{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:IYRB2P2FEDUYLJWFPU76HNVXPX","short_pith_number":"pith:IYRB2P2F","canonical_record":{"source":{"id":"1010.3613","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-10-18T14:36:13Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"45fa640df345ddbbc34c21736d42ceec6bb3027f5c907c33fe1e08168dcd36c7","abstract_canon_sha256":"eba0db7d28b5d5d7b565b547808088354a0c4d9f7033eb90036c6f58facc2007"},"schema_version":"1.0"},"canonical_sha256":"46221d3f4520e985a6c57d3fe3b6b77dc3d30f2fbce651ab1463a203172a1bd6","source":{"kind":"arxiv","id":"1010.3613","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3613","created_at":"2026-05-18T04:39:08Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3613v1","created_at":"2026-05-18T04:39:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3613","created_at":"2026-05-18T04:39:08Z"},{"alias_kind":"pith_short_12","alias_value":"IYRB2P2FEDUY","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IYRB2P2FEDUYLJWF","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IYRB2P2F","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:IYRB2P2FEDUYLJWFPU76HNVXPX","target":"record","payload":{"canonical_record":{"source":{"id":"1010.3613","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-10-18T14:36:13Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"45fa640df345ddbbc34c21736d42ceec6bb3027f5c907c33fe1e08168dcd36c7","abstract_canon_sha256":"eba0db7d28b5d5d7b565b547808088354a0c4d9f7033eb90036c6f58facc2007"},"schema_version":"1.0"},"canonical_sha256":"46221d3f4520e985a6c57d3fe3b6b77dc3d30f2fbce651ab1463a203172a1bd6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:08.737786Z","signature_b64":"gTIaOGZ2vQhfDbQDI9VFz1F84IbDJeLgjYzXO0qgOcQ+9YKqoGoZCIf6F5pmVb9Q81QxnTJmzAsPyXX9qq8lCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46221d3f4520e985a6c57d3fe3b6b77dc3d30f2fbce651ab1463a203172a1bd6","last_reissued_at":"2026-05-18T04:39:08.737159Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:08.737159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.3613","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":"2026-05-18T04:39:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GRcIe3TuX2meER69LNwjJbCB9xcNOj40vRbA5FI0OeDsdhESMpObW+/jwbARS56ilT1mp8vQWG0RpNwylnOWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:37:16.121930Z"},"content_sha256":"8d4f4cf73113d7246771205d3455deb6e3477f513121b2163029f39379373d4d","schema_version":"1.0","event_id":"sha256:8d4f4cf73113d7246771205d3455deb6e3477f513121b2163029f39379373d4d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:IYRB2P2FEDUYLJWFPU76HNVXPX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Common Information of N Dependent Random Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Biao Chen, Ge Xu, Wei Liu","submitted_at":"2010-10-18T14:36:13Z","abstract_excerpt":"This paper generalizes Wyner's definition of common information of a pair of random variables to that of $N$ random variables. We prove coding theorems that show the same operational meanings for the common information of two random variables generalize to that of $N$ random variables. As a byproduct of our proof, we show that the Gray-Wyner source coding network can be generalized to $N$ source squences with $N$ decoders. We also establish a monotone property of Wyner's common information which is in contrast to other notions of the common information, specifically Shannon's mutual informatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3613","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":"2026-05-18T04:39:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kRVlmYydwZldNHAWw8GasBDQpu+XQXOUJZRgQB6TZD44Aifb87xT59rfO6ceCnFdI+mt/djcTr6guEsWUpTmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:37:16.122695Z"},"content_sha256":"201c5a6fa26e17e67465b6ea04e6faa773386421791c494c64ae6cff291c8dd0","schema_version":"1.0","event_id":"sha256:201c5a6fa26e17e67465b6ea04e6faa773386421791c494c64ae6cff291c8dd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IYRB2P2FEDUYLJWFPU76HNVXPX/bundle.json","state_url":"https://pith.science/pith/IYRB2P2FEDUYLJWFPU76HNVXPX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IYRB2P2FEDUYLJWFPU76HNVXPX/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":"2026-06-09T17:37:16Z","links":{"resolver":"https://pith.science/pith/IYRB2P2FEDUYLJWFPU76HNVXPX","bundle":"https://pith.science/pith/IYRB2P2FEDUYLJWFPU76HNVXPX/bundle.json","state":"https://pith.science/pith/IYRB2P2FEDUYLJWFPU76HNVXPX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IYRB2P2FEDUYLJWFPU76HNVXPX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IYRB2P2FEDUYLJWFPU76HNVXPX","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":"eba0db7d28b5d5d7b565b547808088354a0c4d9f7033eb90036c6f58facc2007","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-10-18T14:36:13Z","title_canon_sha256":"45fa640df345ddbbc34c21736d42ceec6bb3027f5c907c33fe1e08168dcd36c7"},"schema_version":"1.0","source":{"id":"1010.3613","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3613","created_at":"2026-05-18T04:39:08Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3613v1","created_at":"2026-05-18T04:39:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3613","created_at":"2026-05-18T04:39:08Z"},{"alias_kind":"pith_short_12","alias_value":"IYRB2P2FEDUY","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IYRB2P2FEDUYLJWF","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IYRB2P2F","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:201c5a6fa26e17e67465b6ea04e6faa773386421791c494c64ae6cff291c8dd0","target":"graph","created_at":"2026-05-18T04:39:08Z","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 paper generalizes Wyner's definition of common information of a pair of random variables to that of $N$ random variables. We prove coding theorems that show the same operational meanings for the common information of two random variables generalize to that of $N$ random variables. As a byproduct of our proof, we show that the Gray-Wyner source coding network can be generalized to $N$ source squences with $N$ decoders. We also establish a monotone property of Wyner's common information which is in contrast to other notions of the common information, specifically Shannon's mutual informatio","authors_text":"Biao Chen, Ge Xu, Wei Liu","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-10-18T14:36:13Z","title":"The Common Information of N Dependent Random Variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3613","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":"sha256:8d4f4cf73113d7246771205d3455deb6e3477f513121b2163029f39379373d4d","target":"record","created_at":"2026-05-18T04:39:08Z","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":"eba0db7d28b5d5d7b565b547808088354a0c4d9f7033eb90036c6f58facc2007","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-10-18T14:36:13Z","title_canon_sha256":"45fa640df345ddbbc34c21736d42ceec6bb3027f5c907c33fe1e08168dcd36c7"},"schema_version":"1.0","source":{"id":"1010.3613","kind":"arxiv","version":1}},"canonical_sha256":"46221d3f4520e985a6c57d3fe3b6b77dc3d30f2fbce651ab1463a203172a1bd6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46221d3f4520e985a6c57d3fe3b6b77dc3d30f2fbce651ab1463a203172a1bd6","first_computed_at":"2026-05-18T04:39:08.737159Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:08.737159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gTIaOGZ2vQhfDbQDI9VFz1F84IbDJeLgjYzXO0qgOcQ+9YKqoGoZCIf6F5pmVb9Q81QxnTJmzAsPyXX9qq8lCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:08.737786Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.3613","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d4f4cf73113d7246771205d3455deb6e3477f513121b2163029f39379373d4d","sha256:201c5a6fa26e17e67465b6ea04e6faa773386421791c494c64ae6cff291c8dd0"],"state_sha256":"8e908fb92032fc1167948b5f3c34942b4caf9fd2f12925bb4c7cedc53323865a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HDzOBt5uLrZEGaZbGzI+iP2gxaY9kKv19J3nupywcYIPni9/h1CJOdyB07D4p+wGr1+g41E4Hj86Saozb191Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T17:37:16.127117Z","bundle_sha256":"fdcdac4dc73cd2ab48d9428a534d16f5ea362368ea4f69b3fa5f0de5e43d5c26"}}