{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:PLPCBM3MXPZ2GLJLHL2HNTZ5I3","short_pith_number":"pith:PLPCBM3M","canonical_record":{"source":{"id":"1908.03222","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2019-08-08T18:01:09Z","cross_cats_sorted":["astro-ph.IM"],"title_canon_sha256":"c002263871ce0627b05ae3a23419208407c93761f7e42b77d00a4734e1b8bd2d","abstract_canon_sha256":"ca932f7745100e928bdaca60416858537b4d99ac92b9d7909b0c35eb3f1c3b5c"},"schema_version":"1.0"},"canonical_sha256":"7ade20b36cbbf3a32d2b3af476cf3d46f185c2c9d9ebed6e76590e8ec1c4c361","source":{"kind":"arxiv","id":"1908.03222","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03222","created_at":"2026-07-05T00:45:08Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03222v2","created_at":"2026-07-05T00:45:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03222","created_at":"2026-07-05T00:45:08Z"},{"alias_kind":"pith_short_12","alias_value":"PLPCBM3MXPZ2","created_at":"2026-07-05T00:45:08Z"},{"alias_kind":"pith_short_16","alias_value":"PLPCBM3MXPZ2GLJL","created_at":"2026-07-05T00:45:08Z"},{"alias_kind":"pith_short_8","alias_value":"PLPCBM3M","created_at":"2026-07-05T00:45:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:PLPCBM3MXPZ2GLJLHL2HNTZ5I3","target":"record","payload":{"canonical_record":{"source":{"id":"1908.03222","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2019-08-08T18:01:09Z","cross_cats_sorted":["astro-ph.IM"],"title_canon_sha256":"c002263871ce0627b05ae3a23419208407c93761f7e42b77d00a4734e1b8bd2d","abstract_canon_sha256":"ca932f7745100e928bdaca60416858537b4d99ac92b9d7909b0c35eb3f1c3b5c"},"schema_version":"1.0"},"canonical_sha256":"7ade20b36cbbf3a32d2b3af476cf3d46f185c2c9d9ebed6e76590e8ec1c4c361","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:45:08.280078Z","signature_b64":"66wX8PNXJhHMdtBY7k58fqgoo40FqoZgRg2Lk1fRZ4BHP1u+/8oBiTHktcVjvmqwJwsbM3PnWiBo9MrqsNFhAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ade20b36cbbf3a32d2b3af476cf3d46f185c2c9d9ebed6e76590e8ec1c4c361","last_reissued_at":"2026-07-05T00:45:08.279688Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:45:08.279688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.03222","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:45:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5PKLQIlvyfPrr19bjuwsuEuY6YaSUYROjg9LtFDkGDlO0qyeNx2G9a0NvExCMW61U/N3DlCEuke6TgwkTJCQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T05:26:39.612973Z"},"content_sha256":"399ac353b01389fe64569da9b8bf7d2e5c6e7ab0b7d31b59b5f3f3eb8b02db4e","schema_version":"1.0","event_id":"sha256:399ac353b01389fe64569da9b8bf7d2e5c6e7ab0b7d31b59b5f3f3eb8b02db4e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:PLPCBM3MXPZ2GLJLHL2HNTZ5I3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytic Planetary Transit Light Curves and Derivatives for Stars with Polynomial Limb Darkening","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.IM"],"primary_cat":"astro-ph.EP","authors_text":"Daniel Foreman-Mackey, Eric Agol, Rodrigo Luger","submitted_at":"2019-08-08T18:01:09Z","abstract_excerpt":"We derive analytic, closed-form solutions for the light curve of a planet transiting a star with a limb darkening profile which is a polynomial function of the stellar elevation, up to arbitrary integer order. We provide improved analytic expressions for the uniform, linear, and quadratic limb-darkened cases, as well as novel expressions for higher order integer powers of limb darkening. The formulae are crafted to be numerically stable over the expected range of usage. We additionally present analytic formulae for the partial derivatives of instantaneous flux with respect to the radius ratio,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03222","kind":"arxiv","version":2},"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/1908.03222/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":"2026-07-05T00:45:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kWh00r5qrIeLCgigFjX4BNI0TV4k2IBXSbawf32BpbMZg4jiFBDvAh7EOkt6EtwoPRnpsmmjorrY5Z64do+zBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T05:26:39.613906Z"},"content_sha256":"ae7e049caf27daa1b2b29d6ca827824afb7f77a6948bcc158443c3c894a37792","schema_version":"1.0","event_id":"sha256:ae7e049caf27daa1b2b29d6ca827824afb7f77a6948bcc158443c3c894a37792"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PLPCBM3MXPZ2GLJLHL2HNTZ5I3/bundle.json","state_url":"https://pith.science/pith/PLPCBM3MXPZ2GLJLHL2HNTZ5I3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PLPCBM3MXPZ2GLJLHL2HNTZ5I3/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":"2026-08-16T05:26:39Z","links":{"resolver":"https://pith.science/pith/PLPCBM3MXPZ2GLJLHL2HNTZ5I3","bundle":"https://pith.science/pith/PLPCBM3MXPZ2GLJLHL2HNTZ5I3/bundle.json","state":"https://pith.science/pith/PLPCBM3MXPZ2GLJLHL2HNTZ5I3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PLPCBM3MXPZ2GLJLHL2HNTZ5I3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PLPCBM3MXPZ2GLJLHL2HNTZ5I3","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":"ca932f7745100e928bdaca60416858537b4d99ac92b9d7909b0c35eb3f1c3b5c","cross_cats_sorted":["astro-ph.IM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2019-08-08T18:01:09Z","title_canon_sha256":"c002263871ce0627b05ae3a23419208407c93761f7e42b77d00a4734e1b8bd2d"},"schema_version":"1.0","source":{"id":"1908.03222","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03222","created_at":"2026-07-05T00:45:08Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03222v2","created_at":"2026-07-05T00:45:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03222","created_at":"2026-07-05T00:45:08Z"},{"alias_kind":"pith_short_12","alias_value":"PLPCBM3MXPZ2","created_at":"2026-07-05T00:45:08Z"},{"alias_kind":"pith_short_16","alias_value":"PLPCBM3MXPZ2GLJL","created_at":"2026-07-05T00:45:08Z"},{"alias_kind":"pith_short_8","alias_value":"PLPCBM3M","created_at":"2026-07-05T00:45:08Z"}],"graph_snapshots":[{"event_id":"sha256:ae7e049caf27daa1b2b29d6ca827824afb7f77a6948bcc158443c3c894a37792","target":"graph","created_at":"2026-07-05T00:45:08Z","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/1908.03222/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive analytic, closed-form solutions for the light curve of a planet transiting a star with a limb darkening profile which is a polynomial function of the stellar elevation, up to arbitrary integer order. We provide improved analytic expressions for the uniform, linear, and quadratic limb-darkened cases, as well as novel expressions for higher order integer powers of limb darkening. The formulae are crafted to be numerically stable over the expected range of usage. We additionally present analytic formulae for the partial derivatives of instantaneous flux with respect to the radius ratio,","authors_text":"Daniel Foreman-Mackey, Eric Agol, Rodrigo Luger","cross_cats":["astro-ph.IM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2019-08-08T18:01:09Z","title":"Analytic Planetary Transit Light Curves and Derivatives for Stars with Polynomial Limb Darkening"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03222","kind":"arxiv","version":2},"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":"sha256:399ac353b01389fe64569da9b8bf7d2e5c6e7ab0b7d31b59b5f3f3eb8b02db4e","target":"record","created_at":"2026-07-05T00:45:08Z","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":"ca932f7745100e928bdaca60416858537b4d99ac92b9d7909b0c35eb3f1c3b5c","cross_cats_sorted":["astro-ph.IM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2019-08-08T18:01:09Z","title_canon_sha256":"c002263871ce0627b05ae3a23419208407c93761f7e42b77d00a4734e1b8bd2d"},"schema_version":"1.0","source":{"id":"1908.03222","kind":"arxiv","version":2}},"canonical_sha256":"7ade20b36cbbf3a32d2b3af476cf3d46f185c2c9d9ebed6e76590e8ec1c4c361","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ade20b36cbbf3a32d2b3af476cf3d46f185c2c9d9ebed6e76590e8ec1c4c361","first_computed_at":"2026-07-05T00:45:08.279688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:45:08.279688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"66wX8PNXJhHMdtBY7k58fqgoo40FqoZgRg2Lk1fRZ4BHP1u+/8oBiTHktcVjvmqwJwsbM3PnWiBo9MrqsNFhAA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:45:08.280078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03222","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:399ac353b01389fe64569da9b8bf7d2e5c6e7ab0b7d31b59b5f3f3eb8b02db4e","sha256:ae7e049caf27daa1b2b29d6ca827824afb7f77a6948bcc158443c3c894a37792"],"state_sha256":"0bb68a931ac1a92203a47951391e5bbd56a1f29c2d504fbf12052de49d3cb4ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0VhalQ5IJ2xhVnC4kVtguZlB+Zd4z6iaKJAfgiBl2bcmBY6DTre1KMjfGFNrt0gg1MSRhdgH5Bpu6i3J1wL1AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T05:26:39.619728Z","bundle_sha256":"e73f21e81f9532d2c9be39e4322e36fe6963f35c3860e00a9b11e9824eb91c9a"}}