{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:CXF45V25EFHKAHFXECEXCTH67L","short_pith_number":"pith:CXF45V25","canonical_record":{"source":{"id":"2504.15897","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-04-22T13:40:04Z","cross_cats_sorted":[],"title_canon_sha256":"e9a22e190ee4c44fdf8564b158ea552646297e5fb4e549c3efd7e20c9686befb","abstract_canon_sha256":"5fb8831e31464dff3620b6684f0b1ce15a658eec6e01ac5c4fb29f2bee6a2aed"},"schema_version":"1.0"},"canonical_sha256":"15cbced75d214ea01cb72089714cfefacec7fa97b65d6e8ac45ca4e35222f817","source":{"kind":"arxiv","id":"2504.15897","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.15897","created_at":"2026-07-05T10:52:31Z"},{"alias_kind":"arxiv_version","alias_value":"2504.15897v1","created_at":"2026-07-05T10:52:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.15897","created_at":"2026-07-05T10:52:31Z"},{"alias_kind":"pith_short_12","alias_value":"CXF45V25EFHK","created_at":"2026-07-05T10:52:31Z"},{"alias_kind":"pith_short_16","alias_value":"CXF45V25EFHKAHFX","created_at":"2026-07-05T10:52:31Z"},{"alias_kind":"pith_short_8","alias_value":"CXF45V25","created_at":"2026-07-05T10:52:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:CXF45V25EFHKAHFXECEXCTH67L","target":"record","payload":{"canonical_record":{"source":{"id":"2504.15897","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-04-22T13:40:04Z","cross_cats_sorted":[],"title_canon_sha256":"e9a22e190ee4c44fdf8564b158ea552646297e5fb4e549c3efd7e20c9686befb","abstract_canon_sha256":"5fb8831e31464dff3620b6684f0b1ce15a658eec6e01ac5c4fb29f2bee6a2aed"},"schema_version":"1.0"},"canonical_sha256":"15cbced75d214ea01cb72089714cfefacec7fa97b65d6e8ac45ca4e35222f817","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:52:31.767534Z","signature_b64":"TIEZPxIOQo5ygfPFzY8u1euSdzjT3n0Mt3NASmF7ouOGGZeoNpRVBhivcKJOwYgrSjwInROHJW77GAUh/d+MDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15cbced75d214ea01cb72089714cfefacec7fa97b65d6e8ac45ca4e35222f817","last_reissued_at":"2026-07-05T10:52:31.767091Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:52:31.767091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.15897","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":"2026-07-05T10:52:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Azmh4+trWaCxueAohfqaBdcd1s0EjjlDTR0pq8nb63ZuTsnDZfgB+TNd3UxW2sU9KP/yH6CgsHE9g2x085CvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T07:15:26.231305Z"},"content_sha256":"a30c9301312b35f0072e7c2b1d1ea4cbbfdae034355126156719c25f11125aa0","schema_version":"1.0","event_id":"sha256:a30c9301312b35f0072e7c2b1d1ea4cbbfdae034355126156719c25f11125aa0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:CXF45V25EFHKAHFXECEXCTH67L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Ligang Liu, Zhengyang Xue, Zherui Yang","submitted_at":"2025-04-22T13:40:04Z","abstract_excerpt":"Neural operators are efficient surrogate models for solving partial differential equations (PDEs), but their key components face challenges: (1) in order to improve accuracy, attention mechanisms suffer from computational inefficiency on large-scale meshes, and (2) spectral convolutions rely on the Fast Fourier Transform (FFT) on regular grids and assume a flat geometry, which causes accuracy degradation on irregular domains. To tackle these problems, we regard the matrix-vector operations in the standard attention mechanism on vectors in Euclidean space as bilinear forms and linear operators "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.15897","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/2504.15897/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":"2026-07-05T10:52:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v9eONBz1ipDJa6+0iryhTUkx92D9lp+09j00Ccy57b440AWToTRHOnW2BKWKU+Ex5I0FSuVPibY65Dafw/KbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T07:15:26.231861Z"},"content_sha256":"3725b94b60291b03a7b708052552cef15c20074dd39a479f639c1afa9eda13d6","schema_version":"1.0","event_id":"sha256:3725b94b60291b03a7b708052552cef15c20074dd39a479f639c1afa9eda13d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CXF45V25EFHKAHFXECEXCTH67L/bundle.json","state_url":"https://pith.science/pith/CXF45V25EFHKAHFXECEXCTH67L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CXF45V25EFHKAHFXECEXCTH67L/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":"2026-08-18T07:15:26Z","links":{"resolver":"https://pith.science/pith/CXF45V25EFHKAHFXECEXCTH67L","bundle":"https://pith.science/pith/CXF45V25EFHKAHFXECEXCTH67L/bundle.json","state":"https://pith.science/pith/CXF45V25EFHKAHFXECEXCTH67L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CXF45V25EFHKAHFXECEXCTH67L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CXF45V25EFHKAHFXECEXCTH67L","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":"5fb8831e31464dff3620b6684f0b1ce15a658eec6e01ac5c4fb29f2bee6a2aed","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-04-22T13:40:04Z","title_canon_sha256":"e9a22e190ee4c44fdf8564b158ea552646297e5fb4e549c3efd7e20c9686befb"},"schema_version":"1.0","source":{"id":"2504.15897","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.15897","created_at":"2026-07-05T10:52:31Z"},{"alias_kind":"arxiv_version","alias_value":"2504.15897v1","created_at":"2026-07-05T10:52:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.15897","created_at":"2026-07-05T10:52:31Z"},{"alias_kind":"pith_short_12","alias_value":"CXF45V25EFHK","created_at":"2026-07-05T10:52:31Z"},{"alias_kind":"pith_short_16","alias_value":"CXF45V25EFHKAHFX","created_at":"2026-07-05T10:52:31Z"},{"alias_kind":"pith_short_8","alias_value":"CXF45V25","created_at":"2026-07-05T10:52:31Z"}],"graph_snapshots":[{"event_id":"sha256:3725b94b60291b03a7b708052552cef15c20074dd39a479f639c1afa9eda13d6","target":"graph","created_at":"2026-07-05T10:52:31Z","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/2504.15897/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Neural operators are efficient surrogate models for solving partial differential equations (PDEs), but their key components face challenges: (1) in order to improve accuracy, attention mechanisms suffer from computational inefficiency on large-scale meshes, and (2) spectral convolutions rely on the Fast Fourier Transform (FFT) on regular grids and assume a flat geometry, which causes accuracy degradation on irregular domains. To tackle these problems, we regard the matrix-vector operations in the standard attention mechanism on vectors in Euclidean space as bilinear forms and linear operators ","authors_text":"Ligang Liu, Zhengyang Xue, Zherui Yang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-04-22T13:40:04Z","title":"SUPRA: Subspace Parameterized Attention for Neural Operator on General Domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.15897","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:a30c9301312b35f0072e7c2b1d1ea4cbbfdae034355126156719c25f11125aa0","target":"record","created_at":"2026-07-05T10:52:31Z","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":"5fb8831e31464dff3620b6684f0b1ce15a658eec6e01ac5c4fb29f2bee6a2aed","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-04-22T13:40:04Z","title_canon_sha256":"e9a22e190ee4c44fdf8564b158ea552646297e5fb4e549c3efd7e20c9686befb"},"schema_version":"1.0","source":{"id":"2504.15897","kind":"arxiv","version":1}},"canonical_sha256":"15cbced75d214ea01cb72089714cfefacec7fa97b65d6e8ac45ca4e35222f817","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15cbced75d214ea01cb72089714cfefacec7fa97b65d6e8ac45ca4e35222f817","first_computed_at":"2026-07-05T10:52:31.767091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:52:31.767091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TIEZPxIOQo5ygfPFzY8u1euSdzjT3n0Mt3NASmF7ouOGGZeoNpRVBhivcKJOwYgrSjwInROHJW77GAUh/d+MDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:52:31.767534Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.15897","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a30c9301312b35f0072e7c2b1d1ea4cbbfdae034355126156719c25f11125aa0","sha256:3725b94b60291b03a7b708052552cef15c20074dd39a479f639c1afa9eda13d6"],"state_sha256":"4176c37e44c1166a98f1fe3fc6ee8279467655651e116457c67256ae4bdfdec5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sY7Io+RitQt8DUYzn1U9pMYMwsBtjOSKvPe6O5CHs7KQHkU9R00/hbxPmJ23TT2KsZ6jjXPxniLxY4jIwZCzCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T07:15:26.236986Z","bundle_sha256":"fb2071679d9b3f3b71f95cf785c2015a68bb2bcf6d1aabc58ab4717ea939713d"}}