{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3S7KMWS3UZBVUQTU6ONHXEDI5B","short_pith_number":"pith:3S7KMWS3","canonical_record":{"source":{"id":"1310.6945","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-25T14:52:55Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"18da1afff88bf3fb19e2f8bc9716dd56c7e4c068c6397cba2415f605b9d4d715","abstract_canon_sha256":"118f1b8510e902c31908b10a109ee3602612487bba2490940bf12004bcfb9f93"},"schema_version":"1.0"},"canonical_sha256":"dcbea65a5ba6435a4274f39a7b9068e874f99aa08bb0c3b2678dbcd7e10b23e7","source":{"kind":"arxiv","id":"1310.6945","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6945","created_at":"2026-05-18T03:08:56Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6945v1","created_at":"2026-05-18T03:08:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6945","created_at":"2026-05-18T03:08:56Z"},{"alias_kind":"pith_short_12","alias_value":"3S7KMWS3UZBV","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3S7KMWS3UZBVUQTU","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3S7KMWS3","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3S7KMWS3UZBVUQTU6ONHXEDI5B","target":"record","payload":{"canonical_record":{"source":{"id":"1310.6945","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-25T14:52:55Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"18da1afff88bf3fb19e2f8bc9716dd56c7e4c068c6397cba2415f605b9d4d715","abstract_canon_sha256":"118f1b8510e902c31908b10a109ee3602612487bba2490940bf12004bcfb9f93"},"schema_version":"1.0"},"canonical_sha256":"dcbea65a5ba6435a4274f39a7b9068e874f99aa08bb0c3b2678dbcd7e10b23e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:56.400753Z","signature_b64":"e9/PLKuX6VKYhTM/ayZiu6F/RJDeJh268gAAybwSMBkFDS/2yyz0e5zoWPBWqwkbFt9I424wWu49l1qhxL5xDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcbea65a5ba6435a4274f39a7b9068e874f99aa08bb0c3b2678dbcd7e10b23e7","last_reissued_at":"2026-05-18T03:08:56.399952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:56.399952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.6945","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":"2026-05-18T03:08:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kyqGHNICaDn3RGedvzYvW1v19xCmN1s5NJWpgc/jyNEaHGF6BLz2p3WFYvogbzQz7AGQcr1DZezLxMRt++gFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:05:02.000748Z"},"content_sha256":"51a710c53946374ab99f06bb0d7ec6a08310704d234130c583dd7194295fea4b","schema_version":"1.0","event_id":"sha256:51a710c53946374ab99f06bb0d7ec6a08310704d234130c583dd7194295fea4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3S7KMWS3UZBVUQTU6ONHXEDI5B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Scalar Quantization for Parameter Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jean-Marc Brossier, Rodrigo Cabral Farias","submitted_at":"2013-10-25T14:52:55Z","abstract_excerpt":"In this paper, we study an asymptotic approximation of the Fisher information for the estimation of a scalar parameter using quantized measurements. We show that, as the number of quantization intervals tends to infinity, the loss of Fisher information induced by quantization decreases exponentially as a function of the number of quantization bits. A characterization of the optimal quantizer through its interval density and an analytical expression for the Fisher information are obtained. A comparison between optimal uniform and non-uniform quantization for the location and scale estimation pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6945","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":"2026-05-18T03:08:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eWmTcQ/oaxheqAggY68W0C1BWJKGacbJkvaJVxg5qEDUe20/O1C1w8Qk3fpqOo2KkZrhfGsIqCariu1ZF9C9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:05:02.001459Z"},"content_sha256":"380b0391226511f5ea8b1e4cf278d476e5d6b19010ceebec166f950966a71ab3","schema_version":"1.0","event_id":"sha256:380b0391226511f5ea8b1e4cf278d476e5d6b19010ceebec166f950966a71ab3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3S7KMWS3UZBVUQTU6ONHXEDI5B/bundle.json","state_url":"https://pith.science/pith/3S7KMWS3UZBVUQTU6ONHXEDI5B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3S7KMWS3UZBVUQTU6ONHXEDI5B/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":"2026-06-05T20:05:02Z","links":{"resolver":"https://pith.science/pith/3S7KMWS3UZBVUQTU6ONHXEDI5B","bundle":"https://pith.science/pith/3S7KMWS3UZBVUQTU6ONHXEDI5B/bundle.json","state":"https://pith.science/pith/3S7KMWS3UZBVUQTU6ONHXEDI5B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3S7KMWS3UZBVUQTU6ONHXEDI5B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3S7KMWS3UZBVUQTU6ONHXEDI5B","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":"118f1b8510e902c31908b10a109ee3602612487bba2490940bf12004bcfb9f93","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-25T14:52:55Z","title_canon_sha256":"18da1afff88bf3fb19e2f8bc9716dd56c7e4c068c6397cba2415f605b9d4d715"},"schema_version":"1.0","source":{"id":"1310.6945","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6945","created_at":"2026-05-18T03:08:56Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6945v1","created_at":"2026-05-18T03:08:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6945","created_at":"2026-05-18T03:08:56Z"},{"alias_kind":"pith_short_12","alias_value":"3S7KMWS3UZBV","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3S7KMWS3UZBVUQTU","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3S7KMWS3","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:380b0391226511f5ea8b1e4cf278d476e5d6b19010ceebec166f950966a71ab3","target":"graph","created_at":"2026-05-18T03:08:56Z","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 study an asymptotic approximation of the Fisher information for the estimation of a scalar parameter using quantized measurements. We show that, as the number of quantization intervals tends to infinity, the loss of Fisher information induced by quantization decreases exponentially as a function of the number of quantization bits. A characterization of the optimal quantizer through its interval density and an analytical expression for the Fisher information are obtained. A comparison between optimal uniform and non-uniform quantization for the location and scale estimation pr","authors_text":"Jean-Marc Brossier, Rodrigo Cabral Farias","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-25T14:52:55Z","title":"Optimal Scalar Quantization for Parameter Estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6945","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":"sha256:51a710c53946374ab99f06bb0d7ec6a08310704d234130c583dd7194295fea4b","target":"record","created_at":"2026-05-18T03:08:56Z","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":"118f1b8510e902c31908b10a109ee3602612487bba2490940bf12004bcfb9f93","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-25T14:52:55Z","title_canon_sha256":"18da1afff88bf3fb19e2f8bc9716dd56c7e4c068c6397cba2415f605b9d4d715"},"schema_version":"1.0","source":{"id":"1310.6945","kind":"arxiv","version":1}},"canonical_sha256":"dcbea65a5ba6435a4274f39a7b9068e874f99aa08bb0c3b2678dbcd7e10b23e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcbea65a5ba6435a4274f39a7b9068e874f99aa08bb0c3b2678dbcd7e10b23e7","first_computed_at":"2026-05-18T03:08:56.399952Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:56.399952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e9/PLKuX6VKYhTM/ayZiu6F/RJDeJh268gAAybwSMBkFDS/2yyz0e5zoWPBWqwkbFt9I424wWu49l1qhxL5xDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:56.400753Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.6945","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51a710c53946374ab99f06bb0d7ec6a08310704d234130c583dd7194295fea4b","sha256:380b0391226511f5ea8b1e4cf278d476e5d6b19010ceebec166f950966a71ab3"],"state_sha256":"ac74eda772233059315cabc67ca6c6fd4cc0c1406f1dc21bd9a49f1376864cce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ABZXJ6F2utKpGxJqUbRd+M9CO9i2GJIxqinYtC6nOcUMLOxvU46lhzROdaE/HqtWARSYYNLvHgmJERVJKwYIAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T20:05:02.005373Z","bundle_sha256":"f9d3c3b271ba7c37d25361c79d1b0cff18f2fe45ad62875f34f0404f1891fc66"}}