{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:FPFXDGODO5BGJGGXWC3PBNTHDC","short_pith_number":"pith:FPFXDGOD","canonical_record":{"source":{"id":"2605.24774","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-23T23:26:48Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"2510c91f43baa117f9d7ce66cbeab048fa5c2c0e3a5b1e3db38d4eaceb4dba04","abstract_canon_sha256":"c3479c9aa1d080f3d2ddc48b7b17214f2ada7a128f2752568eb4b4c5ced4ca22"},"schema_version":"1.0"},"canonical_sha256":"2bcb7199c377426498d7b0b6f0b66718b30b93df97d2d8e3633dfc562ca738bb","source":{"kind":"arxiv","id":"2605.24774","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.24774","created_at":"2026-05-26T01:03:57Z"},{"alias_kind":"arxiv_version","alias_value":"2605.24774v1","created_at":"2026-05-26T01:03:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24774","created_at":"2026-05-26T01:03:57Z"},{"alias_kind":"pith_short_12","alias_value":"FPFXDGODO5BG","created_at":"2026-05-26T01:03:57Z"},{"alias_kind":"pith_short_16","alias_value":"FPFXDGODO5BGJGGX","created_at":"2026-05-26T01:03:57Z"},{"alias_kind":"pith_short_8","alias_value":"FPFXDGOD","created_at":"2026-05-26T01:03:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:FPFXDGODO5BGJGGXWC3PBNTHDC","target":"record","payload":{"canonical_record":{"source":{"id":"2605.24774","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-23T23:26:48Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"2510c91f43baa117f9d7ce66cbeab048fa5c2c0e3a5b1e3db38d4eaceb4dba04","abstract_canon_sha256":"c3479c9aa1d080f3d2ddc48b7b17214f2ada7a128f2752568eb4b4c5ced4ca22"},"schema_version":"1.0"},"canonical_sha256":"2bcb7199c377426498d7b0b6f0b66718b30b93df97d2d8e3633dfc562ca738bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:03:57.532966Z","signature_b64":"0xLDXaxOyXPCuYBiQSjH68U4KG88yIyZ5o4B5hw6SkFtdqpZgj1iXgLHy192u9eVSNMXCb76/dT29KdCEyzxAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2bcb7199c377426498d7b0b6f0b66718b30b93df97d2d8e3633dfc562ca738bb","last_reissued_at":"2026-05-26T01:03:57.532244Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:03:57.532244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.24774","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":"2026-05-26T01:03:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LDvQgUUn+l2C05e2ZEtf3sE7/+6t2pBxmthJighZU9207HSAoCG+y7kjueIvW8+8FQgHjKkR52cPHY68aalIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:16:26.780791Z"},"content_sha256":"b3c9f4f25e8e8a651f0a4497bcd87e6202f1bdf8b9bdc7d780f9f6a646db82a0","schema_version":"1.0","event_id":"sha256:b3c9f4f25e8e8a651f0a4497bcd87e6202f1bdf8b9bdc7d780f9f6a646db82a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:FPFXDGODO5BGJGGXWC3PBNTHDC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hermite-NGP: Gradient-Augmented Hash Encoding for Learning PDEs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"Bo Zhu, Jinjin He, Sinan Wang, Zhiqi Li","submitted_at":"2026-05-23T23:26:48Z","abstract_excerpt":"We propose Hermite-NGP, a gradient-augmented multi-resolution hash encoding designed to enable fast and accurate computation of spatial derivatives for neural PDE solvers. Unlike existing NGP-based approaches that rely on automatic differentiation or finite differences and suffer from instability or high cost, Hermite-NGP explicitly stores function values and mixed partial derivatives at hash grid vertices, allowing fully analytic evaluation of gradients, Jacobians, and Hessians via Hermite interpolation. This design preserves the efficiency and spatial adaptivity of NGP while supporting analy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24774","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/2605.24774/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":"2026-05-26T01:03:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"idZRB0DNMNNoZBo4iWWyULeBvRifKV10y81GUpQNExYdNvS/AlDOZEW5UNa5VT240d8PIXc/nd1Ip4tBNPe+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:16:26.781764Z"},"content_sha256":"23af74d67a9c85d24f4bb279234860db73af1d6fc4bf1b2b1d4c5b4c266fb117","schema_version":"1.0","event_id":"sha256:23af74d67a9c85d24f4bb279234860db73af1d6fc4bf1b2b1d4c5b4c266fb117"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FPFXDGODO5BGJGGXWC3PBNTHDC/bundle.json","state_url":"https://pith.science/pith/FPFXDGODO5BGJGGXWC3PBNTHDC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FPFXDGODO5BGJGGXWC3PBNTHDC/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":"2026-05-31T17:16:26Z","links":{"resolver":"https://pith.science/pith/FPFXDGODO5BGJGGXWC3PBNTHDC","bundle":"https://pith.science/pith/FPFXDGODO5BGJGGXWC3PBNTHDC/bundle.json","state":"https://pith.science/pith/FPFXDGODO5BGJGGXWC3PBNTHDC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FPFXDGODO5BGJGGXWC3PBNTHDC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FPFXDGODO5BGJGGXWC3PBNTHDC","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":"c3479c9aa1d080f3d2ddc48b7b17214f2ada7a128f2752568eb4b4c5ced4ca22","cross_cats_sorted":["physics.comp-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-23T23:26:48Z","title_canon_sha256":"2510c91f43baa117f9d7ce66cbeab048fa5c2c0e3a5b1e3db38d4eaceb4dba04"},"schema_version":"1.0","source":{"id":"2605.24774","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.24774","created_at":"2026-05-26T01:03:57Z"},{"alias_kind":"arxiv_version","alias_value":"2605.24774v1","created_at":"2026-05-26T01:03:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24774","created_at":"2026-05-26T01:03:57Z"},{"alias_kind":"pith_short_12","alias_value":"FPFXDGODO5BG","created_at":"2026-05-26T01:03:57Z"},{"alias_kind":"pith_short_16","alias_value":"FPFXDGODO5BGJGGX","created_at":"2026-05-26T01:03:57Z"},{"alias_kind":"pith_short_8","alias_value":"FPFXDGOD","created_at":"2026-05-26T01:03:57Z"}],"graph_snapshots":[{"event_id":"sha256:23af74d67a9c85d24f4bb279234860db73af1d6fc4bf1b2b1d4c5b4c266fb117","target":"graph","created_at":"2026-05-26T01:03:57Z","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/2605.24774/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose Hermite-NGP, a gradient-augmented multi-resolution hash encoding designed to enable fast and accurate computation of spatial derivatives for neural PDE solvers. Unlike existing NGP-based approaches that rely on automatic differentiation or finite differences and suffer from instability or high cost, Hermite-NGP explicitly stores function values and mixed partial derivatives at hash grid vertices, allowing fully analytic evaluation of gradients, Jacobians, and Hessians via Hermite interpolation. This design preserves the efficiency and spatial adaptivity of NGP while supporting analy","authors_text":"Bo Zhu, Jinjin He, Sinan Wang, Zhiqi Li","cross_cats":["physics.comp-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-23T23:26:48Z","title":"Hermite-NGP: Gradient-Augmented Hash Encoding for Learning PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24774","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:b3c9f4f25e8e8a651f0a4497bcd87e6202f1bdf8b9bdc7d780f9f6a646db82a0","target":"record","created_at":"2026-05-26T01:03:57Z","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":"c3479c9aa1d080f3d2ddc48b7b17214f2ada7a128f2752568eb4b4c5ced4ca22","cross_cats_sorted":["physics.comp-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-23T23:26:48Z","title_canon_sha256":"2510c91f43baa117f9d7ce66cbeab048fa5c2c0e3a5b1e3db38d4eaceb4dba04"},"schema_version":"1.0","source":{"id":"2605.24774","kind":"arxiv","version":1}},"canonical_sha256":"2bcb7199c377426498d7b0b6f0b66718b30b93df97d2d8e3633dfc562ca738bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bcb7199c377426498d7b0b6f0b66718b30b93df97d2d8e3633dfc562ca738bb","first_computed_at":"2026-05-26T01:03:57.532244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:03:57.532244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0xLDXaxOyXPCuYBiQSjH68U4KG88yIyZ5o4B5hw6SkFtdqpZgj1iXgLHy192u9eVSNMXCb76/dT29KdCEyzxAw==","signature_status":"signed_v1","signed_at":"2026-05-26T01:03:57.532966Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.24774","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3c9f4f25e8e8a651f0a4497bcd87e6202f1bdf8b9bdc7d780f9f6a646db82a0","sha256:23af74d67a9c85d24f4bb279234860db73af1d6fc4bf1b2b1d4c5b4c266fb117"],"state_sha256":"dcab15bf92e58eff6c1d993e23d7c9ea7f6c2ce06a316c1300e8a4ba32791445"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RTaRsYxoA/xZnHw0iCTuZs9eKa3cEkweQgYyB10HTh5DdjiEYxbkjskZqxVxpFDrkcwa7jnZXiZ8JF/r5KMoBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T17:16:26.786414Z","bundle_sha256":"4aab8cd5c0d84ad30dd332f78422e3f11200c9d45d9c62fe85d14117313ae52c"}}