{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:TN7VP5P6355NMXPVCJUI7W3MYZ","short_pith_number":"pith:TN7VP5P6","schema_version":"1.0","canonical_sha256":"9b7f57f5fedf7ad65df512688fdb6cc64637c6a0c608764e8d6cc58554a7643d","source":{"kind":"arxiv","id":"2606.09806","version":1},"attestation_state":"computed","paper":{"title":"Topological Neural Operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Lennart Bastian, Mustafa Hajij, Samuel Leventhal, Tolga Birdal","submitted_at":"2026-06-08T17:54:33Z","abstract_excerpt":"We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or edges to topological domains. TNOs represent data as features defined on cells of varying dimension and model their interactions through Discrete Exterior Calculus, enabling explicit cross-dimensional coupling via gradient-, curl-, and divergence-type operators. The key design principle is to decouple where information flows, as governed by fixed topological operators, from how it is transformed (which is learned), yi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.09806","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-08T17:54:33Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"d4720b1952229045229df5c00612e84b4cdbca3a68f196c1aa09316094eba193","abstract_canon_sha256":"479d44a6ee2d10e070ed9c01dc769e80d863f678c776765ad2889ea6390f42a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:09:10.981264Z","signature_b64":"9JvAyRh3z53EWwua5UUSKJRoY/Tj2+IP7oJftHAyi07drUHc/bhPrPfVreUbRQRqsgynwpPxWds9DaxaPazuDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b7f57f5fedf7ad65df512688fdb6cc64637c6a0c608764e8d6cc58554a7643d","last_reissued_at":"2026-06-09T02:09:10.980764Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:09:10.980764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological Neural Operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Lennart Bastian, Mustafa Hajij, Samuel Leventhal, Tolga Birdal","submitted_at":"2026-06-08T17:54:33Z","abstract_excerpt":"We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or edges to topological domains. TNOs represent data as features defined on cells of varying dimension and model their interactions through Discrete Exterior Calculus, enabling explicit cross-dimensional coupling via gradient-, curl-, and divergence-type operators. The key design principle is to decouple where information flows, as governed by fixed topological operators, from how it is transformed (which is learned), yi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09806","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/2606.09806/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.09806","created_at":"2026-06-09T02:09:10.980837+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.09806v1","created_at":"2026-06-09T02:09:10.980837+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09806","created_at":"2026-06-09T02:09:10.980837+00:00"},{"alias_kind":"pith_short_12","alias_value":"TN7VP5P6355N","created_at":"2026-06-09T02:09:10.980837+00:00"},{"alias_kind":"pith_short_16","alias_value":"TN7VP5P6355NMXPV","created_at":"2026-06-09T02:09:10.980837+00:00"},{"alias_kind":"pith_short_8","alias_value":"TN7VP5P6","created_at":"2026-06-09T02:09:10.980837+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TN7VP5P6355NMXPVCJUI7W3MYZ","json":"https://pith.science/pith/TN7VP5P6355NMXPVCJUI7W3MYZ.json","graph_json":"https://pith.science/api/pith-number/TN7VP5P6355NMXPVCJUI7W3MYZ/graph.json","events_json":"https://pith.science/api/pith-number/TN7VP5P6355NMXPVCJUI7W3MYZ/events.json","paper":"https://pith.science/paper/TN7VP5P6"},"agent_actions":{"view_html":"https://pith.science/pith/TN7VP5P6355NMXPVCJUI7W3MYZ","download_json":"https://pith.science/pith/TN7VP5P6355NMXPVCJUI7W3MYZ.json","view_paper":"https://pith.science/paper/TN7VP5P6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.09806&json=true","fetch_graph":"https://pith.science/api/pith-number/TN7VP5P6355NMXPVCJUI7W3MYZ/graph.json","fetch_events":"https://pith.science/api/pith-number/TN7VP5P6355NMXPVCJUI7W3MYZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TN7VP5P6355NMXPVCJUI7W3MYZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TN7VP5P6355NMXPVCJUI7W3MYZ/action/storage_attestation","attest_author":"https://pith.science/pith/TN7VP5P6355NMXPVCJUI7W3MYZ/action/author_attestation","sign_citation":"https://pith.science/pith/TN7VP5P6355NMXPVCJUI7W3MYZ/action/citation_signature","submit_replication":"https://pith.science/pith/TN7VP5P6355NMXPVCJUI7W3MYZ/action/replication_record"}},"created_at":"2026-06-09T02:09:10.980837+00:00","updated_at":"2026-06-09T02:09:10.980837+00:00"}