{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:SVAHS2GVK5JLBO4QBNMVAQLWEO","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":"37ab3c27be60e4b65721f55b55515da6a12e4d13077f0a57a81b984a400b7921","cross_cats_sorted":["math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2004-12-23T20:05:17Z","title_canon_sha256":"126ff0a2fb8d0583f0d727490c60e5a3a809505194583176a43bd0a5d60d7cb4"},"schema_version":"1.0","source":{"id":"cs/0412108","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0412108","created_at":"2026-07-04T15:02:44Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0412108v1","created_at":"2026-07-04T15:02:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0412108","created_at":"2026-07-04T15:02:44Z"},{"alias_kind":"pith_short_12","alias_value":"SVAHS2GVK5JL","created_at":"2026-07-04T15:02:44Z"},{"alias_kind":"pith_short_16","alias_value":"SVAHS2GVK5JLBO4Q","created_at":"2026-07-04T15:02:44Z"},{"alias_kind":"pith_short_8","alias_value":"SVAHS2GV","created_at":"2026-07-04T15:02:44Z"}],"graph_snapshots":[{"event_id":"sha256:7091762fc71730c1f3ec4b33070bd1482eb6e4a1791d81bd832adcd055916e54","target":"graph","created_at":"2026-07-04T15:02:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/cs/0412108/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper deals with arbitrarily distributed finite-power input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the input-output mutual information and the minimum mean-square error (MMSE) achievable by optimal estimation of the input given the output. That is, the derivative of the mutual information (nats) with respect to the signal-to-noise ratio (SNR) is equal to half the MMSE, regardless of the input statistics. This relationship holds for both scalar and vector signals, as well as for discrete-time and continuous-time noncausal MMSE esti","authors_text":"Dongning Guo, Sergio Verdu, Shlomo Shamai (Shitz)","cross_cats":["math.IT"],"headline":"","license":"","primary_cat":"cs.IT","submitted_at":"2004-12-23T20:05:17Z","title":"Mutual Information and Minimum Mean-square Error in Gaussian Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0412108","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":"sha256:0fb610b7de9b632e64a19b2505ea1fd8d9117028578c29e74cca18b6c4aff743","target":"record","created_at":"2026-07-04T15:02:44Z","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":"37ab3c27be60e4b65721f55b55515da6a12e4d13077f0a57a81b984a400b7921","cross_cats_sorted":["math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2004-12-23T20:05:17Z","title_canon_sha256":"126ff0a2fb8d0583f0d727490c60e5a3a809505194583176a43bd0a5d60d7cb4"},"schema_version":"1.0","source":{"id":"cs/0412108","kind":"arxiv","version":1}},"canonical_sha256":"95407968d55752b0bb900b595041762389225dcb430b29fe9207ff9580dfab43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95407968d55752b0bb900b595041762389225dcb430b29fe9207ff9580dfab43","first_computed_at":"2026-07-04T15:02:44.815941Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:02:44.815941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0y28FSAHoO5GWzKK1FtwTu6ZoRttCqmhD5Ri8G4P7aVyI6tXF+To5s9518tpz5YN/3ZO86KkOTgLGJQ15FKuDg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:02:44.816403Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0412108","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fb610b7de9b632e64a19b2505ea1fd8d9117028578c29e74cca18b6c4aff743","sha256:7091762fc71730c1f3ec4b33070bd1482eb6e4a1791d81bd832adcd055916e54"],"state_sha256":"092e80613db15f84d4b9a73d9f1f21ca1391a730e4fadd64f4ce7ac817a84c0d"}