{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6FCIHE6BTHSHDFMNGII4HDLBNC","short_pith_number":"pith:6FCIHE6B","canonical_record":{"source":{"id":"1802.00515","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-02-01T23:23:50Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"35b5a77f3e5c2b8383b018891396969b6a297a11246205a54747dca2f7e19490","abstract_canon_sha256":"7632baca46a82bd0b993ccb38058bc24b6c083e23169397e01d23cdb323d814e"},"schema_version":"1.0"},"canonical_sha256":"f1448393c199e471958d3211c38d6168b2b939ff3afbb0b74b9fc652838c4cf9","source":{"kind":"arxiv","id":"1802.00515","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.00515","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"arxiv_version","alias_value":"1802.00515v2","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.00515","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"pith_short_12","alias_value":"6FCIHE6BTHSH","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6FCIHE6BTHSHDFMN","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6FCIHE6B","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6FCIHE6BTHSHDFMNGII4HDLBNC","target":"record","payload":{"canonical_record":{"source":{"id":"1802.00515","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-02-01T23:23:50Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"35b5a77f3e5c2b8383b018891396969b6a297a11246205a54747dca2f7e19490","abstract_canon_sha256":"7632baca46a82bd0b993ccb38058bc24b6c083e23169397e01d23cdb323d814e"},"schema_version":"1.0"},"canonical_sha256":"f1448393c199e471958d3211c38d6168b2b939ff3afbb0b74b9fc652838c4cf9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:03.087143Z","signature_b64":"MkV3bcYsuH0LtrqDMpCaJmNWhfrSUuUe8V524p2yKOvgC8Wflnh5Dg7vRAhlYgg0E2ODsfGXo2fp9Ic4Pw/dBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1448393c199e471958d3211c38d6168b2b939ff3afbb0b74b9fc652838c4cf9","last_reissued_at":"2026-05-17T23:57:03.086515Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:03.086515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.00515","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+s/lA5SzyWbUotFiG12WnhL91GV+UW4AG20KtjgfGo24K9IJywDN6KnghYyCw4I28Jre85tZIvcb6hs0b03nDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:44:08.253022Z"},"content_sha256":"0a278b34d9015697c7a025dd61f28db9024e2ea18acbc0aa39d8371b8ae27db7","schema_version":"1.0","event_id":"sha256:0a278b34d9015697c7a025dd61f28db9024e2ea18acbc0aa39d8371b8ae27db7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6FCIHE6BTHSHDFMNGII4HDLBNC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dimension Reduction via Gaussian Ridge Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"stat.ME","authors_text":"Geoffrey T. Parks, Pranay Seshadri, Shaowu Yuchi","submitted_at":"2018-02-01T23:23:50Z","abstract_excerpt":"Ridge functions have recently emerged as a powerful set of ideas for subspace-based dimension reduction. In this paper we begin by drawing parallels between ridge subspaces, sufficient dimension reduction and active subspaces, contrasting between techniques rooted in statistical regression and those rooted in approximation theory. This sets the stage for our new algorithm that approximates what we call a Gaussian ridge function---the posterior mean of a Gaussian process on a dimension-reducing subspace---suitable for both regression and approximation problems. To compute this subspace we devel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00515","kind":"arxiv","version":2},"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":"2026-05-17T23:57:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Nq2nmZ2GQ+EbkOFo0/8nrHuvmBpgFowCpkH/YPqyJBYf0whB/V0WrRyK+R0omM5Af4FgkGmoZNcYpblTirNDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:44:08.253750Z"},"content_sha256":"6a144e4940d78c001c2056301a8ead44cfe2bea0f42f12a9c60230ead8c77b68","schema_version":"1.0","event_id":"sha256:6a144e4940d78c001c2056301a8ead44cfe2bea0f42f12a9c60230ead8c77b68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6FCIHE6BTHSHDFMNGII4HDLBNC/bundle.json","state_url":"https://pith.science/pith/6FCIHE6BTHSHDFMNGII4HDLBNC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6FCIHE6BTHSHDFMNGII4HDLBNC/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":"2026-05-31T20:44:08Z","links":{"resolver":"https://pith.science/pith/6FCIHE6BTHSHDFMNGII4HDLBNC","bundle":"https://pith.science/pith/6FCIHE6BTHSHDFMNGII4HDLBNC/bundle.json","state":"https://pith.science/pith/6FCIHE6BTHSHDFMNGII4HDLBNC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6FCIHE6BTHSHDFMNGII4HDLBNC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6FCIHE6BTHSHDFMNGII4HDLBNC","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":"7632baca46a82bd0b993ccb38058bc24b6c083e23169397e01d23cdb323d814e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-02-01T23:23:50Z","title_canon_sha256":"35b5a77f3e5c2b8383b018891396969b6a297a11246205a54747dca2f7e19490"},"schema_version":"1.0","source":{"id":"1802.00515","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.00515","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"arxiv_version","alias_value":"1802.00515v2","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.00515","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"pith_short_12","alias_value":"6FCIHE6BTHSH","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6FCIHE6BTHSHDFMN","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6FCIHE6B","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:6a144e4940d78c001c2056301a8ead44cfe2bea0f42f12a9c60230ead8c77b68","target":"graph","created_at":"2026-05-17T23:57:03Z","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":"Ridge functions have recently emerged as a powerful set of ideas for subspace-based dimension reduction. In this paper we begin by drawing parallels between ridge subspaces, sufficient dimension reduction and active subspaces, contrasting between techniques rooted in statistical regression and those rooted in approximation theory. This sets the stage for our new algorithm that approximates what we call a Gaussian ridge function---the posterior mean of a Gaussian process on a dimension-reducing subspace---suitable for both regression and approximation problems. To compute this subspace we devel","authors_text":"Geoffrey T. Parks, Pranay Seshadri, Shaowu Yuchi","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-02-01T23:23:50Z","title":"Dimension Reduction via Gaussian Ridge Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00515","kind":"arxiv","version":2},"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":"sha256:0a278b34d9015697c7a025dd61f28db9024e2ea18acbc0aa39d8371b8ae27db7","target":"record","created_at":"2026-05-17T23:57:03Z","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":"7632baca46a82bd0b993ccb38058bc24b6c083e23169397e01d23cdb323d814e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-02-01T23:23:50Z","title_canon_sha256":"35b5a77f3e5c2b8383b018891396969b6a297a11246205a54747dca2f7e19490"},"schema_version":"1.0","source":{"id":"1802.00515","kind":"arxiv","version":2}},"canonical_sha256":"f1448393c199e471958d3211c38d6168b2b939ff3afbb0b74b9fc652838c4cf9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1448393c199e471958d3211c38d6168b2b939ff3afbb0b74b9fc652838c4cf9","first_computed_at":"2026-05-17T23:57:03.086515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:03.086515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MkV3bcYsuH0LtrqDMpCaJmNWhfrSUuUe8V524p2yKOvgC8Wflnh5Dg7vRAhlYgg0E2ODsfGXo2fp9Ic4Pw/dBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:03.087143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.00515","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a278b34d9015697c7a025dd61f28db9024e2ea18acbc0aa39d8371b8ae27db7","sha256:6a144e4940d78c001c2056301a8ead44cfe2bea0f42f12a9c60230ead8c77b68"],"state_sha256":"c100a7bb90afdd719b1d4838b5d734da2ecf701f6eb662f07e42905ae05b9139"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pRJR6ywOV0g1T0omR37QBNPAkMABTqkQR6ZfgNS9sAdp8DVP+KN0StNIGgA1rFTz+CrxBWze1zoae2GcubgaAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:44:08.257964Z","bundle_sha256":"ff3bc90fb889e4b6f3946cf5f7966542b17f325248bea3b102d74bb7267c1c76"}}