{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:L6LXFZVCOMJYAFLTVQGWVN4X57","short_pith_number":"pith:L6LXFZVC","schema_version":"1.0","canonical_sha256":"5f9772e6a27313801573ac0d6ab797efcf571397bee9f9bfdb37b334222d202e","source":{"kind":"arxiv","id":"1608.03979","version":3},"attestation_state":"computed","paper":{"title":"Manifolds of Differentiable Densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.DG","math.FA","math.IT","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Nigel J. Newton","submitted_at":"2016-08-13T12:24:39Z","abstract_excerpt":"We develop a family of infinite-dimensional (non-parametric) manifolds of probability measures. The latter are defined on underlying Banach spaces, and have densities of class $C_b^k$ with respect to appropriate reference measures. The case $k=\\infty$, in which the manifolds are modelled on Fr\\'{e}chet spaces, is included. The manifolds admit the Fisher-Rao metric and, unusually for the non-parametric setting, Amari's $\\alpha$-covariant derivatives for all $\\alpha\\in R$. By construction, they are $C^\\infty$-embedded submanifolds of particular manifolds of finite measures. The statistical manif"},"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":"1608.03979","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-13T12:24:39Z","cross_cats_sorted":["cs.IT","math.DG","math.FA","math.IT","math.ST","stat.TH"],"title_canon_sha256":"6b32389a558b75a8815bbf2128e9408193b11fe73029f1eb046808f5048ae85e","abstract_canon_sha256":"64e38407906b3624e5fe9a27c00a67333fed5a80127591d6df5f9e044e9e50e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:48.401474Z","signature_b64":"gmTAeyubTJTKL2aBDFsozFrLntGfR7W70p/ay/BQ9yp1QcUtl65rKteqpXGaJdI+16hYfRcWURuTVw4Zss3hAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f9772e6a27313801573ac0d6ab797efcf571397bee9f9bfdb37b334222d202e","last_reissued_at":"2026-05-18T00:13:48.400857Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:48.400857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Manifolds of Differentiable Densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.DG","math.FA","math.IT","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Nigel J. Newton","submitted_at":"2016-08-13T12:24:39Z","abstract_excerpt":"We develop a family of infinite-dimensional (non-parametric) manifolds of probability measures. The latter are defined on underlying Banach spaces, and have densities of class $C_b^k$ with respect to appropriate reference measures. The case $k=\\infty$, in which the manifolds are modelled on Fr\\'{e}chet spaces, is included. The manifolds admit the Fisher-Rao metric and, unusually for the non-parametric setting, Amari's $\\alpha$-covariant derivatives for all $\\alpha\\in R$. By construction, they are $C^\\infty$-embedded submanifolds of particular manifolds of finite measures. The statistical manif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03979","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1608.03979","created_at":"2026-05-18T00:13:48.400928+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.03979v3","created_at":"2026-05-18T00:13:48.400928+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03979","created_at":"2026-05-18T00:13:48.400928+00:00"},{"alias_kind":"pith_short_12","alias_value":"L6LXFZVCOMJY","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"L6LXFZVCOMJYAFLT","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"L6LXFZVC","created_at":"2026-05-18T12:30:29.479603+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/L6LXFZVCOMJYAFLTVQGWVN4X57","json":"https://pith.science/pith/L6LXFZVCOMJYAFLTVQGWVN4X57.json","graph_json":"https://pith.science/api/pith-number/L6LXFZVCOMJYAFLTVQGWVN4X57/graph.json","events_json":"https://pith.science/api/pith-number/L6LXFZVCOMJYAFLTVQGWVN4X57/events.json","paper":"https://pith.science/paper/L6LXFZVC"},"agent_actions":{"view_html":"https://pith.science/pith/L6LXFZVCOMJYAFLTVQGWVN4X57","download_json":"https://pith.science/pith/L6LXFZVCOMJYAFLTVQGWVN4X57.json","view_paper":"https://pith.science/paper/L6LXFZVC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.03979&json=true","fetch_graph":"https://pith.science/api/pith-number/L6LXFZVCOMJYAFLTVQGWVN4X57/graph.json","fetch_events":"https://pith.science/api/pith-number/L6LXFZVCOMJYAFLTVQGWVN4X57/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L6LXFZVCOMJYAFLTVQGWVN4X57/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L6LXFZVCOMJYAFLTVQGWVN4X57/action/storage_attestation","attest_author":"https://pith.science/pith/L6LXFZVCOMJYAFLTVQGWVN4X57/action/author_attestation","sign_citation":"https://pith.science/pith/L6LXFZVCOMJYAFLTVQGWVN4X57/action/citation_signature","submit_replication":"https://pith.science/pith/L6LXFZVCOMJYAFLTVQGWVN4X57/action/replication_record"}},"created_at":"2026-05-18T00:13:48.400928+00:00","updated_at":"2026-05-18T00:13:48.400928+00:00"}