{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:DQE2I2RCCOKUZXH6Z6GTSZVE3K","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":"6a8426a375c4a45c2588426a7b96cd1de25402636a805933473d89f9f1b9493e","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2002-11-18T04:37:36Z","title_canon_sha256":"fcb3e78d8b980de25fbb23584d8c47d12de7f007d088d0a54218e5008b7f9d53"},"schema_version":"1.0","source":{"id":"astro-ph/0211389","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0211389","created_at":"2026-07-04T16:31:10Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0211389v1","created_at":"2026-07-04T16:31:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0211389","created_at":"2026-07-04T16:31:10Z"},{"alias_kind":"pith_short_12","alias_value":"DQE2I2RCCOKU","created_at":"2026-07-04T16:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DQE2I2RCCOKUZXH6","created_at":"2026-07-04T16:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DQE2I2RC","created_at":"2026-07-04T16:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:a90dafad0988f1ddb1386f0b6e28e13d6dac9f5ef6c92318d34c44c06d9d5265","target":"graph","created_at":"2026-07-04T16:31:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/astro-ph/0211389/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present explicit expressions for the lens equation for a cored isothermal ellipsoidal gravitational lens as a single real sixth-order algebraic equation in two approaches; 2-dimensional Cartesian coordinates and 3-dimensional polar ones. We find a condition for physical solutions which correspond to at most five images. For a singular isothermal ellipsoid, the sixth-order equation is reduced to fourth-order one for which analytic solutions are well-known. Furthermore, we derive analytic criteria for determining the number of images for the singular lens, which give us simple expressions for","authors_text":"Hideki Asada, Masumi Kasai, Takashi Hamana","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2002-11-18T04:37:36Z","title":"Images for an Isothermal Ellipsoidal Gravitational Lens from a Single Real Algebraic Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0211389","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:ff4a6378d509778d66c4ca8d821fd8f607f86fd1ff223954c9c275c4c379f2fa","target":"record","created_at":"2026-07-04T16:31:10Z","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":"6a8426a375c4a45c2588426a7b96cd1de25402636a805933473d89f9f1b9493e","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2002-11-18T04:37:36Z","title_canon_sha256":"fcb3e78d8b980de25fbb23584d8c47d12de7f007d088d0a54218e5008b7f9d53"},"schema_version":"1.0","source":{"id":"astro-ph/0211389","kind":"arxiv","version":1}},"canonical_sha256":"1c09a46a2213954cdcfecf8d3966a4dab52b1eb08b0be055acda66e90c133502","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c09a46a2213954cdcfecf8d3966a4dab52b1eb08b0be055acda66e90c133502","first_computed_at":"2026-07-04T16:31:10.330979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:31:10.330979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+IoJGD8t3e6ZaBopRhe4UXpKXK/KFTTwQP2Sc3sPe/hNf9Onogd1sCag5F9DjlFmRMizozP5LbWYG7VMgbHLAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:31:10.331489Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/0211389","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff4a6378d509778d66c4ca8d821fd8f607f86fd1ff223954c9c275c4c379f2fa","sha256:a90dafad0988f1ddb1386f0b6e28e13d6dac9f5ef6c92318d34c44c06d9d5265"],"state_sha256":"5ffb0cbeeeba187015ed06f1721a06c2deda6a7b43a6a39583517933341fda0e"}