{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1997:A45D7C3IQUQ3BEXKCLMTVJSHLT","short_pith_number":"pith:A45D7C3I","schema_version":"1.0","canonical_sha256":"073a3f8b688521b092ea12d93aa6475cc0d0bce1c65d35dba0096f0043c304a6","source":{"kind":"arxiv","id":"hep-ph/9705354","version":1},"attestation_state":"computed","paper":{"title":"Order 1/N corrections to the time-dependent Hartree approximation for a system of N+1 oscillators","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Bogdan Mihaila, Fred Cooper, John F. Dawson","submitted_at":"1997-05-19T15:23:52Z","abstract_excerpt":"We solve numerically to order 1/N the time evolution of a quantum dynamical system of N oscillators of mass m coupled quadratically to a massless dynamic variable. We use Schwinger's closed time path (CTP) formalism to derive the equations. We compare two methods which differ by terms of order 1/N^2. The first method is a direct perturbation theory in 1/N using the path integral. The second solves exactly the theory defined by the effective action to order 1/N. We compare the results of both methods as a function of N. At N=1, where we expect the expansion to be quite innacurate, we compare ou"},"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":"hep-ph/9705354","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"1997-05-19T15:23:52Z","cross_cats_sorted":[],"title_canon_sha256":"2adc150ead14e6e77692576a42ad2a7d81d21d8480a1b39fc4396f556f74796d","abstract_canon_sha256":"92122d18fabf707a35876ef85283bc935ee800ce9acdc4a0325bc9cbbf66d1f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:01.057046Z","signature_b64":"YJOMQLeZcxc7yjBCcgXxaz2Ob2kbRgqZ/G8xAAu2mudBQ093dAou7A98zBnpYrsFR0uvhty2FCJHYc/vWDloBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"073a3f8b688521b092ea12d93aa6475cc0d0bce1c65d35dba0096f0043c304a6","last_reissued_at":"2026-05-18T02:37:01.056263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:01.056263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Order 1/N corrections to the time-dependent Hartree approximation for a system of N+1 oscillators","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Bogdan Mihaila, Fred Cooper, John F. Dawson","submitted_at":"1997-05-19T15:23:52Z","abstract_excerpt":"We solve numerically to order 1/N the time evolution of a quantum dynamical system of N oscillators of mass m coupled quadratically to a massless dynamic variable. We use Schwinger's closed time path (CTP) formalism to derive the equations. We compare two methods which differ by terms of order 1/N^2. The first method is a direct perturbation theory in 1/N using the path integral. The second solves exactly the theory defined by the effective action to order 1/N. We compare the results of both methods as a function of N. At N=1, where we expect the expansion to be quite innacurate, we compare ou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9705354","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/9705354","created_at":"2026-05-18T02:37:01.056401+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/9705354v1","created_at":"2026-05-18T02:37:01.056401+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/9705354","created_at":"2026-05-18T02:37:01.056401+00:00"},{"alias_kind":"pith_short_12","alias_value":"A45D7C3IQUQ3","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_16","alias_value":"A45D7C3IQUQ3BEXK","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_8","alias_value":"A45D7C3I","created_at":"2026-05-18T12:25:48.327863+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A45D7C3IQUQ3BEXKCLMTVJSHLT","json":"https://pith.science/pith/A45D7C3IQUQ3BEXKCLMTVJSHLT.json","graph_json":"https://pith.science/api/pith-number/A45D7C3IQUQ3BEXKCLMTVJSHLT/graph.json","events_json":"https://pith.science/api/pith-number/A45D7C3IQUQ3BEXKCLMTVJSHLT/events.json","paper":"https://pith.science/paper/A45D7C3I"},"agent_actions":{"view_html":"https://pith.science/pith/A45D7C3IQUQ3BEXKCLMTVJSHLT","download_json":"https://pith.science/pith/A45D7C3IQUQ3BEXKCLMTVJSHLT.json","view_paper":"https://pith.science/paper/A45D7C3I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-ph/9705354&json=true","fetch_graph":"https://pith.science/api/pith-number/A45D7C3IQUQ3BEXKCLMTVJSHLT/graph.json","fetch_events":"https://pith.science/api/pith-number/A45D7C3IQUQ3BEXKCLMTVJSHLT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A45D7C3IQUQ3BEXKCLMTVJSHLT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A45D7C3IQUQ3BEXKCLMTVJSHLT/action/storage_attestation","attest_author":"https://pith.science/pith/A45D7C3IQUQ3BEXKCLMTVJSHLT/action/author_attestation","sign_citation":"https://pith.science/pith/A45D7C3IQUQ3BEXKCLMTVJSHLT/action/citation_signature","submit_replication":"https://pith.science/pith/A45D7C3IQUQ3BEXKCLMTVJSHLT/action/replication_record"}},"created_at":"2026-05-18T02:37:01.056401+00:00","updated_at":"2026-05-18T02:37:01.056401+00:00"}