{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:BZ4NCRIUOHBXTMQ2C4ZVW3RZN7","short_pith_number":"pith:BZ4NCRIU","canonical_record":{"source":{"id":"2607.06002","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-07-07T08:43:39Z","cross_cats_sorted":[],"title_canon_sha256":"d106b3d8716537972e3f367700607869294ae089c81529f5c31b70ee8b14277b","abstract_canon_sha256":"fb0c841c359616a30cb5460fe34723a51e08897ea379dcfc029939d9c1ce8194"},"schema_version":"1.0"},"canonical_sha256":"0e78d1451471c379b21a17335b6e396fd3c4afba40cd03bf87851ccff9f77b2f","source":{"kind":"arxiv","id":"2607.06002","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06002","created_at":"2026-07-08T01:18:52Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06002v1","created_at":"2026-07-08T01:18:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06002","created_at":"2026-07-08T01:18:52Z"},{"alias_kind":"pith_short_12","alias_value":"BZ4NCRIUOHBX","created_at":"2026-07-08T01:18:52Z"},{"alias_kind":"pith_short_16","alias_value":"BZ4NCRIUOHBXTMQ2","created_at":"2026-07-08T01:18:52Z"},{"alias_kind":"pith_short_8","alias_value":"BZ4NCRIU","created_at":"2026-07-08T01:18:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:BZ4NCRIUOHBXTMQ2C4ZVW3RZN7","target":"record","payload":{"canonical_record":{"source":{"id":"2607.06002","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-07-07T08:43:39Z","cross_cats_sorted":[],"title_canon_sha256":"d106b3d8716537972e3f367700607869294ae089c81529f5c31b70ee8b14277b","abstract_canon_sha256":"fb0c841c359616a30cb5460fe34723a51e08897ea379dcfc029939d9c1ce8194"},"schema_version":"1.0"},"canonical_sha256":"0e78d1451471c379b21a17335b6e396fd3c4afba40cd03bf87851ccff9f77b2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-08T01:18:52.906954Z","signature_b64":"d7eX4Egbm+Af2GMUXpKbyh/2kRQHEb8hqkQUtsSrHNIhM7MKq3+Rjm4JTel4GrsU9VkER19eYtqS/mEPh8irCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e78d1451471c379b21a17335b6e396fd3c4afba40cd03bf87851ccff9f77b2f","last_reissued_at":"2026-07-08T01:18:52.906376Z","signature_status":"signed_v1","first_computed_at":"2026-07-08T01:18:52.906376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.06002","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":"2026-07-08T01:18:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1ScbBT9/LpTah/lmpXCKVmzxaUNZOpkJNstRscD/TKJCQxvTMBLjMkDgznjDvrWly9BSchSU/C9BAc2ZP+vhCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T23:48:33.930580Z"},"content_sha256":"069371b983a5988456f7e25679901269bb65216aa14e80bdee687e1c920b294f","schema_version":"1.0","event_id":"sha256:069371b983a5988456f7e25679901269bb65216aa14e80bdee687e1c920b294f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:BZ4NCRIUOHBXTMQ2C4ZVW3RZN7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving Hamiltonian Constraint Equation with Physics-Informed Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Hao Ma, Hong-Bo Jin, Shuanglin Huang, Tailin Wu, Xuefeng Feng, Yu-Chen Zhou, Yue-Liang Wu, Zhi-Chao Zhao, Zhoujian Cao","submitted_at":"2026-07-07T08:43:39Z","abstract_excerpt":"Numerical relativity (NR), solving Einstein equation numerically, plays an important role in source modelling for gravitational wave astronomy. Traditional methods for NR including finite difference method, spectral method and finite element method have been well developed. But newly developed neural network methods for partial differential equations (PDE) have not been well studied yet for NR. We present a Physics-Informed Neural Network (PINN) method to solve the Hamiltonian constraint equation for binary black hole (BBH) initial data in NR. This equation is a highly non-linear elliptic PDE,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06002","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/2607.06002/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":"2026-07-08T01:18:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vZvKdTNMChCXOkoGfWZ3Wi+76jdGd6D1UE2Y4h1mUlKYY3MVUuIfAxxoW4BEM38DjhfmAnFjOmFJqhr1ad3OBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T23:48:33.931190Z"},"content_sha256":"69d6f3028adafe536c753cec82ccb2371bb3b730a7441ee629075360b2872343","schema_version":"1.0","event_id":"sha256:69d6f3028adafe536c753cec82ccb2371bb3b730a7441ee629075360b2872343"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BZ4NCRIUOHBXTMQ2C4ZVW3RZN7/bundle.json","state_url":"https://pith.science/pith/BZ4NCRIUOHBXTMQ2C4ZVW3RZN7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BZ4NCRIUOHBXTMQ2C4ZVW3RZN7/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":"2026-08-18T23:48:33Z","links":{"resolver":"https://pith.science/pith/BZ4NCRIUOHBXTMQ2C4ZVW3RZN7","bundle":"https://pith.science/pith/BZ4NCRIUOHBXTMQ2C4ZVW3RZN7/bundle.json","state":"https://pith.science/pith/BZ4NCRIUOHBXTMQ2C4ZVW3RZN7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BZ4NCRIUOHBXTMQ2C4ZVW3RZN7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BZ4NCRIUOHBXTMQ2C4ZVW3RZN7","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":"fb0c841c359616a30cb5460fe34723a51e08897ea379dcfc029939d9c1ce8194","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-07-07T08:43:39Z","title_canon_sha256":"d106b3d8716537972e3f367700607869294ae089c81529f5c31b70ee8b14277b"},"schema_version":"1.0","source":{"id":"2607.06002","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06002","created_at":"2026-07-08T01:18:52Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06002v1","created_at":"2026-07-08T01:18:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06002","created_at":"2026-07-08T01:18:52Z"},{"alias_kind":"pith_short_12","alias_value":"BZ4NCRIUOHBX","created_at":"2026-07-08T01:18:52Z"},{"alias_kind":"pith_short_16","alias_value":"BZ4NCRIUOHBXTMQ2","created_at":"2026-07-08T01:18:52Z"},{"alias_kind":"pith_short_8","alias_value":"BZ4NCRIU","created_at":"2026-07-08T01:18:52Z"}],"graph_snapshots":[{"event_id":"sha256:69d6f3028adafe536c753cec82ccb2371bb3b730a7441ee629075360b2872343","target":"graph","created_at":"2026-07-08T01:18:52Z","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/2607.06002/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Numerical relativity (NR), solving Einstein equation numerically, plays an important role in source modelling for gravitational wave astronomy. Traditional methods for NR including finite difference method, spectral method and finite element method have been well developed. But newly developed neural network methods for partial differential equations (PDE) have not been well studied yet for NR. We present a Physics-Informed Neural Network (PINN) method to solve the Hamiltonian constraint equation for binary black hole (BBH) initial data in NR. This equation is a highly non-linear elliptic PDE,","authors_text":"Hao Ma, Hong-Bo Jin, Shuanglin Huang, Tailin Wu, Xuefeng Feng, Yu-Chen Zhou, Yue-Liang Wu, Zhi-Chao Zhao, Zhoujian Cao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-07-07T08:43:39Z","title":"Solving Hamiltonian Constraint Equation with Physics-Informed Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06002","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":"sha256:069371b983a5988456f7e25679901269bb65216aa14e80bdee687e1c920b294f","target":"record","created_at":"2026-07-08T01:18:52Z","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":"fb0c841c359616a30cb5460fe34723a51e08897ea379dcfc029939d9c1ce8194","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-07-07T08:43:39Z","title_canon_sha256":"d106b3d8716537972e3f367700607869294ae089c81529f5c31b70ee8b14277b"},"schema_version":"1.0","source":{"id":"2607.06002","kind":"arxiv","version":1}},"canonical_sha256":"0e78d1451471c379b21a17335b6e396fd3c4afba40cd03bf87851ccff9f77b2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e78d1451471c379b21a17335b6e396fd3c4afba40cd03bf87851ccff9f77b2f","first_computed_at":"2026-07-08T01:18:52.906376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-08T01:18:52.906376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d7eX4Egbm+Af2GMUXpKbyh/2kRQHEb8hqkQUtsSrHNIhM7MKq3+Rjm4JTel4GrsU9VkER19eYtqS/mEPh8irCg==","signature_status":"signed_v1","signed_at":"2026-07-08T01:18:52.906954Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.06002","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:069371b983a5988456f7e25679901269bb65216aa14e80bdee687e1c920b294f","sha256:69d6f3028adafe536c753cec82ccb2371bb3b730a7441ee629075360b2872343"],"state_sha256":"2d6b75f77e0fdd74449109f4e5f5ad9371c7a289270a9087e88f5bc62e2ccabf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hufzsfE/THJ7e66kYLeomI18XVDaVkxdB9dAxnyw1WvExYcSmUtZcPfkAyJMVbrXNcAXEr3PiXLdAcf3EVFOAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T23:48:34.001803Z","bundle_sha256":"6e4acd39866ce40079a1edae2831f3e79a11c3b679b7be144cc30921286e9c14"}}