{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:DLYQZPBGNJBTO7ZPSBXCJIMYNE","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":"d68e7f0ddda32f30964cff6bf4834f52c83528c487f25fecba9763bc43a956f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-08-02T07:38:28Z","title_canon_sha256":"97c6095d29ad1eab849a3454a64a6d26d7e70ab5331aca8eca902c42560372b8"},"schema_version":"1.0","source":{"id":"2508.01243","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.01243","created_at":"2026-06-01T02:03:25Z"},{"alias_kind":"arxiv_version","alias_value":"2508.01243v2","created_at":"2026-06-01T02:03:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.01243","created_at":"2026-06-01T02:03:25Z"},{"alias_kind":"pith_short_12","alias_value":"DLYQZPBGNJBT","created_at":"2026-06-01T02:03:25Z"},{"alias_kind":"pith_short_16","alias_value":"DLYQZPBGNJBTO7ZP","created_at":"2026-06-01T02:03:25Z"},{"alias_kind":"pith_short_8","alias_value":"DLYQZPBG","created_at":"2026-06-01T02:03:25Z"}],"graph_snapshots":[{"event_id":"sha256:3aa1a20d5d2643f2d1d4a50197bf6a6e9cd7c972273cc7ecb220f2d985c01308","target":"graph","created_at":"2026-06-01T02:03:25Z","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/2508.01243/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Since the introduction of the Sliced Wasserstein distance in the literature, its simplicity and efficiency have made it one of the most interesting surrogate for the Wasserstein distance in image processing and machine learning. However, its inability to produce transport plans limits its practical use to applications where only a distance is necessary. Several heuristics have been proposed in the recent years to address this limitation when the probability measures are discrete. In this paper, we propose to study these different propositions by redefining and analysing them rigorously for gen","authors_text":"Eloi Tanguy, Julie Delon, Laetitia Chapel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-08-02T07:38:28Z","title":"Sliced Transport Plans"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.01243","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":"sha256:3bba5008d57ac78f002894479dc1db5079bcd631f37b45ae4b94aaf575e8ad69","target":"record","created_at":"2026-06-01T02:03:25Z","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":"d68e7f0ddda32f30964cff6bf4834f52c83528c487f25fecba9763bc43a956f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-08-02T07:38:28Z","title_canon_sha256":"97c6095d29ad1eab849a3454a64a6d26d7e70ab5331aca8eca902c42560372b8"},"schema_version":"1.0","source":{"id":"2508.01243","kind":"arxiv","version":2}},"canonical_sha256":"1af10cbc266a43377f2f906e24a198693ac389cfdb6c83a8a988b7215a23dec1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1af10cbc266a43377f2f906e24a198693ac389cfdb6c83a8a988b7215a23dec1","first_computed_at":"2026-06-01T02:03:25.161133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T02:03:25.161133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v/GnMZ0E6DPhPvUrTq/v5mFgHJAUXL6sZ/C4Dd59GRLyKNrvxrEu89xkVy6LD21FhnFYJkXfSZDQNDZUzVmwCg==","signature_status":"signed_v1","signed_at":"2026-06-01T02:03:25.162246Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.01243","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bba5008d57ac78f002894479dc1db5079bcd631f37b45ae4b94aaf575e8ad69","sha256:3aa1a20d5d2643f2d1d4a50197bf6a6e9cd7c972273cc7ecb220f2d985c01308"],"state_sha256":"f96095059ac2f1d9b88f9ca82a2ffefe218bddce2f9da95881daaa3d717fac3e"}