{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5Z3VEGUCKO5L5WXEBUB5LJ474S","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":"9b11ad1b45356a3a30b8d463c653757bb6761109ded7d0e7b75c63abe63d03b4","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-03-15T12:06:18Z","title_canon_sha256":"eb4857f32cb11debbcd07568722437b0430045de9d71b0d7a69113780692462f"},"schema_version":"1.0","source":{"id":"1603.04652","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04652","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04652v3","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04652","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"pith_short_12","alias_value":"5Z3VEGUCKO5L","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5Z3VEGUCKO5L5WXE","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5Z3VEGUC","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:a923187342331e93e973b6240e5f1d4532d2c6a263727abf882d9a495cb99702","target":"graph","created_at":"2026-05-18T00:59:25Z","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":"We present a new extension of the weak lensing formalism capable of describing strongly lensed images. This paper accompanies Paper I, arXiv:1603.04698 where we provided a condensed overview of the approach and illustrated how it works. Here we give all the necessary details, together with some more explicit examples. We solve the non-linear geodesic deviation equation order-by-order, keeping the leading derivatives of the optical tidal matrix, giving rise to a series of maps from which a complete strongly lensed image is formed. The family of maps are decomposed by separating the trace and tr","authors_text":"Chris Clarkson","cross_cats":["astro-ph.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-03-15T12:06:18Z","title":"Roulettes: A weak lensing formalism for strong lensing - II. Derivation and analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04652","kind":"arxiv","version":3},"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:cef57bfde9530279c7240c49a8eacc2b18fde5714d37581577c2c0f733e824a2","target":"record","created_at":"2026-05-18T00:59:25Z","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":"9b11ad1b45356a3a30b8d463c653757bb6761109ded7d0e7b75c63abe63d03b4","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-03-15T12:06:18Z","title_canon_sha256":"eb4857f32cb11debbcd07568722437b0430045de9d71b0d7a69113780692462f"},"schema_version":"1.0","source":{"id":"1603.04652","kind":"arxiv","version":3}},"canonical_sha256":"ee77521a8253babedae40d03d5a79fe4a2dee44d6f715114a59c27e2375a5e1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee77521a8253babedae40d03d5a79fe4a2dee44d6f715114a59c27e2375a5e1a","first_computed_at":"2026-05-18T00:59:25.714497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:25.714497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UuVqj7kx6E+99JuoKBZ9ymsxCZ8Qy/SpzTbSnvBHC3GotwkggBukPmxyvrfCv7cFO4of5Hp7VW08KkBMJIQmDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:25.715170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04652","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cef57bfde9530279c7240c49a8eacc2b18fde5714d37581577c2c0f733e824a2","sha256:a923187342331e93e973b6240e5f1d4532d2c6a263727abf882d9a495cb99702"],"state_sha256":"5f6a98fba46c96b681ad6d522016236cd6e311f0198df8058c61772355f93da3"}