{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XLPG44RZYOCXBU6IDXFMDRJPSF","short_pith_number":"pith:XLPG44RZ","canonical_record":{"source":{"id":"1111.0511","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-11-02T14:18:25Z","cross_cats_sorted":[],"title_canon_sha256":"c6a4c30eef10a96b478b95605c94534992b4947a104c1f1fc1093af5e57d4377","abstract_canon_sha256":"bf1e93f0f996da97c9548d6bc5960e785a6dac2c4623c550c931b45900ec32da"},"schema_version":"1.0"},"canonical_sha256":"bade6e7239c38570d3c81dcac1c52f916c3a50c5f05084c647c62db495a17225","source":{"kind":"arxiv","id":"1111.0511","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0511","created_at":"2026-05-18T03:23:12Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0511v2","created_at":"2026-05-18T03:23:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0511","created_at":"2026-05-18T03:23:12Z"},{"alias_kind":"pith_short_12","alias_value":"XLPG44RZYOCX","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XLPG44RZYOCXBU6I","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XLPG44RZ","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XLPG44RZYOCXBU6IDXFMDRJPSF","target":"record","payload":{"canonical_record":{"source":{"id":"1111.0511","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-11-02T14:18:25Z","cross_cats_sorted":[],"title_canon_sha256":"c6a4c30eef10a96b478b95605c94534992b4947a104c1f1fc1093af5e57d4377","abstract_canon_sha256":"bf1e93f0f996da97c9548d6bc5960e785a6dac2c4623c550c931b45900ec32da"},"schema_version":"1.0"},"canonical_sha256":"bade6e7239c38570d3c81dcac1c52f916c3a50c5f05084c647c62db495a17225","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:23:12.720629Z","signature_b64":"d+HWVD65tSQAb+B9OTCXYoHVD0zJrGCEQy+QreaLdc/l1ZqPD72txrRTFT9fvSnOHuSXVZDYIawebWxhWWc/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bade6e7239c38570d3c81dcac1c52f916c3a50c5f05084c647c62db495a17225","last_reissued_at":"2026-05-18T03:23:12.720176Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:23:12.720176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.0511","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:23:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7DWfgmcpxiwJrvK51EBg0y66B2jk5Cag0rLnVDQbyfCcDdnJOMkU8+tmGCFBJk4qerU/3Cpdk/WRznX9Bx4LAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:49:59.645983Z"},"content_sha256":"9fc2600263f6cb7da2edbfe9a044ce2e8720390b42cb0b640d8a91f333ea9f02","schema_version":"1.0","event_id":"sha256:9fc2600263f6cb7da2edbfe9a044ce2e8720390b42cb0b640d8a91f333ea9f02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XLPG44RZYOCXBU6IDXFMDRJPSF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spin Non-commutativity and the Three-Dimensional Harmonic Oscillator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"F. Mendez, H. Falomir, J. C. Rojas, J. Gamboa, M. Loewe","submitted_at":"2011-11-02T14:18:25Z","abstract_excerpt":"A three-dimensional harmonic oscillator with spin non-commutativity in the phase space is considered. The system has a regular symplectic structure and by using supersymmetric quantum mechanics techniques, the ground state is calculated exactly. We find that this state is infinitely degenerate and it has explicit spontaneous broken symmetry. Analyzing the Heisenberg equations, we show that the total angular momentum is conserved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0511","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:23:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TPYH+YQt7SdcWhCSTALpzdIQE1wOb68JIJgxd7Re3Qrlw4l9hqqIr44yn3+zYqm6ueZI8WbwoTpQXdtF+zFTAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:49:59.646511Z"},"content_sha256":"09e30493ac297b95414ca5f3fb756892e9bfea304f404eda0e23d604f04df1b7","schema_version":"1.0","event_id":"sha256:09e30493ac297b95414ca5f3fb756892e9bfea304f404eda0e23d604f04df1b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XLPG44RZYOCXBU6IDXFMDRJPSF/bundle.json","state_url":"https://pith.science/pith/XLPG44RZYOCXBU6IDXFMDRJPSF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XLPG44RZYOCXBU6IDXFMDRJPSF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T04:49:59Z","links":{"resolver":"https://pith.science/pith/XLPG44RZYOCXBU6IDXFMDRJPSF","bundle":"https://pith.science/pith/XLPG44RZYOCXBU6IDXFMDRJPSF/bundle.json","state":"https://pith.science/pith/XLPG44RZYOCXBU6IDXFMDRJPSF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XLPG44RZYOCXBU6IDXFMDRJPSF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XLPG44RZYOCXBU6IDXFMDRJPSF","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":"bf1e93f0f996da97c9548d6bc5960e785a6dac2c4623c550c931b45900ec32da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-11-02T14:18:25Z","title_canon_sha256":"c6a4c30eef10a96b478b95605c94534992b4947a104c1f1fc1093af5e57d4377"},"schema_version":"1.0","source":{"id":"1111.0511","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0511","created_at":"2026-05-18T03:23:12Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0511v2","created_at":"2026-05-18T03:23:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0511","created_at":"2026-05-18T03:23:12Z"},{"alias_kind":"pith_short_12","alias_value":"XLPG44RZYOCX","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XLPG44RZYOCXBU6I","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XLPG44RZ","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:09e30493ac297b95414ca5f3fb756892e9bfea304f404eda0e23d604f04df1b7","target":"graph","created_at":"2026-05-18T03:23:12Z","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":"A three-dimensional harmonic oscillator with spin non-commutativity in the phase space is considered. The system has a regular symplectic structure and by using supersymmetric quantum mechanics techniques, the ground state is calculated exactly. We find that this state is infinitely degenerate and it has explicit spontaneous broken symmetry. Analyzing the Heisenberg equations, we show that the total angular momentum is conserved.","authors_text":"F. Mendez, H. Falomir, J. C. Rojas, J. Gamboa, M. Loewe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-11-02T14:18:25Z","title":"Spin Non-commutativity and the Three-Dimensional Harmonic Oscillator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0511","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":"sha256:9fc2600263f6cb7da2edbfe9a044ce2e8720390b42cb0b640d8a91f333ea9f02","target":"record","created_at":"2026-05-18T03:23:12Z","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":"bf1e93f0f996da97c9548d6bc5960e785a6dac2c4623c550c931b45900ec32da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-11-02T14:18:25Z","title_canon_sha256":"c6a4c30eef10a96b478b95605c94534992b4947a104c1f1fc1093af5e57d4377"},"schema_version":"1.0","source":{"id":"1111.0511","kind":"arxiv","version":2}},"canonical_sha256":"bade6e7239c38570d3c81dcac1c52f916c3a50c5f05084c647c62db495a17225","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bade6e7239c38570d3c81dcac1c52f916c3a50c5f05084c647c62db495a17225","first_computed_at":"2026-05-18T03:23:12.720176Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:23:12.720176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d+HWVD65tSQAb+B9OTCXYoHVD0zJrGCEQy+QreaLdc/l1ZqPD72txrRTFT9fvSnOHuSXVZDYIawebWxhWWc/AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:23:12.720629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.0511","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fc2600263f6cb7da2edbfe9a044ce2e8720390b42cb0b640d8a91f333ea9f02","sha256:09e30493ac297b95414ca5f3fb756892e9bfea304f404eda0e23d604f04df1b7"],"state_sha256":"e84f9696a3aed3b1350534552fd95f6af21ad163945f6cc1172eefd63d948e03"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r8s3fHna13ulnmktoV6Fs43BTu/ivnilOyrO70qbpkE+gXjEAt7CTVEqdkBtKx257kdyVP7JT7jphzO0CHIhBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:49:59.649645Z","bundle_sha256":"16b400cdddb386fc3b3535579287321eb5d4c15bd80ff49cbc994ad879ddfbbe"}}