{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:A6U5IYKAEGHK4CTOKXGMZU7BPK","short_pith_number":"pith:A6U5IYKA","canonical_record":{"source":{"id":"1510.08953","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-30T02:19:53Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"74fbc6e82ef09542b983cd3dd438a2f3a1a27388c299f4b8e6da71ffe406d4fc","abstract_canon_sha256":"d15e2db3085171ae279e1bf977fff4029790dd5a9a14b11dbdb3b4825c9de580"},"schema_version":"1.0"},"canonical_sha256":"07a9d46140218eae0a6e55ccccd3e17a9469f811dc9a340d8dffaeacb00c9221","source":{"kind":"arxiv","id":"1510.08953","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08953","created_at":"2026-05-18T01:28:24Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08953v1","created_at":"2026-05-18T01:28:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08953","created_at":"2026-05-18T01:28:24Z"},{"alias_kind":"pith_short_12","alias_value":"A6U5IYKAEGHK","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"A6U5IYKAEGHK4CTO","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"A6U5IYKA","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:A6U5IYKAEGHK4CTOKXGMZU7BPK","target":"record","payload":{"canonical_record":{"source":{"id":"1510.08953","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-30T02:19:53Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"74fbc6e82ef09542b983cd3dd438a2f3a1a27388c299f4b8e6da71ffe406d4fc","abstract_canon_sha256":"d15e2db3085171ae279e1bf977fff4029790dd5a9a14b11dbdb3b4825c9de580"},"schema_version":"1.0"},"canonical_sha256":"07a9d46140218eae0a6e55ccccd3e17a9469f811dc9a340d8dffaeacb00c9221","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:24.045575Z","signature_b64":"Xt/tkozWRUfc8T2i3QlwECWKX2W0JKc64cmqO5oqnHimPmsLqOTboSO9OrlFGE2hd3+HMUNto+GLX2ucMTNgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07a9d46140218eae0a6e55ccccd3e17a9469f811dc9a340d8dffaeacb00c9221","last_reissued_at":"2026-05-18T01:28:24.044874Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:24.044874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.08953","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":"2026-05-18T01:28:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r1PRmFQstq9iriZyCDXLzhzF0bnh69JTA2wWLS/0E3coPkBfciQuRxi4eShjX4aC94w5oI8sBuRHCdaFjTJxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T15:38:12.674708Z"},"content_sha256":"542eff14317452fade2b1f76a0df315ea06f93c41e8d7c3c8d5e0efc6460a90b","schema_version":"1.0","event_id":"sha256:542eff14317452fade2b1f76a0df315ea06f93c41e8d7c3c8d5e0efc6460a90b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:A6U5IYKAEGHK4CTOKXGMZU7BPK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Game-theoretic Perspective on Communication for Omniscience","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chung Chan, Ni Ding, Parastoo Sadeghi, Rodney A. Kennedy, Tie Liu","submitted_at":"2015-10-30T02:19:53Z","abstract_excerpt":"We propose a coalition game model for the problem of communication for omniscience (CO). In this game model, the core contains all achievable rate vectors for CO with sum-rate being equal to a given value. Any rate vector in the core distributes the sum-rate among users in a way that makes all users willing to cooperate in CO. We give the necessary and sufficient condition for the core to be nonempty. Based on this condition, we derive the expression of the minimum sum-rate for CO and show that this expression is consistent with the results in multivariate mutual information (MMI) and coded co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08953","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":"2026-05-18T01:28:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xMlzJAJzkTeVwlEYT7BWzAjQ3gjIZZv8aIOazy6Pb+NztGLHTUF35ZRr0K6tfselQUtBZ/65RmiFNVrJp/snDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T15:38:12.675055Z"},"content_sha256":"faefa039118829315f9f14efa0f60e22b32a2f8a161dc31cec09a1cb39aa4879","schema_version":"1.0","event_id":"sha256:faefa039118829315f9f14efa0f60e22b32a2f8a161dc31cec09a1cb39aa4879"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A6U5IYKAEGHK4CTOKXGMZU7BPK/bundle.json","state_url":"https://pith.science/pith/A6U5IYKAEGHK4CTOKXGMZU7BPK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A6U5IYKAEGHK4CTOKXGMZU7BPK/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":"2026-06-24T15:38:12Z","links":{"resolver":"https://pith.science/pith/A6U5IYKAEGHK4CTOKXGMZU7BPK","bundle":"https://pith.science/pith/A6U5IYKAEGHK4CTOKXGMZU7BPK/bundle.json","state":"https://pith.science/pith/A6U5IYKAEGHK4CTOKXGMZU7BPK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A6U5IYKAEGHK4CTOKXGMZU7BPK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:A6U5IYKAEGHK4CTOKXGMZU7BPK","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":"d15e2db3085171ae279e1bf977fff4029790dd5a9a14b11dbdb3b4825c9de580","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-30T02:19:53Z","title_canon_sha256":"74fbc6e82ef09542b983cd3dd438a2f3a1a27388c299f4b8e6da71ffe406d4fc"},"schema_version":"1.0","source":{"id":"1510.08953","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08953","created_at":"2026-05-18T01:28:24Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08953v1","created_at":"2026-05-18T01:28:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08953","created_at":"2026-05-18T01:28:24Z"},{"alias_kind":"pith_short_12","alias_value":"A6U5IYKAEGHK","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"A6U5IYKAEGHK4CTO","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"A6U5IYKA","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:faefa039118829315f9f14efa0f60e22b32a2f8a161dc31cec09a1cb39aa4879","target":"graph","created_at":"2026-05-18T01:28:24Z","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 propose a coalition game model for the problem of communication for omniscience (CO). In this game model, the core contains all achievable rate vectors for CO with sum-rate being equal to a given value. Any rate vector in the core distributes the sum-rate among users in a way that makes all users willing to cooperate in CO. We give the necessary and sufficient condition for the core to be nonempty. Based on this condition, we derive the expression of the minimum sum-rate for CO and show that this expression is consistent with the results in multivariate mutual information (MMI) and coded co","authors_text":"Chung Chan, Ni Ding, Parastoo Sadeghi, Rodney A. Kennedy, Tie Liu","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-30T02:19:53Z","title":"A Game-theoretic Perspective on Communication for Omniscience"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08953","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":"sha256:542eff14317452fade2b1f76a0df315ea06f93c41e8d7c3c8d5e0efc6460a90b","target":"record","created_at":"2026-05-18T01:28:24Z","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":"d15e2db3085171ae279e1bf977fff4029790dd5a9a14b11dbdb3b4825c9de580","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-30T02:19:53Z","title_canon_sha256":"74fbc6e82ef09542b983cd3dd438a2f3a1a27388c299f4b8e6da71ffe406d4fc"},"schema_version":"1.0","source":{"id":"1510.08953","kind":"arxiv","version":1}},"canonical_sha256":"07a9d46140218eae0a6e55ccccd3e17a9469f811dc9a340d8dffaeacb00c9221","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07a9d46140218eae0a6e55ccccd3e17a9469f811dc9a340d8dffaeacb00c9221","first_computed_at":"2026-05-18T01:28:24.044874Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:24.044874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xt/tkozWRUfc8T2i3QlwECWKX2W0JKc64cmqO5oqnHimPmsLqOTboSO9OrlFGE2hd3+HMUNto+GLX2ucMTNgBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:24.045575Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.08953","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:542eff14317452fade2b1f76a0df315ea06f93c41e8d7c3c8d5e0efc6460a90b","sha256:faefa039118829315f9f14efa0f60e22b32a2f8a161dc31cec09a1cb39aa4879"],"state_sha256":"5a5d3ffacd9a6e7bcaac60d6f1f620a92008f36eb06cfd6ea39821aed04f3a4b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ehtqMti/nlZVwzhS5WR2AiHoyA1+WjmLptQnmyMmMoihaOexxRgvDD3gQm68TYGpd9HdosejjSIxlcBVaBEyAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T15:38:12.677432Z","bundle_sha256":"768ebf9a8d052f89a77ad3622d4c4b856ecf1b9570f011134c514ab32e91bdb6"}}