{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:JRY67KURH3SBPPF3LORVQGYBES","short_pith_number":"pith:JRY67KUR","canonical_record":{"source":{"id":"1804.10320","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-27T01:53:51Z","cross_cats_sorted":["astro-ph.IM","math.CA","physics.flu-dyn"],"title_canon_sha256":"ea80b1340bf020299acf9cde92d23d9c3c4dfe70005e127fb29ca4670f1b539e","abstract_canon_sha256":"26b55d76e67dd01ee07326bc9ba7376da90fc5f7121d51d09c9a3788df80e5ae"},"schema_version":"1.0"},"canonical_sha256":"4c71efaa913ee417bcbb5ba3581b01248e87ff5c43c5ea6a2a046118aa86ee57","source":{"kind":"arxiv","id":"1804.10320","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10320","created_at":"2026-05-18T00:17:21Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10320v1","created_at":"2026-05-18T00:17:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10320","created_at":"2026-05-18T00:17:21Z"},{"alias_kind":"pith_short_12","alias_value":"JRY67KURH3SB","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JRY67KURH3SBPPF3","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JRY67KUR","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:JRY67KURH3SBPPF3LORVQGYBES","target":"record","payload":{"canonical_record":{"source":{"id":"1804.10320","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-27T01:53:51Z","cross_cats_sorted":["astro-ph.IM","math.CA","physics.flu-dyn"],"title_canon_sha256":"ea80b1340bf020299acf9cde92d23d9c3c4dfe70005e127fb29ca4670f1b539e","abstract_canon_sha256":"26b55d76e67dd01ee07326bc9ba7376da90fc5f7121d51d09c9a3788df80e5ae"},"schema_version":"1.0"},"canonical_sha256":"4c71efaa913ee417bcbb5ba3581b01248e87ff5c43c5ea6a2a046118aa86ee57","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:21.122801Z","signature_b64":"MVsD7uTiRMkLR8vZWQlyUgIp7twtmsm2lL3iU1t7Es41exwdQpsPDVVlfoSt3Ljg9w5ehxgXM5ZZ0plv46hIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c71efaa913ee417bcbb5ba3581b01248e87ff5c43c5ea6a2a046118aa86ee57","last_reissued_at":"2026-05-18T00:17:21.122097Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:21.122097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.10320","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":"2026-05-18T00:17:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qg8VfvPjfaoO8VS+9gUXK+PnNeWbojVoOXCeTJB72b2jiQ2IHRA01pKdHqh1oG6157NfzqTGESskswJqdwZ6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:08:09.247981Z"},"content_sha256":"e6ec9efed716113fc04166dd685b2223ad6e5a483aae1edf762b2b869e799b0e","schema_version":"1.0","event_id":"sha256:e6ec9efed716113fc04166dd685b2223ad6e5a483aae1edf762b2b869e799b0e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:JRY67KURH3SBPPF3LORVQGYBES","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tensor calculus in spherical coordinates using Jacobi polynomials. Part-I: Mathematical analysis and derivations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.IM","math.CA","physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"Ben Brown, Daniel Lecoanet, Geoff Vasil, Jeff Oishi, Keaton Burns","submitted_at":"2018-04-27T01:53:51Z","abstract_excerpt":"This paper presents a method for the accurate and efficient computations on scalar, vector and tensor fields in three-dimensional spherical polar coordinates. The methods uses spin-weighted spherical harmonics in the angular directions and rescaled Jacobi polynomials in the radial direction. For the 2-sphere, spin-weighted harmonics allow for automating calculations in a fashion as similar to Fourier series as possible. Derivative operators act as wavenumber multiplication on a set of spectral coefficients. After transforming the angular directions, a set of orthogonal tensor rotations put the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10320","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":""},"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":"2026-05-18T00:17:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+nryw54okgR1BnyhvYPbY5wSMUmHff0kbQauAd703E4DV7Ah3GbslbA8zRoTj8/SUbWTTIXiSV6FLi/eCrhHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:08:09.248353Z"},"content_sha256":"8f9f70297cf55ab9dfbd030781d4cdeb122395bc07209f25b7c3f9284e31ddad","schema_version":"1.0","event_id":"sha256:8f9f70297cf55ab9dfbd030781d4cdeb122395bc07209f25b7c3f9284e31ddad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JRY67KURH3SBPPF3LORVQGYBES/bundle.json","state_url":"https://pith.science/pith/JRY67KURH3SBPPF3LORVQGYBES/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JRY67KURH3SBPPF3LORVQGYBES/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":"2026-05-27T09:08:09Z","links":{"resolver":"https://pith.science/pith/JRY67KURH3SBPPF3LORVQGYBES","bundle":"https://pith.science/pith/JRY67KURH3SBPPF3LORVQGYBES/bundle.json","state":"https://pith.science/pith/JRY67KURH3SBPPF3LORVQGYBES/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JRY67KURH3SBPPF3LORVQGYBES/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JRY67KURH3SBPPF3LORVQGYBES","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":"26b55d76e67dd01ee07326bc9ba7376da90fc5f7121d51d09c9a3788df80e5ae","cross_cats_sorted":["astro-ph.IM","math.CA","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-27T01:53:51Z","title_canon_sha256":"ea80b1340bf020299acf9cde92d23d9c3c4dfe70005e127fb29ca4670f1b539e"},"schema_version":"1.0","source":{"id":"1804.10320","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10320","created_at":"2026-05-18T00:17:21Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10320v1","created_at":"2026-05-18T00:17:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10320","created_at":"2026-05-18T00:17:21Z"},{"alias_kind":"pith_short_12","alias_value":"JRY67KURH3SB","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JRY67KURH3SBPPF3","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JRY67KUR","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:8f9f70297cf55ab9dfbd030781d4cdeb122395bc07209f25b7c3f9284e31ddad","target":"graph","created_at":"2026-05-18T00:17:21Z","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":"This paper presents a method for the accurate and efficient computations on scalar, vector and tensor fields in three-dimensional spherical polar coordinates. The methods uses spin-weighted spherical harmonics in the angular directions and rescaled Jacobi polynomials in the radial direction. For the 2-sphere, spin-weighted harmonics allow for automating calculations in a fashion as similar to Fourier series as possible. Derivative operators act as wavenumber multiplication on a set of spectral coefficients. After transforming the angular directions, a set of orthogonal tensor rotations put the","authors_text":"Ben Brown, Daniel Lecoanet, Geoff Vasil, Jeff Oishi, Keaton Burns","cross_cats":["astro-ph.IM","math.CA","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-27T01:53:51Z","title":"Tensor calculus in spherical coordinates using Jacobi polynomials. Part-I: Mathematical analysis and derivations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10320","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:e6ec9efed716113fc04166dd685b2223ad6e5a483aae1edf762b2b869e799b0e","target":"record","created_at":"2026-05-18T00:17:21Z","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":"26b55d76e67dd01ee07326bc9ba7376da90fc5f7121d51d09c9a3788df80e5ae","cross_cats_sorted":["astro-ph.IM","math.CA","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-27T01:53:51Z","title_canon_sha256":"ea80b1340bf020299acf9cde92d23d9c3c4dfe70005e127fb29ca4670f1b539e"},"schema_version":"1.0","source":{"id":"1804.10320","kind":"arxiv","version":1}},"canonical_sha256":"4c71efaa913ee417bcbb5ba3581b01248e87ff5c43c5ea6a2a046118aa86ee57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c71efaa913ee417bcbb5ba3581b01248e87ff5c43c5ea6a2a046118aa86ee57","first_computed_at":"2026-05-18T00:17:21.122097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:21.122097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MVsD7uTiRMkLR8vZWQlyUgIp7twtmsm2lL3iU1t7Es41exwdQpsPDVVlfoSt3Ljg9w5ehxgXM5ZZ0plv46hIAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:21.122801Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.10320","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6ec9efed716113fc04166dd685b2223ad6e5a483aae1edf762b2b869e799b0e","sha256:8f9f70297cf55ab9dfbd030781d4cdeb122395bc07209f25b7c3f9284e31ddad"],"state_sha256":"c59cd3f42fe50a14402b0c959f94c35f77fea5c1972caeeb36ef7c2526b52947"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F8I4z10aKLnO4wxxxPhyGJRdSN5pd9nRoW3XRxyDNrXi2CpSd0SfCnX/s816dWIu3Xr4m6+so0k20QB5oHUjAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:08:09.250609Z","bundle_sha256":"bb7a287e717b5cb0ab1365500d9cb8f3078bd49ad64f8b5019f9faccf2c4b66f"}}