{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:KM6UWGHDEOMSG5UZLCFHS7TSVA","short_pith_number":"pith:KM6UWGHD","schema_version":"1.0","canonical_sha256":"533d4b18e32399237699588a797e72a807dea86b907e2e777520036e99272f7c","source":{"kind":"arxiv","id":"1512.04510","version":1},"attestation_state":"computed","paper":{"title":"Algorithmic statistics: normal objects and universal models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alexey Milovanov","submitted_at":"2015-12-14T20:45:49Z","abstract_excerpt":"Kolmogorov suggested to measure quality of a statistical hypothesis $P$ for a data $x$ by two parameters: Kolmogorov complexity $C(P)$ of the hypothesis and the probability $P(x)$ of $x$ with respect to $P$.\n  P. G\\'acs, J. Tromp, P.M.B. Vit\\'anyi discovered a small class of models that are universal in the following sense. Each hypothesis $S_{ij}$ from that class is identified by two integer parameters $i,j$ and for every data $x$ and for each complexity level $\\alpha$ there is a hypothesis $S_{ij}$ with $j\\le i\\le l(x)$ of complexity at most $\\alpha$ that has almost the best fit among all hy"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1512.04510","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-14T20:45:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"2d9d069d92a1eebabfcdd5a800142bcffdc141774042b082f51bc0ad36fbe76a","abstract_canon_sha256":"830bb698c4c33f527142d1500674b3e12ec5bdde42730fc7276b62f8ca9f06e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:22.105443Z","signature_b64":"BFY+hiaAlOOCNnC3VDQYAuh7/bWyWqXtUIP6p9S1vv/J8SqFTjTUFCcV7kzIW3YR4RUBgLd2FQ2kbY6vscyoBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"533d4b18e32399237699588a797e72a807dea86b907e2e777520036e99272f7c","last_reissued_at":"2026-05-18T01:24:22.104793Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:22.104793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algorithmic statistics: normal objects and universal models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alexey Milovanov","submitted_at":"2015-12-14T20:45:49Z","abstract_excerpt":"Kolmogorov suggested to measure quality of a statistical hypothesis $P$ for a data $x$ by two parameters: Kolmogorov complexity $C(P)$ of the hypothesis and the probability $P(x)$ of $x$ with respect to $P$.\n  P. G\\'acs, J. Tromp, P.M.B. Vit\\'anyi discovered a small class of models that are universal in the following sense. Each hypothesis $S_{ij}$ from that class is identified by two integer parameters $i,j$ and for every data $x$ and for each complexity level $\\alpha$ there is a hypothesis $S_{ij}$ with $j\\le i\\le l(x)$ of complexity at most $\\alpha$ that has almost the best fit among all hy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04510","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1512.04510","created_at":"2026-05-18T01:24:22.104879+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.04510v1","created_at":"2026-05-18T01:24:22.104879+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04510","created_at":"2026-05-18T01:24:22.104879+00:00"},{"alias_kind":"pith_short_12","alias_value":"KM6UWGHDEOMS","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"KM6UWGHDEOMSG5UZ","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"KM6UWGHD","created_at":"2026-05-18T12:29:29.992203+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KM6UWGHDEOMSG5UZLCFHS7TSVA","json":"https://pith.science/pith/KM6UWGHDEOMSG5UZLCFHS7TSVA.json","graph_json":"https://pith.science/api/pith-number/KM6UWGHDEOMSG5UZLCFHS7TSVA/graph.json","events_json":"https://pith.science/api/pith-number/KM6UWGHDEOMSG5UZLCFHS7TSVA/events.json","paper":"https://pith.science/paper/KM6UWGHD"},"agent_actions":{"view_html":"https://pith.science/pith/KM6UWGHDEOMSG5UZLCFHS7TSVA","download_json":"https://pith.science/pith/KM6UWGHDEOMSG5UZLCFHS7TSVA.json","view_paper":"https://pith.science/paper/KM6UWGHD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.04510&json=true","fetch_graph":"https://pith.science/api/pith-number/KM6UWGHDEOMSG5UZLCFHS7TSVA/graph.json","fetch_events":"https://pith.science/api/pith-number/KM6UWGHDEOMSG5UZLCFHS7TSVA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KM6UWGHDEOMSG5UZLCFHS7TSVA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KM6UWGHDEOMSG5UZLCFHS7TSVA/action/storage_attestation","attest_author":"https://pith.science/pith/KM6UWGHDEOMSG5UZLCFHS7TSVA/action/author_attestation","sign_citation":"https://pith.science/pith/KM6UWGHDEOMSG5UZLCFHS7TSVA/action/citation_signature","submit_replication":"https://pith.science/pith/KM6UWGHDEOMSG5UZLCFHS7TSVA/action/replication_record"}},"created_at":"2026-05-18T01:24:22.104879+00:00","updated_at":"2026-05-18T01:24:22.104879+00:00"}