{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:SMLHENGSXDA242VGWNOGNRMJ66","short_pith_number":"pith:SMLHENGS","canonical_record":{"source":{"id":"2503.16580","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-03-20T12:34:22Z","cross_cats_sorted":["cs.LG","math.OC","math.PR","stat.AP"],"title_canon_sha256":"07aca9f4ed5616dbcddf394335cb32d8630d47fb752d4734142a8ee3d1b125d8","abstract_canon_sha256":"53021611b07745659eb4bfd41b84ba181378b15a3732a3b62abe620c67e0d514"},"schema_version":"1.0"},"canonical_sha256":"93167234d2b8c1ae6aa6b35c66c589f79b4d397f71a37e0dba297dde98f55ea2","source":{"kind":"arxiv","id":"2503.16580","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.16580","created_at":"2026-07-05T10:36:44Z"},{"alias_kind":"arxiv_version","alias_value":"2503.16580v1","created_at":"2026-07-05T10:36:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.16580","created_at":"2026-07-05T10:36:44Z"},{"alias_kind":"pith_short_12","alias_value":"SMLHENGSXDA2","created_at":"2026-07-05T10:36:44Z"},{"alias_kind":"pith_short_16","alias_value":"SMLHENGSXDA242VG","created_at":"2026-07-05T10:36:44Z"},{"alias_kind":"pith_short_8","alias_value":"SMLHENGS","created_at":"2026-07-05T10:36:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:SMLHENGSXDA242VGWNOGNRMJ66","target":"record","payload":{"canonical_record":{"source":{"id":"2503.16580","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-03-20T12:34:22Z","cross_cats_sorted":["cs.LG","math.OC","math.PR","stat.AP"],"title_canon_sha256":"07aca9f4ed5616dbcddf394335cb32d8630d47fb752d4734142a8ee3d1b125d8","abstract_canon_sha256":"53021611b07745659eb4bfd41b84ba181378b15a3732a3b62abe620c67e0d514"},"schema_version":"1.0"},"canonical_sha256":"93167234d2b8c1ae6aa6b35c66c589f79b4d397f71a37e0dba297dde98f55ea2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:36:44.546651Z","signature_b64":"5ymEAmwLewjIp1KZTQ0xLO/samypRNzfcRr0dHI+Lv35ffl7UZ+9IbVSUjkE+ramQ38Ov1ikxDSPc4TCiw3EDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93167234d2b8c1ae6aa6b35c66c589f79b4d397f71a37e0dba297dde98f55ea2","last_reissued_at":"2026-07-05T10:36:44.545692Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:36:44.545692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.16580","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:36:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+jBIGp5Bm2MWZ8dhQahhhd60Pbn6mNXPke2HWGkDXYVSVl80J17bc0d86Sg1kt4vMmXVB0+XaSXJtPbANt6NAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T23:34:06.391611Z"},"content_sha256":"bbf5eab31fbf3b61d227cdc3381cedce77cf6fde405763b64b318bb74c60e50e","schema_version":"1.0","event_id":"sha256:bbf5eab31fbf3b61d227cdc3381cedce77cf6fde405763b64b318bb74c60e50e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:SMLHENGSXDA242VGWNOGNRMJ66","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Procrustes Wasserstein Metric: A Modified Benamou-Brenier Approach with Applications to Latent Gaussian Distributions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.OC","math.PR","stat.AP"],"primary_cat":"stat.ML","authors_text":"Kevine Meugang Toukam","submitted_at":"2025-03-20T12:34:22Z","abstract_excerpt":"We introduce a modified Benamou-Brenier type approach leading to a Wasserstein type distance that allows global invariance, specifically, isometries, and we show that the problem can be summarized to orthogonal transformations. This distance is defined by penalizing the action with a costless movement of the particle that does not change the direction and speed of its trajectory. We show that for Gaussian distribution resume to measuring the Euclidean distance between their ordered vector of eigenvalues and we show a direct application in recovering Latent Gaussian distributions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.16580","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.16580/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:36:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rhyW+BxXcM7VqL2bCdOj3b56wHCHfaEtDV/5+/DTz1tnqSOp517xtqFtMkTeB2gNJAwh1FzhAkOe9G6Qm1rpDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T23:34:06.391999Z"},"content_sha256":"6c9982e00e077a3121178d802d30c99cdd88833c2338c01060d2c26afe8f2e89","schema_version":"1.0","event_id":"sha256:6c9982e00e077a3121178d802d30c99cdd88833c2338c01060d2c26afe8f2e89"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SMLHENGSXDA242VGWNOGNRMJ66/bundle.json","state_url":"https://pith.science/pith/SMLHENGSXDA242VGWNOGNRMJ66/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SMLHENGSXDA242VGWNOGNRMJ66/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":"2026-08-22T23:34:06Z","links":{"resolver":"https://pith.science/pith/SMLHENGSXDA242VGWNOGNRMJ66","bundle":"https://pith.science/pith/SMLHENGSXDA242VGWNOGNRMJ66/bundle.json","state":"https://pith.science/pith/SMLHENGSXDA242VGWNOGNRMJ66/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SMLHENGSXDA242VGWNOGNRMJ66/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SMLHENGSXDA242VGWNOGNRMJ66","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":"53021611b07745659eb4bfd41b84ba181378b15a3732a3b62abe620c67e0d514","cross_cats_sorted":["cs.LG","math.OC","math.PR","stat.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-03-20T12:34:22Z","title_canon_sha256":"07aca9f4ed5616dbcddf394335cb32d8630d47fb752d4734142a8ee3d1b125d8"},"schema_version":"1.0","source":{"id":"2503.16580","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.16580","created_at":"2026-07-05T10:36:44Z"},{"alias_kind":"arxiv_version","alias_value":"2503.16580v1","created_at":"2026-07-05T10:36:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.16580","created_at":"2026-07-05T10:36:44Z"},{"alias_kind":"pith_short_12","alias_value":"SMLHENGSXDA2","created_at":"2026-07-05T10:36:44Z"},{"alias_kind":"pith_short_16","alias_value":"SMLHENGSXDA242VG","created_at":"2026-07-05T10:36:44Z"},{"alias_kind":"pith_short_8","alias_value":"SMLHENGS","created_at":"2026-07-05T10:36:44Z"}],"graph_snapshots":[{"event_id":"sha256:6c9982e00e077a3121178d802d30c99cdd88833c2338c01060d2c26afe8f2e89","target":"graph","created_at":"2026-07-05T10:36:44Z","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/2503.16580/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a modified Benamou-Brenier type approach leading to a Wasserstein type distance that allows global invariance, specifically, isometries, and we show that the problem can be summarized to orthogonal transformations. This distance is defined by penalizing the action with a costless movement of the particle that does not change the direction and speed of its trajectory. We show that for Gaussian distribution resume to measuring the Euclidean distance between their ordered vector of eigenvalues and we show a direct application in recovering Latent Gaussian distributions.","authors_text":"Kevine Meugang Toukam","cross_cats":["cs.LG","math.OC","math.PR","stat.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-03-20T12:34:22Z","title":"Procrustes Wasserstein Metric: A Modified Benamou-Brenier Approach with Applications to Latent Gaussian Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.16580","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:bbf5eab31fbf3b61d227cdc3381cedce77cf6fde405763b64b318bb74c60e50e","target":"record","created_at":"2026-07-05T10:36:44Z","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":"53021611b07745659eb4bfd41b84ba181378b15a3732a3b62abe620c67e0d514","cross_cats_sorted":["cs.LG","math.OC","math.PR","stat.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-03-20T12:34:22Z","title_canon_sha256":"07aca9f4ed5616dbcddf394335cb32d8630d47fb752d4734142a8ee3d1b125d8"},"schema_version":"1.0","source":{"id":"2503.16580","kind":"arxiv","version":1}},"canonical_sha256":"93167234d2b8c1ae6aa6b35c66c589f79b4d397f71a37e0dba297dde98f55ea2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93167234d2b8c1ae6aa6b35c66c589f79b4d397f71a37e0dba297dde98f55ea2","first_computed_at":"2026-07-05T10:36:44.545692Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:36:44.545692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5ymEAmwLewjIp1KZTQ0xLO/samypRNzfcRr0dHI+Lv35ffl7UZ+9IbVSUjkE+ramQ38Ov1ikxDSPc4TCiw3EDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:36:44.546651Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.16580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbf5eab31fbf3b61d227cdc3381cedce77cf6fde405763b64b318bb74c60e50e","sha256:6c9982e00e077a3121178d802d30c99cdd88833c2338c01060d2c26afe8f2e89"],"state_sha256":"06522daaff5a6c6bae08d2a7fc8645f9bcfdc4a1c2a5a3dbd809ccd75b6ea009"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2gY1KKXH9CsSmLRIsdkoqQ9D8Xna45tz6pe0DSKzrY5ba78yyKcEcHrZZeDADvV2rXzrstMhdBOYoCIJSX+WDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T23:34:06.394592Z","bundle_sha256":"bb1144cfb3fd810f56aba6e9562538c82c4729ce8970681223799863a4bb76b0"}}