{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:CHFFU27BYDMQCY5HNL6MGBTYW3","short_pith_number":"pith:CHFFU27B","schema_version":"1.0","canonical_sha256":"11ca5a6be1c0d90163a76afcc30678b6d516a9585be6d2fd25c19627519529af","source":{"kind":"arxiv","id":"0807.1931","version":1},"attestation_state":"computed","paper":{"title":"Multipole Formulae for Gravitational Lensing Shear and Flexion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Gary M. Bernstein, Reiko Nakajima","submitted_at":"2008-07-11T20:18:40Z","abstract_excerpt":"The gravitational lensing equations for convergence, potential, shear, and flexion are simple in polar coordinates and separate under a multipole expansion once the shear and flexion spinors are rotated into a ``tangential'' basis. We use this to investigate whether the useful monopole aperture-mass shear formulae generalize to all multipoles and to flexions. We re-derive the result of Schneider and Bartelmann that the shear multipole m at radius R is completely determined by the mass multipole at R, plus specific moments Q^m_in and Q^m_out of the mass multipoles internal and external, respect"},"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":"0807.1931","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-07-11T20:18:40Z","cross_cats_sorted":[],"title_canon_sha256":"8efe899bc7040fdf8f8837fc431d8f8665320dbdc4e44c0d764a486bc0073972","abstract_canon_sha256":"a0afa6b872c0fcbaaebceffdef8231a0c2f2a61f92dd810e7a8f8ef84a017d11"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:29:33.257029Z","signature_b64":"Wp0gaQt7vAYork+OAcAeU4HPSWer23u6e9RICF2RC4i/Xc2YitKnjyy6JGefbCer66yDtmW3ynjr2z3RTh01BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11ca5a6be1c0d90163a76afcc30678b6d516a9585be6d2fd25c19627519529af","last_reissued_at":"2026-05-18T04:29:33.256638Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:29:33.256638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multipole Formulae for Gravitational Lensing Shear and Flexion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Gary M. Bernstein, Reiko Nakajima","submitted_at":"2008-07-11T20:18:40Z","abstract_excerpt":"The gravitational lensing equations for convergence, potential, shear, and flexion are simple in polar coordinates and separate under a multipole expansion once the shear and flexion spinors are rotated into a ``tangential'' basis. We use this to investigate whether the useful monopole aperture-mass shear formulae generalize to all multipoles and to flexions. We re-derive the result of Schneider and Bartelmann that the shear multipole m at radius R is completely determined by the mass multipole at R, plus specific moments Q^m_in and Q^m_out of the mass multipoles internal and external, respect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.1931","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":""},"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":"0807.1931","created_at":"2026-05-18T04:29:33.256695+00:00"},{"alias_kind":"arxiv_version","alias_value":"0807.1931v1","created_at":"2026-05-18T04:29:33.256695+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.1931","created_at":"2026-05-18T04:29:33.256695+00:00"},{"alias_kind":"pith_short_12","alias_value":"CHFFU27BYDMQ","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"CHFFU27BYDMQCY5H","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"CHFFU27B","created_at":"2026-05-18T12:25:57.157939+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/CHFFU27BYDMQCY5HNL6MGBTYW3","json":"https://pith.science/pith/CHFFU27BYDMQCY5HNL6MGBTYW3.json","graph_json":"https://pith.science/api/pith-number/CHFFU27BYDMQCY5HNL6MGBTYW3/graph.json","events_json":"https://pith.science/api/pith-number/CHFFU27BYDMQCY5HNL6MGBTYW3/events.json","paper":"https://pith.science/paper/CHFFU27B"},"agent_actions":{"view_html":"https://pith.science/pith/CHFFU27BYDMQCY5HNL6MGBTYW3","download_json":"https://pith.science/pith/CHFFU27BYDMQCY5HNL6MGBTYW3.json","view_paper":"https://pith.science/paper/CHFFU27B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0807.1931&json=true","fetch_graph":"https://pith.science/api/pith-number/CHFFU27BYDMQCY5HNL6MGBTYW3/graph.json","fetch_events":"https://pith.science/api/pith-number/CHFFU27BYDMQCY5HNL6MGBTYW3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CHFFU27BYDMQCY5HNL6MGBTYW3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CHFFU27BYDMQCY5HNL6MGBTYW3/action/storage_attestation","attest_author":"https://pith.science/pith/CHFFU27BYDMQCY5HNL6MGBTYW3/action/author_attestation","sign_citation":"https://pith.science/pith/CHFFU27BYDMQCY5HNL6MGBTYW3/action/citation_signature","submit_replication":"https://pith.science/pith/CHFFU27BYDMQCY5HNL6MGBTYW3/action/replication_record"}},"created_at":"2026-05-18T04:29:33.256695+00:00","updated_at":"2026-05-18T04:29:33.256695+00:00"}