"2026-05-18T04:18:15.293430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:15.293430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.3145","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:18:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+1hBEuCZVtCRZbOgV+gvo2MeBqpg7pyr3dSb+t82lJEGp1PdUYKQB6AjJRVb1wYwjLOyyesjEOeotL1tg5wpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T09:10:41.428033Z"},"content_sha256":"bbb5bd6fc58eb455f58c07ab55af6cffea1279896d942ea06b5ce4f556fdc9ca","schema_version":"1.0","event_id":"sha256:bbb5bd6fc58eb455f58c07ab55af6cffea1279896d942ea06b5ce4f556fdc9ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:TRIY635U2SDTQTETJDOMZG2TQ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal Rate-Efficient Scalar Quantization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Petros T. Boufounos","submitted_at":"2010-09-16T11:14:09Z","abstract_excerpt":"Scalar quantization is the most practical and straightforward approach to signal quantization. However, it has been shown that scalar quantization of oversampled or Compressively Sensed signals can be inefficient in terms of the rate-distortion trade-off, especially as the oversampling rate or the sparsity of the signal increases. In this paper, we modify the scalar quantizer to have discontinuous quantization regions. We demonstrate that with this modification it is possible to achieve exponential decay of the quantization error as a function of the oversampling rate instead of the quadratic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3145","kind":"arxiv","version":3},"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":"2026-05-18T04:18:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rf8da8Vl8IUfFiAS6pvLqH/dkWYQGHYKWNBI8xF0d4A3ldBaLlfCNZ8iMBLAcOL3IgmlODmcfP/iI7T+oEGnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T09:10:41.428387Z"},"content_sha256":"13b8de10f930c86650b10bae98800a8a3ffd8744da0555770d6a11609f708966","schema_version":"1.0","event_id":"sha256:13b8de10f930c86650b10bae98800a8a3ffd8744da0555770d6a11609f708966"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TRIY635U2SDTQTETJDOMZG2TQ7/bundle.json","state_url":"https://pith.science/pith/TRIY635U2SDTQTETJDOMZG2TQ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TRIY635U2SDTQTETJDOMZG2TQ7/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":"2026-06-20T09:10:41Z","links":{"resolver":"https://pith.science/pith/TRIY635U2SDTQTETJDOMZG2TQ7","bundle":"https://pith.science/pith/TRIY635U2SDTQTETJDOMZG2TQ7/bundle.json","state":"https://pith.science/pith/TRIY635U2SDTQTETJDOMZG2TQ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TRIY635U2SDTQTETJDOMZG2TQ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TRIY635U2SDTQTETJDOMZG2TQ7","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":"46a6eeb3c1ec5ea6b91c4d1c8b93dc08c4e26eccf3183e99c352497b0b1310d2","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-09-16T11:14:09Z","title_canon_sha256":"f0af689ee0c2abca3306584e81d89a6f7e91f32e50e2faaf79239fbd1493b541"},"schema_version":"1.0","source":{"id":"1009.3145","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3145","created_at":"2026-05-18T04:18:15Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3145v3","created_at":"2026-05-18T04:18:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3145","created_at":"2026-05-18T04:18:15Z"},{"alias_kind":"pith_short_12","alias_value":"TRIY635U2SDT","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"TRIY635U2SDTQTET","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"TRIY635U","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:13b8de10f930c86650b10bae98800a8a3ffd8744da0555770d6a11609f708966","target":"graph","created_at":"2026-05-18T04:18:15Z","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":"Scalar quantization is the most practical and straightforward approach to signal quantization. However, it has been shown that scalar quantization of oversampled or Compressively Sensed signals can be inefficient in terms of the rate-distortion trade-off, especially as the oversampling rate or the sparsity of the signal increases. In this paper, we modify the scalar quantizer to have discontinuous quantization regions. We demonstrate that with this modification it is possible to achieve exponential decay of the quantization error as a function of the oversampling rate instead of the quadratic ","authors_text":"Petros T. Boufounos","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-09-16T11:14:09Z","title":"Universal Rate-Efficient Scalar Quantization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3145","kind":"arxiv","version":3},"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:bbb5bd6fc58eb455f58c07ab55af6cffea1279896d942ea06b5ce4f556fdc9ca","target":"record","created_at":"2026-05-18T04:18:15Z","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":"46a6eeb3c1ec5ea6b91c4d1c8b93dc08c4e26eccf3183e99c352497b0b1310d2","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-09-16T11:14:09Z","title_canon_sha256":"f0af689ee0c2abca3306584e81d89a6f7e91f32e50e2faaf79239fbd1493b541"},"schema_version":"1.0","source":{"id":"1009.3145","kind":"arxiv","version":3}},"canonical_sha256":"9c518f6fb4d487384c9348dccc9b5387c3d8fcb1b3fd3e7f6b1a38c4974dc34d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c518f6fb4d487384c9348dccc9b5387c3d8fcb1b3fd3e7f6b1a38c4974dc34d","first_computed_at":"2026-05-18T04:18:15.293430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:15.293430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aSBv57ZuHr3GiRt+aMhMSUXgTdnQEX9bhf7gyui3xXX0Rw2sF9oHe2z+UesJSol0fsowzoE7yIycWvXr3nAeBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:15.293929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.3145","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbb5bd6fc58eb455f58c07ab55af6cffea1279896d942ea06b5ce4f556fdc9ca","sha256:13b8de10f930c86650b10bae98800a8a3ffd8744da0555770d6a11609f708966"],"state_sha256":"baac765b60a3248b26d6d6d52b343eae1266882d8ec3b25572b1ae1ae47bb10c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0o8OR/BAWhKHcD+APIoSy0cp5hj92Hd6XwxSXi8cdJDGQLx2896BvR6GSfFRdicVwkUvdAEk9vTaeG/XGnjVCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T09:10:41.430345Z","bundle_sha256":"47550ae55a9719eb363f259c143dd0492ad1548f4ca8cafcd7f5c93a7faa3f62"}}