{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:7WUFVQ5CG2ZHQGTYXOOKO2WQRQ","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":"050c5985c799616f99ab99cac9dc20d2de3310fdd3b62b1ec5f64569fdbc46f2","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2005-02-22T05:28:33Z","title_canon_sha256":"6f77f78bf0e5e17b68270959332dfc39cabd91e4ac9b7fed8f1a96e3b8127aa2"},"schema_version":"1.0","source":{"id":"hep-th/0502192","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0502192","created_at":"2026-05-18T01:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0502192v2","created_at":"2026-05-18T01:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0502192","created_at":"2026-05-18T01:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"7WUFVQ5CG2ZH","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"7WUFVQ5CG2ZHQGTY","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"7WUFVQ5C","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:78488b27c98134343499fcdacd259ee3b8cead96d60cb72a0876255ca6a065aa","target":"graph","created_at":"2026-05-18T01:05:57Z","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 have proposed a generally covariant non-relativistic particle model that can represent the $\\kappa$-Minkowski noncommutative spacetime. The idea is similar in spirit to the noncommutative particle coordinates in the lowest Landau level. Physically our model yields a novel type of dynamical system, (termed here as Exotic \"Oscillator\"), that obeys a\n Harmonic Oscillator like equation of motion with a {\\it{frequency}} that is proportional to the square root of {\\it{energy}}. On the other hand, the phase diagram does not reveal a closed structure since there is a singularity in the momentum eve","authors_text":"Probir Pal, Subir Ghosh","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2005-02-22T05:28:33Z","title":"$\\kappa$-Minkowski Spacetime Through Exotic \"Oscillator\""},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0502192","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:ed9b5f768cfda79af0501de048ab618793d78a2fc0e2397ec0fba9cf428b03d0","target":"record","created_at":"2026-05-18T01:05:57Z","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":"050c5985c799616f99ab99cac9dc20d2de3310fdd3b62b1ec5f64569fdbc46f2","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2005-02-22T05:28:33Z","title_canon_sha256":"6f77f78bf0e5e17b68270959332dfc39cabd91e4ac9b7fed8f1a96e3b8127aa2"},"schema_version":"1.0","source":{"id":"hep-th/0502192","kind":"arxiv","version":2}},"canonical_sha256":"fda85ac3a236b2781a78bb9ca76ad08c3714a41e54a5c5e88a3f7092bde92fd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fda85ac3a236b2781a78bb9ca76ad08c3714a41e54a5c5e88a3f7092bde92fd4","first_computed_at":"2026-05-18T01:05:57.053862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:57.053862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pul+FG0S+v5HImLOeyBodJOEa0O6ARuZZ3rT2wf0haD+uNXTwJ32ULbDdm9FEtxn68rodlIvdkBQnhRz11uHDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:57.054280Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0502192","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed9b5f768cfda79af0501de048ab618793d78a2fc0e2397ec0fba9cf428b03d0","sha256:78488b27c98134343499fcdacd259ee3b8cead96d60cb72a0876255ca6a065aa"],"state_sha256":"af7b6358eec092d062b9f38e8dc9a2059c88e373fc040a90431c0b0ba5c18532"}