{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NISAAVOQ2DX4OPQCMWUIK3MPNI","short_pith_number":"pith:NISAAVOQ","canonical_record":{"source":{"id":"1201.6607","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-01-31T16:39:40Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e1a06f48c9828c8b873ab9d730d095a12ee7146c9fb0ce27f2ebf0f3a01c2195","abstract_canon_sha256":"107b1868a1e28b44f79b4db34b1f8bee5162c9e4e640b94b3eeaa9801f68f65a"},"schema_version":"1.0"},"canonical_sha256":"6a240055d0d0efc73e0265a8856d8f6a0f0f4b8cf96a63ec043045ac80a88e04","source":{"kind":"arxiv","id":"1201.6607","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6607","created_at":"2026-05-18T04:03:30Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6607v1","created_at":"2026-05-18T04:03:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6607","created_at":"2026-05-18T04:03:30Z"},{"alias_kind":"pith_short_12","alias_value":"NISAAVOQ2DX4","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NISAAVOQ2DX4OPQC","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NISAAVOQ","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NISAAVOQ2DX4OPQCMWUIK3MPNI","target":"record","payload":{"canonical_record":{"source":{"id":"1201.6607","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-01-31T16:39:40Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e1a06f48c9828c8b873ab9d730d095a12ee7146c9fb0ce27f2ebf0f3a01c2195","abstract_canon_sha256":"107b1868a1e28b44f79b4db34b1f8bee5162c9e4e640b94b3eeaa9801f68f65a"},"schema_version":"1.0"},"canonical_sha256":"6a240055d0d0efc73e0265a8856d8f6a0f0f4b8cf96a63ec043045ac80a88e04","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:30.043441Z","signature_b64":"xMUN+W7s4wdY3ZbFTuzGrqXUFHakGrKHCFzvs35JA0YVhw/C4vVCnYqBY3EX1SYhC0zkXlIoEK2Ym8Mi/PvsDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a240055d0d0efc73e0265a8856d8f6a0f0f4b8cf96a63ec043045ac80a88e04","last_reissued_at":"2026-05-18T04:03:30.042732Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:30.042732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.6607","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:03:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"psvtTyYPFguSot2nAj8VRmPt+nnh7w7vIekhlNcE3e1l2pccvafXQ+Z1CQgbl0idlE1+Xv6MVrvTaQjsYeOFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:33:22.000400Z"},"content_sha256":"51ea929ba950ac76a8d4aa3a31d70f3694a2ed5dadf377124ca94e0a4a08c9ee","schema_version":"1.0","event_id":"sha256:51ea929ba950ac76a8d4aa3a31d70f3694a2ed5dadf377124ca94e0a4a08c9ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NISAAVOQ2DX4OPQCMWUIK3MPNI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wavefunctios of log-periodic oscillators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"I. Guedes, V. Bessa","submitted_at":"2012-01-31T16:39:40Z","abstract_excerpt":"We use the Lewis and Riesenfeld invariant method [\\textit{J. Math. Phys.} \\textbf{10}, 1458 (1969)] and a unitary transformation to obtain the exact Schr\\\"{o}dinger wave functions for time-dependent harmonic oscillators exhibiting log-periodic-type behavior. For each oscillator we calculate the quantum fluctuations in the coordinate and momentum as well as the quantum correlations between the coordinate and momentum. We observe that the oscillator with $m=m_0t/t_0$ and $\\omega= \\omega_0t_0/t$, which exhibits an exact log-periodic oscillation, behaves as the harmonic oscillator with $m$ and $\\o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6607","kind":"arxiv","version":1},"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":"2026-05-18T04:03:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xGoHiFn7araqjVz5BYjnueCzUkFxxf6m8+Rkh6k7hVgksWaEALh4SS/DpIfbvs/jWcpKSUrU2Y+l3DyNqmHuAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:33:22.000747Z"},"content_sha256":"aa1875996771e63bb7888f433d42f329130cd74d877738c445f898cbfeb15bce","schema_version":"1.0","event_id":"sha256:aa1875996771e63bb7888f433d42f329130cd74d877738c445f898cbfeb15bce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NISAAVOQ2DX4OPQCMWUIK3MPNI/bundle.json","state_url":"https://pith.science/pith/NISAAVOQ2DX4OPQCMWUIK3MPNI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NISAAVOQ2DX4OPQCMWUIK3MPNI/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":"2026-06-02T03:33:22Z","links":{"resolver":"https://pith.science/pith/NISAAVOQ2DX4OPQCMWUIK3MPNI","bundle":"https://pith.science/pith/NISAAVOQ2DX4OPQCMWUIK3MPNI/bundle.json","state":"https://pith.science/pith/NISAAVOQ2DX4OPQCMWUIK3MPNI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NISAAVOQ2DX4OPQCMWUIK3MPNI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NISAAVOQ2DX4OPQCMWUIK3MPNI","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":"107b1868a1e28b44f79b4db34b1f8bee5162c9e4e640b94b3eeaa9801f68f65a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-01-31T16:39:40Z","title_canon_sha256":"e1a06f48c9828c8b873ab9d730d095a12ee7146c9fb0ce27f2ebf0f3a01c2195"},"schema_version":"1.0","source":{"id":"1201.6607","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6607","created_at":"2026-05-18T04:03:30Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6607v1","created_at":"2026-05-18T04:03:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6607","created_at":"2026-05-18T04:03:30Z"},{"alias_kind":"pith_short_12","alias_value":"NISAAVOQ2DX4","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NISAAVOQ2DX4OPQC","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NISAAVOQ","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:aa1875996771e63bb7888f433d42f329130cd74d877738c445f898cbfeb15bce","target":"graph","created_at":"2026-05-18T04:03:30Z","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 use the Lewis and Riesenfeld invariant method [\\textit{J. Math. Phys.} \\textbf{10}, 1458 (1969)] and a unitary transformation to obtain the exact Schr\\\"{o}dinger wave functions for time-dependent harmonic oscillators exhibiting log-periodic-type behavior. For each oscillator we calculate the quantum fluctuations in the coordinate and momentum as well as the quantum correlations between the coordinate and momentum. We observe that the oscillator with $m=m_0t/t_0$ and $\\omega= \\omega_0t_0/t$, which exhibits an exact log-periodic oscillation, behaves as the harmonic oscillator with $m$ and $\\o","authors_text":"I. Guedes, V. Bessa","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-01-31T16:39:40Z","title":"Wavefunctios of log-periodic oscillators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6607","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":"sha256:51ea929ba950ac76a8d4aa3a31d70f3694a2ed5dadf377124ca94e0a4a08c9ee","target":"record","created_at":"2026-05-18T04:03:30Z","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":"107b1868a1e28b44f79b4db34b1f8bee5162c9e4e640b94b3eeaa9801f68f65a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-01-31T16:39:40Z","title_canon_sha256":"e1a06f48c9828c8b873ab9d730d095a12ee7146c9fb0ce27f2ebf0f3a01c2195"},"schema_version":"1.0","source":{"id":"1201.6607","kind":"arxiv","version":1}},"canonical_sha256":"6a240055d0d0efc73e0265a8856d8f6a0f0f4b8cf96a63ec043045ac80a88e04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a240055d0d0efc73e0265a8856d8f6a0f0f4b8cf96a63ec043045ac80a88e04","first_computed_at":"2026-05-18T04:03:30.042732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:30.042732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xMUN+W7s4wdY3ZbFTuzGrqXUFHakGrKHCFzvs35JA0YVhw/C4vVCnYqBY3EX1SYhC0zkXlIoEK2Ym8Mi/PvsDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:30.043441Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.6607","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51ea929ba950ac76a8d4aa3a31d70f3694a2ed5dadf377124ca94e0a4a08c9ee","sha256:aa1875996771e63bb7888f433d42f329130cd74d877738c445f898cbfeb15bce"],"state_sha256":"d8b3594593c3b267aa1d0ffd8855ec591486cd06c5abd9dde7eef69af26ae01c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/INjhXDiICLEP4ccSf5RgtaIGtcer56+i0CLUbH0bDxU9ssMkqzSoWjSwNWc3b7aLZr2KXT94rXu6L9cBWDHDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T03:33:22.002709Z","bundle_sha256":"c86e8d39490db22a0096ffc850b63a3a96223036c7c4b6136faaf3ed68c8355f"}}