{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:643FVPRVT3S52LTYIFQVUBLWTZ","short_pith_number":"pith:643FVPRV","canonical_record":{"source":{"id":"2605.31063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-05-29T09:34:53Z","cross_cats_sorted":["cs.LG","physics.chem-ph","physics.comp-ph"],"title_canon_sha256":"20846bce743223c728e7c4c9e1110b1094e444ab06988816436873da6fe3153f","abstract_canon_sha256":"ec0abb18985a031f67164ce65f88fba8a0594b81f93627c7ce200162ff8127c8"},"schema_version":"1.0"},"canonical_sha256":"f7365abe359ee5dd2e7841615a05769e55c6fe7c56e2714a3c5b50384599044e","source":{"kind":"arxiv","id":"2605.31063","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.31063","created_at":"2026-06-01T01:03:33Z"},{"alias_kind":"arxiv_version","alias_value":"2605.31063v1","created_at":"2026-06-01T01:03:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.31063","created_at":"2026-06-01T01:03:33Z"},{"alias_kind":"pith_short_12","alias_value":"643FVPRVT3S5","created_at":"2026-06-01T01:03:33Z"},{"alias_kind":"pith_short_16","alias_value":"643FVPRVT3S52LTY","created_at":"2026-06-01T01:03:33Z"},{"alias_kind":"pith_short_8","alias_value":"643FVPRV","created_at":"2026-06-01T01:03:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:643FVPRVT3S52LTYIFQVUBLWTZ","target":"record","payload":{"canonical_record":{"source":{"id":"2605.31063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-05-29T09:34:53Z","cross_cats_sorted":["cs.LG","physics.chem-ph","physics.comp-ph"],"title_canon_sha256":"20846bce743223c728e7c4c9e1110b1094e444ab06988816436873da6fe3153f","abstract_canon_sha256":"ec0abb18985a031f67164ce65f88fba8a0594b81f93627c7ce200162ff8127c8"},"schema_version":"1.0"},"canonical_sha256":"f7365abe359ee5dd2e7841615a05769e55c6fe7c56e2714a3c5b50384599044e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T01:03:33.937119Z","signature_b64":"0JSCyGPZi03q8lriq1Dka2MJUBnsxw00rYEAok1jmsMdx7SAjWSPzAdQCAnETOv4mR9og2Anqie4mkdo0VqiBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7365abe359ee5dd2e7841615a05769e55c6fe7c56e2714a3c5b50384599044e","last_reissued_at":"2026-06-01T01:03:33.936585Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T01:03:33.936585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.31063","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":"2026-06-01T01:03:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dz7yoxyj8yK6Y/g4azueexBDeAcRRBCsjk/0QkD1KkTa5hEE/SsV6DU/Y21ej8Ph97CCMxIo64mcEAepjVdRBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:53:31.944740Z"},"content_sha256":"ac80e54be61481d6474531f6b37040a1adba067684948e622cd783b39c2fdc34","schema_version":"1.0","event_id":"sha256:ac80e54be61481d6474531f6b37040a1adba067684948e622cd783b39c2fdc34"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:643FVPRVT3S52LTYIFQVUBLWTZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Free energy Estimation on Any State Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","physics.chem-ph","physics.comp-ph"],"primary_cat":"stat.ML","authors_text":"Carles Domingo-Enrich, Francisco Vargas, Jiajun He, Jos\\'e Miguel Hern\\'andez-Lobato, Yingzhen Li, Yuanqi Du, Zijing Ou","submitted_at":"2026-05-29T09:34:53Z","abstract_excerpt":"Free energy estimation is a fundamental yet challenging problem, from physics to statistics. Classical approaches rely on thermodynamic transformations, ranging from direct estimation, quasistatic integration, to finite-time averaging. Recent work [He and Du et al., 2025] learns neural transports to significantly accelerate the efficiency in the finite-time regime. In this paper, we generalize this framework to arbitrary state spaces. Building on this view, we develop a generalized neural transport learning approach for efficient estimation. Experiments validate the effectiveness and efficienc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31063","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/2605.31063/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":"2026-06-01T01:03:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j8sMG0YRHNC2RHHHyr+XakzbqicRh+Y7BjTlnZQf/GVOgRBQquHVyrqI7O3AjOhVAw0OtQAmumlw4rvpolRuCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:53:31.945121Z"},"content_sha256":"17a47f9d9a3a48c048fbaf6cab7a3c8669fefe783a29889f16891a047544935e","schema_version":"1.0","event_id":"sha256:17a47f9d9a3a48c048fbaf6cab7a3c8669fefe783a29889f16891a047544935e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/643FVPRVT3S52LTYIFQVUBLWTZ/bundle.json","state_url":"https://pith.science/pith/643FVPRVT3S52LTYIFQVUBLWTZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/643FVPRVT3S52LTYIFQVUBLWTZ/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":"2026-06-12T03:53:31Z","links":{"resolver":"https://pith.science/pith/643FVPRVT3S52LTYIFQVUBLWTZ","bundle":"https://pith.science/pith/643FVPRVT3S52LTYIFQVUBLWTZ/bundle.json","state":"https://pith.science/pith/643FVPRVT3S52LTYIFQVUBLWTZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/643FVPRVT3S52LTYIFQVUBLWTZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:643FVPRVT3S52LTYIFQVUBLWTZ","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":"ec0abb18985a031f67164ce65f88fba8a0594b81f93627c7ce200162ff8127c8","cross_cats_sorted":["cs.LG","physics.chem-ph","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-05-29T09:34:53Z","title_canon_sha256":"20846bce743223c728e7c4c9e1110b1094e444ab06988816436873da6fe3153f"},"schema_version":"1.0","source":{"id":"2605.31063","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.31063","created_at":"2026-06-01T01:03:33Z"},{"alias_kind":"arxiv_version","alias_value":"2605.31063v1","created_at":"2026-06-01T01:03:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.31063","created_at":"2026-06-01T01:03:33Z"},{"alias_kind":"pith_short_12","alias_value":"643FVPRVT3S5","created_at":"2026-06-01T01:03:33Z"},{"alias_kind":"pith_short_16","alias_value":"643FVPRVT3S52LTY","created_at":"2026-06-01T01:03:33Z"},{"alias_kind":"pith_short_8","alias_value":"643FVPRV","created_at":"2026-06-01T01:03:33Z"}],"graph_snapshots":[{"event_id":"sha256:17a47f9d9a3a48c048fbaf6cab7a3c8669fefe783a29889f16891a047544935e","target":"graph","created_at":"2026-06-01T01:03:33Z","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/2605.31063/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Free energy estimation is a fundamental yet challenging problem, from physics to statistics. Classical approaches rely on thermodynamic transformations, ranging from direct estimation, quasistatic integration, to finite-time averaging. Recent work [He and Du et al., 2025] learns neural transports to significantly accelerate the efficiency in the finite-time regime. In this paper, we generalize this framework to arbitrary state spaces. Building on this view, we develop a generalized neural transport learning approach for efficient estimation. Experiments validate the effectiveness and efficienc","authors_text":"Carles Domingo-Enrich, Francisco Vargas, Jiajun He, Jos\\'e Miguel Hern\\'andez-Lobato, Yingzhen Li, Yuanqi Du, Zijing Ou","cross_cats":["cs.LG","physics.chem-ph","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-05-29T09:34:53Z","title":"Free energy Estimation on Any State Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31063","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:ac80e54be61481d6474531f6b37040a1adba067684948e622cd783b39c2fdc34","target":"record","created_at":"2026-06-01T01:03:33Z","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":"ec0abb18985a031f67164ce65f88fba8a0594b81f93627c7ce200162ff8127c8","cross_cats_sorted":["cs.LG","physics.chem-ph","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-05-29T09:34:53Z","title_canon_sha256":"20846bce743223c728e7c4c9e1110b1094e444ab06988816436873da6fe3153f"},"schema_version":"1.0","source":{"id":"2605.31063","kind":"arxiv","version":1}},"canonical_sha256":"f7365abe359ee5dd2e7841615a05769e55c6fe7c56e2714a3c5b50384599044e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7365abe359ee5dd2e7841615a05769e55c6fe7c56e2714a3c5b50384599044e","first_computed_at":"2026-06-01T01:03:33.936585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T01:03:33.936585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0JSCyGPZi03q8lriq1Dka2MJUBnsxw00rYEAok1jmsMdx7SAjWSPzAdQCAnETOv4mR9og2Anqie4mkdo0VqiBA==","signature_status":"signed_v1","signed_at":"2026-06-01T01:03:33.937119Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.31063","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac80e54be61481d6474531f6b37040a1adba067684948e622cd783b39c2fdc34","sha256:17a47f9d9a3a48c048fbaf6cab7a3c8669fefe783a29889f16891a047544935e"],"state_sha256":"c1e51ee5876219950484a8d63af1395aa55405a31f2116c82dc46fdb64278286"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jQxnIhSquHHb9j6Fxy2Glk5E2nUdXygURl6K6CJZ7UIJU7DIuUZ+xUUMfMRDn/xO6UzsjIqqQFrVi7TJwygUAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T03:53:31.947365Z","bundle_sha256":"52fffb4d5f0447a2ec503799e29d623311fd8a9c6c579ac420fa488c7f0001e0"}}