{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:N3AN2WQFVTNOAXETNBIW2C63IB","short_pith_number":"pith:N3AN2WQF","canonical_record":{"source":{"id":"2210.06991","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-10-13T13:00:31Z","cross_cats_sorted":["hep-ph","quant-ph"],"title_canon_sha256":"0e7edf88c2c98c00016a65475f6daf6142a7a900081f4ca2dff1ed03972ae9a8","abstract_canon_sha256":"8821e7cac70b9eab8db40ef82c1a6a097b99f87051d1fa1f2e81f2ee65d8c4a9"},"schema_version":"1.0"},"canonical_sha256":"6ec0dd5a05acdae05c9368516d0bdb406095ea1a8f95664bb2f08f61043fe6e1","source":{"kind":"arxiv","id":"2210.06991","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.06991","created_at":"2026-07-05T06:18:51Z"},{"alias_kind":"arxiv_version","alias_value":"2210.06991v2","created_at":"2026-07-05T06:18:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.06991","created_at":"2026-07-05T06:18:51Z"},{"alias_kind":"pith_short_12","alias_value":"N3AN2WQFVTNO","created_at":"2026-07-05T06:18:51Z"},{"alias_kind":"pith_short_16","alias_value":"N3AN2WQFVTNOAXET","created_at":"2026-07-05T06:18:51Z"},{"alias_kind":"pith_short_8","alias_value":"N3AN2WQF","created_at":"2026-07-05T06:18:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:N3AN2WQFVTNOAXETNBIW2C63IB","target":"record","payload":{"canonical_record":{"source":{"id":"2210.06991","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-10-13T13:00:31Z","cross_cats_sorted":["hep-ph","quant-ph"],"title_canon_sha256":"0e7edf88c2c98c00016a65475f6daf6142a7a900081f4ca2dff1ed03972ae9a8","abstract_canon_sha256":"8821e7cac70b9eab8db40ef82c1a6a097b99f87051d1fa1f2e81f2ee65d8c4a9"},"schema_version":"1.0"},"canonical_sha256":"6ec0dd5a05acdae05c9368516d0bdb406095ea1a8f95664bb2f08f61043fe6e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:18:51.508615Z","signature_b64":"3SbhK21HAEi9826y3vla7LYy/C/HHtAXjpBz1vv/IbKb0MhpzE0pW7MtxuTOIr43ZyrHm+LIe0emJugUHkaOCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ec0dd5a05acdae05c9368516d0bdb406095ea1a8f95664bb2f08f61043fe6e1","last_reissued_at":"2026-07-05T06:18:51.508173Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:18:51.508173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.06991","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:18:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6DlB0MHsqZcd443ghzOJ+CBndR3MgDHlSqpa/TdXGk+LvbgG6VPmG1HesfYxRsRDR4xxCt64mwAozHOCVCdwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T04:49:16.653403Z"},"content_sha256":"61272e648f3c6d3c7a00b747df61c5009a58cb120f7ec6f93a779a30e5e5e714","schema_version":"1.0","event_id":"sha256:61272e648f3c6d3c7a00b747df61c5009a58cb120f7ec6f93a779a30e5e5e714"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:N3AN2WQFVTNOAXETNBIW2C63IB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Density matrix formalism for interacting quantum fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-ph","quant-ph"],"primary_cat":"hep-th","authors_text":"Christian K\\\"ading, Mario Pitschmann","submitted_at":"2022-10-13T13:00:31Z","abstract_excerpt":"We provide a description of interacting quantum fields in terms of density matrices for any occupation numbers in Fock space in a momentum basis. As a simple example, we focus on a real scalar field interacting with another real scalar field, and present a practicable formalism for directly computing the density matrix elements of the combined scalar-scalar system. For deriving the main formula, we use techniques from non-equilibrium quantum field theory like thermo field dynamics and the Schwinger-Keldysh formalism. Our results allow for studies of particle creation/annihilation processes at "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.06991","kind":"arxiv","version":2},"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/2210.06991/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:18:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lMufojnR4/ic8oZc9m33yp1axlxA+fxrKm47iEGSKLVSUHG6Z3QTF4CHPLZqf7YdvgepONf1NuMnxESrxbDBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T04:49:16.653946Z"},"content_sha256":"4b3e64c24356ab34586ad509d8432d54644c3d6a113343632c669e97fcea909d","schema_version":"1.0","event_id":"sha256:4b3e64c24356ab34586ad509d8432d54644c3d6a113343632c669e97fcea909d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N3AN2WQFVTNOAXETNBIW2C63IB/bundle.json","state_url":"https://pith.science/pith/N3AN2WQFVTNOAXETNBIW2C63IB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N3AN2WQFVTNOAXETNBIW2C63IB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-18T04:49:16Z","links":{"resolver":"https://pith.science/pith/N3AN2WQFVTNOAXETNBIW2C63IB","bundle":"https://pith.science/pith/N3AN2WQFVTNOAXETNBIW2C63IB/bundle.json","state":"https://pith.science/pith/N3AN2WQFVTNOAXETNBIW2C63IB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N3AN2WQFVTNOAXETNBIW2C63IB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:N3AN2WQFVTNOAXETNBIW2C63IB","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":"8821e7cac70b9eab8db40ef82c1a6a097b99f87051d1fa1f2e81f2ee65d8c4a9","cross_cats_sorted":["hep-ph","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-10-13T13:00:31Z","title_canon_sha256":"0e7edf88c2c98c00016a65475f6daf6142a7a900081f4ca2dff1ed03972ae9a8"},"schema_version":"1.0","source":{"id":"2210.06991","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.06991","created_at":"2026-07-05T06:18:51Z"},{"alias_kind":"arxiv_version","alias_value":"2210.06991v2","created_at":"2026-07-05T06:18:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.06991","created_at":"2026-07-05T06:18:51Z"},{"alias_kind":"pith_short_12","alias_value":"N3AN2WQFVTNO","created_at":"2026-07-05T06:18:51Z"},{"alias_kind":"pith_short_16","alias_value":"N3AN2WQFVTNOAXET","created_at":"2026-07-05T06:18:51Z"},{"alias_kind":"pith_short_8","alias_value":"N3AN2WQF","created_at":"2026-07-05T06:18:51Z"}],"graph_snapshots":[{"event_id":"sha256:4b3e64c24356ab34586ad509d8432d54644c3d6a113343632c669e97fcea909d","target":"graph","created_at":"2026-07-05T06:18:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2210.06991/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide a description of interacting quantum fields in terms of density matrices for any occupation numbers in Fock space in a momentum basis. As a simple example, we focus on a real scalar field interacting with another real scalar field, and present a practicable formalism for directly computing the density matrix elements of the combined scalar-scalar system. For deriving the main formula, we use techniques from non-equilibrium quantum field theory like thermo field dynamics and the Schwinger-Keldysh formalism. Our results allow for studies of particle creation/annihilation processes at ","authors_text":"Christian K\\\"ading, Mario Pitschmann","cross_cats":["hep-ph","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-10-13T13:00:31Z","title":"Density matrix formalism for interacting quantum fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.06991","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":"sha256:61272e648f3c6d3c7a00b747df61c5009a58cb120f7ec6f93a779a30e5e5e714","target":"record","created_at":"2026-07-05T06:18:51Z","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":"8821e7cac70b9eab8db40ef82c1a6a097b99f87051d1fa1f2e81f2ee65d8c4a9","cross_cats_sorted":["hep-ph","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-10-13T13:00:31Z","title_canon_sha256":"0e7edf88c2c98c00016a65475f6daf6142a7a900081f4ca2dff1ed03972ae9a8"},"schema_version":"1.0","source":{"id":"2210.06991","kind":"arxiv","version":2}},"canonical_sha256":"6ec0dd5a05acdae05c9368516d0bdb406095ea1a8f95664bb2f08f61043fe6e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ec0dd5a05acdae05c9368516d0bdb406095ea1a8f95664bb2f08f61043fe6e1","first_computed_at":"2026-07-05T06:18:51.508173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:18:51.508173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3SbhK21HAEi9826y3vla7LYy/C/HHtAXjpBz1vv/IbKb0MhpzE0pW7MtxuTOIr43ZyrHm+LIe0emJugUHkaOCA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:18:51.508615Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.06991","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61272e648f3c6d3c7a00b747df61c5009a58cb120f7ec6f93a779a30e5e5e714","sha256:4b3e64c24356ab34586ad509d8432d54644c3d6a113343632c669e97fcea909d"],"state_sha256":"742c9bfd7fbe28aad7f9b995c06b25103f0178f297fa538c757ada395aff54ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6odgeCkem8OnRbQ34mrTS9EW5fxT1gNxZSZL6Ai/tUFaHzPiQyNchbI02x4qE9AdPxHbnltVFUF8LDuTBUKKCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T04:49:16.658624Z","bundle_sha256":"e73c51b2cd15759f5e1a74344298017764dac511563d5a143d326b5f757e76e2"}}