{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LVAIAFTDFMSZKTIY3KRBRZ4H35","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":"50fcb2608a3e6b6e1b62b8ea7e72f91c9fe39343dc424b1c3b399dfbb320ff9d","cross_cats_sorted":["math.PR","stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-11-20T07:10:09Z","title_canon_sha256":"ff737d43ae8f9172a0cd4f9e2b977e656f898f8e16a9150579147d859c2b5c93"},"schema_version":"1.0","source":{"id":"2411.13080","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.13080","created_at":"2026-07-05T09:38:04Z"},{"alias_kind":"arxiv_version","alias_value":"2411.13080v1","created_at":"2026-07-05T09:38:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.13080","created_at":"2026-07-05T09:38:04Z"},{"alias_kind":"pith_short_12","alias_value":"LVAIAFTDFMSZ","created_at":"2026-07-05T09:38:04Z"},{"alias_kind":"pith_short_16","alias_value":"LVAIAFTDFMSZKTIY","created_at":"2026-07-05T09:38:04Z"},{"alias_kind":"pith_short_8","alias_value":"LVAIAFTD","created_at":"2026-07-05T09:38:04Z"}],"graph_snapshots":[{"event_id":"sha256:24acd5ef28fb60c9624cc3193ab18f3e3ca9724c4d911be2c8ea42a3a03a263c","target":"graph","created_at":"2026-07-05T09:38:04Z","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/2411.13080/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we propose and study a class of nonparametric, yet interpretable measures of association between two random vectors $X$ and $Y$ taking values in $\\mathbb{R}^{d_1}$ and $\\mathbb{R}^{d_2}$ respectively ($d_1, d_2\\ge 1$). These nonparametric measures -- defined using the theory of reproducing kernel Hilbert spaces coupled with optimal transport -- capture the strength of dependence between $X$ and $Y$ and have the property that they are 0 if and only if the variables are independent and 1 if and only if one variable is a measurable function of the other. Further, these population me","authors_text":"Bodhisattva Sen, Nabarun Deb, Promit Ghosal","cross_cats":["math.PR","stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-11-20T07:10:09Z","title":"Distribution-free Measures of Association based on Optimal Transport"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13080","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:ab3af71ff8881a1cb9d04eb34c5a55c83d8b4948ce9551698b9fbfb1f34d50d3","target":"record","created_at":"2026-07-05T09:38:04Z","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":"50fcb2608a3e6b6e1b62b8ea7e72f91c9fe39343dc424b1c3b399dfbb320ff9d","cross_cats_sorted":["math.PR","stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-11-20T07:10:09Z","title_canon_sha256":"ff737d43ae8f9172a0cd4f9e2b977e656f898f8e16a9150579147d859c2b5c93"},"schema_version":"1.0","source":{"id":"2411.13080","kind":"arxiv","version":1}},"canonical_sha256":"5d408016632b25954d18daa218e787df48279a855a9393fb9da0e2b31e639049","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d408016632b25954d18daa218e787df48279a855a9393fb9da0e2b31e639049","first_computed_at":"2026-07-05T09:38:04.820547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:38:04.820547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iW5jVKmwZFT5gw8lrdu9sQbs4cTP7RoHgic7jZjxv2nzjXj2k1XExnIy0bAhsm6stJkM0KVgclk+KoO+vJa5Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:38:04.821109Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.13080","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab3af71ff8881a1cb9d04eb34c5a55c83d8b4948ce9551698b9fbfb1f34d50d3","sha256:24acd5ef28fb60c9624cc3193ab18f3e3ca9724c4d911be2c8ea42a3a03a263c"],"state_sha256":"30e681ed4c65cdd60a964584a554aaade683ab4b740fe1cb719947d9ddfd8daf"}