{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:E3TEPWWBVRCSOAFPGZ76ZGVBG2","short_pith_number":"pith:E3TEPWWB","schema_version":"1.0","canonical_sha256":"26e647dac1ac452700af367fec9aa1369ff40b51b2c6efab5596f213673093c9","source":{"kind":"arxiv","id":"2110.08356","version":3},"attestation_state":"computed","paper":{"title":"Operator Complexity for Quantum Scalar Fields and Cosmological Perturbations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"hep-th","authors_text":"Bret Underwood, Chandan Jana, S. Shajidul Haque","submitted_at":"2021-10-15T20:37:36Z","abstract_excerpt":"We calculate the operator complexity for the displacement, squeeze and rotation operators of a quantum harmonic oscillator. The complexity of the time-dependent displacement operator is constant, equal to the magnitude of the coherent state parameter, while the complexity of unitary evolution by a generic quadratic Hamiltonian is proportional to the amount of squeezing and is sensitive to the time-dependent phase of the unitary operator. We apply these results to study the complexity of a free massive scalar field, finding that the complexity has a period of rapid linear growth followed by a s"},"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":"2110.08356","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-10-15T20:37:36Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"5960233b3e8b3b438d069cb91b0189831732878adf88241817fb6a1dc1759f6a","abstract_canon_sha256":"d0c27c0c340eb7305599031c2bce9438fdd8f92928b30a2bec2daf92ff46b34f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:38:45.409981Z","signature_b64":"82fjkJy5Xu90FJRQkGcFRlBN2fFJTGLZxFMioMftWbgibjQLfbhiQNuIMlWGAu1SGKgHk4jLyDbfzdgJgUAJDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26e647dac1ac452700af367fec9aa1369ff40b51b2c6efab5596f213673093c9","last_reissued_at":"2026-07-05T04:38:45.409451Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:38:45.409451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Operator Complexity for Quantum Scalar Fields and Cosmological Perturbations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"hep-th","authors_text":"Bret Underwood, Chandan Jana, S. Shajidul Haque","submitted_at":"2021-10-15T20:37:36Z","abstract_excerpt":"We calculate the operator complexity for the displacement, squeeze and rotation operators of a quantum harmonic oscillator. The complexity of the time-dependent displacement operator is constant, equal to the magnitude of the coherent state parameter, while the complexity of unitary evolution by a generic quadratic Hamiltonian is proportional to the amount of squeezing and is sensitive to the time-dependent phase of the unitary operator. We apply these results to study the complexity of a free massive scalar field, finding that the complexity has a period of rapid linear growth followed by a s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.08356","kind":"arxiv","version":3},"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/2110.08356/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":"2110.08356","created_at":"2026-07-05T04:38:45.409518+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.08356v3","created_at":"2026-07-05T04:38:45.409518+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.08356","created_at":"2026-07-05T04:38:45.409518+00:00"},{"alias_kind":"pith_short_12","alias_value":"E3TEPWWBVRCS","created_at":"2026-07-05T04:38:45.409518+00:00"},{"alias_kind":"pith_short_16","alias_value":"E3TEPWWBVRCSOAFP","created_at":"2026-07-05T04:38:45.409518+00:00"},{"alias_kind":"pith_short_8","alias_value":"E3TEPWWB","created_at":"2026-07-05T04:38:45.409518+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":21,"is_internal_anchor":false},{"citing_arxiv_id":"2509.14810","citing_title":"Krylov Complexity for Open Quantum System: Dissipation and Decoherence","ref_index":44,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E3TEPWWBVRCSOAFPGZ76ZGVBG2","json":"https://pith.science/pith/E3TEPWWBVRCSOAFPGZ76ZGVBG2.json","graph_json":"https://pith.science/api/pith-number/E3TEPWWBVRCSOAFPGZ76ZGVBG2/graph.json","events_json":"https://pith.science/api/pith-number/E3TEPWWBVRCSOAFPGZ76ZGVBG2/events.json","paper":"https://pith.science/paper/E3TEPWWB"},"agent_actions":{"view_html":"https://pith.science/pith/E3TEPWWBVRCSOAFPGZ76ZGVBG2","download_json":"https://pith.science/pith/E3TEPWWBVRCSOAFPGZ76ZGVBG2.json","view_paper":"https://pith.science/paper/E3TEPWWB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.08356&json=true","fetch_graph":"https://pith.science/api/pith-number/E3TEPWWBVRCSOAFPGZ76ZGVBG2/graph.json","fetch_events":"https://pith.science/api/pith-number/E3TEPWWBVRCSOAFPGZ76ZGVBG2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E3TEPWWBVRCSOAFPGZ76ZGVBG2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E3TEPWWBVRCSOAFPGZ76ZGVBG2/action/storage_attestation","attest_author":"https://pith.science/pith/E3TEPWWBVRCSOAFPGZ76ZGVBG2/action/author_attestation","sign_citation":"https://pith.science/pith/E3TEPWWBVRCSOAFPGZ76ZGVBG2/action/citation_signature","submit_replication":"https://pith.science/pith/E3TEPWWBVRCSOAFPGZ76ZGVBG2/action/replication_record"}},"created_at":"2026-07-05T04:38:45.409518+00:00","updated_at":"2026-07-05T04:38:45.409518+00:00"}