{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XQ3XFHESWJEKRDCF4FU4LXV4TE","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":"ccea8a998c5823208e5c8698db3093244625f38b0d1499a40472fe62aba6bc99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-02-18T18:38:25Z","title_canon_sha256":"3f5776cfcbd66fd1afaa28ca77bbb63d76d318f51b1be1e3621aaf71cce131d6"},"schema_version":"1.0","source":{"id":"1702.05643","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05643","created_at":"2026-05-18T00:50:25Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05643v1","created_at":"2026-05-18T00:50:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05643","created_at":"2026-05-18T00:50:25Z"},{"alias_kind":"pith_short_12","alias_value":"XQ3XFHESWJEK","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XQ3XFHESWJEKRDCF","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XQ3XFHES","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:da4dda1e7e9a6082689fda7118be853c14af78181cde1809f03153fa8d4ba9b4","target":"graph","created_at":"2026-05-18T00:50:25Z","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":"The works of William Rowan Hamilton in Geometrical Optics are presented, with emphasis on the Malus-Dupin theorem. According to that theorem, a family of light rays depending on two parameters can be focused to a single point by an optical instrument made of reflecting or refracting surfaces if and only if, before entering the optical instrument, the family of rays is rectangular (\\emph{i.e.}, admits orthogonal surfaces). Moreover, that theorem states that a rectangular system of rays remains rectangular after an arbitrary number of reflections through, or refractions across, smooth surfaces o","authors_text":"Charles-Michel Marle","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-02-18T18:38:25Z","title":"The works of William Rowan Hamilton in geometrical optics and the Malus-Dupin theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05643","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:a4d804e8b399b2741560c2221a7452cbbb9db8870846cff63bddbbf76dc876c4","target":"record","created_at":"2026-05-18T00:50:25Z","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":"ccea8a998c5823208e5c8698db3093244625f38b0d1499a40472fe62aba6bc99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-02-18T18:38:25Z","title_canon_sha256":"3f5776cfcbd66fd1afaa28ca77bbb63d76d318f51b1be1e3621aaf71cce131d6"},"schema_version":"1.0","source":{"id":"1702.05643","kind":"arxiv","version":1}},"canonical_sha256":"bc37729c92b248a88c45e169c5debc99178cd852676d2a157dace860ba50866c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc37729c92b248a88c45e169c5debc99178cd852676d2a157dace860ba50866c","first_computed_at":"2026-05-18T00:50:25.870201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:25.870201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sQEElfIWMUgVQ0CZI9dXaOJAywTX0a6Gv6c9GKntKRVow1IKEEms7+3N2zvFj3VoUlrM2RV+b0UyqNJaXCvHAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:25.870968Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.05643","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4d804e8b399b2741560c2221a7452cbbb9db8870846cff63bddbbf76dc876c4","sha256:da4dda1e7e9a6082689fda7118be853c14af78181cde1809f03153fa8d4ba9b4"],"state_sha256":"18f282bdcbb4f4bb503df64fed99ee7ee29c4d6d1cdaa3bafa426b2123e4d2b9"}