{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7HKXI3I35NATKGTGKIAWTIC3OS","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":"2c18623eb13cbc398b48adee469d4247c2fd56c7842ebf464d07b1b4777c2bfa","cross_cats_sorted":["math.IT","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-03-23T13:48:04Z","title_canon_sha256":"89b4f274becd1e92012b4b0990b72894c4434747a8def4234fe22354e8c33cc0"},"schema_version":"1.0","source":{"id":"1603.07181","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07181","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07181v2","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07181","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"7HKXI3I35NAT","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7HKXI3I35NATKGTG","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7HKXI3I3","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:f5cffa1b266ca1afe5eb3dc8c1249660e994cd5141c8864585c0428c49b3acd0","target":"graph","created_at":"2026-05-18T01:04:27Z","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":"Here we define a procedure for evaluating KL-projections (I- and rI-projections) of channels. These can be useful in the decomposition of mutual information between input and outputs, e.g. to quantify synergies and interactions of different orders, as well as information integration and other related measures of complexity.\n  The algorithm is a generalization of the standard iterative scaling algorithm, which we here extend from probability distributions to channels (also known as transition kernels).","authors_text":"Nihat Ay, Paolo Perrone","cross_cats":["math.IT","stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-03-23T13:48:04Z","title":"Iterative Scaling Algorithm for Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07181","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:da95e7a8dc6bafa4cef51b4687a147bcca8379cd49481b3aeea52b100566ae0b","target":"record","created_at":"2026-05-18T01:04:27Z","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":"2c18623eb13cbc398b48adee469d4247c2fd56c7842ebf464d07b1b4777c2bfa","cross_cats_sorted":["math.IT","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-03-23T13:48:04Z","title_canon_sha256":"89b4f274becd1e92012b4b0990b72894c4434747a8def4234fe22354e8c33cc0"},"schema_version":"1.0","source":{"id":"1603.07181","kind":"arxiv","version":2}},"canonical_sha256":"f9d5746d1beb41351a66520169a05b749d69d20fb2fb009c4157c96ccce63984","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9d5746d1beb41351a66520169a05b749d69d20fb2fb009c4157c96ccce63984","first_computed_at":"2026-05-18T01:04:27.880388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:27.880388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aqYjZVv8Cke9f2+rKM4/IErTOq8kCP3BvJaBQuz8dpyrMmzQW9vt69I1aXEoeFZxqAtwyW/4MGXl57X6Q2L4BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:27.881091Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07181","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da95e7a8dc6bafa4cef51b4687a147bcca8379cd49481b3aeea52b100566ae0b","sha256:f5cffa1b266ca1afe5eb3dc8c1249660e994cd5141c8864585c0428c49b3acd0"],"state_sha256":"dbc25acfad0eec2261c66b431cc6ed4d0a1e077f1101668548777faf1b7a0b63"}