{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GA42Q46CRHU3JIUXC4B372QU62","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":"fabf42a1d9189135a370be8724de6a19ce7cb274ea3b4c6555e7b40aa96e4531","cross_cats_sorted":["astro-ph.GA","gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2018-02-28T01:28:32Z","title_canon_sha256":"09c8a312d629d2ce696f984a12276ca6bcb1c6ef1750ba134e60a2ec67f0a1a2"},"schema_version":"1.0","source":{"id":"1803.00003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00003","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00003v1","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00003","created_at":"2026-05-18T00:22:15Z"},{"alias_kind":"pith_short_12","alias_value":"GA42Q46CRHU3","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GA42Q46CRHU3JIUX","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GA42Q46C","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:97df4caf6e0bac07c9c357959fb97c484a752130571b6ef3d510c1b112973792","target":"graph","created_at":"2026-05-18T00:22:15Z","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"},"paper":{"abstract_excerpt":"New exact solutions are derived for the gravitational potential inside and outside a homogeneous torus as rapidly converging series of toroidal harmonics. The approach consists of splitting the inter- nal potential into a known solution to Poisson's equation plus some solution to Laplace's equation. The full solutions are then obtained using two equivalent methods, applying differential boundary conditions at the surface, or evaluating a surface integral derived from Green's third identity. This surface integral may not have been published before and is general to all geometries and volume den","authors_text":"Matt Majic","cross_cats":["astro-ph.GA","gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2018-02-28T01:28:32Z","title":"Exact gravitational potential of a homogeneous torus in toroidal coordinates and a surface integral approach to Poisson's equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00003","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:d2f91e5633ba8923a9092fefc02a946c423b799e4335c6ca15b943ad64743bc2","target":"record","created_at":"2026-05-18T00:22:15Z","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":"fabf42a1d9189135a370be8724de6a19ce7cb274ea3b4c6555e7b40aa96e4531","cross_cats_sorted":["astro-ph.GA","gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2018-02-28T01:28:32Z","title_canon_sha256":"09c8a312d629d2ce696f984a12276ca6bcb1c6ef1750ba134e60a2ec67f0a1a2"},"schema_version":"1.0","source":{"id":"1803.00003","kind":"arxiv","version":1}},"canonical_sha256":"3039a873c289e9b4a2971703bfea14f6a5e1fdea5c8120256f3f26271cbc7b9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3039a873c289e9b4a2971703bfea14f6a5e1fdea5c8120256f3f26271cbc7b9a","first_computed_at":"2026-05-18T00:22:15.546128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:15.546128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TX1O01snx77e04Q2zwPhqahFOF1H8Qz6I7q9Yefajmyz2HQVGEWSNtttdKBL+tf+KiVfalNFRyz4H4AUj+UhAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:15.546755Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.00003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2f91e5633ba8923a9092fefc02a946c423b799e4335c6ca15b943ad64743bc2","sha256:97df4caf6e0bac07c9c357959fb97c484a752130571b6ef3d510c1b112973792"],"state_sha256":"25d3173d5a27e2254953a3ac334ab16370f225c200ef88916ede77feac45cafd"}