{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:QYPIUKRO7ASOUI6WZKXSVYGDFN","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":"62d876f00318cd3ff4f208220d471522e667da395620df95671592d7244cb765","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-13T03:40:20Z","title_canon_sha256":"1369de4744227ac6875c3ab8ad93179e9a883bd84ab1993e1311f9f827676c61"},"schema_version":"1.0","source":{"id":"0901.1705","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.1705","created_at":"2026-05-18T00:58:20Z"},{"alias_kind":"arxiv_version","alias_value":"0901.1705v2","created_at":"2026-05-18T00:58:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.1705","created_at":"2026-05-18T00:58:20Z"},{"alias_kind":"pith_short_12","alias_value":"QYPIUKRO7ASO","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QYPIUKRO7ASOUI6W","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QYPIUKRO","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:a73b99da49895cae9f138d2e2315f50770dada55d54dd18f94495a4ff112f3f5","target":"graph","created_at":"2026-05-18T00:58:20Z","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":"We present a new inner bound for the rate region of the $t$-stage successive-refinement problem with side-information. We also present a new upper bound for the rate-distortion function for lossy-source coding with multiple decoders and side-information. Characterising this rate-distortion function is a long-standing open problem, and it is widely believed that the tightest upper bound is provided by Theorem 2 of Heegard and Berger's paper \"Rate Distortion when Side Information may be Absent\", \\emph{IEEE Trans. Inform. Theory}, 1985. We give a counterexample to Heegard and Berger's result.","authors_text":"Alexander Grant, Roy Timo, Terence Chan","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-13T03:40:20Z","title":"Rate-Distortion with Side-Information at Many Decoders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1705","kind":"arxiv","version":2},"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":"sha256:38761f74a3facf7552d7bd58349a49c4d5b1713861a6b05e5678e93d2ebc0f2a","target":"record","created_at":"2026-05-18T00:58:20Z","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":"62d876f00318cd3ff4f208220d471522e667da395620df95671592d7244cb765","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-01-13T03:40:20Z","title_canon_sha256":"1369de4744227ac6875c3ab8ad93179e9a883bd84ab1993e1311f9f827676c61"},"schema_version":"1.0","source":{"id":"0901.1705","kind":"arxiv","version":2}},"canonical_sha256":"861e8a2a2ef824ea23d6caaf2ae0c32b62409ebc543c03cf693edecc62b354e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"861e8a2a2ef824ea23d6caaf2ae0c32b62409ebc543c03cf693edecc62b354e0","first_computed_at":"2026-05-18T00:58:20.423077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:20.423077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x4hiTvZXc1JlE/pXdFDXQFy0S55yriRGnFJLtIomD3cK3BKavcOVGYaQELmwmVEVF0wUPe8pwSCHQNb6UL+hCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:20.423765Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.1705","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38761f74a3facf7552d7bd58349a49c4d5b1713861a6b05e5678e93d2ebc0f2a","sha256:a73b99da49895cae9f138d2e2315f50770dada55d54dd18f94495a4ff112f3f5"],"state_sha256":"9bed6b304837a441f5152584b7dbcac379a13a348ba30305019ceb62e8b51cd0"}