{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:TFDRH7PPTALWVWH54U4HPHTKVC","short_pith_number":"pith:TFDRH7PP","schema_version":"1.0","canonical_sha256":"994713fdef98176ad8fde538779e6aa888900458d3340de7ab2f4be45523ef72","source":{"kind":"arxiv","id":"1105.3612","version":4},"attestation_state":"computed","paper":{"title":"Braided Tensor Products and the Covariance of Quantum Noncommutative Free Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Jerzy Lukierski, Mariusz Woronowicz (IFT, Wroclaw Univ.)","submitted_at":"2011-05-18T12:52:37Z","abstract_excerpt":"We introduce the free quantum noncommutative fields as described by braided tensor products. The multiplication of such fields is decomposed into three operations, describing the multiplication in the algebra M of functions on noncommutative space-time, the product in the algebra H of deformed field oscillators, and the braiding by factor Psi_{M,H} between algebras M and H. For noncommutativity generated by the twist factor we shall employ the star-product realizations of the algebra M in terms of functions on standard Minkowski space. The covariance of single noncommutative quantum fields und"},"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":"1105.3612","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-05-18T12:52:37Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3d8e317154b40f2dd130c8d70137d7ecd89b0680bbcbcd0223e689d9baf6492d","abstract_canon_sha256":"4f1ef2d5992017c38e44dc4d4b4abdb330579a88c4a17c4d998eac1bf12ca06b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:56.565410Z","signature_b64":"r6Fx3bEe2KX7PaL/19ig4zn8V3i1YTwv6b7MSkYkVe0ZEIrapeFrIBwlFxP4SJl+UN9HFyd0TzN/vu71WBUfAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"994713fdef98176ad8fde538779e6aa888900458d3340de7ab2f4be45523ef72","last_reissued_at":"2026-05-18T02:01:56.564629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:56.564629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Braided Tensor Products and the Covariance of Quantum Noncommutative Free Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Jerzy Lukierski, Mariusz Woronowicz (IFT, Wroclaw Univ.)","submitted_at":"2011-05-18T12:52:37Z","abstract_excerpt":"We introduce the free quantum noncommutative fields as described by braided tensor products. The multiplication of such fields is decomposed into three operations, describing the multiplication in the algebra M of functions on noncommutative space-time, the product in the algebra H of deformed field oscillators, and the braiding by factor Psi_{M,H} between algebras M and H. For noncommutativity generated by the twist factor we shall employ the star-product realizations of the algebra M in terms of functions on standard Minkowski space. The covariance of single noncommutative quantum fields und"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3612","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":"1105.3612","created_at":"2026-05-18T02:01:56.564755+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.3612v4","created_at":"2026-05-18T02:01:56.564755+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3612","created_at":"2026-05-18T02:01:56.564755+00:00"},{"alias_kind":"pith_short_12","alias_value":"TFDRH7PPTALW","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"TFDRH7PPTALWVWH5","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"TFDRH7PP","created_at":"2026-05-18T12:26:42.757692+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/TFDRH7PPTALWVWH54U4HPHTKVC","json":"https://pith.science/pith/TFDRH7PPTALWVWH54U4HPHTKVC.json","graph_json":"https://pith.science/api/pith-number/TFDRH7PPTALWVWH54U4HPHTKVC/graph.json","events_json":"https://pith.science/api/pith-number/TFDRH7PPTALWVWH54U4HPHTKVC/events.json","paper":"https://pith.science/paper/TFDRH7PP"},"agent_actions":{"view_html":"https://pith.science/pith/TFDRH7PPTALWVWH54U4HPHTKVC","download_json":"https://pith.science/pith/TFDRH7PPTALWVWH54U4HPHTKVC.json","view_paper":"https://pith.science/paper/TFDRH7PP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.3612&json=true","fetch_graph":"https://pith.science/api/pith-number/TFDRH7PPTALWVWH54U4HPHTKVC/graph.json","fetch_events":"https://pith.science/api/pith-number/TFDRH7PPTALWVWH54U4HPHTKVC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TFDRH7PPTALWVWH54U4HPHTKVC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TFDRH7PPTALWVWH54U4HPHTKVC/action/storage_attestation","attest_author":"https://pith.science/pith/TFDRH7PPTALWVWH54U4HPHTKVC/action/author_attestation","sign_citation":"https://pith.science/pith/TFDRH7PPTALWVWH54U4HPHTKVC/action/citation_signature","submit_replication":"https://pith.science/pith/TFDRH7PPTALWVWH54U4HPHTKVC/action/replication_record"}},"created_at":"2026-05-18T02:01:56.564755+00:00","updated_at":"2026-05-18T02:01:56.564755+00:00"}