{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LTFC6ON4ZSGVSC3UI6OQC3DR2K","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":"ab65964cc43cf07f90751a73c1da762cc2f263db3dcb5fee7e1f727544c2ea2e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-26T11:04:41Z","title_canon_sha256":"93b72c8f3bc401da59d3e7ec3d7ef045a84f08b1701712b190f5dd81edc6259b"},"schema_version":"1.0","source":{"id":"2405.16519","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.16519","created_at":"2026-07-05T10:48:16Z"},{"alias_kind":"arxiv_version","alias_value":"2405.16519v3","created_at":"2026-07-05T10:48:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.16519","created_at":"2026-07-05T10:48:16Z"},{"alias_kind":"pith_short_12","alias_value":"LTFC6ON4ZSGV","created_at":"2026-07-05T10:48:16Z"},{"alias_kind":"pith_short_16","alias_value":"LTFC6ON4ZSGVSC3U","created_at":"2026-07-05T10:48:16Z"},{"alias_kind":"pith_short_8","alias_value":"LTFC6ON4","created_at":"2026-07-05T10:48:16Z"}],"graph_snapshots":[{"event_id":"sha256:42464032638c46a491cc6a7f8fc656d3fb901079ac8e4688a9e00c9cc50b774a","target":"graph","created_at":"2026-07-05T10:48:16Z","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/2405.16519/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present the Fourier Sliced-Wasserstein (FSW) embedding - a novel method to embed multisets and measures over R^d into Euclidean space.\n  Our proposed embedding approximately preserves the sliced Wasserstein distance on distributions, thereby yielding geometrically meaningful representations that better capture the structure of the input. Moreover, it is injective on measures and bi-Lipschitz on multisets - a significant advantage over prevalent methods based on sum- or max-pooling, which are provably not bi-Lipschitz, and, in many cases, not even injective. The required output dimension for","authors_text":"Nadav Dym, Tal Amir","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-26T11:04:41Z","title":"Fourier Sliced-Wasserstein Embedding for Multisets and Measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.16519","kind":"arxiv","version":3},"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:cdd2365e0e3843a31984bbbd1da9eec487a421e66beb578844f4a1721ae6c75b","target":"record","created_at":"2026-07-05T10:48:16Z","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":"ab65964cc43cf07f90751a73c1da762cc2f263db3dcb5fee7e1f727544c2ea2e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-26T11:04:41Z","title_canon_sha256":"93b72c8f3bc401da59d3e7ec3d7ef045a84f08b1701712b190f5dd81edc6259b"},"schema_version":"1.0","source":{"id":"2405.16519","kind":"arxiv","version":3}},"canonical_sha256":"5cca2f39bccc8d590b74479d016c71d2b0c4090d746f82bd617fc912bd27d21f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cca2f39bccc8d590b74479d016c71d2b0c4090d746f82bd617fc912bd27d21f","first_computed_at":"2026-07-05T10:48:16.255121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:48:16.255121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+tkYjCbzkkm4Lq+TN+VQg3h/6ePK/WlK8WJX2zUUgJ84IUDrpRIoGHffBIk9f2pbtjfDdZV7hnR5PwR2xIFYDg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:48:16.255602Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.16519","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdd2365e0e3843a31984bbbd1da9eec487a421e66beb578844f4a1721ae6c75b","sha256:42464032638c46a491cc6a7f8fc656d3fb901079ac8e4688a9e00c9cc50b774a"],"state_sha256":"aad17a0db53e9d9ad828018dd71d53e701ed72d582b8514b9b3b3c4e7b223822"}