{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LQPXINBMELPNDRVG4BGBGW7OQK","short_pith_number":"pith:LQPXINBM","canonical_record":{"source":{"id":"1405.0026","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2014-04-30T20:32:19Z","cross_cats_sorted":["physics.ao-ph"],"title_canon_sha256":"43849b5eb556317889eb30afbf3be353084cdae6edac30f126d4cd39c532c976","abstract_canon_sha256":"fe250bb88012c42b239915c96b207148f6e890530dfef2e7e459b4398af08517"},"schema_version":"1.0"},"canonical_sha256":"5c1f74342c22ded1c6a6e04c135bee8299e084f7cc107e63852e168aa1e05fd4","source":{"kind":"arxiv","id":"1405.0026","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0026","created_at":"2026-05-18T01:43:21Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0026v3","created_at":"2026-05-18T01:43:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0026","created_at":"2026-05-18T01:43:21Z"},{"alias_kind":"pith_short_12","alias_value":"LQPXINBMELPN","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LQPXINBMELPNDRVG","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LQPXINBM","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LQPXINBMELPNDRVG4BGBGW7OQK","target":"record","payload":{"canonical_record":{"source":{"id":"1405.0026","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2014-04-30T20:32:19Z","cross_cats_sorted":["physics.ao-ph"],"title_canon_sha256":"43849b5eb556317889eb30afbf3be353084cdae6edac30f126d4cd39c532c976","abstract_canon_sha256":"fe250bb88012c42b239915c96b207148f6e890530dfef2e7e459b4398af08517"},"schema_version":"1.0"},"canonical_sha256":"5c1f74342c22ded1c6a6e04c135bee8299e084f7cc107e63852e168aa1e05fd4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:43:21.205766Z","signature_b64":"npdAkN8X0x1OL5lxGH5+DJwEQkRtYv5+34efJLR/CUhdfuM+boLUKLa1XCX0fmt4MaiwLqyd85Cv5adqJCazBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c1f74342c22ded1c6a6e04c135bee8299e084f7cc107e63852e168aa1e05fd4","last_reissued_at":"2026-05-18T01:43:21.205006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:43:21.205006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.0026","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":"2026-05-18T01:43:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5QWMA79brot+nknbLl4B53vVh7wSDHyJO6xQQji82fEHO6BXFmwQAOrcnVyu7tKUQ5TjxJSJRAgcfIpKlCgOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:34:50.661921Z"},"content_sha256":"be238e34f6b582e243befd8d447ac568fe7a9cfa0200ae9f9b1ef3fb8e25992b","schema_version":"1.0","event_id":"sha256:be238e34f6b582e243befd8d447ac568fe7a9cfa0200ae9f9b1ef3fb8e25992b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LQPXINBMELPNDRVG4BGBGW7OQK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytical Models of Exoplanetary Atmospheres. II. Radiative Transfer via the Two-stream Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.ao-ph"],"primary_cat":"astro-ph.EP","authors_text":"Jae-Min Lee, Jo\\~ao M. Mendon\\c{c}a, Kevin Heng","submitted_at":"2014-04-30T20:32:19Z","abstract_excerpt":"We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior) and solutions for the temperature-pressure profiles. Generally, the problem is mathematically under-determined unless a set of closures (Eddi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0026","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":""},"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":"2026-05-18T01:43:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GHQHyjZYYHv1pkDFi09ImMbZ/U4JabX66K7TgZk2/d/LKoEBJ9S80Fkarx++Y6J3iFwbvS8xGRm7SeaOUd50AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:34:50.662567Z"},"content_sha256":"d8bb932d65a975b2b3d149b559b779b9a46fb2c9b91e628f49dec463c0387a8b","schema_version":"1.0","event_id":"sha256:d8bb932d65a975b2b3d149b559b779b9a46fb2c9b91e628f49dec463c0387a8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LQPXINBMELPNDRVG4BGBGW7OQK/bundle.json","state_url":"https://pith.science/pith/LQPXINBMELPNDRVG4BGBGW7OQK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LQPXINBMELPNDRVG4BGBGW7OQK/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":"2026-06-06T22:34:50Z","links":{"resolver":"https://pith.science/pith/LQPXINBMELPNDRVG4BGBGW7OQK","bundle":"https://pith.science/pith/LQPXINBMELPNDRVG4BGBGW7OQK/bundle.json","state":"https://pith.science/pith/LQPXINBMELPNDRVG4BGBGW7OQK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LQPXINBMELPNDRVG4BGBGW7OQK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LQPXINBMELPNDRVG4BGBGW7OQK","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":"fe250bb88012c42b239915c96b207148f6e890530dfef2e7e459b4398af08517","cross_cats_sorted":["physics.ao-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2014-04-30T20:32:19Z","title_canon_sha256":"43849b5eb556317889eb30afbf3be353084cdae6edac30f126d4cd39c532c976"},"schema_version":"1.0","source":{"id":"1405.0026","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0026","created_at":"2026-05-18T01:43:21Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0026v3","created_at":"2026-05-18T01:43:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0026","created_at":"2026-05-18T01:43:21Z"},{"alias_kind":"pith_short_12","alias_value":"LQPXINBMELPN","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LQPXINBMELPNDRVG","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LQPXINBM","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:d8bb932d65a975b2b3d149b559b779b9a46fb2c9b91e628f49dec463c0387a8b","target":"graph","created_at":"2026-05-18T01:43:21Z","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":"We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior) and solutions for the temperature-pressure profiles. Generally, the problem is mathematically under-determined unless a set of closures (Eddi","authors_text":"Jae-Min Lee, Jo\\~ao M. Mendon\\c{c}a, Kevin Heng","cross_cats":["physics.ao-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2014-04-30T20:32:19Z","title":"Analytical Models of Exoplanetary Atmospheres. II. Radiative Transfer via the Two-stream Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0026","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:be238e34f6b582e243befd8d447ac568fe7a9cfa0200ae9f9b1ef3fb8e25992b","target":"record","created_at":"2026-05-18T01:43:21Z","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":"fe250bb88012c42b239915c96b207148f6e890530dfef2e7e459b4398af08517","cross_cats_sorted":["physics.ao-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2014-04-30T20:32:19Z","title_canon_sha256":"43849b5eb556317889eb30afbf3be353084cdae6edac30f126d4cd39c532c976"},"schema_version":"1.0","source":{"id":"1405.0026","kind":"arxiv","version":3}},"canonical_sha256":"5c1f74342c22ded1c6a6e04c135bee8299e084f7cc107e63852e168aa1e05fd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c1f74342c22ded1c6a6e04c135bee8299e084f7cc107e63852e168aa1e05fd4","first_computed_at":"2026-05-18T01:43:21.205006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:43:21.205006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"npdAkN8X0x1OL5lxGH5+DJwEQkRtYv5+34efJLR/CUhdfuM+boLUKLa1XCX0fmt4MaiwLqyd85Cv5adqJCazBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:43:21.205766Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0026","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be238e34f6b582e243befd8d447ac568fe7a9cfa0200ae9f9b1ef3fb8e25992b","sha256:d8bb932d65a975b2b3d149b559b779b9a46fb2c9b91e628f49dec463c0387a8b"],"state_sha256":"8f33318313726c3c7f67427af3c74117594bdddafe5d14b7253e70c54c8323d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LP+mN1xgMloEVRWj70E0Ptrj6VvplVQcfyswHSGpOiCdX9cw3JyMbmn1SHe86DtAFZBY1/9N+13cMjK3qfmOAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T22:34:50.666425Z","bundle_sha256":"7cccbde1f21d120915168d22bbf72df2c9e2194af67221622ef70bdf8f499fe2"}}