{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UTQDIXSJMNJJERL7HDJXQNFA36","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":"c8d8d3522f056ba29d2d1710105a6499b9dda8b1b8d80adf35a3a94e8cb9ef18","cross_cats_sorted":["cs.NA","physics.comp-ph","q-bio.QM","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2018-04-05T16:12:37Z","title_canon_sha256":"d381b842d18f82dd2912fa124402884ecc53c9a38d6b89321d96fa8178dbb98d"},"schema_version":"1.0","source":{"id":"1804.01932","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.01932","created_at":"2026-05-18T00:02:35Z"},{"alias_kind":"arxiv_version","alias_value":"1804.01932v4","created_at":"2026-05-18T00:02:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01932","created_at":"2026-05-18T00:02:35Z"},{"alias_kind":"pith_short_12","alias_value":"UTQDIXSJMNJJ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UTQDIXSJMNJJERL7","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UTQDIXSJ","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:fd3134277e3ce5fa525dfb25fe4952545430b042a6cb4c61d73022f55000a16e","target":"graph","created_at":"2026-05-18T00:02:35Z","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":"How might a smooth probability distribution be estimated, with accurately quantified uncertainty, from a limited amount of sampled data? Here we describe a field-theoretic approach that addresses this problem remarkably well in one dimension, providing an exact nonparametric Bayesian posterior without relying on tunable parameters or large-data approximations. Strong non-Gaussian constraints, which require a non-perturbative treatment, are found to play a major role in reducing distribution uncertainty. A software implementation of this method is provided.","authors_text":"Ammar Tareen, Justin B. Kinney, Wei-Chia Chen","cross_cats":["cs.NA","physics.comp-ph","q-bio.QM","stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2018-04-05T16:12:37Z","title":"Density estimation on small datasets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01932","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:a3a77a1953b7cf6241735869f7a06fed376a96865651fc46aef7732155906333","target":"record","created_at":"2026-05-18T00:02:35Z","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":"c8d8d3522f056ba29d2d1710105a6499b9dda8b1b8d80adf35a3a94e8cb9ef18","cross_cats_sorted":["cs.NA","physics.comp-ph","q-bio.QM","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2018-04-05T16:12:37Z","title_canon_sha256":"d381b842d18f82dd2912fa124402884ecc53c9a38d6b89321d96fa8178dbb98d"},"schema_version":"1.0","source":{"id":"1804.01932","kind":"arxiv","version":4}},"canonical_sha256":"a4e0345e49635292457f38d37834a0df8e46820341e4018906393bbcdf48a0e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4e0345e49635292457f38d37834a0df8e46820341e4018906393bbcdf48a0e1","first_computed_at":"2026-05-18T00:02:35.278017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:35.278017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HHaEQ8RUEYKdtTyVAkXVfAY1Pq+xzw/rk3uxFWQxm/XROjVJeqAIoEEwCnXj3fCz2uqCbeW7GPlqTLFexUVOAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:35.278644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.01932","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3a77a1953b7cf6241735869f7a06fed376a96865651fc46aef7732155906333","sha256:fd3134277e3ce5fa525dfb25fe4952545430b042a6cb4c61d73022f55000a16e"],"state_sha256":"7521231da365bc50e56bdeee164c891fe2606a5379ce1a3aaf2de8ec78974e1b"}