{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:KDFDDDSXOFAHXSIZNSYSLXU65N","short_pith_number":"pith:KDFDDDSX","schema_version":"1.0","canonical_sha256":"50ca318e5771407bc9196cb125de9eeb4d1ca3e6b4fc6f1abcda2145d698dc91","source":{"kind":"arxiv","id":"2205.03173","version":1},"attestation_state":"computed","paper":{"title":"Comparison of continuity equation and Gaussian mixture model for long-term density propagation using semi-analytical methods","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Camilla Colombo, Mirko Trisolini, Pan Sun, Shuang Li","submitted_at":"2022-05-06T12:39:59Z","abstract_excerpt":"This paper compares the continuum evolution for density equation modelling and the Gaussian mixture model on the 2D phase space long-term density propagation problem in the context of high-altitude and high area-to-mass ratio satellite long-term propagation. The density evolution equation, a pure numerical and pointwise method for the density propagation, is formulated under the influence of solar radiation pressure and Earth's oblateness using semi-analytical methods. Different from the density evolution equation and Monte Carlo techniques, for the Gaussian mixture model, the analytical calcu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2205.03173","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2022-05-06T12:39:59Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"2818f5f3411ca55d37d2bda8921a888b6d4edd14dfbef14974013a1c415eacb7","abstract_canon_sha256":"7cf1eb322758a0d13350fc7cc0e126f98e5747d64e903f8aedfc8bd5f54e7856"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:20:56.692382Z","signature_b64":"qyKt/HXHhXMGiPWO/rZPNMcd5xTiLz+IUW2ueZFF/cDVi9UDfmmup8RD2ioSTx/XoQmfLrZxjguGi7hUBWRVBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50ca318e5771407bc9196cb125de9eeb4d1ca3e6b4fc6f1abcda2145d698dc91","last_reissued_at":"2026-07-05T04:20:56.691922Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:20:56.691922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comparison of continuity equation and Gaussian mixture model for long-term density propagation using semi-analytical methods","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Camilla Colombo, Mirko Trisolini, Pan Sun, Shuang Li","submitted_at":"2022-05-06T12:39:59Z","abstract_excerpt":"This paper compares the continuum evolution for density equation modelling and the Gaussian mixture model on the 2D phase space long-term density propagation problem in the context of high-altitude and high area-to-mass ratio satellite long-term propagation. The density evolution equation, a pure numerical and pointwise method for the density propagation, is formulated under the influence of solar radiation pressure and Earth's oblateness using semi-analytical methods. Different from the density evolution equation and Monte Carlo techniques, for the Gaussian mixture model, the analytical calcu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.03173","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.03173/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2205.03173","created_at":"2026-07-05T04:20:56.691982+00:00"},{"alias_kind":"arxiv_version","alias_value":"2205.03173v1","created_at":"2026-07-05T04:20:56.691982+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.03173","created_at":"2026-07-05T04:20:56.691982+00:00"},{"alias_kind":"pith_short_12","alias_value":"KDFDDDSXOFAH","created_at":"2026-07-05T04:20:56.691982+00:00"},{"alias_kind":"pith_short_16","alias_value":"KDFDDDSXOFAHXSIZ","created_at":"2026-07-05T04:20:56.691982+00:00"},{"alias_kind":"pith_short_8","alias_value":"KDFDDDSX","created_at":"2026-07-05T04:20:56.691982+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KDFDDDSXOFAHXSIZNSYSLXU65N","json":"https://pith.science/pith/KDFDDDSXOFAHXSIZNSYSLXU65N.json","graph_json":"https://pith.science/api/pith-number/KDFDDDSXOFAHXSIZNSYSLXU65N/graph.json","events_json":"https://pith.science/api/pith-number/KDFDDDSXOFAHXSIZNSYSLXU65N/events.json","paper":"https://pith.science/paper/KDFDDDSX"},"agent_actions":{"view_html":"https://pith.science/pith/KDFDDDSXOFAHXSIZNSYSLXU65N","download_json":"https://pith.science/pith/KDFDDDSXOFAHXSIZNSYSLXU65N.json","view_paper":"https://pith.science/paper/KDFDDDSX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2205.03173&json=true","fetch_graph":"https://pith.science/api/pith-number/KDFDDDSXOFAHXSIZNSYSLXU65N/graph.json","fetch_events":"https://pith.science/api/pith-number/KDFDDDSXOFAHXSIZNSYSLXU65N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KDFDDDSXOFAHXSIZNSYSLXU65N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KDFDDDSXOFAHXSIZNSYSLXU65N/action/storage_attestation","attest_author":"https://pith.science/pith/KDFDDDSXOFAHXSIZNSYSLXU65N/action/author_attestation","sign_citation":"https://pith.science/pith/KDFDDDSXOFAHXSIZNSYSLXU65N/action/citation_signature","submit_replication":"https://pith.science/pith/KDFDDDSXOFAHXSIZNSYSLXU65N/action/replication_record"}},"created_at":"2026-07-05T04:20:56.691982+00:00","updated_at":"2026-07-05T04:20:56.691982+00:00"}