{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:32RRHQYFNDJ2OYNBQ2LU5WWVLL","short_pith_number":"pith:32RRHQYF","schema_version":"1.0","canonical_sha256":"dea313c30568d3a761a186974edad55ac39d2e077b3a269d4517fdc71e9d05bb","source":{"kind":"arxiv","id":"2105.08034","version":1},"attestation_state":"computed","paper":{"title":"The Theory of Functional Connections: A journey from theory to application","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Hunter Johnston","submitted_at":"2021-05-17T17:35:41Z","abstract_excerpt":"The Theory of Functional Connections (TFC) is a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The functionals derived from this method, called \\emph{constrained expressions}, analytically satisfy the imposed constraints and can be leveraged to transform constrained optimization problems to unconstrained ones. By simplifying the optimization problem, this technique has been shown to produce a numerical scheme that is faster, more accurate, and robust to poor initialization. The content of this dissertation details the complete develo"},"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":"2105.08034","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-05-17T17:35:41Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"3b9fe8a7592e9e8bb7cb3903df427f3703d22135a57e296603627beb204e1246","abstract_canon_sha256":"67e7776857e3406913c34e68ddd45968bc3d83073a09f8f59bc07a88dbfea05d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:40:47.200540Z","signature_b64":"AqRXxzaMaXcxKvqw8vJOsOSZsrYyaqJLzbVPzk4N3MHUgQZIuw/R8wxTfF86Fu5J0uxJYoeyWT7F/AE36JQjBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dea313c30568d3a761a186974edad55ac39d2e077b3a269d4517fdc71e9d05bb","last_reissued_at":"2026-07-05T02:40:47.200051Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:40:47.200051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Theory of Functional Connections: A journey from theory to application","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Hunter Johnston","submitted_at":"2021-05-17T17:35:41Z","abstract_excerpt":"The Theory of Functional Connections (TFC) is a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The functionals derived from this method, called \\emph{constrained expressions}, analytically satisfy the imposed constraints and can be leveraged to transform constrained optimization problems to unconstrained ones. By simplifying the optimization problem, this technique has been shown to produce a numerical scheme that is faster, more accurate, and robust to poor initialization. The content of this dissertation details the complete develo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.08034","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/2105.08034/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":"2105.08034","created_at":"2026-07-05T02:40:47.200114+00:00"},{"alias_kind":"arxiv_version","alias_value":"2105.08034v1","created_at":"2026-07-05T02:40:47.200114+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.08034","created_at":"2026-07-05T02:40:47.200114+00:00"},{"alias_kind":"pith_short_12","alias_value":"32RRHQYFNDJ2","created_at":"2026-07-05T02:40:47.200114+00:00"},{"alias_kind":"pith_short_16","alias_value":"32RRHQYFNDJ2OYNB","created_at":"2026-07-05T02:40:47.200114+00:00"},{"alias_kind":"pith_short_8","alias_value":"32RRHQYF","created_at":"2026-07-05T02:40:47.200114+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/32RRHQYFNDJ2OYNBQ2LU5WWVLL","json":"https://pith.science/pith/32RRHQYFNDJ2OYNBQ2LU5WWVLL.json","graph_json":"https://pith.science/api/pith-number/32RRHQYFNDJ2OYNBQ2LU5WWVLL/graph.json","events_json":"https://pith.science/api/pith-number/32RRHQYFNDJ2OYNBQ2LU5WWVLL/events.json","paper":"https://pith.science/paper/32RRHQYF"},"agent_actions":{"view_html":"https://pith.science/pith/32RRHQYFNDJ2OYNBQ2LU5WWVLL","download_json":"https://pith.science/pith/32RRHQYFNDJ2OYNBQ2LU5WWVLL.json","view_paper":"https://pith.science/paper/32RRHQYF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2105.08034&json=true","fetch_graph":"https://pith.science/api/pith-number/32RRHQYFNDJ2OYNBQ2LU5WWVLL/graph.json","fetch_events":"https://pith.science/api/pith-number/32RRHQYFNDJ2OYNBQ2LU5WWVLL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/32RRHQYFNDJ2OYNBQ2LU5WWVLL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/32RRHQYFNDJ2OYNBQ2LU5WWVLL/action/storage_attestation","attest_author":"https://pith.science/pith/32RRHQYFNDJ2OYNBQ2LU5WWVLL/action/author_attestation","sign_citation":"https://pith.science/pith/32RRHQYFNDJ2OYNBQ2LU5WWVLL/action/citation_signature","submit_replication":"https://pith.science/pith/32RRHQYFNDJ2OYNBQ2LU5WWVLL/action/replication_record"}},"created_at":"2026-07-05T02:40:47.200114+00:00","updated_at":"2026-07-05T02:40:47.200114+00:00"}