{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:66DW5VB3PSWCXVGVT2UFCHCGA2","short_pith_number":"pith:66DW5VB3","schema_version":"1.0","canonical_sha256":"f7876ed43b7cac2bd4d59ea8511c46069ce106f27f0892e4c10317f081c0413b","source":{"kind":"arxiv","id":"0807.0232","version":2},"attestation_state":"computed","paper":{"title":"A Mathematical Theory of Stochastic Microlensing I. Random Time-Delay Functions and Lensing Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"astro-ph","authors_text":"Alberto M. Teguia, Arlie O. Petters, Brian Rider","submitted_at":"2008-07-01T20:05:24Z","abstract_excerpt":"Stochastic microlensing is a central tool in probing dark matter on galactic scales. From first principles, we initiate the development of a mathematical theory of stochastic microlensing. Beginning with the random time delay function and associated lensing map, we determine exact expressions for the mean and variance of these transformations. We characterize the exact p.d.f. of a normalized random time delay function at the origin, showing that it is a shifted gamma distribution, which also holds at leading order in the limit of a large number of point masses at a general point of the lens pl"},"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":"0807.0232","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-07-01T20:05:24Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"1911f53af8e9a21596c4400f51cce87f15cdf2662a4c13c2c9320f2bfecc928b","abstract_canon_sha256":"d3101f8cbe6f22e05476a4d009ecfe4cdf0ceaf01031c68645d8b5fe62c99a1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:45.727088Z","signature_b64":"vqBIdyyawaAfj0iG3ozoZ9U0tq6yIhwEuisWl7rh9qc2PIvrd1RGIWTA1XBsOiJBVbtRFsMx18qZxx/ErTi5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7876ed43b7cac2bd4d59ea8511c46069ce106f27f0892e4c10317f081c0413b","last_reissued_at":"2026-05-18T02:15:45.726440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:45.726440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Mathematical Theory of Stochastic Microlensing I. Random Time-Delay Functions and Lensing Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"astro-ph","authors_text":"Alberto M. Teguia, Arlie O. Petters, Brian Rider","submitted_at":"2008-07-01T20:05:24Z","abstract_excerpt":"Stochastic microlensing is a central tool in probing dark matter on galactic scales. From first principles, we initiate the development of a mathematical theory of stochastic microlensing. Beginning with the random time delay function and associated lensing map, we determine exact expressions for the mean and variance of these transformations. We characterize the exact p.d.f. of a normalized random time delay function at the origin, showing that it is a shifted gamma distribution, which also holds at leading order in the limit of a large number of point masses at a general point of the lens pl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.0232","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":""},"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":"0807.0232","created_at":"2026-05-18T02:15:45.726544+00:00"},{"alias_kind":"arxiv_version","alias_value":"0807.0232v2","created_at":"2026-05-18T02:15:45.726544+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.0232","created_at":"2026-05-18T02:15:45.726544+00:00"},{"alias_kind":"pith_short_12","alias_value":"66DW5VB3PSWC","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"66DW5VB3PSWCXVGV","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"66DW5VB3","created_at":"2026-05-18T12:25:56.245647+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/66DW5VB3PSWCXVGVT2UFCHCGA2","json":"https://pith.science/pith/66DW5VB3PSWCXVGVT2UFCHCGA2.json","graph_json":"https://pith.science/api/pith-number/66DW5VB3PSWCXVGVT2UFCHCGA2/graph.json","events_json":"https://pith.science/api/pith-number/66DW5VB3PSWCXVGVT2UFCHCGA2/events.json","paper":"https://pith.science/paper/66DW5VB3"},"agent_actions":{"view_html":"https://pith.science/pith/66DW5VB3PSWCXVGVT2UFCHCGA2","download_json":"https://pith.science/pith/66DW5VB3PSWCXVGVT2UFCHCGA2.json","view_paper":"https://pith.science/paper/66DW5VB3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0807.0232&json=true","fetch_graph":"https://pith.science/api/pith-number/66DW5VB3PSWCXVGVT2UFCHCGA2/graph.json","fetch_events":"https://pith.science/api/pith-number/66DW5VB3PSWCXVGVT2UFCHCGA2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/66DW5VB3PSWCXVGVT2UFCHCGA2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/66DW5VB3PSWCXVGVT2UFCHCGA2/action/storage_attestation","attest_author":"https://pith.science/pith/66DW5VB3PSWCXVGVT2UFCHCGA2/action/author_attestation","sign_citation":"https://pith.science/pith/66DW5VB3PSWCXVGVT2UFCHCGA2/action/citation_signature","submit_replication":"https://pith.science/pith/66DW5VB3PSWCXVGVT2UFCHCGA2/action/replication_record"}},"created_at":"2026-05-18T02:15:45.726544+00:00","updated_at":"2026-05-18T02:15:45.726544+00:00"}