{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FCAVIF4IG5QFJSVRIXKVRORPAA","short_pith_number":"pith:FCAVIF4I","canonical_record":{"source":{"id":"1702.01042","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-03T15:14:11Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9e1e241d67154ef7c350273343f0a37332e0732f3e5eea892632d75f16bf74de","abstract_canon_sha256":"cec17d95f943b36cdb29d2b2ce9790988cfeb37a89939af3b465f5cf8037449d"},"schema_version":"1.0"},"canonical_sha256":"2881541788376054cab145d558ba2f003d0e7ab150ef97bbe40929bb66d8912c","source":{"kind":"arxiv","id":"1702.01042","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01042","created_at":"2026-05-18T00:33:39Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01042v2","created_at":"2026-05-18T00:33:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01042","created_at":"2026-05-18T00:33:39Z"},{"alias_kind":"pith_short_12","alias_value":"FCAVIF4IG5QF","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FCAVIF4IG5QFJSVR","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FCAVIF4I","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FCAVIF4IG5QFJSVRIXKVRORPAA","target":"record","payload":{"canonical_record":{"source":{"id":"1702.01042","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-03T15:14:11Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9e1e241d67154ef7c350273343f0a37332e0732f3e5eea892632d75f16bf74de","abstract_canon_sha256":"cec17d95f943b36cdb29d2b2ce9790988cfeb37a89939af3b465f5cf8037449d"},"schema_version":"1.0"},"canonical_sha256":"2881541788376054cab145d558ba2f003d0e7ab150ef97bbe40929bb66d8912c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:39.425781Z","signature_b64":"c8PpZxbatMJ2+zgC/nAI7BwpnIDGUsf1Auqh5c/M4sN2N9oJua+4AA0RxBE7oT/4UYB8QQRpAuX51FGLUkaqDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2881541788376054cab145d558ba2f003d0e7ab150ef97bbe40929bb66d8912c","last_reissued_at":"2026-05-18T00:33:39.424987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:39.424987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.01042","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u9A0AsjL69XEDdGCluvh9YouHNC5+w/TLE9dxADBOM2GWpDSJnKu3zDCjhhsVpGwlHtRsxGE1iJeufs9sJxoAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:26:54.664626Z"},"content_sha256":"ba898af9563fe832bfcaf7feb710160a5d9f19220bbd38dd05258f66e0615bdd","schema_version":"1.0","event_id":"sha256:ba898af9563fe832bfcaf7feb710160a5d9f19220bbd38dd05258f66e0615bdd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FCAVIF4IG5QFJSVRIXKVRORPAA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polar Codes and Polar Lattices for the Heegard-Berger Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Cong Ling, Deniz G\\\"und\\\"uz, Jinwen Shi, Ling Liu","submitted_at":"2017-02-03T15:14:11Z","abstract_excerpt":"Explicit coding schemes are proposed to achieve the rate-distortion function of the Heegard-Berger problem using polar codes. Specifically, a nested polar code construction is employed to achieve the rate-distortion function for the doubly-symmetric binary sources when the side information may be absent. The nested structure contains two optimal polar codes for lossy source coding and channel coding, respectively. Moreover, a similar nested polar lattice construction is employed when the source and the side information are jointly Gaussian. The proposed polar lattice is constructed by nesting "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01042","kind":"arxiv","version":2},"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":"2026-05-18T00:33:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nT573N+t7bg9EfhCIPrE1NN3wo/yObL9HFhqywG3G66QeXj+llTZpWtWMRP6CqHZ4xz2Zq544KrnRDuhO9ljBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:26:54.664970Z"},"content_sha256":"3b62b0cfd0a8e1ef6094685ae1394495e658058da0e446560a544a548e5fa0eb","schema_version":"1.0","event_id":"sha256:3b62b0cfd0a8e1ef6094685ae1394495e658058da0e446560a544a548e5fa0eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FCAVIF4IG5QFJSVRIXKVRORPAA/bundle.json","state_url":"https://pith.science/pith/FCAVIF4IG5QFJSVRIXKVRORPAA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FCAVIF4IG5QFJSVRIXKVRORPAA/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":"2026-05-28T13:26:54Z","links":{"resolver":"https://pith.science/pith/FCAVIF4IG5QFJSVRIXKVRORPAA","bundle":"https://pith.science/pith/FCAVIF4IG5QFJSVRIXKVRORPAA/bundle.json","state":"https://pith.science/pith/FCAVIF4IG5QFJSVRIXKVRORPAA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FCAVIF4IG5QFJSVRIXKVRORPAA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FCAVIF4IG5QFJSVRIXKVRORPAA","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":"cec17d95f943b36cdb29d2b2ce9790988cfeb37a89939af3b465f5cf8037449d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-03T15:14:11Z","title_canon_sha256":"9e1e241d67154ef7c350273343f0a37332e0732f3e5eea892632d75f16bf74de"},"schema_version":"1.0","source":{"id":"1702.01042","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01042","created_at":"2026-05-18T00:33:39Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01042v2","created_at":"2026-05-18T00:33:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01042","created_at":"2026-05-18T00:33:39Z"},{"alias_kind":"pith_short_12","alias_value":"FCAVIF4IG5QF","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FCAVIF4IG5QFJSVR","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FCAVIF4I","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:3b62b0cfd0a8e1ef6094685ae1394495e658058da0e446560a544a548e5fa0eb","target":"graph","created_at":"2026-05-18T00:33:39Z","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":"Explicit coding schemes are proposed to achieve the rate-distortion function of the Heegard-Berger problem using polar codes. Specifically, a nested polar code construction is employed to achieve the rate-distortion function for the doubly-symmetric binary sources when the side information may be absent. The nested structure contains two optimal polar codes for lossy source coding and channel coding, respectively. Moreover, a similar nested polar lattice construction is employed when the source and the side information are jointly Gaussian. The proposed polar lattice is constructed by nesting ","authors_text":"Cong Ling, Deniz G\\\"und\\\"uz, Jinwen Shi, Ling Liu","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-03T15:14:11Z","title":"Polar Codes and Polar Lattices for the Heegard-Berger Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01042","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:ba898af9563fe832bfcaf7feb710160a5d9f19220bbd38dd05258f66e0615bdd","target":"record","created_at":"2026-05-18T00:33:39Z","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":"cec17d95f943b36cdb29d2b2ce9790988cfeb37a89939af3b465f5cf8037449d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-02-03T15:14:11Z","title_canon_sha256":"9e1e241d67154ef7c350273343f0a37332e0732f3e5eea892632d75f16bf74de"},"schema_version":"1.0","source":{"id":"1702.01042","kind":"arxiv","version":2}},"canonical_sha256":"2881541788376054cab145d558ba2f003d0e7ab150ef97bbe40929bb66d8912c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2881541788376054cab145d558ba2f003d0e7ab150ef97bbe40929bb66d8912c","first_computed_at":"2026-05-18T00:33:39.424987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:39.424987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c8PpZxbatMJ2+zgC/nAI7BwpnIDGUsf1Auqh5c/M4sN2N9oJua+4AA0RxBE7oT/4UYB8QQRpAuX51FGLUkaqDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:39.425781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.01042","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba898af9563fe832bfcaf7feb710160a5d9f19220bbd38dd05258f66e0615bdd","sha256:3b62b0cfd0a8e1ef6094685ae1394495e658058da0e446560a544a548e5fa0eb"],"state_sha256":"dd9ad05077317f6f966d75d6ebe921b41f266f0aa6d5784496c87b8c46015651"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5E8TYpMgqVKmlL5z/u0lRNeTkChU44RurRTOXw9IDRpkjhxgv+7TeOBuRqrKXc2O0shFu3lrdd3Zm6ybqGm4Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:26:54.666932Z","bundle_sha256":"6c0e73895b563991c004de6bf2fa2d1da23e10e672991c9cdf9a21c66b6ac816"}}