{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:54NTSPV3H7VAAOW3U4AONA3MQM","short_pith_number":"pith:54NTSPV3","schema_version":"1.0","canonical_sha256":"ef1b393ebb3fea003adba700e6836c83038dc147095990e1ad8cf62e85bd8ea6","source":{"kind":"arxiv","id":"0812.0547","version":4},"attestation_state":"computed","paper":{"title":"kappa-Deformed Oscillators: Deformed Multiplication Versus Deformed Flip Operator and Multiparticle Clusters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Jerzy Lukierski","submitted_at":"2008-12-02T17:05:37Z","abstract_excerpt":"We transform the oscillator algebra with kappa-deformed multiplication rule, proposed in [1],[2], into the oscillator algebra with kappa-deformed flip operator and standard multiplication. We recall that the kappa-multiplication of the kappa-oscillators puts them off-shell. We study the explicit forms of modified mass-shell conditions in both formulations: with kappa-multiplication and with kappa-flip operation. On the example of kappa-deformed 2-particle states we study the clustered nonfactorizable form of the kappa-deformed multiparticle states. We argue that the kappa-deformed star product"},"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":"0812.0547","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-12-02T17:05:37Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"5018becf56f5d2599c1b49c04c51ca5d86c09e77fce3d92776a41a419ce84ff3","abstract_canon_sha256":"70af38dc9e760bddd1c0edc4faefd1be79db1f311c4f5a99da3a7aa65d7280e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:12.202666Z","signature_b64":"aXWrs3pijkggbKRbVrQ3Pxzbop/5HGhRR/FMRcjwZEurQ+jQfVvAnzsCbriClHYqDMjWzMihBtqTVBjyyU/ZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef1b393ebb3fea003adba700e6836c83038dc147095990e1ad8cf62e85bd8ea6","last_reissued_at":"2026-05-18T02:15:12.201979Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:12.201979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"kappa-Deformed Oscillators: Deformed Multiplication Versus Deformed Flip Operator and Multiparticle Clusters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Jerzy Lukierski","submitted_at":"2008-12-02T17:05:37Z","abstract_excerpt":"We transform the oscillator algebra with kappa-deformed multiplication rule, proposed in [1],[2], into the oscillator algebra with kappa-deformed flip operator and standard multiplication. We recall that the kappa-multiplication of the kappa-oscillators puts them off-shell. We study the explicit forms of modified mass-shell conditions in both formulations: with kappa-multiplication and with kappa-flip operation. On the example of kappa-deformed 2-particle states we study the clustered nonfactorizable form of the kappa-deformed multiparticle states. We argue that the kappa-deformed star product"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.0547","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":"0812.0547","created_at":"2026-05-18T02:15:12.202080+00:00"},{"alias_kind":"arxiv_version","alias_value":"0812.0547v4","created_at":"2026-05-18T02:15:12.202080+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.0547","created_at":"2026-05-18T02:15:12.202080+00:00"},{"alias_kind":"pith_short_12","alias_value":"54NTSPV3H7VA","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"54NTSPV3H7VAAOW3","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"54NTSPV3","created_at":"2026-05-18T12:25:56.245647+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/54NTSPV3H7VAAOW3U4AONA3MQM","json":"https://pith.science/pith/54NTSPV3H7VAAOW3U4AONA3MQM.json","graph_json":"https://pith.science/api/pith-number/54NTSPV3H7VAAOW3U4AONA3MQM/graph.json","events_json":"https://pith.science/api/pith-number/54NTSPV3H7VAAOW3U4AONA3MQM/events.json","paper":"https://pith.science/paper/54NTSPV3"},"agent_actions":{"view_html":"https://pith.science/pith/54NTSPV3H7VAAOW3U4AONA3MQM","download_json":"https://pith.science/pith/54NTSPV3H7VAAOW3U4AONA3MQM.json","view_paper":"https://pith.science/paper/54NTSPV3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0812.0547&json=true","fetch_graph":"https://pith.science/api/pith-number/54NTSPV3H7VAAOW3U4AONA3MQM/graph.json","fetch_events":"https://pith.science/api/pith-number/54NTSPV3H7VAAOW3U4AONA3MQM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/54NTSPV3H7VAAOW3U4AONA3MQM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/54NTSPV3H7VAAOW3U4AONA3MQM/action/storage_attestation","attest_author":"https://pith.science/pith/54NTSPV3H7VAAOW3U4AONA3MQM/action/author_attestation","sign_citation":"https://pith.science/pith/54NTSPV3H7VAAOW3U4AONA3MQM/action/citation_signature","submit_replication":"https://pith.science/pith/54NTSPV3H7VAAOW3U4AONA3MQM/action/replication_record"}},"created_at":"2026-05-18T02:15:12.202080+00:00","updated_at":"2026-05-18T02:15:12.202080+00:00"}