{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:DMQKK4UIJKBQVXFRF642TTEZR4","short_pith_number":"pith:DMQKK4UI","schema_version":"1.0","canonical_sha256":"1b20a572884a830adcb12fb9a9cc998f1fb4e5bb85cbc285d1f55ea0ed6217e7","source":{"kind":"arxiv","id":"1701.02827","version":4},"attestation_state":"computed","paper":{"title":"Strong Functional Representation Lemma and Applications to Coding Theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Abbas El Gamal, Cheuk Ting Li","submitted_at":"2017-01-11T02:10:17Z","abstract_excerpt":"This paper shows that for any random variables $X$ and $Y$, it is possible to represent $Y$ as a function of $(X,Z)$ such that $Z$ is independent of $X$ and $I(X;Z|Y)\\le\\log(I(X;Y)+1)+4$ bits. We use this strong functional representation lemma (SFRL) to establish a bound on the rate needed for one-shot exact channel simulation for general (discrete or continuous) random variables, strengthening the results by Harsha et al. and Braverman and Garg, and to establish new and simple achievability results for one-shot variable-length lossy source coding, multiple description coding and Gray-Wyner sy"},"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":"1701.02827","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-11T02:10:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"cf2c3691d25c3518d66a3cd715053d4b0302b2b349c2682e540e510f4fbc3cdc","abstract_canon_sha256":"9f57c992ac4bb19ccbf434a39520c2da742c0154aadbb0fd7df2f514a7b17912"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:50.387784Z","signature_b64":"dS/IBm77CaHYXHixBwR+S97uGEXfykooBT45thMHlNAV483qB5W2oapBrqN7yOqzdHy13WUUb1HVuuAPBHB9Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b20a572884a830adcb12fb9a9cc998f1fb4e5bb85cbc285d1f55ea0ed6217e7","last_reissued_at":"2026-05-17T23:58:50.387211Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:50.387211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong Functional Representation Lemma and Applications to Coding Theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Abbas El Gamal, Cheuk Ting Li","submitted_at":"2017-01-11T02:10:17Z","abstract_excerpt":"This paper shows that for any random variables $X$ and $Y$, it is possible to represent $Y$ as a function of $(X,Z)$ such that $Z$ is independent of $X$ and $I(X;Z|Y)\\le\\log(I(X;Y)+1)+4$ bits. We use this strong functional representation lemma (SFRL) to establish a bound on the rate needed for one-shot exact channel simulation for general (discrete or continuous) random variables, strengthening the results by Harsha et al. and Braverman and Garg, and to establish new and simple achievability results for one-shot variable-length lossy source coding, multiple description coding and Gray-Wyner sy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02827","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1701.02827","created_at":"2026-05-17T23:58:50.387284+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.02827v4","created_at":"2026-05-17T23:58:50.387284+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02827","created_at":"2026-05-17T23:58:50.387284+00:00"},{"alias_kind":"pith_short_12","alias_value":"DMQKK4UIJKBQ","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"DMQKK4UIJKBQVXFR","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"DMQKK4UI","created_at":"2026-05-18T12:31:12.930513+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/DMQKK4UIJKBQVXFRF642TTEZR4","json":"https://pith.science/pith/DMQKK4UIJKBQVXFRF642TTEZR4.json","graph_json":"https://pith.science/api/pith-number/DMQKK4UIJKBQVXFRF642TTEZR4/graph.json","events_json":"https://pith.science/api/pith-number/DMQKK4UIJKBQVXFRF642TTEZR4/events.json","paper":"https://pith.science/paper/DMQKK4UI"},"agent_actions":{"view_html":"https://pith.science/pith/DMQKK4UIJKBQVXFRF642TTEZR4","download_json":"https://pith.science/pith/DMQKK4UIJKBQVXFRF642TTEZR4.json","view_paper":"https://pith.science/paper/DMQKK4UI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.02827&json=true","fetch_graph":"https://pith.science/api/pith-number/DMQKK4UIJKBQVXFRF642TTEZR4/graph.json","fetch_events":"https://pith.science/api/pith-number/DMQKK4UIJKBQVXFRF642TTEZR4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DMQKK4UIJKBQVXFRF642TTEZR4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DMQKK4UIJKBQVXFRF642TTEZR4/action/storage_attestation","attest_author":"https://pith.science/pith/DMQKK4UIJKBQVXFRF642TTEZR4/action/author_attestation","sign_citation":"https://pith.science/pith/DMQKK4UIJKBQVXFRF642TTEZR4/action/citation_signature","submit_replication":"https://pith.science/pith/DMQKK4UIJKBQVXFRF642TTEZR4/action/replication_record"}},"created_at":"2026-05-17T23:58:50.387284+00:00","updated_at":"2026-05-17T23:58:50.387284+00:00"}