{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BB73PQ73QBZ3SSCOJHCLPVYQ3M","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":"20f28502906bbe4288716ebcc4267e338c5ccf899c07f64ca4f5e904eb72a592","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-08-17T23:15:31Z","title_canon_sha256":"1c3ba9295905d5fccbf9cdbd1110d5bdf925ddc8c1fc456ed44f86ab67c37b7a"},"schema_version":"1.0","source":{"id":"0908.2464","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.2464","created_at":"2026-05-18T02:12:25Z"},{"alias_kind":"arxiv_version","alias_value":"0908.2464v1","created_at":"2026-05-18T02:12:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.2464","created_at":"2026-05-18T02:12:25Z"},{"alias_kind":"pith_short_12","alias_value":"BB73PQ73QBZ3","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BB73PQ73QBZ3SSCO","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BB73PQ73","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:47a878d19fb77fbf8cfdb597cd9c196d4d081648125aee75b8d1ef516f2a9378","target":"graph","created_at":"2026-05-18T02:12:25Z","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 consider the following geometric optics problem: Construct a system of two reflectors which transforms a spherical wavefront generated by a point source into a beam of parallel rays. This beam has a prescribed intensity distribution. We give a rigorous analysis of this problem. The reflectors we construct are (parts of) the boundaries of convex sets. We prove existence of solutions for a large class of input data and give a uniqueness result. To the author's knowledge, this is the first time that a rigorous mathematical analysis of this problem is given. The approach is based on optimal tra","authors_text":"Tilmann Glimm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-08-17T23:15:31Z","title":"A rigorous analysis using optimal transport theory for a two-reflector design problem with a point source"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.2464","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":"sha256:6745f2c08399d1ad3fcd622dccc1c9978ef0c8949297b599c20a7bc47125dcf8","target":"record","created_at":"2026-05-18T02:12:25Z","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":"20f28502906bbe4288716ebcc4267e338c5ccf899c07f64ca4f5e904eb72a592","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-08-17T23:15:31Z","title_canon_sha256":"1c3ba9295905d5fccbf9cdbd1110d5bdf925ddc8c1fc456ed44f86ab67c37b7a"},"schema_version":"1.0","source":{"id":"0908.2464","kind":"arxiv","version":1}},"canonical_sha256":"087fb7c3fb8073b9484e49c4b7d710db3d2f18de9437b800fe6568d5ab69b317","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"087fb7c3fb8073b9484e49c4b7d710db3d2f18de9437b800fe6568d5ab69b317","first_computed_at":"2026-05-18T02:12:25.832810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:12:25.832810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pBRa62R+SpLrHpjQW0m/Oi+ZZhQ9kGSrYVlODG/m/ZcqfrhNREFfaAbACH6xyQfwaypGGS6tTQSKbslECHJ/Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:12:25.833671Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.2464","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6745f2c08399d1ad3fcd622dccc1c9978ef0c8949297b599c20a7bc47125dcf8","sha256:47a878d19fb77fbf8cfdb597cd9c196d4d081648125aee75b8d1ef516f2a9378"],"state_sha256":"275182a5a049e45aa401dae29840b885bea4bedd192ed596432684c9d202d753"}