{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:CLLVJRXS337J6PVT5ADG5HV5LK","short_pith_number":"pith:CLLVJRXS","canonical_record":{"source":{"id":"2412.19235","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-12-26T14:30:54Z","cross_cats_sorted":["cs.AI","cs.LG","cs.NA","physics.comp-ph"],"title_canon_sha256":"97978af8253da01498687a75d00a272d8d3d07419d56ada49f75df804c1df48f","abstract_canon_sha256":"a895584459475c97ce2c41c4da4171a66349b6888111e121edaf52fe75310bc0"},"schema_version":"1.0"},"canonical_sha256":"12d754c6f2defe9f3eb3e8066e9ebd5a9fa999ec63cf6539145f8ed8f464710e","source":{"kind":"arxiv","id":"2412.19235","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.19235","created_at":"2026-07-05T11:32:22Z"},{"alias_kind":"arxiv_version","alias_value":"2412.19235v1","created_at":"2026-07-05T11:32:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.19235","created_at":"2026-07-05T11:32:22Z"},{"alias_kind":"pith_short_12","alias_value":"CLLVJRXS337J","created_at":"2026-07-05T11:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"CLLVJRXS337J6PVT","created_at":"2026-07-05T11:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"CLLVJRXS","created_at":"2026-07-05T11:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:CLLVJRXS337J6PVT5ADG5HV5LK","target":"record","payload":{"canonical_record":{"source":{"id":"2412.19235","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-12-26T14:30:54Z","cross_cats_sorted":["cs.AI","cs.LG","cs.NA","physics.comp-ph"],"title_canon_sha256":"97978af8253da01498687a75d00a272d8d3d07419d56ada49f75df804c1df48f","abstract_canon_sha256":"a895584459475c97ce2c41c4da4171a66349b6888111e121edaf52fe75310bc0"},"schema_version":"1.0"},"canonical_sha256":"12d754c6f2defe9f3eb3e8066e9ebd5a9fa999ec63cf6539145f8ed8f464710e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:32:22.511408Z","signature_b64":"wxgAt7JC7LBICBANr6XUvAKdDuT8C4Rp6D7jPT7oCFFpqEvvojB9ikWmBReSzeF3qZ3IAYBh4JvbPE+kZXKsBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12d754c6f2defe9f3eb3e8066e9ebd5a9fa999ec63cf6539145f8ed8f464710e","last_reissued_at":"2026-07-05T11:32:22.510878Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:32:22.510878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.19235","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":"2026-07-05T11:32:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R5Csfim4ElU2dN1jcKMrhCTQBbNUqBuaq7RSrbI+0UzB1PBwBHjTUvpCjIU4BTRRkqZRW20UlnS1ADud3VSQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:36:43.979969Z"},"content_sha256":"991592cdaa7ac29fa73091e229331c50ed54977374ec7d9d300d1495f4cd7cb9","schema_version":"1.0","event_id":"sha256:991592cdaa7ac29fa73091e229331c50ed54977374ec7d9d300d1495f4cd7cb9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:CLLVJRXS337J6PVT5ADG5HV5LK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks?","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.LG","cs.NA","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Alexey O. Malkhanov, Mikhail E. Smorkalov, Vasiliy A. Es'kin","submitted_at":"2024-12-26T14:30:54Z","abstract_excerpt":"The article discusses the development of various methods and techniques for initializing and training neural networks with a single hidden layer, as well as training a separable physics-informed neural network consisting of neural networks with a single hidden layer to solve physical problems described by ordinary differential equations (ODEs) and partial differential equations (PDEs). A method for strictly deterministic initialization of a neural network with one hidden layer for solving physical problems described by an ODE is proposed. Modifications to existing methods for weighting the los"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19235","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/2412.19235/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":"2026-07-05T11:32:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wQVoqe7mCmJd308G+n7WtpzQOWDohxQwb81BgR4gb4rDeyWqD6c5KByJEsjGTrTjSkcnYJP99oI6YOvLpakIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:36:43.980305Z"},"content_sha256":"7faabd9c10aec5eac1cee4111a5489ccf2e47da585da4f27826eadd7784ccb5e","schema_version":"1.0","event_id":"sha256:7faabd9c10aec5eac1cee4111a5489ccf2e47da585da4f27826eadd7784ccb5e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CLLVJRXS337J6PVT5ADG5HV5LK/bundle.json","state_url":"https://pith.science/pith/CLLVJRXS337J6PVT5ADG5HV5LK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CLLVJRXS337J6PVT5ADG5HV5LK/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":"2026-08-11T12:36:43Z","links":{"resolver":"https://pith.science/pith/CLLVJRXS337J6PVT5ADG5HV5LK","bundle":"https://pith.science/pith/CLLVJRXS337J6PVT5ADG5HV5LK/bundle.json","state":"https://pith.science/pith/CLLVJRXS337J6PVT5ADG5HV5LK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CLLVJRXS337J6PVT5ADG5HV5LK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:CLLVJRXS337J6PVT5ADG5HV5LK","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":"a895584459475c97ce2c41c4da4171a66349b6888111e121edaf52fe75310bc0","cross_cats_sorted":["cs.AI","cs.LG","cs.NA","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-12-26T14:30:54Z","title_canon_sha256":"97978af8253da01498687a75d00a272d8d3d07419d56ada49f75df804c1df48f"},"schema_version":"1.0","source":{"id":"2412.19235","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.19235","created_at":"2026-07-05T11:32:22Z"},{"alias_kind":"arxiv_version","alias_value":"2412.19235v1","created_at":"2026-07-05T11:32:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.19235","created_at":"2026-07-05T11:32:22Z"},{"alias_kind":"pith_short_12","alias_value":"CLLVJRXS337J","created_at":"2026-07-05T11:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"CLLVJRXS337J6PVT","created_at":"2026-07-05T11:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"CLLVJRXS","created_at":"2026-07-05T11:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:7faabd9c10aec5eac1cee4111a5489ccf2e47da585da4f27826eadd7784ccb5e","target":"graph","created_at":"2026-07-05T11:32:22Z","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/2412.19235/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The article discusses the development of various methods and techniques for initializing and training neural networks with a single hidden layer, as well as training a separable physics-informed neural network consisting of neural networks with a single hidden layer to solve physical problems described by ordinary differential equations (ODEs) and partial differential equations (PDEs). A method for strictly deterministic initialization of a neural network with one hidden layer for solving physical problems described by an ODE is proposed. Modifications to existing methods for weighting the los","authors_text":"Alexey O. Malkhanov, Mikhail E. Smorkalov, Vasiliy A. Es'kin","cross_cats":["cs.AI","cs.LG","cs.NA","physics.comp-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-12-26T14:30:54Z","title":"Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19235","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":"sha256:991592cdaa7ac29fa73091e229331c50ed54977374ec7d9d300d1495f4cd7cb9","target":"record","created_at":"2026-07-05T11:32:22Z","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":"a895584459475c97ce2c41c4da4171a66349b6888111e121edaf52fe75310bc0","cross_cats_sorted":["cs.AI","cs.LG","cs.NA","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-12-26T14:30:54Z","title_canon_sha256":"97978af8253da01498687a75d00a272d8d3d07419d56ada49f75df804c1df48f"},"schema_version":"1.0","source":{"id":"2412.19235","kind":"arxiv","version":1}},"canonical_sha256":"12d754c6f2defe9f3eb3e8066e9ebd5a9fa999ec63cf6539145f8ed8f464710e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12d754c6f2defe9f3eb3e8066e9ebd5a9fa999ec63cf6539145f8ed8f464710e","first_computed_at":"2026-07-05T11:32:22.510878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:32:22.510878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wxgAt7JC7LBICBANr6XUvAKdDuT8C4Rp6D7jPT7oCFFpqEvvojB9ikWmBReSzeF3qZ3IAYBh4JvbPE+kZXKsBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:32:22.511408Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.19235","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:991592cdaa7ac29fa73091e229331c50ed54977374ec7d9d300d1495f4cd7cb9","sha256:7faabd9c10aec5eac1cee4111a5489ccf2e47da585da4f27826eadd7784ccb5e"],"state_sha256":"c393545303a4c97deda98e024c74d4fd3a59d861333b1d14c5bf07f3c7104047"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZMEBoijF5JIwZqW/Osh7WDOaAaQ+3NkrmiRyw/V3UOah+BBFdQJOYGXQ1wmIw4XOnFcZOb6YRJL7G9g1qUq/DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T12:36:43.982690Z","bundle_sha256":"ede479b5ac58fbae8fae4852354ae3ef6a37e07f8315ddb6358e2da25ceb07ef"}}