{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VIYYWCKZ34TB2YHAKIWXFSWHNI","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":"fd457fdddf98c97917050b94445e99312498666014e71e42efb134574a539085","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-14T05:55:05Z","title_canon_sha256":"1facc666041a14364c7e3aab2b509882c624bd4c2be4c2d8ff0f5ae062bb2ddd"},"schema_version":"1.0","source":{"id":"1304.3883","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.3883","created_at":"2026-05-18T02:49:02Z"},{"alias_kind":"arxiv_version","alias_value":"1304.3883v2","created_at":"2026-05-18T02:49:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3883","created_at":"2026-05-18T02:49:02Z"},{"alias_kind":"pith_short_12","alias_value":"VIYYWCKZ34TB","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VIYYWCKZ34TB2YHA","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VIYYWCKZ","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:19464f2869d3479dcc134d559555c015f289224d40304c61ffe8cdecbc1312fe","target":"graph","created_at":"2026-05-18T02:49:02Z","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":"Given a point S (the light position) in P^3 and an algebraic surface Z (the mirror) of P^3, the caustic by reflection of Z from S is the Zariski closure of the envelope of the reflected lines got by reflection of the incident lines (Sm) on Z at m in Z. We use the ramification method to identify the caustic by reflection with the Zariski closure of the image, by a rational map, of an algebraic 2-covering space of Z. We also give a general formula for the degree (with multiplicity) of caustics (by reflection) of algebraic surfaces.","authors_text":"Alfrederic Josse (LM), Francoise Pene (LM)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-14T05:55:05Z","title":"On caustics by reflection of algebraic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3883","kind":"arxiv","version":2},"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":"sha256:1b7259723d9e028a6767767ca7471980813331bea61d2497563f714904561345","target":"record","created_at":"2026-05-18T02:49:02Z","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":"fd457fdddf98c97917050b94445e99312498666014e71e42efb134574a539085","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-14T05:55:05Z","title_canon_sha256":"1facc666041a14364c7e3aab2b509882c624bd4c2be4c2d8ff0f5ae062bb2ddd"},"schema_version":"1.0","source":{"id":"1304.3883","kind":"arxiv","version":2}},"canonical_sha256":"aa318b0959df261d60e0522d72cac76a3acbba25d0e8ee661c22436ca8bec40f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa318b0959df261d60e0522d72cac76a3acbba25d0e8ee661c22436ca8bec40f","first_computed_at":"2026-05-18T02:49:02.064855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:02.064855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R/MVLHfxOq0D4HHR4uBpveOfzPc3S1n49hAHuAjV2Phv2nqmL/0fVIELq5dc1oGOcGmSN7bLIdFeOAVM9CYpAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:02.065388Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.3883","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b7259723d9e028a6767767ca7471980813331bea61d2497563f714904561345","sha256:19464f2869d3479dcc134d559555c015f289224d40304c61ffe8cdecbc1312fe"],"state_sha256":"ef1029d02d25afb0c4747aa9a172ebf63824756b614974f665b8a07af012ca89"}