{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:XQHXV5QWL3ZGDKO4MN4PGAD2CC","short_pith_number":"pith:XQHXV5QW","canonical_record":{"source":{"id":"2509.26364","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-09-30T15:03:55Z","cross_cats_sorted":[],"title_canon_sha256":"47e568afff311e4d5ec310657a02f4ea34b07fc6092d2fc7ac52571274877e0e","abstract_canon_sha256":"92edda97c0114dbd8920111903799e38310e864302b98a1fbb5e923aaf8d85a5"},"schema_version":"1.0"},"canonical_sha256":"bc0f7af6165ef261a9dc6378f3007a108c0244fd74ab2397f150a06a08520520","source":{"kind":"arxiv","id":"2509.26364","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.26364","created_at":"2026-07-07T01:15:58Z"},{"alias_kind":"arxiv_version","alias_value":"2509.26364v2","created_at":"2026-07-07T01:15:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.26364","created_at":"2026-07-07T01:15:58Z"},{"alias_kind":"pith_short_12","alias_value":"XQHXV5QWL3ZG","created_at":"2026-07-07T01:15:58Z"},{"alias_kind":"pith_short_16","alias_value":"XQHXV5QWL3ZGDKO4","created_at":"2026-07-07T01:15:58Z"},{"alias_kind":"pith_short_8","alias_value":"XQHXV5QW","created_at":"2026-07-07T01:15:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:XQHXV5QWL3ZGDKO4MN4PGAD2CC","target":"record","payload":{"canonical_record":{"source":{"id":"2509.26364","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-09-30T15:03:55Z","cross_cats_sorted":[],"title_canon_sha256":"47e568afff311e4d5ec310657a02f4ea34b07fc6092d2fc7ac52571274877e0e","abstract_canon_sha256":"92edda97c0114dbd8920111903799e38310e864302b98a1fbb5e923aaf8d85a5"},"schema_version":"1.0"},"canonical_sha256":"bc0f7af6165ef261a9dc6378f3007a108c0244fd74ab2397f150a06a08520520","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T01:15:58.700844Z","signature_b64":"IAg0o6IajAVMOMoBPau1k9HXZZEOlCCkNfXRr35cveAJcJdvFkIMjbIudN61CcmqWAyUaIlTEQ8eZuwI/THaCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc0f7af6165ef261a9dc6378f3007a108c0244fd74ab2397f150a06a08520520","last_reissued_at":"2026-07-07T01:15:58.699737Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T01:15:58.699737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.26364","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-07T01:15:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0wvDO1J4Y+dYr4ZvN021yixfmUGh3VBMti8WL9qi9tQ5/5KmbkOQHQ0OSKzjtSQGUFPgoLagG/19ZM4gjVTmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T13:33:31.500338Z"},"content_sha256":"83ec3e7970c33ab8d025533b54d94670f833e8d9c9d4dc0646cdfb606ebe107e","schema_version":"1.0","event_id":"sha256:83ec3e7970c33ab8d025533b54d94670f833e8d9c9d4dc0646cdfb606ebe107e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:XQHXV5QWL3ZGDKO4MN4PGAD2CC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Data-to-Energy Stochastic Dynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Kirill Tamogashev, Nikolay Malkin","submitted_at":"2025-09-30T15:03:55Z","abstract_excerpt":"The Schr\\\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certain transportation cost. This problem, which represents a generalisation of optimal transport to the stochastic case, has received attention due to its connections to diffusion models and flow matching, as well as its applications in the natural sciences. However, all existing algorithms allow to infer such dynamics only for cases where samples from both distributions are available. In this paper, we propose the first general method for modelling Sch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.26364","kind":"arxiv","version":2},"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/2509.26364/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":"2026-07-07T01:15:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VVw+t70Rqdo4oxZY0FUlZoYPwcGJPwMNLl0/UO7FArY2E/h14opFO3zuUSwcv+pjkFv9pkp7Lmyi4sQQvs4QCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T13:33:31.500874Z"},"content_sha256":"12f36c50d245aebde6cd19f496aa06d4bc4c85848f0dfa4ad9ded3a05b860fc9","schema_version":"1.0","event_id":"sha256:12f36c50d245aebde6cd19f496aa06d4bc4c85848f0dfa4ad9ded3a05b860fc9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XQHXV5QWL3ZGDKO4MN4PGAD2CC/bundle.json","state_url":"https://pith.science/pith/XQHXV5QWL3ZGDKO4MN4PGAD2CC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XQHXV5QWL3ZGDKO4MN4PGAD2CC/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":"2026-08-14T13:33:31Z","links":{"resolver":"https://pith.science/pith/XQHXV5QWL3ZGDKO4MN4PGAD2CC","bundle":"https://pith.science/pith/XQHXV5QWL3ZGDKO4MN4PGAD2CC/bundle.json","state":"https://pith.science/pith/XQHXV5QWL3ZGDKO4MN4PGAD2CC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XQHXV5QWL3ZGDKO4MN4PGAD2CC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XQHXV5QWL3ZGDKO4MN4PGAD2CC","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":"92edda97c0114dbd8920111903799e38310e864302b98a1fbb5e923aaf8d85a5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-09-30T15:03:55Z","title_canon_sha256":"47e568afff311e4d5ec310657a02f4ea34b07fc6092d2fc7ac52571274877e0e"},"schema_version":"1.0","source":{"id":"2509.26364","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.26364","created_at":"2026-07-07T01:15:58Z"},{"alias_kind":"arxiv_version","alias_value":"2509.26364v2","created_at":"2026-07-07T01:15:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.26364","created_at":"2026-07-07T01:15:58Z"},{"alias_kind":"pith_short_12","alias_value":"XQHXV5QWL3ZG","created_at":"2026-07-07T01:15:58Z"},{"alias_kind":"pith_short_16","alias_value":"XQHXV5QWL3ZGDKO4","created_at":"2026-07-07T01:15:58Z"},{"alias_kind":"pith_short_8","alias_value":"XQHXV5QW","created_at":"2026-07-07T01:15:58Z"}],"graph_snapshots":[{"event_id":"sha256:12f36c50d245aebde6cd19f496aa06d4bc4c85848f0dfa4ad9ded3a05b860fc9","target":"graph","created_at":"2026-07-07T01:15:58Z","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/2509.26364/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Schr\\\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certain transportation cost. This problem, which represents a generalisation of optimal transport to the stochastic case, has received attention due to its connections to diffusion models and flow matching, as well as its applications in the natural sciences. However, all existing algorithms allow to infer such dynamics only for cases where samples from both distributions are available. In this paper, we propose the first general method for modelling Sch","authors_text":"Kirill Tamogashev, Nikolay Malkin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-09-30T15:03:55Z","title":"Data-to-Energy Stochastic Dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.26364","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":"sha256:83ec3e7970c33ab8d025533b54d94670f833e8d9c9d4dc0646cdfb606ebe107e","target":"record","created_at":"2026-07-07T01:15:58Z","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":"92edda97c0114dbd8920111903799e38310e864302b98a1fbb5e923aaf8d85a5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-09-30T15:03:55Z","title_canon_sha256":"47e568afff311e4d5ec310657a02f4ea34b07fc6092d2fc7ac52571274877e0e"},"schema_version":"1.0","source":{"id":"2509.26364","kind":"arxiv","version":2}},"canonical_sha256":"bc0f7af6165ef261a9dc6378f3007a108c0244fd74ab2397f150a06a08520520","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc0f7af6165ef261a9dc6378f3007a108c0244fd74ab2397f150a06a08520520","first_computed_at":"2026-07-07T01:15:58.699737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T01:15:58.699737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IAg0o6IajAVMOMoBPau1k9HXZZEOlCCkNfXRr35cveAJcJdvFkIMjbIudN61CcmqWAyUaIlTEQ8eZuwI/THaCQ==","signature_status":"signed_v1","signed_at":"2026-07-07T01:15:58.700844Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.26364","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83ec3e7970c33ab8d025533b54d94670f833e8d9c9d4dc0646cdfb606ebe107e","sha256:12f36c50d245aebde6cd19f496aa06d4bc4c85848f0dfa4ad9ded3a05b860fc9"],"state_sha256":"e150b6497153709e37b46f12f3d580dcf8ed2b4aa9a30cdbc20641f63165d3b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sTz3sAAX4oCyWiQhYFyWxT1oftLHRAbT7JMpY+ebmPOXPNxhZ5Re1Q33+R6BxOyc5Mydm9j0kDQ+FWMPTLBOCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T13:33:31.505234Z","bundle_sha256":"64718d6d89402045467d5432a6ca64b3a9b49c853f3ebbe0dea569d7ef94710d"}}