{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2VGWE2CMVNMJQEWHJ37VNKLLBP","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":"75e9f78aa9d2bb7a49a0a2417254d9bb40b98b4f5d8ad224681e2f9aae8f2ae0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.optics","submitted_at":"2026-06-10T03:21:32Z","title_canon_sha256":"43adf435a85858ed1aa8dd2f68faf2440b89b1d61c8f3f426e8065c6711b76ca"},"schema_version":"1.0","source":{"id":"2606.11610","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.11610","created_at":"2026-06-11T01:09:58Z"},{"alias_kind":"arxiv_version","alias_value":"2606.11610v1","created_at":"2026-06-11T01:09:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.11610","created_at":"2026-06-11T01:09:58Z"},{"alias_kind":"pith_short_12","alias_value":"2VGWE2CMVNMJ","created_at":"2026-06-11T01:09:58Z"},{"alias_kind":"pith_short_16","alias_value":"2VGWE2CMVNMJQEWH","created_at":"2026-06-11T01:09:58Z"},{"alias_kind":"pith_short_8","alias_value":"2VGWE2CM","created_at":"2026-06-11T01:09:58Z"}],"graph_snapshots":[{"event_id":"sha256:eeddf4ddb6b8e0d241a90fe2e45e3635fb57e1807229cb854b4aa7aacbca70ba","target":"graph","created_at":"2026-06-11T01:09:58Z","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/2606.11610/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present the exact analytical paraxial propagation of structured light beams that transition from Ring annular profiles to top-hat intensity distributions. The initial field is defined as a superposition of a Gaussian-weighted power-law core and a singular inverse-quadratic modulation term, both carrying an azimuthal phase factor. By solving the Fresnel diffraction integral in cylindrical coordinates, we obtain exact closed-form expressions for the propagated field at arbitrary planes. The paraxial evolution is shown to be governed by a Cauchy-Riemann beam term and an infinite series of modi","authors_text":"D. S\\'anchez-de-la-Llave, F. Soto-Eguibar, H. M. Moya-Cessa, I. Jul\\'ian-Mac\\'ias, I. Ramos-Prieto, M. A. J\\'acome-Silva, U. Ru\\'iz-Corona","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.optics","submitted_at":"2026-06-10T03:21:32Z","title":"From Rings to Top-Hat beams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11610","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":"sha256:792d6f93aca67b5fa5d3f048bb41f3ee1f8a85a440ba0429f2255cd7cc469d61","target":"record","created_at":"2026-06-11T01:09:58Z","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":"75e9f78aa9d2bb7a49a0a2417254d9bb40b98b4f5d8ad224681e2f9aae8f2ae0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.optics","submitted_at":"2026-06-10T03:21:32Z","title_canon_sha256":"43adf435a85858ed1aa8dd2f68faf2440b89b1d61c8f3f426e8065c6711b76ca"},"schema_version":"1.0","source":{"id":"2606.11610","kind":"arxiv","version":1}},"canonical_sha256":"d54d62684cab589812c74eff56a96b0bceebffac9f8b530fe7799bd1c9d21973","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d54d62684cab589812c74eff56a96b0bceebffac9f8b530fe7799bd1c9d21973","first_computed_at":"2026-06-11T01:09:58.935803Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T01:09:58.935803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QLuE6iGP22xWlQYbytsGjJ8tdsBDfM6vUDAxkDZjWBWiKClwoB/DnJT1Lcb7UlrBc018/5qftEq4U8Y/6s89BA==","signature_status":"signed_v1","signed_at":"2026-06-11T01:09:58.936596Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.11610","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:792d6f93aca67b5fa5d3f048bb41f3ee1f8a85a440ba0429f2255cd7cc469d61","sha256:eeddf4ddb6b8e0d241a90fe2e45e3635fb57e1807229cb854b4aa7aacbca70ba"],"state_sha256":"587a3369384fb2f4b1f215aa20209c949c83bfa7f19c1b112d3252db3d752971"}