{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:66QZAQ4TBJZY2XIVN2VUSNNIR4","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":"45e58e9a4f751ce91ba088efc467cb10bb50a64ef1edd2d2ef9b0bbf89c37633","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-16T03:26:55Z","title_canon_sha256":"5971605bb1ca333694a7fb03dae202f2fdf2c3817b7dbcacc597280f31bb6a90"},"schema_version":"1.0","source":{"id":"2606.17465","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17465","created_at":"2026-06-19T16:10:13Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17465v1","created_at":"2026-06-19T16:10:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17465","created_at":"2026-06-19T16:10:13Z"},{"alias_kind":"pith_short_12","alias_value":"66QZAQ4TBJZY","created_at":"2026-06-19T16:10:13Z"},{"alias_kind":"pith_short_16","alias_value":"66QZAQ4TBJZY2XIV","created_at":"2026-06-19T16:10:13Z"},{"alias_kind":"pith_short_8","alias_value":"66QZAQ4T","created_at":"2026-06-19T16:10:13Z"}],"graph_snapshots":[{"event_id":"sha256:314a6f7229cb8ad35efbf0f435af15eefd60003435ef435ec249d127a8e4a47c","target":"graph","created_at":"2026-06-19T16:10:13Z","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/2606.17465/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce Perron--Frobenius Operator Matching (PFOM), a generative framework that matches density evolution via the integral PF operator, subsuming flow, diffusion, and jump models. We prove that among Bregman divergences, only Kullback--Leibler divergence preserves equality between density-level and sample-conditioned objectives, yielding a practical loss equivalent to Koopman path matching. We further develop Nesterov-accelerated training and sampling that stabilize discretization and accelerate convergence. %On Gaussian mixtures and two-moons, PFOM achieves faster KL/$W_2$/MMD decrease a","authors_text":"Jaemin Oh, Jie Chen, Shiqi Zhang, Wuwei Wu, Xiaoning Qian","cross_cats":["cs.SY","eess.SY"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-16T03:26:55Z","title":"Perron--Frobenius Operator Matching for Generative Modeling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17465","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:dbb37af75a58a967fac25e4071b3310db66f01fee93e83e13a919651886c0420","target":"record","created_at":"2026-06-19T16:10:13Z","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":"45e58e9a4f751ce91ba088efc467cb10bb50a64ef1edd2d2ef9b0bbf89c37633","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-16T03:26:55Z","title_canon_sha256":"5971605bb1ca333694a7fb03dae202f2fdf2c3817b7dbcacc597280f31bb6a90"},"schema_version":"1.0","source":{"id":"2606.17465","kind":"arxiv","version":1}},"canonical_sha256":"f7a19043930a738d5d156eab4935a88f1d03edbe90c6ef9709d9eec21dfad211","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7a19043930a738d5d156eab4935a88f1d03edbe90c6ef9709d9eec21dfad211","first_computed_at":"2026-06-19T16:10:13.730652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:13.730652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HDyhphxC+A1H28LskrD3DRv4dJcPhujunHCZFCf1DtDsUvw7ZCDQ5LjBVqsihJpAkN0g+V7QiW6pikmojbs3BQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:13.731014Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.17465","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dbb37af75a58a967fac25e4071b3310db66f01fee93e83e13a919651886c0420","sha256:314a6f7229cb8ad35efbf0f435af15eefd60003435ef435ec249d127a8e4a47c"],"state_sha256":"34aa1364390baec8d3de827949f28079974bedeb2a1841194d0872520cacd5dd"}