{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:54NTSPV3H7VAAOW3U4AONA3MQM","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":"70af38dc9e760bddd1c0edc4faefd1be79db1f311c4f5a99da3a7aa65d7280e2","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-12-02T17:05:37Z","title_canon_sha256":"5018becf56f5d2599c1b49c04c51ca5d86c09e77fce3d92776a41a419ce84ff3"},"schema_version":"1.0","source":{"id":"0812.0547","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.0547","created_at":"2026-05-18T02:15:12Z"},{"alias_kind":"arxiv_version","alias_value":"0812.0547v4","created_at":"2026-05-18T02:15:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.0547","created_at":"2026-05-18T02:15:12Z"},{"alias_kind":"pith_short_12","alias_value":"54NTSPV3H7VA","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"54NTSPV3H7VAAOW3","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"54NTSPV3","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:8d650c8b2ccb18c1dbfcb1780ccbb5af9dba8e57acd5140f00f356097e1eb418","target":"graph","created_at":"2026-05-18T02:15:12Z","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":"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","authors_text":"Jerzy Lukierski","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-12-02T17:05:37Z","title":"kappa-Deformed Oscillators: Deformed Multiplication Versus Deformed Flip Operator and Multiparticle Clusters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.0547","kind":"arxiv","version":4},"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":"sha256:1fff6bad826ca7965ad1099e8cd4187d126ae86f254a7859931151988c8e141b","target":"record","created_at":"2026-05-18T02:15:12Z","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":"70af38dc9e760bddd1c0edc4faefd1be79db1f311c4f5a99da3a7aa65d7280e2","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-12-02T17:05:37Z","title_canon_sha256":"5018becf56f5d2599c1b49c04c51ca5d86c09e77fce3d92776a41a419ce84ff3"},"schema_version":"1.0","source":{"id":"0812.0547","kind":"arxiv","version":4}},"canonical_sha256":"ef1b393ebb3fea003adba700e6836c83038dc147095990e1ad8cf62e85bd8ea6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef1b393ebb3fea003adba700e6836c83038dc147095990e1ad8cf62e85bd8ea6","first_computed_at":"2026-05-18T02:15:12.201979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:12.201979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aXWrs3pijkggbKRbVrQ3Pxzbop/5HGhRR/FMRcjwZEurQ+jQfVvAnzsCbriClHYqDMjWzMihBtqTVBjyyU/ZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:12.202666Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.0547","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fff6bad826ca7965ad1099e8cd4187d126ae86f254a7859931151988c8e141b","sha256:8d650c8b2ccb18c1dbfcb1780ccbb5af9dba8e57acd5140f00f356097e1eb418"],"state_sha256":"e5292447b9677c304394f5f1068abce2a490d9b8ef8b449875ab1381f6089c15"}