{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QGUBKZX5KHPGVDK27FFZJU54GJ","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":"c71d9e539d622678aaef41e4f40c698a67ffaa5b183e09e9681e2fb83be04ca1","cross_cats_sorted":["math.FA","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-08-13T15:36:23Z","title_canon_sha256":"d746dd31d2063ff7e91a04c38367404f1334136eb7ac93f2cfb7c3458c3ae893"},"schema_version":"1.0","source":{"id":"2608.13374","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.13374","created_at":"2026-08-14T01:04:19Z"},{"alias_kind":"arxiv_version","alias_value":"2608.13374v1","created_at":"2026-08-14T01:04:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.13374","created_at":"2026-08-14T01:04:19Z"},{"alias_kind":"pith_short_12","alias_value":"QGUBKZX5KHPG","created_at":"2026-08-14T01:04:19Z"},{"alias_kind":"pith_short_16","alias_value":"QGUBKZX5KHPGVDK2","created_at":"2026-08-14T01:04:19Z"},{"alias_kind":"pith_short_8","alias_value":"QGUBKZX5","created_at":"2026-08-14T01:04:19Z"}],"graph_snapshots":[{"event_id":"sha256:0b75d060378323067bce35a4f447e24ea1ef852a59fd2cc875e546c82f464d83","target":"graph","created_at":"2026-08-14T01:04:19Z","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/2608.13374/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove new comparison results between the Wasserstein distance and its sliced and max-sliced counterparts. First, we show that the H\\\"older exponent~$\\frac{2}{d+2}$ obtained by Bobkov and G\\\"otze for the max-sliced 1-Wasserstein distance on the unit ball is optimal for every $d \\geq 2$, settling a question raised in their work. Second, we show that sharper comparisons are possible under stronger structural assumptions: if $\\nu$ is a discrete measure and the optimal coupling between $\\mu$ and $\\nu$ transports each point to a nearest atom of $\\nu$, then $W_p(\\mu, \\nu) \\leq C \\sqrt{d}\\, K \\, \\m","authors_text":"Jacob Shkrob, Jonathan Niles-Weed","cross_cats":["math.FA","math.ST","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-08-13T15:36:23Z","title":"Nearly sharp comparison results for sliced and max-sliced Wasserstein distances"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13374","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:d1c89cec2e7183bab8dbd0b7f02f1b4b644ffa41a08937d6d7514cfa3f5589b5","target":"record","created_at":"2026-08-14T01:04:19Z","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":"c71d9e539d622678aaef41e4f40c698a67ffaa5b183e09e9681e2fb83be04ca1","cross_cats_sorted":["math.FA","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-08-13T15:36:23Z","title_canon_sha256":"d746dd31d2063ff7e91a04c38367404f1334136eb7ac93f2cfb7c3458c3ae893"},"schema_version":"1.0","source":{"id":"2608.13374","kind":"arxiv","version":1}},"canonical_sha256":"81a81566fd51de6a8d5af94b94d3bc32452e2ae01ce3c48dd24cc79ba7f61add","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81a81566fd51de6a8d5af94b94d3bc32452e2ae01ce3c48dd24cc79ba7f61add","first_computed_at":"2026-08-14T01:04:19.147224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-14T01:04:19.147224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3tVnjLvZNbzfGZCH8FuPdwWwdpZkr3FaL/3pvLMT5Ft8y4SUj1pHdWYiuegh9PfKfP/ehG6oJ2kGsdjAkXGfCg==","signature_status":"signed_v1","signed_at":"2026-08-14T01:04:19.148953Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.13374","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1c89cec2e7183bab8dbd0b7f02f1b4b644ffa41a08937d6d7514cfa3f5589b5","sha256:0b75d060378323067bce35a4f447e24ea1ef852a59fd2cc875e546c82f464d83"],"state_sha256":"7a3d24ab8b13e0f1448725a6aff65eccc9a54ff9b03f97621c502345bfb318fa"}