{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ICU4AQZ53BGCA24JWEE6YD7NVH","short_pith_number":"pith:ICU4AQZ5","schema_version":"1.0","canonical_sha256":"40a9c0433dd84c206b89b109ec0feda9fd2e0da44d265fee33049aa9ac467d35","source":{"kind":"arxiv","id":"1311.7335","version":1},"attestation_state":"computed","paper":{"title":"From the Weyl quantization of a particle on the circle to number-phase Wigner functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Jaromir Tosiek, Maciej Przanowski, Przemyslaw Brzykcy","submitted_at":"2013-11-28T14:51:08Z","abstract_excerpt":"A generalized Weyl quantization formalism for a particle on the circle investigated in \\cite{1} is developed. A Wigner function for the state $\\hat{\\varrho}$ and the kernel $\\mathcal{K}$ for a particle on the circle is defined and its properties are analyzed. Then it is shown how this Wigner function can be easily modified to give the number-phase Wigner function in quantum optics. Some examples of such number-phase Wigner function are considered."},"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":"1311.7335","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-11-28T14:51:08Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"423512a270b73a1d7c0f47a706c7afd17c27a2c23030aad21fe0ee5f78cf1d3c","abstract_canon_sha256":"67d3656f9e5a186af3110d01e59bfa7a274982361b10f3f34e48e69fded0576d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:46:05.181778Z","signature_b64":"FjbxSDXPpiM3AXArxszX/kHVrQFSQzeJfDEcsZhdqKMzHdqJHHbneSjRC2ks3PwmmOsRdbXA2TGZF1pXr/nCCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40a9c0433dd84c206b89b109ec0feda9fd2e0da44d265fee33049aa9ac467d35","last_reissued_at":"2026-05-18T01:46:05.181241Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:46:05.181241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From the Weyl quantization of a particle on the circle to number-phase Wigner functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Jaromir Tosiek, Maciej Przanowski, Przemyslaw Brzykcy","submitted_at":"2013-11-28T14:51:08Z","abstract_excerpt":"A generalized Weyl quantization formalism for a particle on the circle investigated in \\cite{1} is developed. A Wigner function for the state $\\hat{\\varrho}$ and the kernel $\\mathcal{K}$ for a particle on the circle is defined and its properties are analyzed. Then it is shown how this Wigner function can be easily modified to give the number-phase Wigner function in quantum optics. Some examples of such number-phase Wigner function are considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7335","kind":"arxiv","version":1},"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":"1311.7335","created_at":"2026-05-18T01:46:05.181324+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.7335v1","created_at":"2026-05-18T01:46:05.181324+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7335","created_at":"2026-05-18T01:46:05.181324+00:00"},{"alias_kind":"pith_short_12","alias_value":"ICU4AQZ53BGC","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"ICU4AQZ53BGCA24J","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"ICU4AQZ5","created_at":"2026-05-18T12:27:46.883200+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/ICU4AQZ53BGCA24JWEE6YD7NVH","json":"https://pith.science/pith/ICU4AQZ53BGCA24JWEE6YD7NVH.json","graph_json":"https://pith.science/api/pith-number/ICU4AQZ53BGCA24JWEE6YD7NVH/graph.json","events_json":"https://pith.science/api/pith-number/ICU4AQZ53BGCA24JWEE6YD7NVH/events.json","paper":"https://pith.science/paper/ICU4AQZ5"},"agent_actions":{"view_html":"https://pith.science/pith/ICU4AQZ53BGCA24JWEE6YD7NVH","download_json":"https://pith.science/pith/ICU4AQZ53BGCA24JWEE6YD7NVH.json","view_paper":"https://pith.science/paper/ICU4AQZ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.7335&json=true","fetch_graph":"https://pith.science/api/pith-number/ICU4AQZ53BGCA24JWEE6YD7NVH/graph.json","fetch_events":"https://pith.science/api/pith-number/ICU4AQZ53BGCA24JWEE6YD7NVH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ICU4AQZ53BGCA24JWEE6YD7NVH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ICU4AQZ53BGCA24JWEE6YD7NVH/action/storage_attestation","attest_author":"https://pith.science/pith/ICU4AQZ53BGCA24JWEE6YD7NVH/action/author_attestation","sign_citation":"https://pith.science/pith/ICU4AQZ53BGCA24JWEE6YD7NVH/action/citation_signature","submit_replication":"https://pith.science/pith/ICU4AQZ53BGCA24JWEE6YD7NVH/action/replication_record"}},"created_at":"2026-05-18T01:46:05.181324+00:00","updated_at":"2026-05-18T01:46:05.181324+00:00"}