{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6YHWYWO2FJG7BPHQNXGKAZ7Y6X","short_pith_number":"pith:6YHWYWO2","canonical_record":{"source":{"id":"1603.08035","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-03-25T21:09:54Z","cross_cats_sorted":["cs.DM","cs.LG"],"title_canon_sha256":"a2a132ad78aafeea2b46a80bbd1b42f3b59d926071d32ad91bdb4c5cfb385a6f","abstract_canon_sha256":"deacdc8fbc8fef6d16a36e842b2e4510bb9d111e1e7a7a1965cf3a15d0682ab6"},"schema_version":"1.0"},"canonical_sha256":"f60f6c59da2a4df0bcf06dcca067f8f5ef7c72070d03b7bb0252b5b50f10f9b1","source":{"kind":"arxiv","id":"1603.08035","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08035","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08035v2","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08035","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"6YHWYWO2FJG7","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6YHWYWO2FJG7BPHQ","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6YHWYWO2","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6YHWYWO2FJG7BPHQNXGKAZ7Y6X","target":"record","payload":{"canonical_record":{"source":{"id":"1603.08035","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-03-25T21:09:54Z","cross_cats_sorted":["cs.DM","cs.LG"],"title_canon_sha256":"a2a132ad78aafeea2b46a80bbd1b42f3b59d926071d32ad91bdb4c5cfb385a6f","abstract_canon_sha256":"deacdc8fbc8fef6d16a36e842b2e4510bb9d111e1e7a7a1965cf3a15d0682ab6"},"schema_version":"1.0"},"canonical_sha256":"f60f6c59da2a4df0bcf06dcca067f8f5ef7c72070d03b7bb0252b5b50f10f9b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:53.016592Z","signature_b64":"WXK8T7M9gj5hr1oj0iZBagOUkh2n133R0tT5CDypMOaCXrWGERvPA8ywNTPeicj6rQZ7+2K1bJIQrMIFum6ODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f60f6c59da2a4df0bcf06dcca067f8f5ef7c72070d03b7bb0252b5b50f10f9b1","last_reissued_at":"2026-05-18T00:39:53.015925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:53.015925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.08035","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":"2026-05-18T00:39:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+DWpbGRb2vlwUGl518Yz8h90L//V+vlFnx9fZvYitTwdwh6I+Q3Mwj9bEUtYwBTQ+bOvqVcL6GSEUk8KM1vbBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:08:35.859759Z"},"content_sha256":"b2c23277d5d1ba589ea4d78f91b99213e697a97accb06273bf1c4f3f6a9c4722","schema_version":"1.0","event_id":"sha256:b2c23277d5d1ba589ea4d78f91b99213e697a97accb06273bf1c4f3f6a9c4722"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6YHWYWO2FJG7BPHQNXGKAZ7Y6X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On kernel methods for covariates that are rankings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.LG"],"primary_cat":"stat.ML","authors_text":"Aaditya Ramdas, Benjamin Recht, Horia Mania, Martin J. Wainwright, Michael I. Jordan","submitted_at":"2016-03-25T21:09:54Z","abstract_excerpt":"Permutation-valued features arise in a variety of applications, either in a direct way when preferences are elicited over a collection of items, or an indirect way in which numerical ratings are converted to a ranking. To date, there has been relatively limited study of regression, classification, and testing problems based on permutation-valued features, as opposed to permutation-valued responses. This paper studies the use of reproducing kernel Hilbert space methods for learning from permutation-valued features. These methods embed the rankings into an implicitly defined function space, and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08035","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":"2026-05-18T00:39:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yXde4/iuZ27uZtBJTfVGg3UCoCZqiYcsJ9Ogfx+aursFKLFEMGmuDtAFbQ/iClG5RFMiYBixplucCzw36EZbCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:08:35.860120Z"},"content_sha256":"59b2772c5534e6a20d620a56e122e6be5a074573db33f271fc44c5c046f3ab2f","schema_version":"1.0","event_id":"sha256:59b2772c5534e6a20d620a56e122e6be5a074573db33f271fc44c5c046f3ab2f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6YHWYWO2FJG7BPHQNXGKAZ7Y6X/bundle.json","state_url":"https://pith.science/pith/6YHWYWO2FJG7BPHQNXGKAZ7Y6X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6YHWYWO2FJG7BPHQNXGKAZ7Y6X/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":"2026-05-30T06:08:35Z","links":{"resolver":"https://pith.science/pith/6YHWYWO2FJG7BPHQNXGKAZ7Y6X","bundle":"https://pith.science/pith/6YHWYWO2FJG7BPHQNXGKAZ7Y6X/bundle.json","state":"https://pith.science/pith/6YHWYWO2FJG7BPHQNXGKAZ7Y6X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6YHWYWO2FJG7BPHQNXGKAZ7Y6X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6YHWYWO2FJG7BPHQNXGKAZ7Y6X","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":"deacdc8fbc8fef6d16a36e842b2e4510bb9d111e1e7a7a1965cf3a15d0682ab6","cross_cats_sorted":["cs.DM","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-03-25T21:09:54Z","title_canon_sha256":"a2a132ad78aafeea2b46a80bbd1b42f3b59d926071d32ad91bdb4c5cfb385a6f"},"schema_version":"1.0","source":{"id":"1603.08035","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08035","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08035v2","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08035","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"6YHWYWO2FJG7","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6YHWYWO2FJG7BPHQ","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6YHWYWO2","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:59b2772c5534e6a20d620a56e122e6be5a074573db33f271fc44c5c046f3ab2f","target":"graph","created_at":"2026-05-18T00:39:53Z","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"},"paper":{"abstract_excerpt":"Permutation-valued features arise in a variety of applications, either in a direct way when preferences are elicited over a collection of items, or an indirect way in which numerical ratings are converted to a ranking. To date, there has been relatively limited study of regression, classification, and testing problems based on permutation-valued features, as opposed to permutation-valued responses. This paper studies the use of reproducing kernel Hilbert space methods for learning from permutation-valued features. These methods embed the rankings into an implicitly defined function space, and ","authors_text":"Aaditya Ramdas, Benjamin Recht, Horia Mania, Martin J. Wainwright, Michael I. Jordan","cross_cats":["cs.DM","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-03-25T21:09:54Z","title":"On kernel methods for covariates that are rankings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08035","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:b2c23277d5d1ba589ea4d78f91b99213e697a97accb06273bf1c4f3f6a9c4722","target":"record","created_at":"2026-05-18T00:39:53Z","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":"deacdc8fbc8fef6d16a36e842b2e4510bb9d111e1e7a7a1965cf3a15d0682ab6","cross_cats_sorted":["cs.DM","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-03-25T21:09:54Z","title_canon_sha256":"a2a132ad78aafeea2b46a80bbd1b42f3b59d926071d32ad91bdb4c5cfb385a6f"},"schema_version":"1.0","source":{"id":"1603.08035","kind":"arxiv","version":2}},"canonical_sha256":"f60f6c59da2a4df0bcf06dcca067f8f5ef7c72070d03b7bb0252b5b50f10f9b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f60f6c59da2a4df0bcf06dcca067f8f5ef7c72070d03b7bb0252b5b50f10f9b1","first_computed_at":"2026-05-18T00:39:53.015925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:53.015925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WXK8T7M9gj5hr1oj0iZBagOUkh2n133R0tT5CDypMOaCXrWGERvPA8ywNTPeicj6rQZ7+2K1bJIQrMIFum6ODw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:53.016592Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08035","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2c23277d5d1ba589ea4d78f91b99213e697a97accb06273bf1c4f3f6a9c4722","sha256:59b2772c5534e6a20d620a56e122e6be5a074573db33f271fc44c5c046f3ab2f"],"state_sha256":"8d005424413170b2243b065b9f6b4b95ad7da44eba745657bdcae838fab12ccf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"my/v0eycMjbsyzoP1Sl8gWfUkuyTOU2oH4D0zeIbc11efUlxGLSl06ciHZ3QwGLr0TT5kDAo9KLKjH6d4vFBBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:08:35.862397Z","bundle_sha256":"0b819689ab50cfbb8749a2a922f24826ec65c5b31fb18df724e075bd39993fe5"}}