{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:STPSH2WRBJBMP47ISP57EIVZDJ","short_pith_number":"pith:STPSH2WR","schema_version":"1.0","canonical_sha256":"94df23ead10a42c7f3e893fbf222b91a4c443cf239dfee839e08cfb36d55063b","source":{"kind":"arxiv","id":"1908.04024","version":1},"attestation_state":"computed","paper":{"title":"A Lagrange-Dual Lower Bound to the Error Exponent Function of the Typical Random Code","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Neri Merhav","submitted_at":"2019-08-12T06:54:02Z","abstract_excerpt":"A Lagrange-dual (Gallager-style) lower bound is derived for the error exponent function of the typical random code (TRC) pertaining to the i.i.d. random coding ensemble and mismatched stochastic likelihood decoding. While the original expression, derived from the method of types (the Csiszar-style expression) involves minimization over probability distributions defined on the channel input--output alphabets, the new Lagrange-dual formula involves optimization of five parameters, independently of the alphabet sizes. For both stochastic and deterministic mismatched decoding (including maximum li"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1908.04024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-08-12T06:54:02Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1860c54e964d1df794cd1de07096ab23096ad6df3eb037e77728039485fa331f","abstract_canon_sha256":"e6f8b821385b10373e542e396a2c2a1d93743f36413c1282dabe2de828dcd640"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:53:20.115773Z","signature_b64":"R2XXycLR0vpqcb8D95kjDov1FyMln+85CJLQU2wJAA2UR/Yuc0H69o8ZcEF80E3uYIDgjB4HZ4GYBqD4JSPnCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94df23ead10a42c7f3e893fbf222b91a4c443cf239dfee839e08cfb36d55063b","last_reissued_at":"2026-07-04T23:53:20.115380Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:53:20.115380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Lagrange-Dual Lower Bound to the Error Exponent Function of the Typical Random Code","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Neri Merhav","submitted_at":"2019-08-12T06:54:02Z","abstract_excerpt":"A Lagrange-dual (Gallager-style) lower bound is derived for the error exponent function of the typical random code (TRC) pertaining to the i.i.d. random coding ensemble and mismatched stochastic likelihood decoding. While the original expression, derived from the method of types (the Csiszar-style expression) involves minimization over probability distributions defined on the channel input--output alphabets, the new Lagrange-dual formula involves optimization of five parameters, independently of the alphabet sizes. For both stochastic and deterministic mismatched decoding (including maximum li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04024","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.04024/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1908.04024","created_at":"2026-07-04T23:53:20.115440+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.04024v1","created_at":"2026-07-04T23:53:20.115440+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04024","created_at":"2026-07-04T23:53:20.115440+00:00"},{"alias_kind":"pith_short_12","alias_value":"STPSH2WRBJBM","created_at":"2026-07-04T23:53:20.115440+00:00"},{"alias_kind":"pith_short_16","alias_value":"STPSH2WRBJBMP47I","created_at":"2026-07-04T23:53:20.115440+00:00"},{"alias_kind":"pith_short_8","alias_value":"STPSH2WR","created_at":"2026-07-04T23:53:20.115440+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/STPSH2WRBJBMP47ISP57EIVZDJ","json":"https://pith.science/pith/STPSH2WRBJBMP47ISP57EIVZDJ.json","graph_json":"https://pith.science/api/pith-number/STPSH2WRBJBMP47ISP57EIVZDJ/graph.json","events_json":"https://pith.science/api/pith-number/STPSH2WRBJBMP47ISP57EIVZDJ/events.json","paper":"https://pith.science/paper/STPSH2WR"},"agent_actions":{"view_html":"https://pith.science/pith/STPSH2WRBJBMP47ISP57EIVZDJ","download_json":"https://pith.science/pith/STPSH2WRBJBMP47ISP57EIVZDJ.json","view_paper":"https://pith.science/paper/STPSH2WR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.04024&json=true","fetch_graph":"https://pith.science/api/pith-number/STPSH2WRBJBMP47ISP57EIVZDJ/graph.json","fetch_events":"https://pith.science/api/pith-number/STPSH2WRBJBMP47ISP57EIVZDJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/STPSH2WRBJBMP47ISP57EIVZDJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/STPSH2WRBJBMP47ISP57EIVZDJ/action/storage_attestation","attest_author":"https://pith.science/pith/STPSH2WRBJBMP47ISP57EIVZDJ/action/author_attestation","sign_citation":"https://pith.science/pith/STPSH2WRBJBMP47ISP57EIVZDJ/action/citation_signature","submit_replication":"https://pith.science/pith/STPSH2WRBJBMP47ISP57EIVZDJ/action/replication_record"}},"created_at":"2026-07-04T23:53:20.115440+00:00","updated_at":"2026-07-04T23:53:20.115440+00:00"}