{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:LYFRD23HNUBFHIE3L6IRG52RYZ","short_pith_number":"pith:LYFRD23H","schema_version":"1.0","canonical_sha256":"5e0b11eb676d0253a09b5f91137751c66fa15f05e46ef9447be5692b071f09cd","source":{"kind":"arxiv","id":"1102.0718","version":4},"attestation_state":"computed","paper":{"title":"Noncommutative Phase Spaces by Coadjoint Orbits Method","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Ancille Ngendakumana, Joachim Nzotungicimpaye, Leonardt Todjihounde","submitted_at":"2011-02-03T16:06:13Z","abstract_excerpt":"We introduce noncommutative phase spaces by minimal couplings (usual one, dual one and their mixing). We then realize some of them as coadjoint orbits of the anisotropic Newton-Hooke groups in two- and three-dimensional spaces. Through these constructions the positions and the momenta of the phase spaces do not commute due to the presence of a magnetic field and a dual magnetic field."},"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":"1102.0718","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-02-03T16:06:13Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"f0e0c7c471622153e592f83450f43ec1042558877f9885ff8879bb13dbe4e984","abstract_canon_sha256":"257de70f3d20c4b1c39b2d596e68c5e15b201c45e60f16a18417e9c84609d63e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:07.994552Z","signature_b64":"zg8wrry3uI30Qs+mR9PQ/YUIQxtyuYBJlw/tYg2elNbrn50xmZRddRtVQwhlrK7wwg0Fzza1GWKYWZNpi5SDCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e0b11eb676d0253a09b5f91137751c66fa15f05e46ef9447be5692b071f09cd","last_reissued_at":"2026-05-18T04:06:07.993886Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:07.993886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Noncommutative Phase Spaces by Coadjoint Orbits Method","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Ancille Ngendakumana, Joachim Nzotungicimpaye, Leonardt Todjihounde","submitted_at":"2011-02-03T16:06:13Z","abstract_excerpt":"We introduce noncommutative phase spaces by minimal couplings (usual one, dual one and their mixing). We then realize some of them as coadjoint orbits of the anisotropic Newton-Hooke groups in two- and three-dimensional spaces. Through these constructions the positions and the momenta of the phase spaces do not commute due to the presence of a magnetic field and a dual magnetic field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0718","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":"1102.0718","created_at":"2026-05-18T04:06:07.993986+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.0718v4","created_at":"2026-05-18T04:06:07.993986+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0718","created_at":"2026-05-18T04:06:07.993986+00:00"},{"alias_kind":"pith_short_12","alias_value":"LYFRD23HNUBF","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"LYFRD23HNUBFHIE3","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"LYFRD23H","created_at":"2026-05-18T12:26:34.985390+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/LYFRD23HNUBFHIE3L6IRG52RYZ","json":"https://pith.science/pith/LYFRD23HNUBFHIE3L6IRG52RYZ.json","graph_json":"https://pith.science/api/pith-number/LYFRD23HNUBFHIE3L6IRG52RYZ/graph.json","events_json":"https://pith.science/api/pith-number/LYFRD23HNUBFHIE3L6IRG52RYZ/events.json","paper":"https://pith.science/paper/LYFRD23H"},"agent_actions":{"view_html":"https://pith.science/pith/LYFRD23HNUBFHIE3L6IRG52RYZ","download_json":"https://pith.science/pith/LYFRD23HNUBFHIE3L6IRG52RYZ.json","view_paper":"https://pith.science/paper/LYFRD23H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.0718&json=true","fetch_graph":"https://pith.science/api/pith-number/LYFRD23HNUBFHIE3L6IRG52RYZ/graph.json","fetch_events":"https://pith.science/api/pith-number/LYFRD23HNUBFHIE3L6IRG52RYZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LYFRD23HNUBFHIE3L6IRG52RYZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LYFRD23HNUBFHIE3L6IRG52RYZ/action/storage_attestation","attest_author":"https://pith.science/pith/LYFRD23HNUBFHIE3L6IRG52RYZ/action/author_attestation","sign_citation":"https://pith.science/pith/LYFRD23HNUBFHIE3L6IRG52RYZ/action/citation_signature","submit_replication":"https://pith.science/pith/LYFRD23HNUBFHIE3L6IRG52RYZ/action/replication_record"}},"created_at":"2026-05-18T04:06:07.993986+00:00","updated_at":"2026-05-18T04:06:07.993986+00:00"}