{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:VYSX42SHGF5K6OEM7L2VMMVRDK","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":"da778f8120e251bab849abee0003b9bbefcbf95fd4fc0823256104a737903606","cross_cats_sorted":["hep-th","math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1995-07-01T22:56:09Z","title_canon_sha256":"adf0b6e6904ffca853923a661ffecdc8e3c3cfc28268ff91ab54d8be65ac2cb6"},"schema_version":"1.0","source":{"id":"q-alg/9506028","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-alg/9506028","created_at":"2026-05-18T03:44:34Z"},{"alias_kind":"arxiv_version","alias_value":"q-alg/9506028v2","created_at":"2026-05-18T03:44:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-alg/9506028","created_at":"2026-05-18T03:44:34Z"},{"alias_kind":"pith_short_12","alias_value":"VYSX42SHGF5K","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"VYSX42SHGF5K6OEM","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"VYSX42SH","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:6055c26e36b8ec42dcce4d86b1a985a1ddd65dcde793563ac5356418155ae98c","target":"graph","created_at":"2026-05-18T03:44:34Z","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 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","authors_text":"Gaetano Fiore","cross_cats":["hep-th","math.QA"],"headline":"","license":"","primary_cat":"q-alg","submitted_at":"1995-07-01T22:56:09Z","title":"The q-Euclidean algebra $U_q(e^N)$ and the corresponding q-Euclidean lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9506028","kind":"arxiv","version":2},"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":"sha256:15a36d3b26d8d960bff7335fea8443a87a43345eea0c4e4262836c2b826a9fd3","target":"record","created_at":"2026-05-18T03:44:34Z","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":"da778f8120e251bab849abee0003b9bbefcbf95fd4fc0823256104a737903606","cross_cats_sorted":["hep-th","math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1995-07-01T22:56:09Z","title_canon_sha256":"adf0b6e6904ffca853923a661ffecdc8e3c3cfc28268ff91ab54d8be65ac2cb6"},"schema_version":"1.0","source":{"id":"q-alg/9506028","kind":"arxiv","version":2}},"canonical_sha256":"ae257e6a47317aaf388cfaf55632b11ab238e2e0d908ec932ecdf73999cfc44f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae257e6a47317aaf388cfaf55632b11ab238e2e0d908ec932ecdf73999cfc44f","first_computed_at":"2026-05-18T03:44:34.295410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:34.295410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NrIB5HCHaDRUViH16B9W21b7jOOY/A9M5CAgDXSVKbbbCPuc0/lFEqYQ9Ar96paarX7wqZRIGABxHVkq0HDjCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:34.296192Z","signed_message":"canonical_sha256_bytes"},"source_id":"q-alg/9506028","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15a36d3b26d8d960bff7335fea8443a87a43345eea0c4e4262836c2b826a9fd3","sha256:6055c26e36b8ec42dcce4d86b1a985a1ddd65dcde793563ac5356418155ae98c"],"state_sha256":"7186ad506713331fe95a85a9592db93e9afa8d9b1da2a837b6d1cf5afe15cfbe"}