{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:KY4QVDCYXJMSSXY4N6SRITVZ5U","short_pith_number":"pith:KY4QVDCY","schema_version":"1.0","canonical_sha256":"56390a8c58ba59295f1c6fa5144eb9ed0317c295135e8a12defb0e6d12029669","source":{"kind":"arxiv","id":"1601.01590","version":1},"attestation_state":"computed","paper":{"title":"On Hopf algebroid structure of kappa-deformed Heisenberg algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.MP","math.QA"],"primary_cat":"math-ph","authors_text":"Jerzy Lukierski, Mariusz Woronowicz, Zoran \\v{S}koda","submitted_at":"2016-01-07T16:33:38Z","abstract_excerpt":"The $(4+4)$-dimensional $\\kappa$-deformed quantum phase space as well as its $(10+10)$-dimensional covariant extension by the Lorentz sector can be described as Heisenberg doubles: the $(10+10)$-dimensional quantum phase space is the double of $D=4$ $\\kappa$-deformed Poincar\\'e Hopf algebra $\\mathbb{H}$ and the standard $(4+4)$-dimensional space is its subalgebra generated by $\\kappa$-Minkowski coordinates $\\hat{x}_\\mu$ and corresponding commuting momenta $\\hat{p}_\\mu$. Every Heisenberg double appears as the total algebra of a Hopf algebroid over a base algebra which is in our case the coordin"},"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":"1601.01590","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2016-01-07T16:33:38Z","cross_cats_sorted":["hep-th","math.MP","math.QA"],"title_canon_sha256":"6ccf3f8415513157a2cd104ba5a46256fe7832ae4348e96eb2ae8942a399c3d5","abstract_canon_sha256":"f927210057ef19cd8a71936023aa809c6b4bdcbdda0008b377e5bb71ea69c271"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:03.279904Z","signature_b64":"EpyJq5FunlATxtaqs5aHZIinLqJ43DPqLv6ABs6j4sHOTZ2Dg2jCrNHZa2iBMk3NA7j4/lVAad9d1oi5qihqDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56390a8c58ba59295f1c6fa5144eb9ed0317c295135e8a12defb0e6d12029669","last_reissued_at":"2026-05-18T00:39:03.279200Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:03.279200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Hopf algebroid structure of kappa-deformed Heisenberg algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.MP","math.QA"],"primary_cat":"math-ph","authors_text":"Jerzy Lukierski, Mariusz Woronowicz, Zoran \\v{S}koda","submitted_at":"2016-01-07T16:33:38Z","abstract_excerpt":"The $(4+4)$-dimensional $\\kappa$-deformed quantum phase space as well as its $(10+10)$-dimensional covariant extension by the Lorentz sector can be described as Heisenberg doubles: the $(10+10)$-dimensional quantum phase space is the double of $D=4$ $\\kappa$-deformed Poincar\\'e Hopf algebra $\\mathbb{H}$ and the standard $(4+4)$-dimensional space is its subalgebra generated by $\\kappa$-Minkowski coordinates $\\hat{x}_\\mu$ and corresponding commuting momenta $\\hat{p}_\\mu$. Every Heisenberg double appears as the total algebra of a Hopf algebroid over a base algebra which is in our case the coordin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01590","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":"1601.01590","created_at":"2026-05-18T00:39:03.279309+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.01590v1","created_at":"2026-05-18T00:39:03.279309+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01590","created_at":"2026-05-18T00:39:03.279309+00:00"},{"alias_kind":"pith_short_12","alias_value":"KY4QVDCYXJMS","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"KY4QVDCYXJMSSXY4","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"KY4QVDCY","created_at":"2026-05-18T12:30:29.479603+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/KY4QVDCYXJMSSXY4N6SRITVZ5U","json":"https://pith.science/pith/KY4QVDCYXJMSSXY4N6SRITVZ5U.json","graph_json":"https://pith.science/api/pith-number/KY4QVDCYXJMSSXY4N6SRITVZ5U/graph.json","events_json":"https://pith.science/api/pith-number/KY4QVDCYXJMSSXY4N6SRITVZ5U/events.json","paper":"https://pith.science/paper/KY4QVDCY"},"agent_actions":{"view_html":"https://pith.science/pith/KY4QVDCYXJMSSXY4N6SRITVZ5U","download_json":"https://pith.science/pith/KY4QVDCYXJMSSXY4N6SRITVZ5U.json","view_paper":"https://pith.science/paper/KY4QVDCY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.01590&json=true","fetch_graph":"https://pith.science/api/pith-number/KY4QVDCYXJMSSXY4N6SRITVZ5U/graph.json","fetch_events":"https://pith.science/api/pith-number/KY4QVDCYXJMSSXY4N6SRITVZ5U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KY4QVDCYXJMSSXY4N6SRITVZ5U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KY4QVDCYXJMSSXY4N6SRITVZ5U/action/storage_attestation","attest_author":"https://pith.science/pith/KY4QVDCYXJMSSXY4N6SRITVZ5U/action/author_attestation","sign_citation":"https://pith.science/pith/KY4QVDCYXJMSSXY4N6SRITVZ5U/action/citation_signature","submit_replication":"https://pith.science/pith/KY4QVDCYXJMSSXY4N6SRITVZ5U/action/replication_record"}},"created_at":"2026-05-18T00:39:03.279309+00:00","updated_at":"2026-05-18T00:39:03.279309+00:00"}