{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:HM7AEPVPGFRNFJMOB5RQPAJIG6","short_pith_number":"pith:HM7AEPVP","canonical_record":{"source":{"id":"2608.11020","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-11T15:01:29Z","cross_cats_sorted":["cs.NA","math.NA","physics.comp-ph"],"title_canon_sha256":"e44c18115bd16b6b66f4260de417de45b5376f09432de12406536b94ec664865","abstract_canon_sha256":"b0b016e3cc3a72144c25251c45abdae47b50a0f742711c68f9f119f6fdf8d8f5"},"schema_version":"1.0"},"canonical_sha256":"3b3e023eaf3162d2a58e0f6307812837b9938ad4e6c44c76154665824ca1b5f8","source":{"kind":"arxiv","id":"2608.11020","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.11020","created_at":"2026-08-12T01:24:05Z"},{"alias_kind":"arxiv_version","alias_value":"2608.11020v1","created_at":"2026-08-12T01:24:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.11020","created_at":"2026-08-12T01:24:05Z"},{"alias_kind":"pith_short_12","alias_value":"HM7AEPVPGFRN","created_at":"2026-08-12T01:24:05Z"},{"alias_kind":"pith_short_16","alias_value":"HM7AEPVPGFRNFJMO","created_at":"2026-08-12T01:24:05Z"},{"alias_kind":"pith_short_8","alias_value":"HM7AEPVP","created_at":"2026-08-12T01:24:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:HM7AEPVPGFRNFJMOB5RQPAJIG6","target":"record","payload":{"canonical_record":{"source":{"id":"2608.11020","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-11T15:01:29Z","cross_cats_sorted":["cs.NA","math.NA","physics.comp-ph"],"title_canon_sha256":"e44c18115bd16b6b66f4260de417de45b5376f09432de12406536b94ec664865","abstract_canon_sha256":"b0b016e3cc3a72144c25251c45abdae47b50a0f742711c68f9f119f6fdf8d8f5"},"schema_version":"1.0"},"canonical_sha256":"3b3e023eaf3162d2a58e0f6307812837b9938ad4e6c44c76154665824ca1b5f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-12T01:24:05.096607Z","signature_b64":"B6AF1zgNR2isoMCgy4DV9U9jFNm9y8dkRfPJfJTBwHJWdRYtdxbggG38ErHMQSUFWiff493YAHZHwJomjlzQBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b3e023eaf3162d2a58e0f6307812837b9938ad4e6c44c76154665824ca1b5f8","last_reissued_at":"2026-08-12T01:24:05.094847Z","signature_status":"signed_v1","first_computed_at":"2026-08-12T01:24:05.094847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.11020","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":"2026-08-12T01:24:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G+oU1r4rA+KjsNr5NZAEdi5fv5HxaZWsUfPuYYv72E0LLMsV/98ctV5vWGgVgGt03OnCL2zPTY7rHM1pIZsHAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T00:31:02.289852Z"},"content_sha256":"a1bbb5273b93f9d88f6caf0626cb706785a6c8ad948c3524350e4709d2281d13","schema_version":"1.0","event_id":"sha256:a1bbb5273b93f9d88f6caf0626cb706785a6c8ad948c3524350e4709d2281d13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:HM7AEPVPGFRNFJMOB5RQPAJIG6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derivative Computation in PINNs: Automatic Differentiation, Finite Differences and Beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"Maciej J. Mikulski, Tadeusz Uhl","submitted_at":"2026-08-11T15:01:29Z","abstract_excerpt":"We systematically investigate finite-difference (FD) derivative computation in Physics-Informed Neural Networks (PINNs) as an alternative to automatic differentiation (AD). On three benchmark PDEs we show that, with a properly calibrated step size, FD matches AD in accuracy on every problem while running faster across the full tested batch-size range and using substantially less GPU memory, and that a stochastic variant we propose outperforms AD on a stationary problem. We further show that for neural architectures with inter-sample dependencies (e.g. BatchNorm, self-attention) the standard Py"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11020","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/2608.11020/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":"2026-08-12T01:24:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0wPsrenApaVagl6WhU0H6WJ2WQEbH/cNFCcMd6o35auG5dp3+jnJs1fBrMU5O0wmbTW4DRVb6qj3NBBC3Oc5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T00:31:02.290723Z"},"content_sha256":"9355364285b21a77bd598fa4a546d7a396afa8f2dde83794c1d0987249056254","schema_version":"1.0","event_id":"sha256:9355364285b21a77bd598fa4a546d7a396afa8f2dde83794c1d0987249056254"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HM7AEPVPGFRNFJMOB5RQPAJIG6/bundle.json","state_url":"https://pith.science/pith/HM7AEPVPGFRNFJMOB5RQPAJIG6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HM7AEPVPGFRNFJMOB5RQPAJIG6/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":"2026-08-16T00:31:02Z","links":{"resolver":"https://pith.science/pith/HM7AEPVPGFRNFJMOB5RQPAJIG6","bundle":"https://pith.science/pith/HM7AEPVPGFRNFJMOB5RQPAJIG6/bundle.json","state":"https://pith.science/pith/HM7AEPVPGFRNFJMOB5RQPAJIG6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HM7AEPVPGFRNFJMOB5RQPAJIG6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HM7AEPVPGFRNFJMOB5RQPAJIG6","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":"b0b016e3cc3a72144c25251c45abdae47b50a0f742711c68f9f119f6fdf8d8f5","cross_cats_sorted":["cs.NA","math.NA","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-11T15:01:29Z","title_canon_sha256":"e44c18115bd16b6b66f4260de417de45b5376f09432de12406536b94ec664865"},"schema_version":"1.0","source":{"id":"2608.11020","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.11020","created_at":"2026-08-12T01:24:05Z"},{"alias_kind":"arxiv_version","alias_value":"2608.11020v1","created_at":"2026-08-12T01:24:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.11020","created_at":"2026-08-12T01:24:05Z"},{"alias_kind":"pith_short_12","alias_value":"HM7AEPVPGFRN","created_at":"2026-08-12T01:24:05Z"},{"alias_kind":"pith_short_16","alias_value":"HM7AEPVPGFRNFJMO","created_at":"2026-08-12T01:24:05Z"},{"alias_kind":"pith_short_8","alias_value":"HM7AEPVP","created_at":"2026-08-12T01:24:05Z"}],"graph_snapshots":[{"event_id":"sha256:9355364285b21a77bd598fa4a546d7a396afa8f2dde83794c1d0987249056254","target":"graph","created_at":"2026-08-12T01:24:05Z","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/2608.11020/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We systematically investigate finite-difference (FD) derivative computation in Physics-Informed Neural Networks (PINNs) as an alternative to automatic differentiation (AD). On three benchmark PDEs we show that, with a properly calibrated step size, FD matches AD in accuracy on every problem while running faster across the full tested batch-size range and using substantially less GPU memory, and that a stochastic variant we propose outperforms AD on a stationary problem. We further show that for neural architectures with inter-sample dependencies (e.g. BatchNorm, self-attention) the standard Py","authors_text":"Maciej J. Mikulski, Tadeusz Uhl","cross_cats":["cs.NA","math.NA","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-11T15:01:29Z","title":"Derivative Computation in PINNs: Automatic Differentiation, Finite Differences and Beyond"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11020","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:a1bbb5273b93f9d88f6caf0626cb706785a6c8ad948c3524350e4709d2281d13","target":"record","created_at":"2026-08-12T01:24:05Z","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":"b0b016e3cc3a72144c25251c45abdae47b50a0f742711c68f9f119f6fdf8d8f5","cross_cats_sorted":["cs.NA","math.NA","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-08-11T15:01:29Z","title_canon_sha256":"e44c18115bd16b6b66f4260de417de45b5376f09432de12406536b94ec664865"},"schema_version":"1.0","source":{"id":"2608.11020","kind":"arxiv","version":1}},"canonical_sha256":"3b3e023eaf3162d2a58e0f6307812837b9938ad4e6c44c76154665824ca1b5f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b3e023eaf3162d2a58e0f6307812837b9938ad4e6c44c76154665824ca1b5f8","first_computed_at":"2026-08-12T01:24:05.094847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-12T01:24:05.094847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B6AF1zgNR2isoMCgy4DV9U9jFNm9y8dkRfPJfJTBwHJWdRYtdxbggG38ErHMQSUFWiff493YAHZHwJomjlzQBQ==","signature_status":"signed_v1","signed_at":"2026-08-12T01:24:05.096607Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.11020","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1bbb5273b93f9d88f6caf0626cb706785a6c8ad948c3524350e4709d2281d13","sha256:9355364285b21a77bd598fa4a546d7a396afa8f2dde83794c1d0987249056254"],"state_sha256":"0d1c67ed5870060658c193c3165ee6ce47c433ca6f3e4d095aac5b5131a881ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z9a8Egp8kVO3GdWG36r6tNH//lJRF7gkBipyJRvDEaK82pRERSJszKH6IHMu67UNx6+2mEJR2PmjypIvsjhyBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T00:31:02.296500Z","bundle_sha256":"c814179241042df06f4eb680c001dd623139d23a2bdadc33adcefe3778fbc058"}}