{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Z2UAJYQLS4KX7SKMAAP4ZQ7I76","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":"f8e9057ffe90f8ed160db6c4cfc3374c1d76cb0e41ef2b0b0adc7571650bf520","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2013-06-04T05:57:26Z","title_canon_sha256":"22a4721ee6562197e4f1140ff9f9eb741b9faddbd7b69f922a8db25e1d9a4908"},"schema_version":"1.0","source":{"id":"1306.0660","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0660","created_at":"2026-05-18T03:21:54Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0660v1","created_at":"2026-05-18T03:21:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0660","created_at":"2026-05-18T03:21:54Z"},{"alias_kind":"pith_short_12","alias_value":"Z2UAJYQLS4KX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z2UAJYQLS4KX7SKM","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z2UAJYQL","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:9ab106e0a14dba6adc6f87643ce6de26aca3978df8fbab3b293d2921b27702fc","target":"graph","created_at":"2026-05-18T03:21:54Z","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":"A new type of deformation for microscopic laser disks, the \\textit{equiangular spiral deformation} is proposed. First a short review of the geometry of light paths in equiangular spirals in the language of real two-dimensional geometric calculus is given. Second, the constituting equations for \\textit{closed paths} inside equiangular spirals are derived. Third, their numerical solution is performed and found to yield two generic types of closed light paths. \\textit{Degenerate} closed paths that exist over large intervals of the deformation parameter, and \\textit{nondegenerate} closed paths whi","authors_text":"Eckhard Hitzer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2013-06-04T05:57:26Z","title":"Closed Light Paths in Equiangular Spiral Disks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0660","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:c255c90c633ede4472dd552c0819d02d50912f04362e6d842c66833218fba337","target":"record","created_at":"2026-05-18T03:21:54Z","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":"f8e9057ffe90f8ed160db6c4cfc3374c1d76cb0e41ef2b0b0adc7571650bf520","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2013-06-04T05:57:26Z","title_canon_sha256":"22a4721ee6562197e4f1140ff9f9eb741b9faddbd7b69f922a8db25e1d9a4908"},"schema_version":"1.0","source":{"id":"1306.0660","kind":"arxiv","version":1}},"canonical_sha256":"cea804e20b97157fc94c001fccc3e8ff8e9f371730f6ea72e99c873c7546fd7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cea804e20b97157fc94c001fccc3e8ff8e9f371730f6ea72e99c873c7546fd7e","first_computed_at":"2026-05-18T03:21:54.445388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:54.445388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QNRQSzR7Bm9opgc8bid7xJk+kZQ0u94BQ/vRS43BFhqJodc/AhcY3Vxu5/nUamhhUbOnBuf2fi7iNcZUMOMMBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:54.446121Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.0660","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c255c90c633ede4472dd552c0819d02d50912f04362e6d842c66833218fba337","sha256:9ab106e0a14dba6adc6f87643ce6de26aca3978df8fbab3b293d2921b27702fc"],"state_sha256":"52298c5fcb6e9ceabc7e31a2f42fb05785b413161853b23bd45e46257b309590"}