{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NDW3CP55GXBL24I5CLVX5IF2VG","short_pith_number":"pith:NDW3CP55","canonical_record":{"source":{"id":"1512.02713","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2015-12-09T01:28:00Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"28c8fa12a123fe295b4503a95223dc9ee2d36e68eedc0bb73c3c2cfd8b004d9f","abstract_canon_sha256":"1112ccec2904e8eb7878c1790b8c673e19332154d1e1807200e797c5faffa02f"},"schema_version":"1.0"},"canonical_sha256":"68edb13fbd35c2bd711d12eb7ea0baa9b1297dbbea8d4afe79563ee424a9b7ae","source":{"kind":"arxiv","id":"1512.02713","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02713","created_at":"2026-05-18T01:24:43Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02713v1","created_at":"2026-05-18T01:24:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02713","created_at":"2026-05-18T01:24:43Z"},{"alias_kind":"pith_short_12","alias_value":"NDW3CP55GXBL","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NDW3CP55GXBL24I5","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NDW3CP55","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NDW3CP55GXBL24I5CLVX5IF2VG","target":"record","payload":{"canonical_record":{"source":{"id":"1512.02713","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2015-12-09T01:28:00Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"28c8fa12a123fe295b4503a95223dc9ee2d36e68eedc0bb73c3c2cfd8b004d9f","abstract_canon_sha256":"1112ccec2904e8eb7878c1790b8c673e19332154d1e1807200e797c5faffa02f"},"schema_version":"1.0"},"canonical_sha256":"68edb13fbd35c2bd711d12eb7ea0baa9b1297dbbea8d4afe79563ee424a9b7ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:43.286130Z","signature_b64":"TKpkZmPt0T7BgBAhnyeRQK1pHXELXOUFDIZTbtbQk0ykGO8a4Q4ur85L7vWF59wezZ46/SqbHf3AGZNyuVQoCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68edb13fbd35c2bd711d12eb7ea0baa9b1297dbbea8d4afe79563ee424a9b7ae","last_reissued_at":"2026-05-18T01:24:43.285698Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:43.285698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.02713","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":"2026-05-18T01:24:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JpQKEVsiQ2yMEik7hNPiw7y9eKISSVV8mkJL/l49SqqgqJvBGKaY69ESWFs3zxYZw7O/rNjIMHfa+OIrIGiyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T00:21:01.854494Z"},"content_sha256":"9d1b1ab91467d561d7dd6f66ca29690189e81f501f24425da5844ac6d8ce9c0c","schema_version":"1.0","event_id":"sha256:9d1b1ab91467d561d7dd6f66ca29690189e81f501f24425da5844ac6d8ce9c0c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NDW3CP55GXBL24I5CLVX5IF2VG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transformations and Hardy-Krause variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"stat.CO","authors_text":"Art B. Owen, Kinjal Basu","submitted_at":"2015-12-09T01:28:00Z","abstract_excerpt":"Using a multivariable Faa di Bruno formula we give conditions on transformations $\\tau:[0,1]^m\\to\\mathcal{X}$ where $\\mathcal{X}$ is a closed and bounded subset of $\\mathbb{R}^d$ such that $f\\circ\\tau$ is of bounded variation in the sense of Hardy and Krause for all $f\\in C^d(\\mathcal{x})$. We give similar conditions for $f\\circ\\tau$ to be smooth enough for scrambled net sampling to attain $O(n^{-3/2+\\epsilon})$ accuracy. Some popular symmetric transformations to the simplex and sphere are shown to satisfy neither condition. Some other transformations due to Fang and Wang (1993) satisfy the fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02713","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":"2026-05-18T01:24:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KHX3W80XEfbFdgY3EZtuAEFXgkbfyzzt/V241Q/AzEhEfHhg7RlhQAjIMEmwBCF6WE1SGyhrdHXZtUjtNbcTBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T00:21:01.854843Z"},"content_sha256":"a599ea7f0e4545356545d50a3b09c4256fe3b1ea10d1d1e8648d0b7d01cfc705","schema_version":"1.0","event_id":"sha256:a599ea7f0e4545356545d50a3b09c4256fe3b1ea10d1d1e8648d0b7d01cfc705"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NDW3CP55GXBL24I5CLVX5IF2VG/bundle.json","state_url":"https://pith.science/pith/NDW3CP55GXBL24I5CLVX5IF2VG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NDW3CP55GXBL24I5CLVX5IF2VG/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":"2026-06-22T00:21:01Z","links":{"resolver":"https://pith.science/pith/NDW3CP55GXBL24I5CLVX5IF2VG","bundle":"https://pith.science/pith/NDW3CP55GXBL24I5CLVX5IF2VG/bundle.json","state":"https://pith.science/pith/NDW3CP55GXBL24I5CLVX5IF2VG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NDW3CP55GXBL24I5CLVX5IF2VG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NDW3CP55GXBL24I5CLVX5IF2VG","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":"1112ccec2904e8eb7878c1790b8c673e19332154d1e1807200e797c5faffa02f","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2015-12-09T01:28:00Z","title_canon_sha256":"28c8fa12a123fe295b4503a95223dc9ee2d36e68eedc0bb73c3c2cfd8b004d9f"},"schema_version":"1.0","source":{"id":"1512.02713","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02713","created_at":"2026-05-18T01:24:43Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02713v1","created_at":"2026-05-18T01:24:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02713","created_at":"2026-05-18T01:24:43Z"},{"alias_kind":"pith_short_12","alias_value":"NDW3CP55GXBL","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NDW3CP55GXBL24I5","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NDW3CP55","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:a599ea7f0e4545356545d50a3b09c4256fe3b1ea10d1d1e8648d0b7d01cfc705","target":"graph","created_at":"2026-05-18T01:24:43Z","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":"Using a multivariable Faa di Bruno formula we give conditions on transformations $\\tau:[0,1]^m\\to\\mathcal{X}$ where $\\mathcal{X}$ is a closed and bounded subset of $\\mathbb{R}^d$ such that $f\\circ\\tau$ is of bounded variation in the sense of Hardy and Krause for all $f\\in C^d(\\mathcal{x})$. We give similar conditions for $f\\circ\\tau$ to be smooth enough for scrambled net sampling to attain $O(n^{-3/2+\\epsilon})$ accuracy. Some popular symmetric transformations to the simplex and sphere are shown to satisfy neither condition. Some other transformations due to Fang and Wang (1993) satisfy the fi","authors_text":"Art B. Owen, Kinjal Basu","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2015-12-09T01:28:00Z","title":"Transformations and Hardy-Krause variation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02713","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":"sha256:9d1b1ab91467d561d7dd6f66ca29690189e81f501f24425da5844ac6d8ce9c0c","target":"record","created_at":"2026-05-18T01:24:43Z","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":"1112ccec2904e8eb7878c1790b8c673e19332154d1e1807200e797c5faffa02f","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2015-12-09T01:28:00Z","title_canon_sha256":"28c8fa12a123fe295b4503a95223dc9ee2d36e68eedc0bb73c3c2cfd8b004d9f"},"schema_version":"1.0","source":{"id":"1512.02713","kind":"arxiv","version":1}},"canonical_sha256":"68edb13fbd35c2bd711d12eb7ea0baa9b1297dbbea8d4afe79563ee424a9b7ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68edb13fbd35c2bd711d12eb7ea0baa9b1297dbbea8d4afe79563ee424a9b7ae","first_computed_at":"2026-05-18T01:24:43.285698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:43.285698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TKpkZmPt0T7BgBAhnyeRQK1pHXELXOUFDIZTbtbQk0ykGO8a4Q4ur85L7vWF59wezZ46/SqbHf3AGZNyuVQoCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:43.286130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.02713","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d1b1ab91467d561d7dd6f66ca29690189e81f501f24425da5844ac6d8ce9c0c","sha256:a599ea7f0e4545356545d50a3b09c4256fe3b1ea10d1d1e8648d0b7d01cfc705"],"state_sha256":"3ce379fddea747f745dffda36046a8e7f1568c6027cb6bb1d96762d813314499"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zx0MO+mUYlLbSsYkKQap13niiu7u8ZsocNaKHDmSO3JGUyIXXKEWUehq4KBqcBDeZYZZ2pRrRe87ui8n53rFBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T00:21:01.856838Z","bundle_sha256":"ca51ae586b81c506824cc837f24cf6c5046f89972f7882910e8c28c26030ef88"}}