{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QRXUJVBKKGCO45AUOGRMX3P6S7","short_pith_number":"pith:QRXUJVBK","canonical_record":{"source":{"id":"2505.18923","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-25T01:06:32Z","cross_cats_sorted":[],"title_canon_sha256":"de4cea5a16845da2bf27d16b35ee6ce394d5404e13744bc3449df06f02dfcec9","abstract_canon_sha256":"6b723389fa56a5f66dba15c736d8252f5a50f8a9c45f463c553e00faf1a682a3"},"schema_version":"1.0"},"canonical_sha256":"846f44d42a5184ee741471a2cbedfe97f8512c2546b5149861c197fa9163bd4f","source":{"kind":"arxiv","id":"2505.18923","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.18923","created_at":"2026-07-05T11:09:21Z"},{"alias_kind":"arxiv_version","alias_value":"2505.18923v1","created_at":"2026-07-05T11:09:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.18923","created_at":"2026-07-05T11:09:21Z"},{"alias_kind":"pith_short_12","alias_value":"QRXUJVBKKGCO","created_at":"2026-07-05T11:09:21Z"},{"alias_kind":"pith_short_16","alias_value":"QRXUJVBKKGCO45AU","created_at":"2026-07-05T11:09:21Z"},{"alias_kind":"pith_short_8","alias_value":"QRXUJVBK","created_at":"2026-07-05T11:09:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QRXUJVBKKGCO45AUOGRMX3P6S7","target":"record","payload":{"canonical_record":{"source":{"id":"2505.18923","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-25T01:06:32Z","cross_cats_sorted":[],"title_canon_sha256":"de4cea5a16845da2bf27d16b35ee6ce394d5404e13744bc3449df06f02dfcec9","abstract_canon_sha256":"6b723389fa56a5f66dba15c736d8252f5a50f8a9c45f463c553e00faf1a682a3"},"schema_version":"1.0"},"canonical_sha256":"846f44d42a5184ee741471a2cbedfe97f8512c2546b5149861c197fa9163bd4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:09:21.864323Z","signature_b64":"0XSmEYsgNIdYSX7tjx0x6YY5S49/11i5D5ZScmEyM1CWPsq8RT1kgtUNh3tEzFPYD8F1ppQcGVYMmS/Fb+vtAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"846f44d42a5184ee741471a2cbedfe97f8512c2546b5149861c197fa9163bd4f","last_reissued_at":"2026-07-05T11:09:21.863773Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:09:21.863773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.18923","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":"2026-07-05T11:09:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IM3a/amdZNjO6WOL3/Z52ZS167602wf7w9DT9C290QwIYke9wzPDBnCN4Q+A7T0ZqDDEQ06aVopisBZ029QsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T23:02:11.775127Z"},"content_sha256":"9d02a4c30d7bec1fe5b725aca859aff3e05f67f70245ca12e98103416e3ff1e5","schema_version":"1.0","event_id":"sha256:9d02a4c30d7bec1fe5b725aca859aff3e05f67f70245ca12e98103416e3ff1e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QRXUJVBKKGCO45AUOGRMX3P6S7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graph-Based Operator Learning from Limited Data on Irregular Domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Shandian Zhe, Yile Li","submitted_at":"2025-05-25T01:06:32Z","abstract_excerpt":"Operator learning seeks to approximate mappings from input functions to output solutions, particularly in the context of partial differential equations (PDEs). While recent advances such as DeepONet and Fourier Neural Operator (FNO) have demonstrated strong performance, they often rely on regular grid discretizations, limiting their applicability to complex or irregular domains. In this work, we propose a Graph-based Operator Learning with Attention (GOLA) framework that addresses this limitation by constructing graphs from irregularly sampled spatial points and leveraging attention-enhanced G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.18923","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/2505.18923/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":"2026-07-05T11:09:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uxcbYgRvGCu8QFuRO+aTlPQnbTmvImVX3nCN8srjzR37lwLHUnKbeoPexS7C7NRecfBx8QSM3JpD1xwsoWNzDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T23:02:11.775640Z"},"content_sha256":"26c48d0e29026a4b8a8a8271a65b2198651a44d620ecb537e30cf49a4f66c2dd","schema_version":"1.0","event_id":"sha256:26c48d0e29026a4b8a8a8271a65b2198651a44d620ecb537e30cf49a4f66c2dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QRXUJVBKKGCO45AUOGRMX3P6S7/bundle.json","state_url":"https://pith.science/pith/QRXUJVBKKGCO45AUOGRMX3P6S7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QRXUJVBKKGCO45AUOGRMX3P6S7/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":"2026-08-15T23:02:11Z","links":{"resolver":"https://pith.science/pith/QRXUJVBKKGCO45AUOGRMX3P6S7","bundle":"https://pith.science/pith/QRXUJVBKKGCO45AUOGRMX3P6S7/bundle.json","state":"https://pith.science/pith/QRXUJVBKKGCO45AUOGRMX3P6S7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QRXUJVBKKGCO45AUOGRMX3P6S7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QRXUJVBKKGCO45AUOGRMX3P6S7","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":"6b723389fa56a5f66dba15c736d8252f5a50f8a9c45f463c553e00faf1a682a3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-25T01:06:32Z","title_canon_sha256":"de4cea5a16845da2bf27d16b35ee6ce394d5404e13744bc3449df06f02dfcec9"},"schema_version":"1.0","source":{"id":"2505.18923","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.18923","created_at":"2026-07-05T11:09:21Z"},{"alias_kind":"arxiv_version","alias_value":"2505.18923v1","created_at":"2026-07-05T11:09:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.18923","created_at":"2026-07-05T11:09:21Z"},{"alias_kind":"pith_short_12","alias_value":"QRXUJVBKKGCO","created_at":"2026-07-05T11:09:21Z"},{"alias_kind":"pith_short_16","alias_value":"QRXUJVBKKGCO45AU","created_at":"2026-07-05T11:09:21Z"},{"alias_kind":"pith_short_8","alias_value":"QRXUJVBK","created_at":"2026-07-05T11:09:21Z"}],"graph_snapshots":[{"event_id":"sha256:26c48d0e29026a4b8a8a8271a65b2198651a44d620ecb537e30cf49a4f66c2dd","target":"graph","created_at":"2026-07-05T11:09:21Z","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/2505.18923/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Operator learning seeks to approximate mappings from input functions to output solutions, particularly in the context of partial differential equations (PDEs). While recent advances such as DeepONet and Fourier Neural Operator (FNO) have demonstrated strong performance, they often rely on regular grid discretizations, limiting their applicability to complex or irregular domains. In this work, we propose a Graph-based Operator Learning with Attention (GOLA) framework that addresses this limitation by constructing graphs from irregularly sampled spatial points and leveraging attention-enhanced G","authors_text":"Shandian Zhe, Yile Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-25T01:06:32Z","title":"Graph-Based Operator Learning from Limited Data on Irregular Domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.18923","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":"sha256:9d02a4c30d7bec1fe5b725aca859aff3e05f67f70245ca12e98103416e3ff1e5","target":"record","created_at":"2026-07-05T11:09:21Z","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":"6b723389fa56a5f66dba15c736d8252f5a50f8a9c45f463c553e00faf1a682a3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-25T01:06:32Z","title_canon_sha256":"de4cea5a16845da2bf27d16b35ee6ce394d5404e13744bc3449df06f02dfcec9"},"schema_version":"1.0","source":{"id":"2505.18923","kind":"arxiv","version":1}},"canonical_sha256":"846f44d42a5184ee741471a2cbedfe97f8512c2546b5149861c197fa9163bd4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"846f44d42a5184ee741471a2cbedfe97f8512c2546b5149861c197fa9163bd4f","first_computed_at":"2026-07-05T11:09:21.863773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:09:21.863773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0XSmEYsgNIdYSX7tjx0x6YY5S49/11i5D5ZScmEyM1CWPsq8RT1kgtUNh3tEzFPYD8F1ppQcGVYMmS/Fb+vtAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:09:21.864323Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.18923","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d02a4c30d7bec1fe5b725aca859aff3e05f67f70245ca12e98103416e3ff1e5","sha256:26c48d0e29026a4b8a8a8271a65b2198651a44d620ecb537e30cf49a4f66c2dd"],"state_sha256":"7a25c2b484cd26007571974a405b46c41678c43ae2083bdd5d923d76077f043c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2HKYGsHqWhKS9kD+Ym0n4i0j3fdjSoZ+FEdz1E9777EYqfLegkoqgRZao9A0cuCf1v9KKIefbCERifnorz6pDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T23:02:11.780555Z","bundle_sha256":"067fcd278dd742cc89508af13b9f533ac2731b6b520464ef337505fd35b212e9"}}