{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NR3LIKCBB6OCH5D5LMUPDR5UAB","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":"a290cdc0aae8e68371dd8d233eddd3ee1d1c4730ff622831af83627e0952e3b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2016-10-21T17:39:35Z","title_canon_sha256":"82e5983d857e0e60f106365b9b4c529b9445d21f21ba36c4857522f078b2aa08"},"schema_version":"1.0","source":{"id":"1610.06874","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06874","created_at":"2026-05-18T00:50:56Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06874v2","created_at":"2026-05-18T00:50:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06874","created_at":"2026-05-18T00:50:56Z"},{"alias_kind":"pith_short_12","alias_value":"NR3LIKCBB6OC","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NR3LIKCBB6OCH5D5","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NR3LIKCB","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:a4547c0d4e2206313f03834f537bb4facd459b7f2f196bdbffc10bd221366720","target":"graph","created_at":"2026-05-18T00:50:56Z","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":"A simple integral relation between a complex weight and the corresponding positive distribution is derived by introducing a second complex variable. Together with the positivity and normalizability conditions, this sum rule allows to construct explicitly equivalent pairs of distributions in simple cases. In particular the well known solution for a complex gaussian distribution is generalized to an arbitrary complex slope. This opens a possibility of positive representation of Feynman path integrals directly in the Minkowski time. Such construction is then explicitly carried through in the seco","authors_text":"Jacek Wosiek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2016-10-21T17:39:35Z","title":"Beyond complex Langevin equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06874","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:aa67a8a36cb16c528d3323789ef085fecfd13273811ac1e1b33f2424466ae287","target":"record","created_at":"2026-05-18T00:50:56Z","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":"a290cdc0aae8e68371dd8d233eddd3ee1d1c4730ff622831af83627e0952e3b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2016-10-21T17:39:35Z","title_canon_sha256":"82e5983d857e0e60f106365b9b4c529b9445d21f21ba36c4857522f078b2aa08"},"schema_version":"1.0","source":{"id":"1610.06874","kind":"arxiv","version":2}},"canonical_sha256":"6c76b428410f9c23f47d5b28f1c7b400791832b43bb47a0c6478357aa1834bf6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c76b428410f9c23f47d5b28f1c7b400791832b43bb47a0c6478357aa1834bf6","first_computed_at":"2026-05-18T00:50:56.491440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:56.491440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hz0B9YUYOiVbk/Q5o1J/8hhXLNS3WgT7X1ho8iNRx/xy0PtXby+K37YMW4hgDh88OAXxHe5HJvOsrirmbbdBBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:56.492020Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06874","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa67a8a36cb16c528d3323789ef085fecfd13273811ac1e1b33f2424466ae287","sha256:a4547c0d4e2206313f03834f537bb4facd459b7f2f196bdbffc10bd221366720"],"state_sha256":"e1936c1abfff201ff698bc383e72f8f238689f1b121f0b58033702d884b38063"}