{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:WAOGAYKQFWFYEEIRLMOZWFXAWB","short_pith_number":"pith:WAOGAYKQ","canonical_record":{"source":{"id":"2607.07718","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-04T11:07:09Z","cross_cats_sorted":["cs.AI","cs.NA","math.NA"],"title_canon_sha256":"c99c1f3546e158b5968a6c5f5337bda0c568bc1e9103fec6a571d97a87c510b1","abstract_canon_sha256":"faeaf9169239cdb1700e45c2a1a85c00ae4f95d7dd1c96bf5db9bcbd7e8f3e51"},"schema_version":"1.0"},"canonical_sha256":"b01c6061502d8b8211115b1d9b16e0b07eb6d9f791eb83a5cc3359078c11b1dd","source":{"kind":"arxiv","id":"2607.07718","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07718","created_at":"2026-07-10T00:18:47Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07718v1","created_at":"2026-07-10T00:18:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07718","created_at":"2026-07-10T00:18:47Z"},{"alias_kind":"pith_short_12","alias_value":"WAOGAYKQFWFY","created_at":"2026-07-10T00:18:47Z"},{"alias_kind":"pith_short_16","alias_value":"WAOGAYKQFWFYEEIR","created_at":"2026-07-10T00:18:47Z"},{"alias_kind":"pith_short_8","alias_value":"WAOGAYKQ","created_at":"2026-07-10T00:18:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:WAOGAYKQFWFYEEIRLMOZWFXAWB","target":"record","payload":{"canonical_record":{"source":{"id":"2607.07718","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-04T11:07:09Z","cross_cats_sorted":["cs.AI","cs.NA","math.NA"],"title_canon_sha256":"c99c1f3546e158b5968a6c5f5337bda0c568bc1e9103fec6a571d97a87c510b1","abstract_canon_sha256":"faeaf9169239cdb1700e45c2a1a85c00ae4f95d7dd1c96bf5db9bcbd7e8f3e51"},"schema_version":"1.0"},"canonical_sha256":"b01c6061502d8b8211115b1d9b16e0b07eb6d9f791eb83a5cc3359078c11b1dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-10T00:18:47.167880Z","signature_b64":"mDXpqFrkBk0fXcOLJmAYbm+YT02EiaF/lFpJ0tieRwnjQ3srC0pXpWmfwlJxN0dzh8U2pFfBSChUEWKtSykfCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b01c6061502d8b8211115b1d9b16e0b07eb6d9f791eb83a5cc3359078c11b1dd","last_reissued_at":"2026-07-10T00:18:47.167368Z","signature_status":"signed_v1","first_computed_at":"2026-07-10T00:18:47.167368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.07718","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":"2026-07-10T00:18:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lkVJWS3AJdH5mxIdzY1Poy1GdCDT0B0EkBiY2Fz9nBFe2tUYiyKK//H0vryNVtepAZpwZBDNn5swIGS3oCqjAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T07:47:57.489287Z"},"content_sha256":"0f4f774dfccaeddb040cc807a2d25b4d1d731411eb147b10f0580b82ee546026","schema_version":"1.0","event_id":"sha256:0f4f774dfccaeddb040cc807a2d25b4d1d731411eb147b10f0580b82ee546026"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:WAOGAYKQFWFYEEIRLMOZWFXAWB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"LLT: Local Linear Transformer for PDE Operator Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Eli Turkel, Oded Ovadia","submitted_at":"2026-07-04T11:07:09Z","abstract_excerpt":"Neural operators have become a common approach for learning PDE solution maps and accelerating numerical simulations. Transformer-based neural operators are of particular interest, since attention can learn long-range dependencies in the computational domain. However, standard attention has two major limitations when applied to PDEs: it scales quadratically with the number of computational nodes, and it lacks an explicit bias toward local interactions. To address these issues, we introduce Local Linear Transformer (LLT) for PDE operator learning. The architecture combines linear global attenti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07718","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/2607.07718/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":"2026-07-10T00:18:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"reH5LoxBKaYGAPava7ADgM02mPZcJ7A7PiKrhVwXPTfUFPGQ5mQ8veMj18kqUiyI84eMzF1wYwCYN+Ky0rCMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T07:47:57.489775Z"},"content_sha256":"4173043016f5c84be28bc556f54f8fd5db6357c58db40b106c468cb301aa7a18","schema_version":"1.0","event_id":"sha256:4173043016f5c84be28bc556f54f8fd5db6357c58db40b106c468cb301aa7a18"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WAOGAYKQFWFYEEIRLMOZWFXAWB/bundle.json","state_url":"https://pith.science/pith/WAOGAYKQFWFYEEIRLMOZWFXAWB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WAOGAYKQFWFYEEIRLMOZWFXAWB/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":"2026-08-08T07:47:57Z","links":{"resolver":"https://pith.science/pith/WAOGAYKQFWFYEEIRLMOZWFXAWB","bundle":"https://pith.science/pith/WAOGAYKQFWFYEEIRLMOZWFXAWB/bundle.json","state":"https://pith.science/pith/WAOGAYKQFWFYEEIRLMOZWFXAWB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WAOGAYKQFWFYEEIRLMOZWFXAWB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WAOGAYKQFWFYEEIRLMOZWFXAWB","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":"faeaf9169239cdb1700e45c2a1a85c00ae4f95d7dd1c96bf5db9bcbd7e8f3e51","cross_cats_sorted":["cs.AI","cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-04T11:07:09Z","title_canon_sha256":"c99c1f3546e158b5968a6c5f5337bda0c568bc1e9103fec6a571d97a87c510b1"},"schema_version":"1.0","source":{"id":"2607.07718","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07718","created_at":"2026-07-10T00:18:47Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07718v1","created_at":"2026-07-10T00:18:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07718","created_at":"2026-07-10T00:18:47Z"},{"alias_kind":"pith_short_12","alias_value":"WAOGAYKQFWFY","created_at":"2026-07-10T00:18:47Z"},{"alias_kind":"pith_short_16","alias_value":"WAOGAYKQFWFYEEIR","created_at":"2026-07-10T00:18:47Z"},{"alias_kind":"pith_short_8","alias_value":"WAOGAYKQ","created_at":"2026-07-10T00:18:47Z"}],"graph_snapshots":[{"event_id":"sha256:4173043016f5c84be28bc556f54f8fd5db6357c58db40b106c468cb301aa7a18","target":"graph","created_at":"2026-07-10T00:18:47Z","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/2607.07718/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Neural operators have become a common approach for learning PDE solution maps and accelerating numerical simulations. Transformer-based neural operators are of particular interest, since attention can learn long-range dependencies in the computational domain. However, standard attention has two major limitations when applied to PDEs: it scales quadratically with the number of computational nodes, and it lacks an explicit bias toward local interactions. To address these issues, we introduce Local Linear Transformer (LLT) for PDE operator learning. The architecture combines linear global attenti","authors_text":"Eli Turkel, Oded Ovadia","cross_cats":["cs.AI","cs.NA","math.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-04T11:07:09Z","title":"LLT: Local Linear Transformer for PDE Operator Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07718","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":"sha256:0f4f774dfccaeddb040cc807a2d25b4d1d731411eb147b10f0580b82ee546026","target":"record","created_at":"2026-07-10T00:18:47Z","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":"faeaf9169239cdb1700e45c2a1a85c00ae4f95d7dd1c96bf5db9bcbd7e8f3e51","cross_cats_sorted":["cs.AI","cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-04T11:07:09Z","title_canon_sha256":"c99c1f3546e158b5968a6c5f5337bda0c568bc1e9103fec6a571d97a87c510b1"},"schema_version":"1.0","source":{"id":"2607.07718","kind":"arxiv","version":1}},"canonical_sha256":"b01c6061502d8b8211115b1d9b16e0b07eb6d9f791eb83a5cc3359078c11b1dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b01c6061502d8b8211115b1d9b16e0b07eb6d9f791eb83a5cc3359078c11b1dd","first_computed_at":"2026-07-10T00:18:47.167368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-10T00:18:47.167368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mDXpqFrkBk0fXcOLJmAYbm+YT02EiaF/lFpJ0tieRwnjQ3srC0pXpWmfwlJxN0dzh8U2pFfBSChUEWKtSykfCA==","signature_status":"signed_v1","signed_at":"2026-07-10T00:18:47.167880Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.07718","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f4f774dfccaeddb040cc807a2d25b4d1d731411eb147b10f0580b82ee546026","sha256:4173043016f5c84be28bc556f54f8fd5db6357c58db40b106c468cb301aa7a18"],"state_sha256":"a9278faccf94663947a3f951eac6ac591d2223474d75783a18d30952f2f4adc0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Ii69C5thFTP/3KIGBAf8+DIGQi8Jf8vVzja33Uzj1LVfrftrERl0l6zFY2ep8Cl3V0Jn5GDCrYv4Gc85olsCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T07:47:57.492973Z","bundle_sha256":"71d6be5045292ed23b187e1bf6851baa94d726b24afe995f3d7d60cc85576f10"}}