{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1995:VYSX42SHGF5K6OEM7L2VMMVRDK","short_pith_number":"pith:VYSX42SH","schema_version":"1.0","canonical_sha256":"ae257e6a47317aaf388cfaf55632b11ab238e2e0d908ec932ecdf73999cfc44f","source":{"kind":"arxiv","id":"q-alg/9506028","version":2},"attestation_state":"computed","paper":{"title":"The q-Euclidean algebra $U_q(e^N)$ and the corresponding q-Euclidean lattice","license":"","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"q-alg","authors_text":"Gaetano Fiore","submitted_at":"1995-07-01T22:56:09Z","abstract_excerpt":"We review the Euclidean Hopf algebra $U_q(e^N)$ dual of $Fun(\\rn_q^N\\lcross SO_{q^{-1}}(N))$ and describe its fundamental Hilbert space representations \\cite{fioeu}, which turn out to be rather simple \"lattice-regularized\" versions of the classical ones, in the sense that the spectra of squared momentum components are discrete and the corresponding eigenfunctions normalizable.These representations can be regarded as describing a quantum system consisting of one free particle on the quantum Euclidean space. A suitable notion of classical limit is introduced, so that we recover the classical con"},"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":"q-alg/9506028","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"q-alg","submitted_at":"1995-07-01T22:56:09Z","cross_cats_sorted":["hep-th","math.QA"],"title_canon_sha256":"adf0b6e6904ffca853923a661ffecdc8e3c3cfc28268ff91ab54d8be65ac2cb6","abstract_canon_sha256":"da778f8120e251bab849abee0003b9bbefcbf95fd4fc0823256104a737903606"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:34.296192Z","signature_b64":"NrIB5HCHaDRUViH16B9W21b7jOOY/A9M5CAgDXSVKbbbCPuc0/lFEqYQ9Ar96paarX7wqZRIGABxHVkq0HDjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae257e6a47317aaf388cfaf55632b11ab238e2e0d908ec932ecdf73999cfc44f","last_reissued_at":"2026-05-18T03:44:34.295410Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:34.295410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The q-Euclidean algebra $U_q(e^N)$ and the corresponding q-Euclidean lattice","license":"","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"q-alg","authors_text":"Gaetano Fiore","submitted_at":"1995-07-01T22:56:09Z","abstract_excerpt":"We review the Euclidean Hopf algebra $U_q(e^N)$ dual of $Fun(\\rn_q^N\\lcross SO_{q^{-1}}(N))$ and describe its fundamental Hilbert space representations \\cite{fioeu}, which turn out to be rather simple \"lattice-regularized\" versions of the classical ones, in the sense that the spectra of squared momentum components are discrete and the corresponding eigenfunctions normalizable.These representations can be regarded as describing a quantum system consisting of one free particle on the quantum Euclidean space. A suitable notion of classical limit is introduced, so that we recover the classical con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9506028","kind":"arxiv","version":2},"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":"q-alg/9506028","created_at":"2026-05-18T03:44:34.295529+00:00"},{"alias_kind":"arxiv_version","alias_value":"q-alg/9506028v2","created_at":"2026-05-18T03:44:34.295529+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-alg/9506028","created_at":"2026-05-18T03:44:34.295529+00:00"},{"alias_kind":"pith_short_12","alias_value":"VYSX42SHGF5K","created_at":"2026-05-18T12:25:47.700082+00:00"},{"alias_kind":"pith_short_16","alias_value":"VYSX42SHGF5K6OEM","created_at":"2026-05-18T12:25:47.700082+00:00"},{"alias_kind":"pith_short_8","alias_value":"VYSX42SH","created_at":"2026-05-18T12:25:47.700082+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/VYSX42SHGF5K6OEM7L2VMMVRDK","json":"https://pith.science/pith/VYSX42SHGF5K6OEM7L2VMMVRDK.json","graph_json":"https://pith.science/api/pith-number/VYSX42SHGF5K6OEM7L2VMMVRDK/graph.json","events_json":"https://pith.science/api/pith-number/VYSX42SHGF5K6OEM7L2VMMVRDK/events.json","paper":"https://pith.science/paper/VYSX42SH"},"agent_actions":{"view_html":"https://pith.science/pith/VYSX42SHGF5K6OEM7L2VMMVRDK","download_json":"https://pith.science/pith/VYSX42SHGF5K6OEM7L2VMMVRDK.json","view_paper":"https://pith.science/paper/VYSX42SH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=q-alg/9506028&json=true","fetch_graph":"https://pith.science/api/pith-number/VYSX42SHGF5K6OEM7L2VMMVRDK/graph.json","fetch_events":"https://pith.science/api/pith-number/VYSX42SHGF5K6OEM7L2VMMVRDK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VYSX42SHGF5K6OEM7L2VMMVRDK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VYSX42SHGF5K6OEM7L2VMMVRDK/action/storage_attestation","attest_author":"https://pith.science/pith/VYSX42SHGF5K6OEM7L2VMMVRDK/action/author_attestation","sign_citation":"https://pith.science/pith/VYSX42SHGF5K6OEM7L2VMMVRDK/action/citation_signature","submit_replication":"https://pith.science/pith/VYSX42SHGF5K6OEM7L2VMMVRDK/action/replication_record"}},"created_at":"2026-05-18T03:44:34.295529+00:00","updated_at":"2026-05-18T03:44:34.295529+00:00"}