{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WD5QA2WIPB26XAJ5NENO6IFLES","short_pith_number":"pith:WD5QA2WI","canonical_record":{"source":{"id":"1809.02691","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-09-07T21:51:25Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"a7acacb544582dbcab29d327385d17ba4b2a6d64fb408c2f12ee0c752dc7c27d","abstract_canon_sha256":"4d6753d77e774816c673b06731c76f73ff074a61b75fd589855b0f5718fdfc26"},"schema_version":"1.0"},"canonical_sha256":"b0fb006ac87875eb813d691aef20ab24aaeb1fcd6085699255285d5a59c9dd4c","source":{"kind":"arxiv","id":"1809.02691","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02691","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02691v1","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02691","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"WD5QA2WIPB26","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WD5QA2WIPB26XAJ5","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WD5QA2WI","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WD5QA2WIPB26XAJ5NENO6IFLES","target":"record","payload":{"canonical_record":{"source":{"id":"1809.02691","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-09-07T21:51:25Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"a7acacb544582dbcab29d327385d17ba4b2a6d64fb408c2f12ee0c752dc7c27d","abstract_canon_sha256":"4d6753d77e774816c673b06731c76f73ff074a61b75fd589855b0f5718fdfc26"},"schema_version":"1.0"},"canonical_sha256":"b0fb006ac87875eb813d691aef20ab24aaeb1fcd6085699255285d5a59c9dd4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:15.598205Z","signature_b64":"0oBxxc94m4WoRa/SSea8ceFFE2cyTKMXhZqgm+OEDvQEzHs1LufZw2Xq+8UeIFn536KMoA9bZsylZvvACLLsDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0fb006ac87875eb813d691aef20ab24aaeb1fcd6085699255285d5a59c9dd4c","last_reissued_at":"2026-05-18T00:06:15.597754Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:15.597754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.02691","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yq7VX3h4C6iamyMITKjAEHHRi4iiCETME5xF2kH4m5tZoPwSFqjcWKyZxsZ+7VAy0CO22W4Wg7foMPxvuORJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:57:27.559049Z"},"content_sha256":"2b32585b9fbdac5dba98640f3d2d181b7541cc25325ce9614f5ae03c5824324c","schema_version":"1.0","event_id":"sha256:2b32585b9fbdac5dba98640f3d2d181b7541cc25325ce9614f5ae03c5824324c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WD5QA2WIPB26XAJ5NENO6IFLES","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The smoothness test for a density function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Barbara Wolnik, Bogdan \\'Cmiel, Karol Dziedziul","submitted_at":"2018-09-07T21:51:25Z","abstract_excerpt":"The problem of testing hypothesis that a density function has no more than $\\mu$ derivatives versus it has more than $\\mu$ derivatives is considered. For a solution, the $L^2$ norms of wavelet orthogonal projections on some orthogonal \"differences\" of spaces from a multiresolution analysis is used. For the construction of the smoothness test an asymptotic distribution of a smoothness estimator is used. To analyze that asymptotic distribution, a new technique of enrichment procedure is proposed. The finite sample behaviour of the smoothness test is demonstrated in a numerical experiment in case"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02691","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9inQrmMyG9W0hYJkj9INrA5aA6DmGbPSttv7p8vi3mG978LuMU5AwsxkeMfzLgWZ53pv78VoxDCKWWX9ZineBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:57:27.559419Z"},"content_sha256":"a9b963e8932bb99140d529b931ec265dc7c65317c3f0034c0167ad4929a58de0","schema_version":"1.0","event_id":"sha256:a9b963e8932bb99140d529b931ec265dc7c65317c3f0034c0167ad4929a58de0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WD5QA2WIPB26XAJ5NENO6IFLES/bundle.json","state_url":"https://pith.science/pith/WD5QA2WIPB26XAJ5NENO6IFLES/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WD5QA2WIPB26XAJ5NENO6IFLES/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":"2026-06-25T10:57:27Z","links":{"resolver":"https://pith.science/pith/WD5QA2WIPB26XAJ5NENO6IFLES","bundle":"https://pith.science/pith/WD5QA2WIPB26XAJ5NENO6IFLES/bundle.json","state":"https://pith.science/pith/WD5QA2WIPB26XAJ5NENO6IFLES/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WD5QA2WIPB26XAJ5NENO6IFLES/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WD5QA2WIPB26XAJ5NENO6IFLES","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":"4d6753d77e774816c673b06731c76f73ff074a61b75fd589855b0f5718fdfc26","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-09-07T21:51:25Z","title_canon_sha256":"a7acacb544582dbcab29d327385d17ba4b2a6d64fb408c2f12ee0c752dc7c27d"},"schema_version":"1.0","source":{"id":"1809.02691","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02691","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02691v1","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02691","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"WD5QA2WIPB26","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WD5QA2WIPB26XAJ5","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WD5QA2WI","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:a9b963e8932bb99140d529b931ec265dc7c65317c3f0034c0167ad4929a58de0","target":"graph","created_at":"2026-05-18T00:06:15Z","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 problem of testing hypothesis that a density function has no more than $\\mu$ derivatives versus it has more than $\\mu$ derivatives is considered. For a solution, the $L^2$ norms of wavelet orthogonal projections on some orthogonal \"differences\" of spaces from a multiresolution analysis is used. For the construction of the smoothness test an asymptotic distribution of a smoothness estimator is used. To analyze that asymptotic distribution, a new technique of enrichment procedure is proposed. The finite sample behaviour of the smoothness test is demonstrated in a numerical experiment in case","authors_text":"Barbara Wolnik, Bogdan \\'Cmiel, Karol Dziedziul","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-09-07T21:51:25Z","title":"The smoothness test for a density function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02691","kind":"arxiv","version":1},"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":"sha256:2b32585b9fbdac5dba98640f3d2d181b7541cc25325ce9614f5ae03c5824324c","target":"record","created_at":"2026-05-18T00:06:15Z","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":"4d6753d77e774816c673b06731c76f73ff074a61b75fd589855b0f5718fdfc26","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-09-07T21:51:25Z","title_canon_sha256":"a7acacb544582dbcab29d327385d17ba4b2a6d64fb408c2f12ee0c752dc7c27d"},"schema_version":"1.0","source":{"id":"1809.02691","kind":"arxiv","version":1}},"canonical_sha256":"b0fb006ac87875eb813d691aef20ab24aaeb1fcd6085699255285d5a59c9dd4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0fb006ac87875eb813d691aef20ab24aaeb1fcd6085699255285d5a59c9dd4c","first_computed_at":"2026-05-18T00:06:15.597754Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:15.597754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0oBxxc94m4WoRa/SSea8ceFFE2cyTKMXhZqgm+OEDvQEzHs1LufZw2Xq+8UeIFn536KMoA9bZsylZvvACLLsDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:15.598205Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02691","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b32585b9fbdac5dba98640f3d2d181b7541cc25325ce9614f5ae03c5824324c","sha256:a9b963e8932bb99140d529b931ec265dc7c65317c3f0034c0167ad4929a58de0"],"state_sha256":"7ae563fe6a4da41405ec4191c24479e2dbb5da1a507ca69d857125442a8712ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OSiqUa0Fl8bLhlA6VVl+TvUK98l1+sLEs4z+YMLNt1Kl/W8UxQ4XXWwmwT9CVFHsh0DZNxwnlMZTEZDr6queAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T10:57:27.561426Z","bundle_sha256":"460f309a09d2a1ef2cdf64644604b3688d3095d511a420ff03381e8752056efa"}}