{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:JMTGK2KHLKCS46JZMRUOCQJB6Z","short_pith_number":"pith:JMTGK2KH","canonical_record":{"source":{"id":"2506.18860","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2025-06-23T17:22:11Z","cross_cats_sorted":["astro-ph.IM","astro-ph.SR"],"title_canon_sha256":"4934177b20ef75986d4518325b7c462e87fffc3efb0c9d239a30197c598095e9","abstract_canon_sha256":"c02ea162f36c057e7f5277383302ad3c476c39593f9f9ac11d799b3b003372e8"},"schema_version":"1.0"},"canonical_sha256":"4b266569475a852e79396468e14121f67954fcc15ab499e39ad9607661076e63","source":{"kind":"arxiv","id":"2506.18860","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.18860","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"2506.18860v3","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.18860","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"JMTGK2KHLKCS","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"pith_short_16","alias_value":"JMTGK2KHLKCS46JZ","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"pith_short_8","alias_value":"JMTGK2KH","created_at":"2026-06-02T01:03:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:JMTGK2KHLKCS46JZMRUOCQJB6Z","target":"record","payload":{"canonical_record":{"source":{"id":"2506.18860","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2025-06-23T17:22:11Z","cross_cats_sorted":["astro-ph.IM","astro-ph.SR"],"title_canon_sha256":"4934177b20ef75986d4518325b7c462e87fffc3efb0c9d239a30197c598095e9","abstract_canon_sha256":"c02ea162f36c057e7f5277383302ad3c476c39593f9f9ac11d799b3b003372e8"},"schema_version":"1.0"},"canonical_sha256":"4b266569475a852e79396468e14121f67954fcc15ab499e39ad9607661076e63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:03:32.386459Z","signature_b64":"Tmi8YYtOVGlflhlZcejjP3QqKqiCmX2L92fW/XGPohD5O94haUjM13KldDdge9XEwqihLlYhTLWfhyTYnPm8BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b266569475a852e79396468e14121f67954fcc15ab499e39ad9607661076e63","last_reissued_at":"2026-06-02T01:03:32.385893Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:03:32.385893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.18860","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T01:03:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SKqNGoUkk/0zTrxbsLc7H+7C86zB1c6M191IjFg/+BzNRn33fsj/ITZAg46r/exLqYuBuipvn0GXvBkaXGEnBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T04:10:03.411977Z"},"content_sha256":"0c0f333c598899d951cb51978cf5b2ee0467a23289bc5fc9c6309391e45f8f14","schema_version":"1.0","event_id":"sha256:0c0f333c598899d951cb51978cf5b2ee0467a23289bc5fc9c6309391e45f8f14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:JMTGK2KHLKCS46JZMRUOCQJB6Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytical transit light curves for arbitrary power-law limb darkening: a unified framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.IM","astro-ph.SR"],"primary_cat":"astro-ph.EP","authors_text":"Farrukh A. Chishtie, Mohammad I. Saeed, Shaukat N. Goderya","submitted_at":"2025-06-23T17:22:11Z","abstract_excerpt":"We present a unified analytical framework for computing exoplanet transit light curves under arbitrary real power-law limb darkening $I(\\mu)=I_0\\mu^\\alpha$, $\\alpha>-2$, eliminating the two-decade restriction to integer-polynomial forms. Our central result is an exact closed-form expression for the normalised stellar flux in terms of Appell's bivariate hypergeometric function $F_1$, valid for all real $\\alpha$ and all geometric transit configurations. Three mutually equivalent formulations -- a geometric kernel representation, a Riemann-Liouville fractional-calculus framework, and a hypergeome"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.18860","kind":"arxiv","version":3},"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/2506.18860/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":"2026-06-02T01:03:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LSK1iRFN4Ql4mq3A/a+CB1ysWcPwyOFZ3DUb9X8oB/XnzOVtw7gUm2l3fsJR5VDjkhMBJ1/txgXfWMCzD/CWAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T04:10:03.412699Z"},"content_sha256":"f46fade48ba60362eeeae2123826a3bd2e626ac49f1f6ccc29e6547e968b171d","schema_version":"1.0","event_id":"sha256:f46fade48ba60362eeeae2123826a3bd2e626ac49f1f6ccc29e6547e968b171d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JMTGK2KHLKCS46JZMRUOCQJB6Z/bundle.json","state_url":"https://pith.science/pith/JMTGK2KHLKCS46JZMRUOCQJB6Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JMTGK2KHLKCS46JZMRUOCQJB6Z/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":"2026-06-06T04:10:03Z","links":{"resolver":"https://pith.science/pith/JMTGK2KHLKCS46JZMRUOCQJB6Z","bundle":"https://pith.science/pith/JMTGK2KHLKCS46JZMRUOCQJB6Z/bundle.json","state":"https://pith.science/pith/JMTGK2KHLKCS46JZMRUOCQJB6Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JMTGK2KHLKCS46JZMRUOCQJB6Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:JMTGK2KHLKCS46JZMRUOCQJB6Z","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":"c02ea162f36c057e7f5277383302ad3c476c39593f9f9ac11d799b3b003372e8","cross_cats_sorted":["astro-ph.IM","astro-ph.SR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2025-06-23T17:22:11Z","title_canon_sha256":"4934177b20ef75986d4518325b7c462e87fffc3efb0c9d239a30197c598095e9"},"schema_version":"1.0","source":{"id":"2506.18860","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.18860","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"2506.18860v3","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.18860","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"JMTGK2KHLKCS","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"pith_short_16","alias_value":"JMTGK2KHLKCS46JZ","created_at":"2026-06-02T01:03:32Z"},{"alias_kind":"pith_short_8","alias_value":"JMTGK2KH","created_at":"2026-06-02T01:03:32Z"}],"graph_snapshots":[{"event_id":"sha256:f46fade48ba60362eeeae2123826a3bd2e626ac49f1f6ccc29e6547e968b171d","target":"graph","created_at":"2026-06-02T01:03:32Z","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/2506.18860/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a unified analytical framework for computing exoplanet transit light curves under arbitrary real power-law limb darkening $I(\\mu)=I_0\\mu^\\alpha$, $\\alpha>-2$, eliminating the two-decade restriction to integer-polynomial forms. Our central result is an exact closed-form expression for the normalised stellar flux in terms of Appell's bivariate hypergeometric function $F_1$, valid for all real $\\alpha$ and all geometric transit configurations. Three mutually equivalent formulations -- a geometric kernel representation, a Riemann-Liouville fractional-calculus framework, and a hypergeome","authors_text":"Farrukh A. Chishtie, Mohammad I. Saeed, Shaukat N. Goderya","cross_cats":["astro-ph.IM","astro-ph.SR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2025-06-23T17:22:11Z","title":"Analytical transit light curves for arbitrary power-law limb darkening: a unified framework"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.18860","kind":"arxiv","version":3},"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":"sha256:0c0f333c598899d951cb51978cf5b2ee0467a23289bc5fc9c6309391e45f8f14","target":"record","created_at":"2026-06-02T01:03:32Z","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":"c02ea162f36c057e7f5277383302ad3c476c39593f9f9ac11d799b3b003372e8","cross_cats_sorted":["astro-ph.IM","astro-ph.SR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2025-06-23T17:22:11Z","title_canon_sha256":"4934177b20ef75986d4518325b7c462e87fffc3efb0c9d239a30197c598095e9"},"schema_version":"1.0","source":{"id":"2506.18860","kind":"arxiv","version":3}},"canonical_sha256":"4b266569475a852e79396468e14121f67954fcc15ab499e39ad9607661076e63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b266569475a852e79396468e14121f67954fcc15ab499e39ad9607661076e63","first_computed_at":"2026-06-02T01:03:32.385893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:03:32.385893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tmi8YYtOVGlflhlZcejjP3QqKqiCmX2L92fW/XGPohD5O94haUjM13KldDdge9XEwqihLlYhTLWfhyTYnPm8BQ==","signature_status":"signed_v1","signed_at":"2026-06-02T01:03:32.386459Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.18860","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c0f333c598899d951cb51978cf5b2ee0467a23289bc5fc9c6309391e45f8f14","sha256:f46fade48ba60362eeeae2123826a3bd2e626ac49f1f6ccc29e6547e968b171d"],"state_sha256":"c3edb9640b8cf818fe47269b968a85dcc8d8cc1a5af3e82544ecdf00950fa8df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M0Bw3SJjzBovacXYY4kBN2ZkgfhiEgvVVu6wIYF7KToK2/xcG18z9rOA+Tz9ge+E5z8nPl5ukCQ5O1HiXV2wBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T04:10:03.416512Z","bundle_sha256":"d6266043677d025df3e6fe9769e6ce3c2b68e1d500d0acbc0044e4398c7b6032"}}