{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:37RCXGC7U6FGDSRNLUU4Y6DR2A","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":"a47ae037a4ae8595a45b3ff7ed78d9d32becbd81cebe50cb2d5fb800ea5bc25c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-25T14:12:31Z","title_canon_sha256":"1e79a4fb2fc7d84fd7e2af98a9949ac58063e64ae2d62a340cf148798a9163db"},"schema_version":"1.0","source":{"id":"1703.08696","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08696","created_at":"2026-05-18T00:05:19Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08696v4","created_at":"2026-05-18T00:05:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08696","created_at":"2026-05-18T00:05:19Z"},{"alias_kind":"pith_short_12","alias_value":"37RCXGC7U6FG","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"37RCXGC7U6FGDSRN","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"37RCXGC7","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:6a958f84110e429e87595f48b99997c5570e5f333ff6837e03e19bb272276a22","target":"graph","created_at":"2026-05-18T00:05:19Z","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":"The metric properties of the set in which random variables take their values lead to relevant probabilistic concepts. For example, the mean of a random variable is a best predictor in that it minimizes the standard Euclidean distance or $L_2$ norm in an appropriate class of random variables. Similarly, the median is the same concept but when the distance is measured by the $L_1$ norm. These two predictors stem from the fact that the mean and the median, minimize the distance to a given set of points when distances in $\\mathbb{R}$ or in $\\mathbb{R}^n$ are measured in the aforementioned metrics.","authors_text":"Henryk Gzyl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-25T14:12:31Z","title":"Prediction in logarithmic distance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08696","kind":"arxiv","version":4},"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":"sha256:82ce86700334810399596abdbb9a6cd7a6f86df2f3666896681351534570b46e","target":"record","created_at":"2026-05-18T00:05:19Z","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":"a47ae037a4ae8595a45b3ff7ed78d9d32becbd81cebe50cb2d5fb800ea5bc25c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-25T14:12:31Z","title_canon_sha256":"1e79a4fb2fc7d84fd7e2af98a9949ac58063e64ae2d62a340cf148798a9163db"},"schema_version":"1.0","source":{"id":"1703.08696","kind":"arxiv","version":4}},"canonical_sha256":"dfe22b985fa78a61ca2d5d29cc7871d039eb1074379236a7f9ceb9b4c7575533","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfe22b985fa78a61ca2d5d29cc7871d039eb1074379236a7f9ceb9b4c7575533","first_computed_at":"2026-05-18T00:05:19.841560Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:19.841560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6jCSDkXdZm63LOeS6IVSa7m8WqPRtmuVC7Wgc8b4yoBJ7P0oLTdvwtvSpQqiYGfRPnkubkPYLJmm/C6sIv7NDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:19.842071Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.08696","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82ce86700334810399596abdbb9a6cd7a6f86df2f3666896681351534570b46e","sha256:6a958f84110e429e87595f48b99997c5570e5f333ff6837e03e19bb272276a22"],"state_sha256":"2e3368c392f2a6b77d18842b00e56f9409aa485ecc894cd1ea4d84e4135f50ad"}