{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Y37IXLQ37NSLR3CBTJDEHQDL62","short_pith_number":"pith:Y37IXLQ3","canonical_record":{"source":{"id":"1105.1207","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2011-05-06T01:43:48Z","cross_cats_sorted":["physics.ao-ph"],"title_canon_sha256":"faa29b7fd98dd665d7b541d3289febed3bb8dcea4e6f8e7517c0324998084598","abstract_canon_sha256":"96dae8d2abe9309bbd7cf22f0c7b761d3c2c9068985960cd92ded8243628f1ad"},"schema_version":"1.0"},"canonical_sha256":"c6fe8bae1bfb64b8ec419a4643c06bf6b43af8d2a1e721cc3d7063f80031339e","source":{"kind":"arxiv","id":"1105.1207","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1207","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1207v4","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1207","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"pith_short_12","alias_value":"Y37IXLQ37NSL","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Y37IXLQ37NSLR3CB","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Y37IXLQ3","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Y37IXLQ37NSLR3CBTJDEHQDL62","target":"record","payload":{"canonical_record":{"source":{"id":"1105.1207","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2011-05-06T01:43:48Z","cross_cats_sorted":["physics.ao-ph"],"title_canon_sha256":"faa29b7fd98dd665d7b541d3289febed3bb8dcea4e6f8e7517c0324998084598","abstract_canon_sha256":"96dae8d2abe9309bbd7cf22f0c7b761d3c2c9068985960cd92ded8243628f1ad"},"schema_version":"1.0"},"canonical_sha256":"c6fe8bae1bfb64b8ec419a4643c06bf6b43af8d2a1e721cc3d7063f80031339e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:45.612123Z","signature_b64":"hMRRVnnEZyQdFiDaMKyx6Tp/FKjnNYrZQuyaM5AJukgfqnY7Qad+91hYP1yd/uloHeQqCxUQdGYv0dvFxS3lCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6fe8bae1bfb64b8ec419a4643c06bf6b43af8d2a1e721cc3d7063f80031339e","last_reissued_at":"2026-05-18T03:46:45.611560Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:45.611560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.1207","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:46:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"phMaMn2kFJIGEftoXlD7ELLbHRvFYU8qGlEz1YvuW7/6lBVQ6Ez1Yeo7GwayuLCH8CijPfX2EHmK8zF6vfgSBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:28:39.992151Z"},"content_sha256":"70888a0d9deaf1a932707d81bfaf54036491f40ec7c84cf7b0f8869c0af296a9","schema_version":"1.0","event_id":"sha256:70888a0d9deaf1a932707d81bfaf54036491f40ec7c84cf7b0f8869c0af296a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Y37IXLQ37NSLR3CBTJDEHQDL62","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Second Order Radiative Transfer Equation and Its Solution by Meshless Method with Application to Strongly Inhomogeneous Media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.ao-ph"],"primary_cat":"physics.comp-ph","authors_text":"J. M. Zhao, J. Y. Tan, L. H. Liu","submitted_at":"2011-05-06T01:43:48Z","abstract_excerpt":"A new second order form of radiative transfer equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order radiative transfer equation [J. Comput. Phys. 214 (2006) 12-40 (where it was termed SAAI), Numer. Heat Transfer B 51 (2007) 391-409] in dealing with inhomogeneous media where some locations have very small/zero extinction coefficient. The MSORTE contains a naturally introduced diffusion (or second order) term which provides better numerical property than the classic first order radiative transfer equation (RTE). The stability and conve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1207","kind":"arxiv","version":4},"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":"2026-05-18T03:46:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SgNxo6G6dVPsc56vnC/EKob61T0coV2NuELU6ZdlyLnrLZ35ojl351zzCuwZqpYJZAsV6ulttLVdnyoU+ezOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:28:39.992537Z"},"content_sha256":"1807a380e54db663a4a3628cb5183c0ae12c1530344ae0c09242cf2ded7fc4eb","schema_version":"1.0","event_id":"sha256:1807a380e54db663a4a3628cb5183c0ae12c1530344ae0c09242cf2ded7fc4eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y37IXLQ37NSLR3CBTJDEHQDL62/bundle.json","state_url":"https://pith.science/pith/Y37IXLQ37NSLR3CBTJDEHQDL62/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y37IXLQ37NSLR3CBTJDEHQDL62/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":"2026-07-01T21:28:39Z","links":{"resolver":"https://pith.science/pith/Y37IXLQ37NSLR3CBTJDEHQDL62","bundle":"https://pith.science/pith/Y37IXLQ37NSLR3CBTJDEHQDL62/bundle.json","state":"https://pith.science/pith/Y37IXLQ37NSLR3CBTJDEHQDL62/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y37IXLQ37NSLR3CBTJDEHQDL62/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Y37IXLQ37NSLR3CBTJDEHQDL62","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":"96dae8d2abe9309bbd7cf22f0c7b761d3c2c9068985960cd92ded8243628f1ad","cross_cats_sorted":["physics.ao-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2011-05-06T01:43:48Z","title_canon_sha256":"faa29b7fd98dd665d7b541d3289febed3bb8dcea4e6f8e7517c0324998084598"},"schema_version":"1.0","source":{"id":"1105.1207","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1207","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1207v4","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1207","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"pith_short_12","alias_value":"Y37IXLQ37NSL","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Y37IXLQ37NSLR3CB","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Y37IXLQ3","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:1807a380e54db663a4a3628cb5183c0ae12c1530344ae0c09242cf2ded7fc4eb","target":"graph","created_at":"2026-05-18T03:46:45Z","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":"A new second order form of radiative transfer equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order radiative transfer equation [J. Comput. Phys. 214 (2006) 12-40 (where it was termed SAAI), Numer. Heat Transfer B 51 (2007) 391-409] in dealing with inhomogeneous media where some locations have very small/zero extinction coefficient. The MSORTE contains a naturally introduced diffusion (or second order) term which provides better numerical property than the classic first order radiative transfer equation (RTE). The stability and conve","authors_text":"J. M. Zhao, J. Y. Tan, L. H. Liu","cross_cats":["physics.ao-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2011-05-06T01:43:48Z","title":"A Second Order Radiative Transfer Equation and Its Solution by Meshless Method with Application to Strongly Inhomogeneous Media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1207","kind":"arxiv","version":4},"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":"sha256:70888a0d9deaf1a932707d81bfaf54036491f40ec7c84cf7b0f8869c0af296a9","target":"record","created_at":"2026-05-18T03:46:45Z","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":"96dae8d2abe9309bbd7cf22f0c7b761d3c2c9068985960cd92ded8243628f1ad","cross_cats_sorted":["physics.ao-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2011-05-06T01:43:48Z","title_canon_sha256":"faa29b7fd98dd665d7b541d3289febed3bb8dcea4e6f8e7517c0324998084598"},"schema_version":"1.0","source":{"id":"1105.1207","kind":"arxiv","version":4}},"canonical_sha256":"c6fe8bae1bfb64b8ec419a4643c06bf6b43af8d2a1e721cc3d7063f80031339e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6fe8bae1bfb64b8ec419a4643c06bf6b43af8d2a1e721cc3d7063f80031339e","first_computed_at":"2026-05-18T03:46:45.611560Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:45.611560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hMRRVnnEZyQdFiDaMKyx6Tp/FKjnNYrZQuyaM5AJukgfqnY7Qad+91hYP1yd/uloHeQqCxUQdGYv0dvFxS3lCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:45.612123Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.1207","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70888a0d9deaf1a932707d81bfaf54036491f40ec7c84cf7b0f8869c0af296a9","sha256:1807a380e54db663a4a3628cb5183c0ae12c1530344ae0c09242cf2ded7fc4eb"],"state_sha256":"d5ca65167bc958db713da6df6bf736c7386a33c274203153925f5026cd5f9b3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JPfRMOtbRJstk7SQS4jxKTr6cOsvgvSXy9Nt0TnlXeUjkNysQjHuac5iOIo4SMrKaicQDjrIaRFW9r90A594Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T21:28:39.994494Z","bundle_sha256":"00e12ef447f5496e2817e135a12dcd4bf07d3ffb2c45c030ea4aa1319f700912"}}