{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:STNL3YIQEPB3F3DWG75W5FXQQA","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":"190e2dc23a51b98cb8f33fbaeea8d9da81f199bf6d1240627353e95c0cdc0c55","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"hep-th","submitted_at":"2000-09-13T13:45:41Z","title_canon_sha256":"183e8623e442f9c9719d7b4907baa985846893099149747921aa76fc51696427"},"schema_version":"1.0","source":{"id":"hep-th/0009099","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0009099","created_at":"2026-05-18T04:17:36Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0009099v1","created_at":"2026-05-18T04:17:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0009099","created_at":"2026-05-18T04:17:36Z"},{"alias_kind":"pith_short_12","alias_value":"STNL3YIQEPB3","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"STNL3YIQEPB3F3DW","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"STNL3YIQ","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:7108b972b5d2462aa67f81b9515b565b5cafbf57dc8a9239ea43a5e918869000","target":"graph","created_at":"2026-05-18T04:17:36Z","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 describe generally deformed Heisenberg algebras in one dimension. The condition for a generalized Leibniz rule is obtained and solved. We analyze conditions under which deformed quantum-mechanical problems have a Fock-space representation. One solution of these conditions leads to a q-deformed oscillator already studied by Lorek et al., and reduces to the harmonic oscillator only in the infinite-momentum frame. The other solution leads to the Calogero model in ordinary quantum mechanics, but reduces to the harmonic oscillator in the absence of deformation.","authors_text":"Stjepan Meljanac (Rudjer Boskovic Inst.), Velimir Bardek","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2000-09-13T13:45:41Z","title":"Deformed Heisenberg algebras, a Fock-space representation and the Calogero model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0009099","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":"sha256:51fdb319ea2c0a7354a3ce243681c4d9316a7a336dd34dc6510226aabb21f904","target":"record","created_at":"2026-05-18T04:17:36Z","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":"190e2dc23a51b98cb8f33fbaeea8d9da81f199bf6d1240627353e95c0cdc0c55","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"hep-th","submitted_at":"2000-09-13T13:45:41Z","title_canon_sha256":"183e8623e442f9c9719d7b4907baa985846893099149747921aa76fc51696427"},"schema_version":"1.0","source":{"id":"hep-th/0009099","kind":"arxiv","version":1}},"canonical_sha256":"94dabde11023c3b2ec7637fb6e96f0801146864a7ee8c56b5daf08e9a13abd84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94dabde11023c3b2ec7637fb6e96f0801146864a7ee8c56b5daf08e9a13abd84","first_computed_at":"2026-05-18T04:17:36.879346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:36.879346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9D31jCvJUU/qpHMtx4+19uEEsQWkgiK6vSyJZnpU3S5lAnzWQ3xiyiz9+PexiCFx9nYnfyVm3kWTTnoBXe0uBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:36.879836Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0009099","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51fdb319ea2c0a7354a3ce243681c4d9316a7a336dd34dc6510226aabb21f904","sha256:7108b972b5d2462aa67f81b9515b565b5cafbf57dc8a9239ea43a5e918869000"],"state_sha256":"b9349e6e577f10e167fd70278601df90dd2a8cda9917553517d9bf0a0d0755e5"}