{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:NMBK7LBQQ56KPDJJGJHZ5V2BNO","short_pith_number":"pith:NMBK7LBQ","schema_version":"1.0","canonical_sha256":"6b02afac30877ca78d29324f9ed7416b87a16916aa26bc94333b718cbcffb57f","source":{"kind":"arxiv","id":"2107.08969","version":1},"attestation_state":"computed","paper":{"title":"Saturation of Thermal Complexity of Purification","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","quant-ph"],"primary_cat":"hep-th","authors_text":"Bret Underwood, Chandan Jana, S. Shajidul Haque","submitted_at":"2021-07-19T15:36:30Z","abstract_excerpt":"We purify the thermal density matrix of a free harmonic oscillator as a two-mode squeezed state, characterized by a squeezing parameter and squeezing angle. While the squeezing parameter is fixed by the temperature and frequency of the oscillator, the squeezing angle is otherwise undetermined, so that the complexity of purification is obtained by minimizing the complexity of the squeezed state over the squeezing angle. The resulting complexity of the thermal state is minimized at non-zero values of the squeezing angle and saturates to an order one number at high temperatures, indicating that t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2107.08969","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-07-19T15:36:30Z","cross_cats_sorted":["gr-qc","quant-ph"],"title_canon_sha256":"c82fb5b6c14fc62cd005e960507261a6487050fc54321582df0efa0419c27329","abstract_canon_sha256":"7fb07aa333cd2c105d7003f7604bdc26e38fa60b7e614eaa70cfc4986cf984de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:52:13.715152Z","signature_b64":"/5eWyoLlghDM3kswHQawncmDN+CEWBHA9MdeDmoula0BaYjG1yg4h+y3XyZjE7t2hFkHWL0QAn0gvMujZHXICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b02afac30877ca78d29324f9ed7416b87a16916aa26bc94333b718cbcffb57f","last_reissued_at":"2026-07-05T03:52:13.714677Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:52:13.714677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Saturation of Thermal Complexity of Purification","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","quant-ph"],"primary_cat":"hep-th","authors_text":"Bret Underwood, Chandan Jana, S. Shajidul Haque","submitted_at":"2021-07-19T15:36:30Z","abstract_excerpt":"We purify the thermal density matrix of a free harmonic oscillator as a two-mode squeezed state, characterized by a squeezing parameter and squeezing angle. While the squeezing parameter is fixed by the temperature and frequency of the oscillator, the squeezing angle is otherwise undetermined, so that the complexity of purification is obtained by minimizing the complexity of the squeezed state over the squeezing angle. The resulting complexity of the thermal state is minimized at non-zero values of the squeezing angle and saturates to an order one number at high temperatures, indicating that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.08969","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2107.08969/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2107.08969","created_at":"2026-07-05T03:52:13.714737+00:00"},{"alias_kind":"arxiv_version","alias_value":"2107.08969v1","created_at":"2026-07-05T03:52:13.714737+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.08969","created_at":"2026-07-05T03:52:13.714737+00:00"},{"alias_kind":"pith_short_12","alias_value":"NMBK7LBQQ56K","created_at":"2026-07-05T03:52:13.714737+00:00"},{"alias_kind":"pith_short_16","alias_value":"NMBK7LBQQ56KPDJJ","created_at":"2026-07-05T03:52:13.714737+00:00"},{"alias_kind":"pith_short_8","alias_value":"NMBK7LBQ","created_at":"2026-07-05T03:52:13.714737+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.07663","citing_title":"A Landscape of Cosmological Decoherence","ref_index":20,"is_internal_anchor":false},{"citing_arxiv_id":"2509.14810","citing_title":"Krylov Complexity for Open Quantum System: Dissipation and Decoherence","ref_index":35,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NMBK7LBQQ56KPDJJGJHZ5V2BNO","json":"https://pith.science/pith/NMBK7LBQQ56KPDJJGJHZ5V2BNO.json","graph_json":"https://pith.science/api/pith-number/NMBK7LBQQ56KPDJJGJHZ5V2BNO/graph.json","events_json":"https://pith.science/api/pith-number/NMBK7LBQQ56KPDJJGJHZ5V2BNO/events.json","paper":"https://pith.science/paper/NMBK7LBQ"},"agent_actions":{"view_html":"https://pith.science/pith/NMBK7LBQQ56KPDJJGJHZ5V2BNO","download_json":"https://pith.science/pith/NMBK7LBQQ56KPDJJGJHZ5V2BNO.json","view_paper":"https://pith.science/paper/NMBK7LBQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2107.08969&json=true","fetch_graph":"https://pith.science/api/pith-number/NMBK7LBQQ56KPDJJGJHZ5V2BNO/graph.json","fetch_events":"https://pith.science/api/pith-number/NMBK7LBQQ56KPDJJGJHZ5V2BNO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NMBK7LBQQ56KPDJJGJHZ5V2BNO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NMBK7LBQQ56KPDJJGJHZ5V2BNO/action/storage_attestation","attest_author":"https://pith.science/pith/NMBK7LBQQ56KPDJJGJHZ5V2BNO/action/author_attestation","sign_citation":"https://pith.science/pith/NMBK7LBQQ56KPDJJGJHZ5V2BNO/action/citation_signature","submit_replication":"https://pith.science/pith/NMBK7LBQQ56KPDJJGJHZ5V2BNO/action/replication_record"}},"created_at":"2026-07-05T03:52:13.714737+00:00","updated_at":"2026-07-05T03:52:13.714737+00:00"}