{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HWGQWEYNHV2L3B7ARVG3THNM7O","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":"75643429b569c5e26601e5129cdf1c3067180e81a21441c60f114d9224bcde9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2018-11-05T08:29:25Z","title_canon_sha256":"4349b9baa82b72e2199c1b249cc6e18fc64cefbf934ed069abdb71d093474e04"},"schema_version":"1.0","source":{"id":"1811.01937","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.01937","created_at":"2026-05-17T23:50:11Z"},{"alias_kind":"arxiv_version","alias_value":"1811.01937v1","created_at":"2026-05-17T23:50:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01937","created_at":"2026-05-17T23:50:11Z"},{"alias_kind":"pith_short_12","alias_value":"HWGQWEYNHV2L","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HWGQWEYNHV2L3B7A","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HWGQWEYN","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:1ff771fa3f74e1c98eca3c6f52c39406a252a402e8b5abd7ce0c610c8cdaa709","target":"graph","created_at":"2026-05-17T23:50:11Z","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 generalized family of scalar structured Gaussian modes including helical-Ince--Gaussian (HIG) and Hermite--Laguerre--Gaussian (HLG) beams is presented with physical insight upon a hybrid topological evolution nature of multi-singularity vortex beams carrying orbital angular momentum (OAM). Considering the physical origins of intrinsic coordinates aberration and the Gouy phase shift, a closed-form expression is derived to characterize the general modes in astigmatic optical systems. Moreover, a graphical representation, Singularities Hybrid Evolution Nature (SHEN) sphere, is proposed to visua","authors_text":"Mali Gong, Xing Fu, Yijie Shen, Yuan Meng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2018-11-05T08:29:25Z","title":"Hybrid topological evolution of multi-singularity vortex beams: Generalized nature for helical-Ince-Gaussian and Hermite-Laguerre-Gaussian modes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01937","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":"sha256:722af6779b420c4458cdf39741a6f009e820c7b1eb585c52c7edfbc4a7934a1c","target":"record","created_at":"2026-05-17T23:50:11Z","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":"75643429b569c5e26601e5129cdf1c3067180e81a21441c60f114d9224bcde9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2018-11-05T08:29:25Z","title_canon_sha256":"4349b9baa82b72e2199c1b249cc6e18fc64cefbf934ed069abdb71d093474e04"},"schema_version":"1.0","source":{"id":"1811.01937","kind":"arxiv","version":1}},"canonical_sha256":"3d8d0b130d3d74bd87e08d4db99dacfb8287f86e465ce769cd9f096b99b7040a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d8d0b130d3d74bd87e08d4db99dacfb8287f86e465ce769cd9f096b99b7040a","first_computed_at":"2026-05-17T23:50:11.595296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:11.595296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"THnirF6Ldw+2Mt9OVmWGcQCgH6xnjvDsKRGEOxOu2FvtXi/GPNW/MPCbRKZDnC/s4lJDROaSt8z/Bv0FvxVsCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:11.595837Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.01937","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:722af6779b420c4458cdf39741a6f009e820c7b1eb585c52c7edfbc4a7934a1c","sha256:1ff771fa3f74e1c98eca3c6f52c39406a252a402e8b5abd7ce0c610c8cdaa709"],"state_sha256":"10d840c35deff19d029529cb6966a751405746d48e9065a6c07bc7c3ecf602e6"}