{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1996:CSV3C6MH7F2YAV5PA6RW2WL3DZ","short_pith_number":"pith:CSV3C6MH","schema_version":"1.0","canonical_sha256":"14abb17987f9758057af07a36d597b1e500587c3736a06239d1d72167e7d1d6e","source":{"kind":"arxiv","id":"quant-ph/9612006","version":1},"attestation_state":"computed","paper":{"title":"f-Oscillators and Nonlinear Coherent States","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"E. C. G. Sudarshan, F. Zaccaria, G. Marmo, V. I. Man'ko","submitted_at":"1996-11-30T18:55:55Z","abstract_excerpt":"The notion of f-oscillators generalizing q-oscillators is introduced. For classical and quantum cases, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of oscillation depends on the energy. The f-coherent states (nonlinear coherent states) generalizing q-coherent states are constructed. Applied to quantum optics, photon distribution function, photon number means, and dispersions are calculated for the f-coherent states as well as the Wigner function and Q-function. As an example, it is shown how this nonlinearity "},"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":"quant-ph/9612006","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1996-11-30T18:55:55Z","cross_cats_sorted":[],"title_canon_sha256":"4902b0e84fe082cc8eb05049108cce73b3d34a638eba3e662ca90f0ef6654015","abstract_canon_sha256":"ac11a1b2e08d0081ce4f1572abfa835d37434ddc5169da995e6174094d9ff714"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:02.002299Z","signature_b64":"nAUz4dq1O6SveUUt+p5Oqz5n7zXhNJbR/rIjgqAnu34NRBToLLCPlNgaeR+vry6XsvvFDkA/exza2+3fZXyiDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14abb17987f9758057af07a36d597b1e500587c3736a06239d1d72167e7d1d6e","last_reissued_at":"2026-05-18T01:05:02.001560Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:02.001560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"f-Oscillators and Nonlinear Coherent States","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"E. C. G. Sudarshan, F. Zaccaria, G. Marmo, V. I. Man'ko","submitted_at":"1996-11-30T18:55:55Z","abstract_excerpt":"The notion of f-oscillators generalizing q-oscillators is introduced. For classical and quantum cases, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of oscillation depends on the energy. The f-coherent states (nonlinear coherent states) generalizing q-coherent states are constructed. Applied to quantum optics, photon distribution function, photon number means, and dispersions are calculated for the f-coherent states as well as the Wigner function and Q-function. As an example, it is shown how this nonlinearity "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9612006","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":"quant-ph/9612006","created_at":"2026-05-18T01:05:02.001668+00:00"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9612006v1","created_at":"2026-05-18T01:05:02.001668+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9612006","created_at":"2026-05-18T01:05:02.001668+00:00"},{"alias_kind":"pith_short_12","alias_value":"CSV3C6MH7F2Y","created_at":"2026-05-18T12:25:47.700082+00:00"},{"alias_kind":"pith_short_16","alias_value":"CSV3C6MH7F2YAV5P","created_at":"2026-05-18T12:25:47.700082+00:00"},{"alias_kind":"pith_short_8","alias_value":"CSV3C6MH","created_at":"2026-05-18T12:25:47.700082+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.03038","citing_title":"Squeezed-state radiation in shockwave scattering: QCD-Gravity double copy","ref_index":37,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CSV3C6MH7F2YAV5PA6RW2WL3DZ","json":"https://pith.science/pith/CSV3C6MH7F2YAV5PA6RW2WL3DZ.json","graph_json":"https://pith.science/api/pith-number/CSV3C6MH7F2YAV5PA6RW2WL3DZ/graph.json","events_json":"https://pith.science/api/pith-number/CSV3C6MH7F2YAV5PA6RW2WL3DZ/events.json","paper":"https://pith.science/paper/CSV3C6MH"},"agent_actions":{"view_html":"https://pith.science/pith/CSV3C6MH7F2YAV5PA6RW2WL3DZ","download_json":"https://pith.science/pith/CSV3C6MH7F2YAV5PA6RW2WL3DZ.json","view_paper":"https://pith.science/paper/CSV3C6MH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=quant-ph/9612006&json=true","fetch_graph":"https://pith.science/api/pith-number/CSV3C6MH7F2YAV5PA6RW2WL3DZ/graph.json","fetch_events":"https://pith.science/api/pith-number/CSV3C6MH7F2YAV5PA6RW2WL3DZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CSV3C6MH7F2YAV5PA6RW2WL3DZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CSV3C6MH7F2YAV5PA6RW2WL3DZ/action/storage_attestation","attest_author":"https://pith.science/pith/CSV3C6MH7F2YAV5PA6RW2WL3DZ/action/author_attestation","sign_citation":"https://pith.science/pith/CSV3C6MH7F2YAV5PA6RW2WL3DZ/action/citation_signature","submit_replication":"https://pith.science/pith/CSV3C6MH7F2YAV5PA6RW2WL3DZ/action/replication_record"}},"created_at":"2026-05-18T01:05:02.001668+00:00","updated_at":"2026-05-18T01:05:02.001668+00:00"}