{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MG4IPHSNHIQHRYUSQLIU647SOL","short_pith_number":"pith:MG4IPHSN","schema_version":"1.0","canonical_sha256":"61b8879e4d3a2078e29282d14f73f272cbf945f29edfc3ee6dcffa463bec0087","source":{"kind":"arxiv","id":"1512.01444","version":4},"attestation_state":"computed","paper":{"title":"Spontaneous generation of singularities in paraxial optical fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"physics.optics","authors_text":"Andrea Aiello","submitted_at":"2015-12-04T15:01:20Z","abstract_excerpt":"In nonrelativistic quantum mechanics the spontaneous generation of singularities in smooth and finite wave functions, is a well understood phenomenon also occurring for free particles. We use the familiar analogy between the two-dimensional Schroedinger equation and the optical paraxial wave equation to define a new class of square-integrable paraxial optical fields which develop a spatial singularity in the focal point of a weakly-focusing thin lens. These fields are characterized by a single real parameter whose value determines the nature of the singularity. This novel field enhancement mec"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1512.01444","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-12-04T15:01:20Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"dd0dfa764a21f26f1f173d01230ca4727bd9de3b9363245b46b1a388c6bbeaac","abstract_canon_sha256":"3919d31b0bfc7a26252d1eeadc6313af013c1c8fe9c19ab9460445d42e970a3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:43.732797Z","signature_b64":"0WMhUh2JPlzNq+vWaXFBR/UO1eL6ocCkLE+w7fDpvEsNdvjpaYMmWih5bKs8EmxI2pUR5/QUyx6iIaQluA2sAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61b8879e4d3a2078e29282d14f73f272cbf945f29edfc3ee6dcffa463bec0087","last_reissued_at":"2026-05-18T01:15:43.732147Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:43.732147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spontaneous generation of singularities in paraxial optical fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"physics.optics","authors_text":"Andrea Aiello","submitted_at":"2015-12-04T15:01:20Z","abstract_excerpt":"In nonrelativistic quantum mechanics the spontaneous generation of singularities in smooth and finite wave functions, is a well understood phenomenon also occurring for free particles. We use the familiar analogy between the two-dimensional Schroedinger equation and the optical paraxial wave equation to define a new class of square-integrable paraxial optical fields which develop a spatial singularity in the focal point of a weakly-focusing thin lens. These fields are characterized by a single real parameter whose value determines the nature of the singularity. This novel field enhancement mec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01444","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1512.01444","created_at":"2026-05-18T01:15:43.732240+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.01444v4","created_at":"2026-05-18T01:15:43.732240+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01444","created_at":"2026-05-18T01:15:43.732240+00:00"},{"alias_kind":"pith_short_12","alias_value":"MG4IPHSNHIQH","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MG4IPHSNHIQHRYUS","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MG4IPHSN","created_at":"2026-05-18T12:29:32.376354+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MG4IPHSNHIQHRYUSQLIU647SOL","json":"https://pith.science/pith/MG4IPHSNHIQHRYUSQLIU647SOL.json","graph_json":"https://pith.science/api/pith-number/MG4IPHSNHIQHRYUSQLIU647SOL/graph.json","events_json":"https://pith.science/api/pith-number/MG4IPHSNHIQHRYUSQLIU647SOL/events.json","paper":"https://pith.science/paper/MG4IPHSN"},"agent_actions":{"view_html":"https://pith.science/pith/MG4IPHSNHIQHRYUSQLIU647SOL","download_json":"https://pith.science/pith/MG4IPHSNHIQHRYUSQLIU647SOL.json","view_paper":"https://pith.science/paper/MG4IPHSN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.01444&json=true","fetch_graph":"https://pith.science/api/pith-number/MG4IPHSNHIQHRYUSQLIU647SOL/graph.json","fetch_events":"https://pith.science/api/pith-number/MG4IPHSNHIQHRYUSQLIU647SOL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MG4IPHSNHIQHRYUSQLIU647SOL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MG4IPHSNHIQHRYUSQLIU647SOL/action/storage_attestation","attest_author":"https://pith.science/pith/MG4IPHSNHIQHRYUSQLIU647SOL/action/author_attestation","sign_citation":"https://pith.science/pith/MG4IPHSNHIQHRYUSQLIU647SOL/action/citation_signature","submit_replication":"https://pith.science/pith/MG4IPHSNHIQHRYUSQLIU647SOL/action/replication_record"}},"created_at":"2026-05-18T01:15:43.732240+00:00","updated_at":"2026-05-18T01:15:43.732240+00:00"}