{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HNCQOF6JD7OHLI7P67RRQ5YQSO","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":"86e781c4214ee2d2ffb7ece885c81a8fc045d844c03d67b280158531995e1559","cross_cats_sorted":["cs.AI","cs.DS","math.PR","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-05-27T18:12:29Z","title_canon_sha256":"e48fef2fbe4aa117246751dc6293c33129e96351e4b91f908db5b16849a922d1"},"schema_version":"1.0","source":{"id":"2505.21640","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21640","created_at":"2026-07-05T11:11:01Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21640v1","created_at":"2026-07-05T11:11:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21640","created_at":"2026-07-05T11:11:01Z"},{"alias_kind":"pith_short_12","alias_value":"HNCQOF6JD7OH","created_at":"2026-07-05T11:11:01Z"},{"alias_kind":"pith_short_16","alias_value":"HNCQOF6JD7OHLI7P","created_at":"2026-07-05T11:11:01Z"},{"alias_kind":"pith_short_8","alias_value":"HNCQOF6J","created_at":"2026-07-05T11:11:01Z"}],"graph_snapshots":[{"event_id":"sha256:6db0ef15e1d3264dafdc345a990f09b026e6d6982c605b6ece68e726f7931433","target":"graph","created_at":"2026-07-05T11:11:01Z","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/2505.21640/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a framework for designing efficient diffusion models for $d$-dimensional symmetric-space Riemannian manifolds, including the torus, sphere, special orthogonal group and unitary group. Existing manifold diffusion models often depend on heat kernels, which lack closed-form expressions and require either $d$ gradient evaluations or exponential-in-$d$ arithmetic operations per training step. We introduce a new diffusion model for symmetric manifolds with a spatially-varying covariance, allowing us to leverage a projection of Euclidean Brownian motion to bypass heat kernel computations","authors_text":"Neil He, Nisheeth K. Vishnoi, Oren Mangoubi","cross_cats":["cs.AI","cs.DS","math.PR","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-05-27T18:12:29Z","title":"Efficient Diffusion Models for Symmetric Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21640","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":"sha256:8ae80e70a337089a8a532e04a0d32b2fb0c4f3fa067caebbdd816daeafcb3e0b","target":"record","created_at":"2026-07-05T11:11:01Z","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":"86e781c4214ee2d2ffb7ece885c81a8fc045d844c03d67b280158531995e1559","cross_cats_sorted":["cs.AI","cs.DS","math.PR","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-05-27T18:12:29Z","title_canon_sha256":"e48fef2fbe4aa117246751dc6293c33129e96351e4b91f908db5b16849a922d1"},"schema_version":"1.0","source":{"id":"2505.21640","kind":"arxiv","version":1}},"canonical_sha256":"3b450717c91fdc75a3eff7e31877109391ed4c69e1a5d86949780b4b7ddc42b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b450717c91fdc75a3eff7e31877109391ed4c69e1a5d86949780b4b7ddc42b7","first_computed_at":"2026-07-05T11:11:01.329786Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:01.329786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"alak3k754cv517iMhkR23D+3sBfRtrwpakXkkcluZIVXdq5x57sjq7wMpXGd2OS9rAHNKQJbzVNktzzhqtsjDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:01.330250Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.21640","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ae80e70a337089a8a532e04a0d32b2fb0c4f3fa067caebbdd816daeafcb3e0b","sha256:6db0ef15e1d3264dafdc345a990f09b026e6d6982c605b6ece68e726f7931433"],"state_sha256":"10296b8a3ef172d02ba4fe9c34de88f124d7941cca1c3274bc6e0a5e73fe1bb5"}