{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:LGE4ZCYWOHKP5DYUXXCQYUC7IO","short_pith_number":"pith:LGE4ZCYW","canonical_record":{"source":{"id":"2503.19185","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-03-24T22:22:24Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"18778ebfd598476b0d41ebfde8baaaa9973e3c63b6f9caefcb45feba94bd4b97","abstract_canon_sha256":"10e2477b655ff9353883aba503aec32b00911218c260743e01605e956ece67de"},"schema_version":"1.0"},"canonical_sha256":"5989cc8b1671d4fe8f14bdc50c505f43ae46a1bfd764795d68d284134c12c62e","source":{"kind":"arxiv","id":"2503.19185","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.19185","created_at":"2026-07-05T11:28:15Z"},{"alias_kind":"arxiv_version","alias_value":"2503.19185v3","created_at":"2026-07-05T11:28:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.19185","created_at":"2026-07-05T11:28:15Z"},{"alias_kind":"pith_short_12","alias_value":"LGE4ZCYWOHKP","created_at":"2026-07-05T11:28:15Z"},{"alias_kind":"pith_short_16","alias_value":"LGE4ZCYWOHKP5DYU","created_at":"2026-07-05T11:28:15Z"},{"alias_kind":"pith_short_8","alias_value":"LGE4ZCYW","created_at":"2026-07-05T11:28:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:LGE4ZCYWOHKP5DYUXXCQYUC7IO","target":"record","payload":{"canonical_record":{"source":{"id":"2503.19185","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-03-24T22:22:24Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"18778ebfd598476b0d41ebfde8baaaa9973e3c63b6f9caefcb45feba94bd4b97","abstract_canon_sha256":"10e2477b655ff9353883aba503aec32b00911218c260743e01605e956ece67de"},"schema_version":"1.0"},"canonical_sha256":"5989cc8b1671d4fe8f14bdc50c505f43ae46a1bfd764795d68d284134c12c62e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:28:15.257107Z","signature_b64":"9nLTCn16hUFTPJIGQS8Un9AvXDFEPcfBPDytmc0vI2OkAt/UuvIyaqmgC1WejDev/6DoXGQL0vPbn44csSidCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5989cc8b1671d4fe8f14bdc50c505f43ae46a1bfd764795d68d284134c12c62e","last_reissued_at":"2026-07-05T11:28:15.256668Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:28:15.256668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.19185","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:28:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SQ5zFIfntdv4sAMidvjnym3y1+Y3U8NG4RJULOyWXfqzUctSCkrXtlx3IpEOhbr47S2A1B5pb9V7suDydAIvBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T19:22:13.906663Z"},"content_sha256":"1b03683a3d5bac1ca6933a67c3daba11988b7ac747d9eac78bf24bc6db7b79fc","schema_version":"1.0","event_id":"sha256:1b03683a3d5bac1ca6933a67c3daba11988b7ac747d9eac78bf24bc6db7b79fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:LGE4ZCYWOHKP5DYUXXCQYUC7IO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Least Squares with Equality constraints Extreme Learning Machines for the resolution of PDEs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Davide Elia De Falco, Enrico Schiassi, Francesco Calabr\\`o","submitted_at":"2025-03-24T22:22:24Z","abstract_excerpt":"In this paper, we investigate the use of single hidden-layer neural networks as a family of ansatz functions for the resolution of partial differential equations (PDEs). In particular, we train the network via Extreme Learning Machines (ELMs) on the residual of the equation collocated on -- eventually randomly chosen -- points. Because the approximation is done directly in the formulation, such a method falls into the framework of Physically Informed Neural Networks (PINNs) and has been named PIELM. Since its first introduction, the method has been refined variously, and one successful variant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.19185","kind":"arxiv","version":3},"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/2503.19185/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":"2026-07-05T11:28:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wifMVO6oMKs70nAGYcxZT0cWsjKKOlA/giujOXYlFJ1Ew18KcD+6d/Vtu6jzJf9Q7y/qL4W7d2edRONvblnlBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T19:22:13.907168Z"},"content_sha256":"1796a4ccab0b1cc6f4013f8c0048c90de57263f864fe66a6b654985cbd4add7f","schema_version":"1.0","event_id":"sha256:1796a4ccab0b1cc6f4013f8c0048c90de57263f864fe66a6b654985cbd4add7f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LGE4ZCYWOHKP5DYUXXCQYUC7IO/bundle.json","state_url":"https://pith.science/pith/LGE4ZCYWOHKP5DYUXXCQYUC7IO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LGE4ZCYWOHKP5DYUXXCQYUC7IO/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":"2026-08-23T19:22:13Z","links":{"resolver":"https://pith.science/pith/LGE4ZCYWOHKP5DYUXXCQYUC7IO","bundle":"https://pith.science/pith/LGE4ZCYWOHKP5DYUXXCQYUC7IO/bundle.json","state":"https://pith.science/pith/LGE4ZCYWOHKP5DYUXXCQYUC7IO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LGE4ZCYWOHKP5DYUXXCQYUC7IO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:LGE4ZCYWOHKP5DYUXXCQYUC7IO","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":"10e2477b655ff9353883aba503aec32b00911218c260743e01605e956ece67de","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-03-24T22:22:24Z","title_canon_sha256":"18778ebfd598476b0d41ebfde8baaaa9973e3c63b6f9caefcb45feba94bd4b97"},"schema_version":"1.0","source":{"id":"2503.19185","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.19185","created_at":"2026-07-05T11:28:15Z"},{"alias_kind":"arxiv_version","alias_value":"2503.19185v3","created_at":"2026-07-05T11:28:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.19185","created_at":"2026-07-05T11:28:15Z"},{"alias_kind":"pith_short_12","alias_value":"LGE4ZCYWOHKP","created_at":"2026-07-05T11:28:15Z"},{"alias_kind":"pith_short_16","alias_value":"LGE4ZCYWOHKP5DYU","created_at":"2026-07-05T11:28:15Z"},{"alias_kind":"pith_short_8","alias_value":"LGE4ZCYW","created_at":"2026-07-05T11:28:15Z"}],"graph_snapshots":[{"event_id":"sha256:1796a4ccab0b1cc6f4013f8c0048c90de57263f864fe66a6b654985cbd4add7f","target":"graph","created_at":"2026-07-05T11:28:15Z","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/2503.19185/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate the use of single hidden-layer neural networks as a family of ansatz functions for the resolution of partial differential equations (PDEs). In particular, we train the network via Extreme Learning Machines (ELMs) on the residual of the equation collocated on -- eventually randomly chosen -- points. Because the approximation is done directly in the formulation, such a method falls into the framework of Physically Informed Neural Networks (PINNs) and has been named PIELM. Since its first introduction, the method has been refined variously, and one successful variant","authors_text":"Davide Elia De Falco, Enrico Schiassi, Francesco Calabr\\`o","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-03-24T22:22:24Z","title":"Least Squares with Equality constraints Extreme Learning Machines for the resolution of PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.19185","kind":"arxiv","version":3},"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":"sha256:1b03683a3d5bac1ca6933a67c3daba11988b7ac747d9eac78bf24bc6db7b79fc","target":"record","created_at":"2026-07-05T11:28:15Z","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":"10e2477b655ff9353883aba503aec32b00911218c260743e01605e956ece67de","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-03-24T22:22:24Z","title_canon_sha256":"18778ebfd598476b0d41ebfde8baaaa9973e3c63b6f9caefcb45feba94bd4b97"},"schema_version":"1.0","source":{"id":"2503.19185","kind":"arxiv","version":3}},"canonical_sha256":"5989cc8b1671d4fe8f14bdc50c505f43ae46a1bfd764795d68d284134c12c62e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5989cc8b1671d4fe8f14bdc50c505f43ae46a1bfd764795d68d284134c12c62e","first_computed_at":"2026-07-05T11:28:15.256668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:28:15.256668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9nLTCn16hUFTPJIGQS8Un9AvXDFEPcfBPDytmc0vI2OkAt/UuvIyaqmgC1WejDev/6DoXGQL0vPbn44csSidCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:28:15.257107Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.19185","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b03683a3d5bac1ca6933a67c3daba11988b7ac747d9eac78bf24bc6db7b79fc","sha256:1796a4ccab0b1cc6f4013f8c0048c90de57263f864fe66a6b654985cbd4add7f"],"state_sha256":"8cad22d98eb6d12f9a348beef15faf230a99c82bbc443e9751094e10de0e3d35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LlO8rNZ4hiomaC3YwZl125M81UuU5lmujvPCE/fHw5Xpf057NH1UiEhs4J76ifNjkPH2KzZRpO8YEZZMK3WcDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T19:22:13.911718Z","bundle_sha256":"29b7bf2e967ddd8b8d520439b23bd9795b6f76ce093769a0359abc59760ff2a8"}}