{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JDOV3ETMYJJKZDQL6DA5UPP4XG","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":"69c4af87a22abc70ebfe2f9af272ebbbc8ee42d4d12e82e92e057415cc98e00a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-26T07:50:20Z","title_canon_sha256":"c379185dc61f5492ede4027d4faccf7bcc88d01d077dded0be123fca274ded96"},"schema_version":"1.0","source":{"id":"1701.07602","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07602","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07602v3","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07602","created_at":"2026-05-18T00:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"JDOV3ETMYJJK","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JDOV3ETMYJJKZDQL","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JDOV3ETM","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:fb7203033c7262750caa82d659645818c0d2d5ac29cbfa078e83948d91a41189","target":"graph","created_at":"2026-05-18T00:30:55Z","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":"Suppose we have a pair of information channels, $\\kappa_{1},\\kappa_{2}$, with a common input. The Blackwell order is a partial order over channels that compares $\\kappa_{1}$ and $\\kappa_{2}$ by the maximal expected utility an agent can obtain when decisions are based on the channel outputs. Equivalently, $\\kappa_{1}$ is said to be Blackwell-inferior to $\\kappa_{2}$ if and only if $\\kappa_{1}$ can be constructed by garbling the output of $\\kappa_{2}$. A related partial order stipulates that $\\kappa_{2}$ is more capable than $\\kappa_{1}$ if the mutual information between the input and output is ","authors_text":"David Wolpert, Eckehard Olbrich, Johannes Rauh, J\\\"urgen Jost, Nils Bertschinger, Pradeep Kr. Banerjee","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-26T07:50:20Z","title":"Coarse-graining and the Blackwell order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07602","kind":"arxiv","version":3},"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":"sha256:7c05fa38adf2598efec5112a9729881738f3e7f328a42101864dcf612734e365","target":"record","created_at":"2026-05-18T00:30:55Z","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":"69c4af87a22abc70ebfe2f9af272ebbbc8ee42d4d12e82e92e057415cc98e00a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-26T07:50:20Z","title_canon_sha256":"c379185dc61f5492ede4027d4faccf7bcc88d01d077dded0be123fca274ded96"},"schema_version":"1.0","source":{"id":"1701.07602","kind":"arxiv","version":3}},"canonical_sha256":"48dd5d926cc252ac8e0bf0c1da3dfcb9b3c58c58ce0bb410dd7b6fb7072a8db5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48dd5d926cc252ac8e0bf0c1da3dfcb9b3c58c58ce0bb410dd7b6fb7072a8db5","first_computed_at":"2026-05-18T00:30:55.304675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:55.304675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iJ31oQzYJn/vckmajAs41wQrFqxSj7wbWuu2Rg498H9+74qEa5rPtVysTw/UBOLgtuRedtSLIy+EhNvxDN1DBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:55.305363Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.07602","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c05fa38adf2598efec5112a9729881738f3e7f328a42101864dcf612734e365","sha256:fb7203033c7262750caa82d659645818c0d2d5ac29cbfa078e83948d91a41189"],"state_sha256":"4c3eca225f2116c77dd988a1ce2ddcc02b7960a433438e8367c6cf0d9fb1a4ae"}