{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:CHFFU27BYDMQCY5HNL6MGBTYW3","short_pith_number":"pith:CHFFU27B","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"},"canonical_sha256":"11ca5a6be1c0d90163a76afcc30678b6d516a9585be6d2fd25c19627519529af","source":{"kind":"arxiv","id":"0807.1931","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.1931","created_at":"2026-05-18T04:29:33Z"},{"alias_kind":"arxiv_version","alias_value":"0807.1931v1","created_at":"2026-05-18T04:29:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.1931","created_at":"2026-05-18T04:29:33Z"},{"alias_kind":"pith_short_12","alias_value":"CHFFU27BYDMQ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"CHFFU27BYDMQCY5H","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"CHFFU27B","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:CHFFU27BYDMQCY5HNL6MGBTYW3","target":"record","payload":{"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"},"canonical_sha256":"11ca5a6be1c0d90163a76afcc30678b6d516a9585be6d2fd25c19627519529af","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"},"source_kind":"arxiv","source_id":"0807.1931","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:29:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IWmcOOX/7z5X/aS8/elYKM8fbeBi9Id+zlCq1/07gNBAup4h8xuOu7nmDXhSLeuU7/OEWwmiBShJ4Qbqw+D2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:13:55.505805Z"},"content_sha256":"0c681743352fa5f286fd1396b6fdf32db06071eb64152f5e59b39fab9f0cde8d","schema_version":"1.0","event_id":"sha256:0c681743352fa5f286fd1396b6fdf32db06071eb64152f5e59b39fab9f0cde8d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:CHFFU27BYDMQCY5HNL6MGBTYW3","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:29:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dltWC8Y2A0BDvmouYQBtMbGRUiC4G4hIDQVyrtjLRx/y4y480l1L3DJvAtFftsrRjUpDelni9aQ4TazluidMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:13:55.506501Z"},"content_sha256":"d22e0485aed0603c9a19205f82707f98002b880e30e07f7667aa3f8d4afcaf3a","schema_version":"1.0","event_id":"sha256:d22e0485aed0603c9a19205f82707f98002b880e30e07f7667aa3f8d4afcaf3a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CHFFU27BYDMQCY5HNL6MGBTYW3/bundle.json","state_url":"https://pith.science/pith/CHFFU27BYDMQCY5HNL6MGBTYW3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CHFFU27BYDMQCY5HNL6MGBTYW3/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":"2026-06-08T16:13:55Z","links":{"resolver":"https://pith.science/pith/CHFFU27BYDMQCY5HNL6MGBTYW3","bundle":"https://pith.science/pith/CHFFU27BYDMQCY5HNL6MGBTYW3/bundle.json","state":"https://pith.science/pith/CHFFU27BYDMQCY5HNL6MGBTYW3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CHFFU27BYDMQCY5HNL6MGBTYW3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:CHFFU27BYDMQCY5HNL6MGBTYW3","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":"a0afa6b872c0fcbaaebceffdef8231a0c2f2a61f92dd810e7a8f8ef84a017d11","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-07-11T20:18:40Z","title_canon_sha256":"8efe899bc7040fdf8f8837fc431d8f8665320dbdc4e44c0d764a486bc0073972"},"schema_version":"1.0","source":{"id":"0807.1931","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.1931","created_at":"2026-05-18T04:29:33Z"},{"alias_kind":"arxiv_version","alias_value":"0807.1931v1","created_at":"2026-05-18T04:29:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.1931","created_at":"2026-05-18T04:29:33Z"},{"alias_kind":"pith_short_12","alias_value":"CHFFU27BYDMQ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"CHFFU27BYDMQCY5H","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"CHFFU27B","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:d22e0485aed0603c9a19205f82707f98002b880e30e07f7667aa3f8d4afcaf3a","target":"graph","created_at":"2026-05-18T04:29:33Z","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":"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","authors_text":"Gary M. Bernstein, Reiko Nakajima","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-07-11T20:18:40Z","title":"Multipole Formulae for Gravitational Lensing Shear and Flexion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.1931","kind":"arxiv","version":1},"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":"sha256:0c681743352fa5f286fd1396b6fdf32db06071eb64152f5e59b39fab9f0cde8d","target":"record","created_at":"2026-05-18T04:29:33Z","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":"a0afa6b872c0fcbaaebceffdef8231a0c2f2a61f92dd810e7a8f8ef84a017d11","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-07-11T20:18:40Z","title_canon_sha256":"8efe899bc7040fdf8f8837fc431d8f8665320dbdc4e44c0d764a486bc0073972"},"schema_version":"1.0","source":{"id":"0807.1931","kind":"arxiv","version":1}},"canonical_sha256":"11ca5a6be1c0d90163a76afcc30678b6d516a9585be6d2fd25c19627519529af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11ca5a6be1c0d90163a76afcc30678b6d516a9585be6d2fd25c19627519529af","first_computed_at":"2026-05-18T04:29:33.256638Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:29:33.256638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wp0gaQt7vAYork+OAcAeU4HPSWer23u6e9RICF2RC4i/Xc2YitKnjyy6JGefbCer66yDtmW3ynjr2z3RTh01BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:29:33.257029Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.1931","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c681743352fa5f286fd1396b6fdf32db06071eb64152f5e59b39fab9f0cde8d","sha256:d22e0485aed0603c9a19205f82707f98002b880e30e07f7667aa3f8d4afcaf3a"],"state_sha256":"49e777bf4d90b2610cd5a3fed98cfd165996ab0f75f2d7a90e54792c7abe5514"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tA+MpSuedfV/ztt9Sc+1iqpTv3nENU2l7vCB+gGdZoYl34g34ENzZEWfquyhaGDoLXsu0J+kEz723av1dSV0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T16:13:55.511373Z","bundle_sha256":"ce0c7cade5c68c2297aff14627fa9506016d5539c1d09e7658be025550aac7c3"}}