{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:EXQ364GXWH5IEBYC3LSD3FYMSR","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":"8568feeb239e3b3b2d429473def6911e4a73d1346b3f60372ef5bd30cc8e22c7","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"","primary_cat":"hep-th","submitted_at":"2003-09-10T15:49:25Z","title_canon_sha256":"1409a17080cca555971a654cbc894467abfecba8ec66a423302f8e8922cd5d88"},"schema_version":"1.0","source":{"id":"hep-th/0309105","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0309105","created_at":"2026-05-18T04:37:00Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0309105v1","created_at":"2026-05-18T04:37:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0309105","created_at":"2026-05-18T04:37:00Z"},{"alias_kind":"pith_short_12","alias_value":"EXQ364GXWH5I","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"EXQ364GXWH5IEBYC","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"EXQ364GX","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:7d25731740420fa99735d6de1a3d581ff4d2150208eee8f786d487b87202eb30","target":"graph","created_at":"2026-05-18T04:37:00Z","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 investigate a system of two coupled harmonic oscillators on the non-commutative plane \\RR^2_{\\theta} by requiring that the spatial coordinates do not commute. We show that the system can be diagonalized by a suitable transformation, i.e. a rotation with a mixing angle \\alpha. The obtained eigenstates as well as the eigenvalues depend on the non-commutativity parameter \\theta. Focusing on the ground state wave function before the transformation, we calculate the density matrix \\rho_0(\\theta) and find that its traces {\\rm Tr}(\\rho_{0}(\\theta)) and {\\rm Tr}(\\rho_0^2(\\theta)) are not affected b","authors_text":"Ahmed Jellal, El Hassan El Kinani, Michael Schreiber","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2003-09-10T15:49:25Z","title":"Two Coupled Harmonic Oscillators on Non-commutative Plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0309105","kind":"arxiv","version":1},"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":"sha256:0469ca2aaf90a10caa0e1f7dd485dd7e9cac5ad47a20b09f51be017e16673bf5","target":"record","created_at":"2026-05-18T04:37:00Z","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":"8568feeb239e3b3b2d429473def6911e4a73d1346b3f60372ef5bd30cc8e22c7","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"","primary_cat":"hep-th","submitted_at":"2003-09-10T15:49:25Z","title_canon_sha256":"1409a17080cca555971a654cbc894467abfecba8ec66a423302f8e8922cd5d88"},"schema_version":"1.0","source":{"id":"hep-th/0309105","kind":"arxiv","version":1}},"canonical_sha256":"25e1bf70d7b1fa820702dae43d970c94622515a8e999b61f1d805d1a3dc3822a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25e1bf70d7b1fa820702dae43d970c94622515a8e999b61f1d805d1a3dc3822a","first_computed_at":"2026-05-18T04:37:00.179412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:00.179412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QHz0xXxGvpgSF7vRMbpGo3coywMCHyWKF/nlHMwzwbjYKUPz9Ufo7MjDZAGPUTm1PuYxcTg2GdgNFVLf2StECw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:00.180064Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0309105","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0469ca2aaf90a10caa0e1f7dd485dd7e9cac5ad47a20b09f51be017e16673bf5","sha256:7d25731740420fa99735d6de1a3d581ff4d2150208eee8f786d487b87202eb30"],"state_sha256":"6f14104dfc67363eeaef54a98bb8b3b162a136aae3683ea5f353be2874d73c1e"}