{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6HCM4Y5RGB2CGI5L2JFXZ5OWRW","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":"c487f8e007356552cdf933b7c881d0658b6f3847c6714994fc17cc0c00d45c7e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-01T13:46:22Z","title_canon_sha256":"c6e141d9ac9fd9082d74192c353cd84ed8944d1337744eafc8247ae56b767b27"},"schema_version":"1.0","source":{"id":"2607.00947","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00947","created_at":"2026-07-02T01:18:24Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00947v1","created_at":"2026-07-02T01:18:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00947","created_at":"2026-07-02T01:18:24Z"},{"alias_kind":"pith_short_12","alias_value":"6HCM4Y5RGB2C","created_at":"2026-07-02T01:18:24Z"},{"alias_kind":"pith_short_16","alias_value":"6HCM4Y5RGB2CGI5L","created_at":"2026-07-02T01:18:24Z"},{"alias_kind":"pith_short_8","alias_value":"6HCM4Y5R","created_at":"2026-07-02T01:18:24Z"}],"graph_snapshots":[{"event_id":"sha256:d37a2e7fd9ed9faf70490b0eb42cb917cda01363886118a357bea2e8304a6dcd","target":"graph","created_at":"2026-07-02T01:18:24Z","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/2607.00947/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Generative models learn data distributions that reside on a low-dimensional manifold within a higher-dimensional ambient space. Optimizing differentiable objectives on this manifold is challenging: the ambient loss landscape is high-dimensional, rugged, and non-convex. Direct gradient descent, blind to the manifold's geometry, quickly drifts off it. Diffeomorphic optimization starts from the observation that diffusion and flow models provide a map from the data manifold to a much simpler base space in which we perform gradient descent. Using differential geometry, we show this is equivalent to","authors_text":"Andrew Leaver-Fay, Joseph Kleinhenz, Ludwig Winkler, Pan Kessel","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-01T13:46:22Z","title":"Diffeomorphic Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00947","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":"sha256:8853fe4dc52aae487f99f67e7de946d4ba268811492fca96fb64af51371d8069","target":"record","created_at":"2026-07-02T01:18:24Z","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":"c487f8e007356552cdf933b7c881d0658b6f3847c6714994fc17cc0c00d45c7e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-01T13:46:22Z","title_canon_sha256":"c6e141d9ac9fd9082d74192c353cd84ed8944d1337744eafc8247ae56b767b27"},"schema_version":"1.0","source":{"id":"2607.00947","kind":"arxiv","version":1}},"canonical_sha256":"f1c4ce63b130742323abd24b7cf5d68d9a9289fd11f6ca100448ee733bb2e2f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1c4ce63b130742323abd24b7cf5d68d9a9289fd11f6ca100448ee733bb2e2f2","first_computed_at":"2026-07-02T01:18:24.225369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T01:18:24.225369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0CcORcm7LS719aFqaSv5GlDClBoL9mKsWQjFelCKGMLSNGtYfGr3VhqsDxeI8Nk8ce/MLDkbv3d6X5x5NJN5Dw==","signature_status":"signed_v1","signed_at":"2026-07-02T01:18:24.225753Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.00947","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8853fe4dc52aae487f99f67e7de946d4ba268811492fca96fb64af51371d8069","sha256:d37a2e7fd9ed9faf70490b0eb42cb917cda01363886118a357bea2e8304a6dcd"],"state_sha256":"3ca76fe2710a4163c31a1131c2fbf5d68dab923839ca30ecdb720b676393fed8"}