{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5NIQURG3DAHFBMNN7CQ26BTZJR","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":"7c9101c90790e338397c5715b315b9a6be82a0395d60e05852e3c9cb1887fe7f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-15T20:26:51Z","title_canon_sha256":"afec884416f61ea5f1f16bf9e466be0b1e4da38937d80bf67b523aba79b269bb"},"schema_version":"1.0","source":{"id":"1506.04767","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04767","created_at":"2026-05-18T01:48:05Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04767v1","created_at":"2026-05-18T01:48:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04767","created_at":"2026-05-18T01:48:05Z"},{"alias_kind":"pith_short_12","alias_value":"5NIQURG3DAHF","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5NIQURG3DAHFBMNN","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5NIQURG3","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:0767ac039cb41c8630b9acb188ee1c5c457768bfe17737975eab2a2721d8cc29","target":"graph","created_at":"2026-05-18T01:48:05Z","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":"We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with specified in-degrees. Another class additionally requires that the graph is connected. For both classes, ","authors_text":"Ali Pinar, Christopher J. Quinn, Negar Kiyavash","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-15T20:26:51Z","title":"Bounded Degree Approximations of Stochastic Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04767","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":"sha256:7f1b308d76a4afa70c805acac7e4bbb5f2ffada9adfb30da36ddad171b3b6378","target":"record","created_at":"2026-05-18T01:48:05Z","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":"7c9101c90790e338397c5715b315b9a6be82a0395d60e05852e3c9cb1887fe7f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-15T20:26:51Z","title_canon_sha256":"afec884416f61ea5f1f16bf9e466be0b1e4da38937d80bf67b523aba79b269bb"},"schema_version":"1.0","source":{"id":"1506.04767","kind":"arxiv","version":1}},"canonical_sha256":"eb510a44db180e50b1adf8a1af06794c6ba6398c6150484cc95b9c7d30760b4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb510a44db180e50b1adf8a1af06794c6ba6398c6150484cc95b9c7d30760b4f","first_computed_at":"2026-05-18T01:48:05.924107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:48:05.924107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0JZ42EqTwnwhao5irwTCJmC4pd+7etRUCTcYK7luqGhfQCTOeWo0YQupmnoVmALRcxmShpzCfPO7H8lF2pELAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:48:05.924739Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.04767","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f1b308d76a4afa70c805acac7e4bbb5f2ffada9adfb30da36ddad171b3b6378","sha256:0767ac039cb41c8630b9acb188ee1c5c457768bfe17737975eab2a2721d8cc29"],"state_sha256":"9589f2fe1e969e4ed0daf720f21c9f234e8ff43ccb0d55d56511b924be14832d"}