{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:JDOV3ETMYJJKZDQL6DA5UPP4XG","short_pith_number":"pith:JDOV3ETM","canonical_record":{"source":{"id":"1701.07602","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-26T07:50:20Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c379185dc61f5492ede4027d4faccf7bcc88d01d077dded0be123fca274ded96","abstract_canon_sha256":"69c4af87a22abc70ebfe2f9af272ebbbc8ee42d4d12e82e92e057415cc98e00a"},"schema_version":"1.0"},"canonical_sha256":"48dd5d926cc252ac8e0bf0c1da3dfcb9b3c58c58ce0bb410dd7b6fb7072a8db5","source":{"kind":"arxiv","id":"1701.07602","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:JDOV3ETMYJJKZDQL6DA5UPP4XG","target":"record","payload":{"canonical_record":{"source":{"id":"1701.07602","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-26T07:50:20Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c379185dc61f5492ede4027d4faccf7bcc88d01d077dded0be123fca274ded96","abstract_canon_sha256":"69c4af87a22abc70ebfe2f9af272ebbbc8ee42d4d12e82e92e057415cc98e00a"},"schema_version":"1.0"},"canonical_sha256":"48dd5d926cc252ac8e0bf0c1da3dfcb9b3c58c58ce0bb410dd7b6fb7072a8db5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:55.305363Z","signature_b64":"iJ31oQzYJn/vckmajAs41wQrFqxSj7wbWuu2Rg498H9+74qEa5rPtVysTw/UBOLgtuRedtSLIy+EhNvxDN1DBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48dd5d926cc252ac8e0bf0c1da3dfcb9b3c58c58ce0bb410dd7b6fb7072a8db5","last_reissued_at":"2026-05-18T00:30:55.304675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:55.304675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.07602","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MaiqSUrn4fgsrR+2a4bGOaWFHDcD4e3AKS3OAIF8gBlKIOumCIjNe7l5kOcVxg8weVrsIVbxJZXzZBYZMXRHDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:30:27.681544Z"},"content_sha256":"7c05fa38adf2598efec5112a9729881738f3e7f328a42101864dcf612734e365","schema_version":"1.0","event_id":"sha256:7c05fa38adf2598efec5112a9729881738f3e7f328a42101864dcf612734e365"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:JDOV3ETMYJJKZDQL6DA5UPP4XG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coarse-graining and the Blackwell order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"David Wolpert, Eckehard Olbrich, Johannes Rauh, J\\\"urgen Jost, Nils Bertschinger, Pradeep Kr. Banerjee","submitted_at":"2017-01-26T07:50:20Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07602","kind":"arxiv","version":3},"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":"2026-05-18T00:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WWlKXYpONF/MwVE8UC25kMXVCSwhTa3shdQPWH6xFZ0P6Db97d2rMw2dkDh65J3XtgAtJ55fZ/swv0M6L8Q7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:30:27.682087Z"},"content_sha256":"fb7203033c7262750caa82d659645818c0d2d5ac29cbfa078e83948d91a41189","schema_version":"1.0","event_id":"sha256:fb7203033c7262750caa82d659645818c0d2d5ac29cbfa078e83948d91a41189"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JDOV3ETMYJJKZDQL6DA5UPP4XG/bundle.json","state_url":"https://pith.science/pith/JDOV3ETMYJJKZDQL6DA5UPP4XG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JDOV3ETMYJJKZDQL6DA5UPP4XG/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":"2026-05-31T15:30:27Z","links":{"resolver":"https://pith.science/pith/JDOV3ETMYJJKZDQL6DA5UPP4XG","bundle":"https://pith.science/pith/JDOV3ETMYJJKZDQL6DA5UPP4XG/bundle.json","state":"https://pith.science/pith/JDOV3ETMYJJKZDQL6DA5UPP4XG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JDOV3ETMYJJKZDQL6DA5UPP4XG/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N5Apjg1lN/8hEvujCwcOaDstOxnVjLWAruZIzhievq7eiOmiqvUZxTBFd8bNnrFyE1itEG0J5ClUnC9LSpdvBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T15:30:27.685895Z","bundle_sha256":"5b157b7c0f4b5c1085953797c51c53a8938ad062047a5b065a0e54c0a38acdcd"}}