{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ESBUJOLZNJJMCT7PBGUYI3YNJO","short_pith_number":"pith:ESBUJOLZ","canonical_record":{"source":{"id":"1603.07727","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-03-24T08:29:22Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"108a0e53968273298f5a9669d80984d18db7f89784cdd37b122cb7e1158ac6e2","abstract_canon_sha256":"e488bb2257a6d0882e8b505858951c5d6546eb12bcdae159c271532241532816"},"schema_version":"1.0"},"canonical_sha256":"248344b9796a52c14fef09a9846f0d4b946163da29918c995346752d0948ab8b","source":{"kind":"arxiv","id":"1603.07727","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07727","created_at":"2026-05-18T01:14:52Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07727v2","created_at":"2026-05-18T01:14:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07727","created_at":"2026-05-18T01:14:52Z"},{"alias_kind":"pith_short_12","alias_value":"ESBUJOLZNJJM","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"ESBUJOLZNJJMCT7P","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"ESBUJOLZ","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ESBUJOLZNJJMCT7PBGUYI3YNJO","target":"record","payload":{"canonical_record":{"source":{"id":"1603.07727","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-03-24T08:29:22Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"108a0e53968273298f5a9669d80984d18db7f89784cdd37b122cb7e1158ac6e2","abstract_canon_sha256":"e488bb2257a6d0882e8b505858951c5d6546eb12bcdae159c271532241532816"},"schema_version":"1.0"},"canonical_sha256":"248344b9796a52c14fef09a9846f0d4b946163da29918c995346752d0948ab8b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:52.347306Z","signature_b64":"sOfATLaAqZoHrQTzjLRd/5rocDk5x1Q633mS5yFbYskhv7Tz1Mt+iyxBjDnLQFcvmSRH+lSYUR9qtFM4WN3JAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"248344b9796a52c14fef09a9846f0d4b946163da29918c995346752d0948ab8b","last_reissued_at":"2026-05-18T01:14:52.346799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:52.346799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.07727","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":"2026-05-18T01:14:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fxkoWGYRtLCbuCGXyp/iDD6NJwxsaZddX8iQjSVSq4glAs/Pi2IHDwcRtbfGvmNJtPBWNrDds8//bbDExRFQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:51:10.833200Z"},"content_sha256":"64d1a0ffb54ce9ca8afd6dc2341ef68e22184c5e0d12eed28bac3cbb84460693","schema_version":"1.0","event_id":"sha256:64d1a0ffb54ce9ca8afd6dc2341ef68e22184c5e0d12eed28bac3cbb84460693"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ESBUJOLZNJJMCT7PBGUYI3YNJO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The odd-order Pais-Uhlenbeck oscillator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Ivan Masterov","submitted_at":"2016-03-24T08:29:22Z","abstract_excerpt":"We consider a Hamiltonian formulation of the (2n+1)-order generalization of the Pais-Uhlenbeck oscillator with distinct frequencies of oscillation. This system is invariant under time translations. However, the corresponding Noether integral of motion is unbounded from below and can be presented as a direct sum of 2n one-dimensional harmonic oscillators with an alternating sign. If this integral of motion plays a role of a Hamiltonian, a quantum theory of the Pais-Uhlenbeck oscillator faces a ghost problem. We construct an alternative canonical formulation for the system under study to avoid t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07727","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":"2026-05-18T01:14:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uU2aMfYBB0vCEMnmFg4jonrnEGmDTY/dJgR6y7xqMMZlY1VzjZOZqYcFeBVvBjmiaPQud5CPb/MMoMS6nkCjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:51:10.833888Z"},"content_sha256":"6e076a285898f21689db3f5b2d796ae3b20e6ae4678511902acc9c7fb2166fdd","schema_version":"1.0","event_id":"sha256:6e076a285898f21689db3f5b2d796ae3b20e6ae4678511902acc9c7fb2166fdd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ESBUJOLZNJJMCT7PBGUYI3YNJO/bundle.json","state_url":"https://pith.science/pith/ESBUJOLZNJJMCT7PBGUYI3YNJO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ESBUJOLZNJJMCT7PBGUYI3YNJO/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":"2026-05-26T11:51:10Z","links":{"resolver":"https://pith.science/pith/ESBUJOLZNJJMCT7PBGUYI3YNJO","bundle":"https://pith.science/pith/ESBUJOLZNJJMCT7PBGUYI3YNJO/bundle.json","state":"https://pith.science/pith/ESBUJOLZNJJMCT7PBGUYI3YNJO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ESBUJOLZNJJMCT7PBGUYI3YNJO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ESBUJOLZNJJMCT7PBGUYI3YNJO","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":"e488bb2257a6d0882e8b505858951c5d6546eb12bcdae159c271532241532816","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-03-24T08:29:22Z","title_canon_sha256":"108a0e53968273298f5a9669d80984d18db7f89784cdd37b122cb7e1158ac6e2"},"schema_version":"1.0","source":{"id":"1603.07727","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07727","created_at":"2026-05-18T01:14:52Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07727v2","created_at":"2026-05-18T01:14:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07727","created_at":"2026-05-18T01:14:52Z"},{"alias_kind":"pith_short_12","alias_value":"ESBUJOLZNJJM","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"ESBUJOLZNJJMCT7P","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"ESBUJOLZ","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:6e076a285898f21689db3f5b2d796ae3b20e6ae4678511902acc9c7fb2166fdd","target":"graph","created_at":"2026-05-18T01:14:52Z","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 consider a Hamiltonian formulation of the (2n+1)-order generalization of the Pais-Uhlenbeck oscillator with distinct frequencies of oscillation. This system is invariant under time translations. However, the corresponding Noether integral of motion is unbounded from below and can be presented as a direct sum of 2n one-dimensional harmonic oscillators with an alternating sign. If this integral of motion plays a role of a Hamiltonian, a quantum theory of the Pais-Uhlenbeck oscillator faces a ghost problem. We construct an alternative canonical formulation for the system under study to avoid t","authors_text":"Ivan Masterov","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-03-24T08:29:22Z","title":"The odd-order Pais-Uhlenbeck oscillator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07727","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":"sha256:64d1a0ffb54ce9ca8afd6dc2341ef68e22184c5e0d12eed28bac3cbb84460693","target":"record","created_at":"2026-05-18T01:14:52Z","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":"e488bb2257a6d0882e8b505858951c5d6546eb12bcdae159c271532241532816","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-03-24T08:29:22Z","title_canon_sha256":"108a0e53968273298f5a9669d80984d18db7f89784cdd37b122cb7e1158ac6e2"},"schema_version":"1.0","source":{"id":"1603.07727","kind":"arxiv","version":2}},"canonical_sha256":"248344b9796a52c14fef09a9846f0d4b946163da29918c995346752d0948ab8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"248344b9796a52c14fef09a9846f0d4b946163da29918c995346752d0948ab8b","first_computed_at":"2026-05-18T01:14:52.346799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:52.346799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sOfATLaAqZoHrQTzjLRd/5rocDk5x1Q633mS5yFbYskhv7Tz1Mt+iyxBjDnLQFcvmSRH+lSYUR9qtFM4WN3JAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:52.347306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07727","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64d1a0ffb54ce9ca8afd6dc2341ef68e22184c5e0d12eed28bac3cbb84460693","sha256:6e076a285898f21689db3f5b2d796ae3b20e6ae4678511902acc9c7fb2166fdd"],"state_sha256":"f2cc23202889a6fd300a236ee1b53dbfe83a8c48185ec176cb993430cd7014c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sHni9p1YHEK9fHe8Hn72Z7q4aTXY5pPWc/8QG6Hexuf30uZLHCwDjUTXcdFWvYgC0nGth39tTT98m8F1ZwbwBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:51:10.837512Z","bundle_sha256":"1ab3e7afda1c6da74ac53a98a3b1bcac2aa5dc09df2eaf58d6f82c42b25b72e7"}}