{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SQDAH6EWPSYZE35UF6P475ECXU","short_pith_number":"pith:SQDAH6EW","canonical_record":{"source":{"id":"1609.00248","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-09-01T14:09:42Z","cross_cats_sorted":[],"title_canon_sha256":"7ccd37866a5835f4448fc52fc4831d437a2da0a6e909825a8293ea33d4dfc077","abstract_canon_sha256":"ff6b141f936e8f7238766f61adf9f3c1f3030d751c461dfad91696bd4c55f0c6"},"schema_version":"1.0"},"canonical_sha256":"940603f8967cb1926fb42f9fcff482bd2e225f70d5351c07dd734faedd2e82fc","source":{"kind":"arxiv","id":"1609.00248","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00248","created_at":"2026-05-18T00:54:34Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00248v2","created_at":"2026-05-18T00:54:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00248","created_at":"2026-05-18T00:54:34Z"},{"alias_kind":"pith_short_12","alias_value":"SQDAH6EWPSYZ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SQDAH6EWPSYZE35U","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SQDAH6EW","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SQDAH6EWPSYZE35UF6P475ECXU","target":"record","payload":{"canonical_record":{"source":{"id":"1609.00248","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-09-01T14:09:42Z","cross_cats_sorted":[],"title_canon_sha256":"7ccd37866a5835f4448fc52fc4831d437a2da0a6e909825a8293ea33d4dfc077","abstract_canon_sha256":"ff6b141f936e8f7238766f61adf9f3c1f3030d751c461dfad91696bd4c55f0c6"},"schema_version":"1.0"},"canonical_sha256":"940603f8967cb1926fb42f9fcff482bd2e225f70d5351c07dd734faedd2e82fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:34.326063Z","signature_b64":"kcRCd22UlSQcSfCYLqMXNEKL5UqI/q24Ei+HzMB5bHyf/kT+CtvW7s0iAwg32zoke6zCUBz42pyeUAQyklJSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"940603f8967cb1926fb42f9fcff482bd2e225f70d5351c07dd734faedd2e82fc","last_reissued_at":"2026-05-18T00:54:34.325341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:34.325341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.00248","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":"2026-05-18T00:54:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gPmhJJVv/w+k64hFB1v8Jy38c3EP8JuD4KR6ipRHPaJG+rggVqxbvikeVgobadEs/P2riqWP7/u4XH05MkBhAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:18:20.902164Z"},"content_sha256":"fd683e66e3bb6542e443c364600b5310e98a9512bd9b8c7f9b979110c7571980","schema_version":"1.0","event_id":"sha256:fd683e66e3bb6542e443c364600b5310e98a9512bd9b8c7f9b979110c7571980"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SQDAH6EWPSYZE35UF6P475ECXU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction of Exact Ermakov-Pinney Solutions and Time-Dependent Quantum Oscillators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Sang Pyo Kim, Won Kim (Kunsan Natl U.)","submitted_at":"2016-09-01T14:09:42Z","abstract_excerpt":"The harmonic oscillator with a time-dependent frequency has a family of linear quantum invariants for the time-dependent Schr\\\"{o}dinger equation, which are determined by any two independent solutions to the classical equation of motion. Ermakov and Pinney have shown that a general solution to the time-dependent oscillator with an inverse cubic term can be expressed in terms of two independent solutions to the time-dependent oscillator. We explore the connection between linear quantum invariants and the Ermakov-Pinney solution for the time-dependent harmonic oscillator. We advance a novel meth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00248","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":"2026-05-18T00:54:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U523oZupnjlsbHN2yvyK5OpPi9ON0L9DCCIeOrErVd22kCpT1FPwWoCqihKagRbb/MVVrpNuIe+TQlmC8BdrBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:18:20.902745Z"},"content_sha256":"0340c707253ea56851ad1a2debf4d6e26607181f5602ff2c99c1ceeb48cda689","schema_version":"1.0","event_id":"sha256:0340c707253ea56851ad1a2debf4d6e26607181f5602ff2c99c1ceeb48cda689"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SQDAH6EWPSYZE35UF6P475ECXU/bundle.json","state_url":"https://pith.science/pith/SQDAH6EWPSYZE35UF6P475ECXU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SQDAH6EWPSYZE35UF6P475ECXU/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":"2026-05-25T23:18:20Z","links":{"resolver":"https://pith.science/pith/SQDAH6EWPSYZE35UF6P475ECXU","bundle":"https://pith.science/pith/SQDAH6EWPSYZE35UF6P475ECXU/bundle.json","state":"https://pith.science/pith/SQDAH6EWPSYZE35UF6P475ECXU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SQDAH6EWPSYZE35UF6P475ECXU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SQDAH6EWPSYZE35UF6P475ECXU","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":"ff6b141f936e8f7238766f61adf9f3c1f3030d751c461dfad91696bd4c55f0c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-09-01T14:09:42Z","title_canon_sha256":"7ccd37866a5835f4448fc52fc4831d437a2da0a6e909825a8293ea33d4dfc077"},"schema_version":"1.0","source":{"id":"1609.00248","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00248","created_at":"2026-05-18T00:54:34Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00248v2","created_at":"2026-05-18T00:54:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00248","created_at":"2026-05-18T00:54:34Z"},{"alias_kind":"pith_short_12","alias_value":"SQDAH6EWPSYZ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SQDAH6EWPSYZE35U","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SQDAH6EW","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:0340c707253ea56851ad1a2debf4d6e26607181f5602ff2c99c1ceeb48cda689","target":"graph","created_at":"2026-05-18T00:54:34Z","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":"The harmonic oscillator with a time-dependent frequency has a family of linear quantum invariants for the time-dependent Schr\\\"{o}dinger equation, which are determined by any two independent solutions to the classical equation of motion. Ermakov and Pinney have shown that a general solution to the time-dependent oscillator with an inverse cubic term can be expressed in terms of two independent solutions to the time-dependent oscillator. We explore the connection between linear quantum invariants and the Ermakov-Pinney solution for the time-dependent harmonic oscillator. We advance a novel meth","authors_text":"Sang Pyo Kim, Won Kim (Kunsan Natl U.)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-09-01T14:09:42Z","title":"Construction of Exact Ermakov-Pinney Solutions and Time-Dependent Quantum Oscillators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00248","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:fd683e66e3bb6542e443c364600b5310e98a9512bd9b8c7f9b979110c7571980","target":"record","created_at":"2026-05-18T00:54:34Z","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":"ff6b141f936e8f7238766f61adf9f3c1f3030d751c461dfad91696bd4c55f0c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-09-01T14:09:42Z","title_canon_sha256":"7ccd37866a5835f4448fc52fc4831d437a2da0a6e909825a8293ea33d4dfc077"},"schema_version":"1.0","source":{"id":"1609.00248","kind":"arxiv","version":2}},"canonical_sha256":"940603f8967cb1926fb42f9fcff482bd2e225f70d5351c07dd734faedd2e82fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"940603f8967cb1926fb42f9fcff482bd2e225f70d5351c07dd734faedd2e82fc","first_computed_at":"2026-05-18T00:54:34.325341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:34.325341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kcRCd22UlSQcSfCYLqMXNEKL5UqI/q24Ei+HzMB5bHyf/kT+CtvW7s0iAwg32zoke6zCUBz42pyeUAQyklJSAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:34.326063Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.00248","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd683e66e3bb6542e443c364600b5310e98a9512bd9b8c7f9b979110c7571980","sha256:0340c707253ea56851ad1a2debf4d6e26607181f5602ff2c99c1ceeb48cda689"],"state_sha256":"f4cb4bb3ad9a0a901ab3620f37464c142fc03044e89de060f9d6575e27a6464d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eawwDVidG6hiAVPB9aqzTsA5r2O366r4m9LCwGk00TfwNOFvePx3sPVNn/fAZwxPFoVirzGWkQeo4IZVRoN1AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:18:20.905849Z","bundle_sha256":"2d16b3020327b48adc46fbe4a9132d3514f42fb5ba6a8d21bcf82f1100d79546"}}