{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:6P6ABNVSQ3EU4FJCF3DCLNJQ5C","short_pith_number":"pith:6P6ABNVS","canonical_record":{"source":{"id":"2606.00413","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-05-29T23:06:44Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"a1bb1b13ddbc0ba20c68d0716e958c2830e980cf26e8892f9c220e13cbb37749","abstract_canon_sha256":"b52dd5bb1a951c15572a67e4ae56525ba76bf72c1e61f598d7596ae30b521c0b"},"schema_version":"1.0"},"canonical_sha256":"f3fc00b6b286c94e15222ec625b530e8983d7fc15ce9fd87a86a851d12225f49","source":{"kind":"arxiv","id":"2606.00413","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.00413","created_at":"2026-06-02T01:03:53Z"},{"alias_kind":"arxiv_version","alias_value":"2606.00413v1","created_at":"2026-06-02T01:03:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00413","created_at":"2026-06-02T01:03:53Z"},{"alias_kind":"pith_short_12","alias_value":"6P6ABNVSQ3EU","created_at":"2026-06-02T01:03:53Z"},{"alias_kind":"pith_short_16","alias_value":"6P6ABNVSQ3EU4FJC","created_at":"2026-06-02T01:03:53Z"},{"alias_kind":"pith_short_8","alias_value":"6P6ABNVS","created_at":"2026-06-02T01:03:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:6P6ABNVSQ3EU4FJCF3DCLNJQ5C","target":"record","payload":{"canonical_record":{"source":{"id":"2606.00413","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-05-29T23:06:44Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"a1bb1b13ddbc0ba20c68d0716e958c2830e980cf26e8892f9c220e13cbb37749","abstract_canon_sha256":"b52dd5bb1a951c15572a67e4ae56525ba76bf72c1e61f598d7596ae30b521c0b"},"schema_version":"1.0"},"canonical_sha256":"f3fc00b6b286c94e15222ec625b530e8983d7fc15ce9fd87a86a851d12225f49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:03:53.920338Z","signature_b64":"DMK4FEqxhwU0dVoPShEIP+O5MzzqUyxzhUQs9/Ry6OEndx3R+JBjdYcjwf8VWdCpe/D6sdRC+xJ1AO/8WHn+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3fc00b6b286c94e15222ec625b530e8983d7fc15ce9fd87a86a851d12225f49","last_reissued_at":"2026-06-02T01:03:53.919956Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:03:53.919956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.00413","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":"2026-06-02T01:03:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YAE8ss0g0mOWHWWraOO/fvEUK4tnQRDVxy2CFE737F4e1A+I5ijkABqAxS7Lnn/IaUFdtOKw303bj2rIjzUICw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:44:00.255997Z"},"content_sha256":"b253a0bb2630909cf26801cac23549a0f0d2c616839a3e1df2675db86d08d6d7","schema_version":"1.0","event_id":"sha256:b253a0bb2630909cf26801cac23549a0f0d2c616839a3e1df2675db86d08d6d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:6P6ABNVSQ3EU4FJCF3DCLNJQ5C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riemannian Stochastic Optimization for Sufficient Dimension Reduction","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Fran\\c{c}ois Portier, Thibault Pautrel","submitted_at":"2026-05-29T23:06:44Z","abstract_excerpt":"Sufficient dimension reduction (SDR) makes high-dimensional regression tractable by projecting the covariates onto a low-dimensional subspace that preserves the conditional mean of the response. Existing gradient-based estimators either operate in the ambient space and suffer from the curse of dimensionality, or localize in the reduced space at a per-outer-iteration cost at least quadratic in the sample size. We show that minimizers of the population Minimum Average Variance Estimation (MAVE) risk approximate the same Grassmannian target as the Outer Product of Gradients (OPG), and recast the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00413","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.00413/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-02T01:03:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aF91V5mmNo9QGQF8q3vqygwCI0QtNEu1KZjPRkwQykzozFa/3dMGiuTlC8yfaa7zVk+1w1hou+OYBhFV2jK5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:44:00.256403Z"},"content_sha256":"f5a1b5a9906f1218bc6c4c5a8e8f64e057314c03b6f0039180e722fefea41c27","schema_version":"1.0","event_id":"sha256:f5a1b5a9906f1218bc6c4c5a8e8f64e057314c03b6f0039180e722fefea41c27"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6P6ABNVSQ3EU4FJCF3DCLNJQ5C/bundle.json","state_url":"https://pith.science/pith/6P6ABNVSQ3EU4FJCF3DCLNJQ5C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6P6ABNVSQ3EU4FJCF3DCLNJQ5C/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":"2026-06-22T11:44:00Z","links":{"resolver":"https://pith.science/pith/6P6ABNVSQ3EU4FJCF3DCLNJQ5C","bundle":"https://pith.science/pith/6P6ABNVSQ3EU4FJCF3DCLNJQ5C/bundle.json","state":"https://pith.science/pith/6P6ABNVSQ3EU4FJCF3DCLNJQ5C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6P6ABNVSQ3EU4FJCF3DCLNJQ5C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6P6ABNVSQ3EU4FJCF3DCLNJQ5C","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":"b52dd5bb1a951c15572a67e4ae56525ba76bf72c1e61f598d7596ae30b521c0b","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-05-29T23:06:44Z","title_canon_sha256":"a1bb1b13ddbc0ba20c68d0716e958c2830e980cf26e8892f9c220e13cbb37749"},"schema_version":"1.0","source":{"id":"2606.00413","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.00413","created_at":"2026-06-02T01:03:53Z"},{"alias_kind":"arxiv_version","alias_value":"2606.00413v1","created_at":"2026-06-02T01:03:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00413","created_at":"2026-06-02T01:03:53Z"},{"alias_kind":"pith_short_12","alias_value":"6P6ABNVSQ3EU","created_at":"2026-06-02T01:03:53Z"},{"alias_kind":"pith_short_16","alias_value":"6P6ABNVSQ3EU4FJC","created_at":"2026-06-02T01:03:53Z"},{"alias_kind":"pith_short_8","alias_value":"6P6ABNVS","created_at":"2026-06-02T01:03:53Z"}],"graph_snapshots":[{"event_id":"sha256:f5a1b5a9906f1218bc6c4c5a8e8f64e057314c03b6f0039180e722fefea41c27","target":"graph","created_at":"2026-06-02T01:03:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.00413/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Sufficient dimension reduction (SDR) makes high-dimensional regression tractable by projecting the covariates onto a low-dimensional subspace that preserves the conditional mean of the response. Existing gradient-based estimators either operate in the ambient space and suffer from the curse of dimensionality, or localize in the reduced space at a per-outer-iteration cost at least quadratic in the sample size. We show that minimizers of the population Minimum Average Variance Estimation (MAVE) risk approximate the same Grassmannian target as the Outer Product of Gradients (OPG), and recast the ","authors_text":"Fran\\c{c}ois Portier, Thibault Pautrel","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-05-29T23:06:44Z","title":"Riemannian Stochastic Optimization for Sufficient Dimension Reduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00413","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:b253a0bb2630909cf26801cac23549a0f0d2c616839a3e1df2675db86d08d6d7","target":"record","created_at":"2026-06-02T01:03:53Z","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":"b52dd5bb1a951c15572a67e4ae56525ba76bf72c1e61f598d7596ae30b521c0b","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-05-29T23:06:44Z","title_canon_sha256":"a1bb1b13ddbc0ba20c68d0716e958c2830e980cf26e8892f9c220e13cbb37749"},"schema_version":"1.0","source":{"id":"2606.00413","kind":"arxiv","version":1}},"canonical_sha256":"f3fc00b6b286c94e15222ec625b530e8983d7fc15ce9fd87a86a851d12225f49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3fc00b6b286c94e15222ec625b530e8983d7fc15ce9fd87a86a851d12225f49","first_computed_at":"2026-06-02T01:03:53.919956Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:03:53.919956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DMK4FEqxhwU0dVoPShEIP+O5MzzqUyxzhUQs9/Ry6OEndx3R+JBjdYcjwf8VWdCpe/D6sdRC+xJ1AO/8WHn+Bw==","signature_status":"signed_v1","signed_at":"2026-06-02T01:03:53.920338Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.00413","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b253a0bb2630909cf26801cac23549a0f0d2c616839a3e1df2675db86d08d6d7","sha256:f5a1b5a9906f1218bc6c4c5a8e8f64e057314c03b6f0039180e722fefea41c27"],"state_sha256":"e889ca35bd6ea437bdbab6403b9f88928c9c00d7b8f779e21ba7c4356931364f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hVf5T2OE2lXxtg2qtW1xusCUYXspRGyLy6DXjVg1diaiH/yUsKFtMCetJ14CnR8yPe2d+GSyovopcmjSC2wPCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T11:44:00.258452Z","bundle_sha256":"312de580165b9c3be13fbc1fc4caceadca34d26fb313059d5b35c840e94efae4"}}