{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:CFLC6LQEFGB3OEUTAZVQWJTLC5","short_pith_number":"pith:CFLC6LQE","canonical_record":{"source":{"id":"1009.2077","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-09-10T19:08:16Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ab155a12e2823f79e34841ab4b567104fd6062629651f356d758ea9f4a1a7bd2","abstract_canon_sha256":"0006c7867f97f0336840c2ab89a0b74d329e51afdbe55ec55824282c4e9710ca"},"schema_version":"1.0"},"canonical_sha256":"11562f2e042983b71293066b0b266b17474e9fbaf6310a458b672db2406b9f2a","source":{"kind":"arxiv","id":"1009.2077","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2077","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2077v1","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2077","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"pith_short_12","alias_value":"CFLC6LQEFGB3","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"CFLC6LQEFGB3OEUT","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"CFLC6LQE","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:CFLC6LQEFGB3OEUTAZVQWJTLC5","target":"record","payload":{"canonical_record":{"source":{"id":"1009.2077","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-09-10T19:08:16Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ab155a12e2823f79e34841ab4b567104fd6062629651f356d758ea9f4a1a7bd2","abstract_canon_sha256":"0006c7867f97f0336840c2ab89a0b74d329e51afdbe55ec55824282c4e9710ca"},"schema_version":"1.0"},"canonical_sha256":"11562f2e042983b71293066b0b266b17474e9fbaf6310a458b672db2406b9f2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:05.499883Z","signature_b64":"doJlE0vroINLDwfIfe+E0vBlumAq1sxJgkQqTdQYqolG/xUKuSSnOqNWjC8hazpeD62jbavaRKGQlrlQDhEMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11562f2e042983b71293066b0b266b17474e9fbaf6310a458b672db2406b9f2a","last_reissued_at":"2026-05-18T04:41:05.499409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:05.499409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.2077","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:41:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IZY3HW9E3+E7wAmHv9JUxmRIE6SM7ayNTAS+70t0woNgxgDAfSl3oasyGJ+NqYah/GY8udoH3coXY20lCvvxAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:06:18.615356Z"},"content_sha256":"2672f79db82df010733468a2504a20acbed622ac97024b9645c3ed9c6df4d600","schema_version":"1.0","event_id":"sha256:2672f79db82df010733468a2504a20acbed622ac97024b9645c3ed9c6df4d600"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:CFLC6LQEFGB3OEUTAZVQWJTLC5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new sufficient condition for sum-rate tightness in quadratic Gaussian multiterminal source coding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Yang Yang, Yifu Zhang, Zixiang Xiong","submitted_at":"2010-09-10T19:08:16Z","abstract_excerpt":"This work considers the quadratic Gaussian multiterminal (MT) source coding problem and provides a new sufficient condition for the Berger-Tung sum-rate bound to be tight. The converse proof utilizes a set of virtual remote sources given which the MT sources are block independent with a maximum block size of two. The given MT source coding problem is then related to a set of two-terminal problems with matrix-distortion constraints, for which a new lower bound on the sum-rate is given. Finally, a convex optimization problem is formulated and a sufficient condition derived for the optimal BT sch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2077","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":""},"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":"2026-05-18T04:41:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uwHSAc7tDoYy4Tgn1v63MTBKzGR96RYg9LWZrn637TU4eGW9KdNbIUDRP2PPY0yvFlW+P4IbJNU8vmYf2KJcDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:06:18.615710Z"},"content_sha256":"cc0f0af90eae924f3cb4bdca184be15c58a7fe8539ac9cac9e377526c5b062fc","schema_version":"1.0","event_id":"sha256:cc0f0af90eae924f3cb4bdca184be15c58a7fe8539ac9cac9e377526c5b062fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CFLC6LQEFGB3OEUTAZVQWJTLC5/bundle.json","state_url":"https://pith.science/pith/CFLC6LQEFGB3OEUTAZVQWJTLC5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CFLC6LQEFGB3OEUTAZVQWJTLC5/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":"2026-06-22T18:06:18Z","links":{"resolver":"https://pith.science/pith/CFLC6LQEFGB3OEUTAZVQWJTLC5","bundle":"https://pith.science/pith/CFLC6LQEFGB3OEUTAZVQWJTLC5/bundle.json","state":"https://pith.science/pith/CFLC6LQEFGB3OEUTAZVQWJTLC5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CFLC6LQEFGB3OEUTAZVQWJTLC5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CFLC6LQEFGB3OEUTAZVQWJTLC5","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":"0006c7867f97f0336840c2ab89a0b74d329e51afdbe55ec55824282c4e9710ca","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-09-10T19:08:16Z","title_canon_sha256":"ab155a12e2823f79e34841ab4b567104fd6062629651f356d758ea9f4a1a7bd2"},"schema_version":"1.0","source":{"id":"1009.2077","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2077","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2077v1","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2077","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"pith_short_12","alias_value":"CFLC6LQEFGB3","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"CFLC6LQEFGB3OEUT","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"CFLC6LQE","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:cc0f0af90eae924f3cb4bdca184be15c58a7fe8539ac9cac9e377526c5b062fc","target":"graph","created_at":"2026-05-18T04:41:05Z","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":"This work considers the quadratic Gaussian multiterminal (MT) source coding problem and provides a new sufficient condition for the Berger-Tung sum-rate bound to be tight. The converse proof utilizes a set of virtual remote sources given which the MT sources are block independent with a maximum block size of two. The given MT source coding problem is then related to a set of two-terminal problems with matrix-distortion constraints, for which a new lower bound on the sum-rate is given. Finally, a convex optimization problem is formulated and a sufficient condition derived for the optimal BT sch","authors_text":"Yang Yang, Yifu Zhang, Zixiang Xiong","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-09-10T19:08:16Z","title":"A new sufficient condition for sum-rate tightness in quadratic Gaussian multiterminal source coding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2077","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":"sha256:2672f79db82df010733468a2504a20acbed622ac97024b9645c3ed9c6df4d600","target":"record","created_at":"2026-05-18T04:41:05Z","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":"0006c7867f97f0336840c2ab89a0b74d329e51afdbe55ec55824282c4e9710ca","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-09-10T19:08:16Z","title_canon_sha256":"ab155a12e2823f79e34841ab4b567104fd6062629651f356d758ea9f4a1a7bd2"},"schema_version":"1.0","source":{"id":"1009.2077","kind":"arxiv","version":1}},"canonical_sha256":"11562f2e042983b71293066b0b266b17474e9fbaf6310a458b672db2406b9f2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11562f2e042983b71293066b0b266b17474e9fbaf6310a458b672db2406b9f2a","first_computed_at":"2026-05-18T04:41:05.499409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:05.499409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"doJlE0vroINLDwfIfe+E0vBlumAq1sxJgkQqTdQYqolG/xUKuSSnOqNWjC8hazpeD62jbavaRKGQlrlQDhEMDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:05.499883Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2077","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2672f79db82df010733468a2504a20acbed622ac97024b9645c3ed9c6df4d600","sha256:cc0f0af90eae924f3cb4bdca184be15c58a7fe8539ac9cac9e377526c5b062fc"],"state_sha256":"d696a6130fd45cbff0ca2f9ed48775c6be2b4b6c0509e608e3fa576015cd554b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CzJZ3BWnP7LALd3eqnJy2BW50e7wMSNukiTrZ4kVd5NeV2nrlY0z2Rg6C+2ZFhHWukpczYOjftSNkql1gx81DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T18:06:18.617690Z","bundle_sha256":"749a5005ee0a999b71c3b29d7d82849d7a3ea41c6c3b72e993a5f259cf71675d"}}