{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:XVHCL5JLLKTQ637M6XZQZHBMHW","short_pith_number":"pith:XVHCL5JL","schema_version":"1.0","canonical_sha256":"bd4e25f52b5aa70f6fecf5f30c9c2c3dbf5991e1159765270b79b2f3e2e49df4","source":{"kind":"arxiv","id":"1205.3601","version":1},"attestation_state":"computed","paper":{"title":"A Symplectic Method to Generate Multivariate Normal Distributions","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"physics.data-an","authors_text":"Christian Baumgarten","submitted_at":"2012-05-16T09:07:30Z","abstract_excerpt":"The AMAS group at the Paul Scherrer Institute developed an object oriented library for high performance simulation of high intensity ion beam transport with space charge. Such particle-in-cell (PIC) simulations require a method to generate multivariate particle distributions as starting conditions.\n  In a preceeding publications it has been shown that the generators of symplectic transformations in two dimensions are a subset of the real Dirac matrices (RDMs) and that few symplectic transformations are required to transform a quadratic Hamiltonian into diagonal form.\n  Here we argue that the u"},"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":"1205.3601","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"physics.data-an","submitted_at":"2012-05-16T09:07:30Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e4455da0bf9566cafab359950d2a962c06b99c1f81749bf6582514669cc6e358","abstract_canon_sha256":"cd3e2e15c626908c499d3256f065d2c3fb6385dafe1d5c6212ede6f050928bd0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:34.640933Z","signature_b64":"cLPARgi6OkI9xFiNd/vWrarPHsCetxq0GK9CSUB0SERsLb7q4Kc448bp+l5DCo4jyUKqWL8PxpLPmRrweF+4Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd4e25f52b5aa70f6fecf5f30c9c2c3dbf5991e1159765270b79b2f3e2e49df4","last_reissued_at":"2026-05-18T03:55:34.640052Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:34.640052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Symplectic Method to Generate Multivariate Normal Distributions","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"physics.data-an","authors_text":"Christian Baumgarten","submitted_at":"2012-05-16T09:07:30Z","abstract_excerpt":"The AMAS group at the Paul Scherrer Institute developed an object oriented library for high performance simulation of high intensity ion beam transport with space charge. Such particle-in-cell (PIC) simulations require a method to generate multivariate particle distributions as starting conditions.\n  In a preceeding publications it has been shown that the generators of symplectic transformations in two dimensions are a subset of the real Dirac matrices (RDMs) and that few symplectic transformations are required to transform a quadratic Hamiltonian into diagonal form.\n  Here we argue that the u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3601","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":"1205.3601","created_at":"2026-05-18T03:55:34.640202+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.3601v1","created_at":"2026-05-18T03:55:34.640202+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3601","created_at":"2026-05-18T03:55:34.640202+00:00"},{"alias_kind":"pith_short_12","alias_value":"XVHCL5JLLKTQ","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"XVHCL5JLLKTQ637M","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"XVHCL5JL","created_at":"2026-05-18T12:27:27.928770+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/XVHCL5JLLKTQ637M6XZQZHBMHW","json":"https://pith.science/pith/XVHCL5JLLKTQ637M6XZQZHBMHW.json","graph_json":"https://pith.science/api/pith-number/XVHCL5JLLKTQ637M6XZQZHBMHW/graph.json","events_json":"https://pith.science/api/pith-number/XVHCL5JLLKTQ637M6XZQZHBMHW/events.json","paper":"https://pith.science/paper/XVHCL5JL"},"agent_actions":{"view_html":"https://pith.science/pith/XVHCL5JLLKTQ637M6XZQZHBMHW","download_json":"https://pith.science/pith/XVHCL5JLLKTQ637M6XZQZHBMHW.json","view_paper":"https://pith.science/paper/XVHCL5JL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.3601&json=true","fetch_graph":"https://pith.science/api/pith-number/XVHCL5JLLKTQ637M6XZQZHBMHW/graph.json","fetch_events":"https://pith.science/api/pith-number/XVHCL5JLLKTQ637M6XZQZHBMHW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XVHCL5JLLKTQ637M6XZQZHBMHW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XVHCL5JLLKTQ637M6XZQZHBMHW/action/storage_attestation","attest_author":"https://pith.science/pith/XVHCL5JLLKTQ637M6XZQZHBMHW/action/author_attestation","sign_citation":"https://pith.science/pith/XVHCL5JLLKTQ637M6XZQZHBMHW/action/citation_signature","submit_replication":"https://pith.science/pith/XVHCL5JLLKTQ637M6XZQZHBMHW/action/replication_record"}},"created_at":"2026-05-18T03:55:34.640202+00:00","updated_at":"2026-05-18T03:55:34.640202+00:00"}