{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VSAWJTRYGF72O32OJU3U2MZYVO","short_pith_number":"pith:VSAWJTRY","canonical_record":{"source":{"id":"2504.04799","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-04-07T07:45:21Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"0cc9f45d96642ffa4ee03f1ee35b65058007ef82a0d85de96be4dcae33710126","abstract_canon_sha256":"f96fbb362986bcdd158809b50a8ac2ba1809c452e35709338f26c0dc36250196"},"schema_version":"1.0"},"canonical_sha256":"ac8164ce38317fa76f4e4d374d3338abad25e9c03ff778db575f638788ede963","source":{"kind":"arxiv","id":"2504.04799","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.04799","created_at":"2026-07-05T11:13:23Z"},{"alias_kind":"arxiv_version","alias_value":"2504.04799v3","created_at":"2026-07-05T11:13:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.04799","created_at":"2026-07-05T11:13:23Z"},{"alias_kind":"pith_short_12","alias_value":"VSAWJTRYGF72","created_at":"2026-07-05T11:13:23Z"},{"alias_kind":"pith_short_16","alias_value":"VSAWJTRYGF72O32O","created_at":"2026-07-05T11:13:23Z"},{"alias_kind":"pith_short_8","alias_value":"VSAWJTRY","created_at":"2026-07-05T11:13:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VSAWJTRYGF72O32OJU3U2MZYVO","target":"record","payload":{"canonical_record":{"source":{"id":"2504.04799","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-04-07T07:45:21Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"0cc9f45d96642ffa4ee03f1ee35b65058007ef82a0d85de96be4dcae33710126","abstract_canon_sha256":"f96fbb362986bcdd158809b50a8ac2ba1809c452e35709338f26c0dc36250196"},"schema_version":"1.0"},"canonical_sha256":"ac8164ce38317fa76f4e4d374d3338abad25e9c03ff778db575f638788ede963","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:13:23.702482Z","signature_b64":"vgnflVlAe5y+jL/PsB+p8VKqQIxtoDTH81LlO0dIB/Leb9TdUzn2RRb6MzDULzOsacx2wL8ZnW4JSmYxQ4tiAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac8164ce38317fa76f4e4d374d3338abad25e9c03ff778db575f638788ede963","last_reissued_at":"2026-07-05T11:13:23.701992Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:13:23.701992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.04799","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:13:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p7/C5L/807rNbCQKGexIx7v6G/0HDSS6KquyJbd/jt3OEzzFnk5Vd/HYX16hloiYjqxL51BnbyoCahdeoAauBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:01:09.470831Z"},"content_sha256":"e53ed1708d9681aed6ad6087ae060caf5effb8a220f9c88b5b0b10ac14f1a357","schema_version":"1.0","event_id":"sha256:e53ed1708d9681aed6ad6087ae060caf5effb8a220f9c88b5b0b10ac14f1a357"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VSAWJTRYGF72O32OJU3U2MZYVO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological Schr\\\"odinger Bridge Matching","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Maosheng Yang","submitted_at":"2025-04-07T07:45:21Z","abstract_excerpt":"Given two boundary distributions, the Schr\\\"odinger Bridge (SB) problem seeks the ``most likely`` random evolution between them with respect to a reference process. It has revealed rich connections to recent machine learning methods for generative modeling and distribution matching. While these methods perform well in Euclidean domains, they are not directly applicable to topological domains such as graphs and simplicial complexes, which are crucial for data defined over network entities, such as node signals and edge flows. In this work, we propose the Topological Schr\\\"odinger Bridge problem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.04799","kind":"arxiv","version":3},"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/2504.04799/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":"2026-07-05T11:13:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qiYZ/P7MwGg3AYYqyugX6FTChQJxfFbCSrLhA0S0LQ3cRLdklQm7m/eGX97cv4gv8fImjPj9aGUcvr7AXWhTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:01:09.471314Z"},"content_sha256":"05518007247477d669d637c3817cfc66305a112caf0f9dbb4ac322e8af7f70b2","schema_version":"1.0","event_id":"sha256:05518007247477d669d637c3817cfc66305a112caf0f9dbb4ac322e8af7f70b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VSAWJTRYGF72O32OJU3U2MZYVO/bundle.json","state_url":"https://pith.science/pith/VSAWJTRYGF72O32OJU3U2MZYVO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VSAWJTRYGF72O32OJU3U2MZYVO/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":"2026-08-09T03:01:09Z","links":{"resolver":"https://pith.science/pith/VSAWJTRYGF72O32OJU3U2MZYVO","bundle":"https://pith.science/pith/VSAWJTRYGF72O32OJU3U2MZYVO/bundle.json","state":"https://pith.science/pith/VSAWJTRYGF72O32OJU3U2MZYVO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VSAWJTRYGF72O32OJU3U2MZYVO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VSAWJTRYGF72O32OJU3U2MZYVO","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":"f96fbb362986bcdd158809b50a8ac2ba1809c452e35709338f26c0dc36250196","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-04-07T07:45:21Z","title_canon_sha256":"0cc9f45d96642ffa4ee03f1ee35b65058007ef82a0d85de96be4dcae33710126"},"schema_version":"1.0","source":{"id":"2504.04799","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.04799","created_at":"2026-07-05T11:13:23Z"},{"alias_kind":"arxiv_version","alias_value":"2504.04799v3","created_at":"2026-07-05T11:13:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.04799","created_at":"2026-07-05T11:13:23Z"},{"alias_kind":"pith_short_12","alias_value":"VSAWJTRYGF72","created_at":"2026-07-05T11:13:23Z"},{"alias_kind":"pith_short_16","alias_value":"VSAWJTRYGF72O32O","created_at":"2026-07-05T11:13:23Z"},{"alias_kind":"pith_short_8","alias_value":"VSAWJTRY","created_at":"2026-07-05T11:13:23Z"}],"graph_snapshots":[{"event_id":"sha256:05518007247477d669d637c3817cfc66305a112caf0f9dbb4ac322e8af7f70b2","target":"graph","created_at":"2026-07-05T11:13:23Z","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/2504.04799/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given two boundary distributions, the Schr\\\"odinger Bridge (SB) problem seeks the ``most likely`` random evolution between them with respect to a reference process. It has revealed rich connections to recent machine learning methods for generative modeling and distribution matching. While these methods perform well in Euclidean domains, they are not directly applicable to topological domains such as graphs and simplicial complexes, which are crucial for data defined over network entities, such as node signals and edge flows. In this work, we propose the Topological Schr\\\"odinger Bridge problem","authors_text":"Maosheng Yang","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-04-07T07:45:21Z","title":"Topological Schr\\\"odinger Bridge Matching"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.04799","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:e53ed1708d9681aed6ad6087ae060caf5effb8a220f9c88b5b0b10ac14f1a357","target":"record","created_at":"2026-07-05T11:13:23Z","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":"f96fbb362986bcdd158809b50a8ac2ba1809c452e35709338f26c0dc36250196","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-04-07T07:45:21Z","title_canon_sha256":"0cc9f45d96642ffa4ee03f1ee35b65058007ef82a0d85de96be4dcae33710126"},"schema_version":"1.0","source":{"id":"2504.04799","kind":"arxiv","version":3}},"canonical_sha256":"ac8164ce38317fa76f4e4d374d3338abad25e9c03ff778db575f638788ede963","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac8164ce38317fa76f4e4d374d3338abad25e9c03ff778db575f638788ede963","first_computed_at":"2026-07-05T11:13:23.701992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:13:23.701992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vgnflVlAe5y+jL/PsB+p8VKqQIxtoDTH81LlO0dIB/Leb9TdUzn2RRb6MzDULzOsacx2wL8ZnW4JSmYxQ4tiAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:13:23.702482Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.04799","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e53ed1708d9681aed6ad6087ae060caf5effb8a220f9c88b5b0b10ac14f1a357","sha256:05518007247477d669d637c3817cfc66305a112caf0f9dbb4ac322e8af7f70b2"],"state_sha256":"c1efb611b6d0e6ce641f76a7d3a5e0a51a59758a4ee849cf5d7687d2bbfe74d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hcFMVrLhjUmWjBQYG1Ye+Ejh5HX+sV68kywM8fq3e9+fw9npMQr8uehYpzl4JJIB7SANJ4zUgKtH51d88UknDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T03:01:09.485384Z","bundle_sha256":"14dd169ab08dfd71d2984f3f9029b808e6b49d8b9a4b1a5e475d798adb86cb7a"}}