{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:EDZC5YAKUMOUIQA5CVWJQQCJQW","short_pith_number":"pith:EDZC5YAK","canonical_record":{"source":{"id":"0710.5652","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2007-10-30T14:04:46Z","cross_cats_sorted":[],"title_canon_sha256":"2a6284c9d421188afd2250e441046e67c107c834cb38a35fb895de4c4d28c73e","abstract_canon_sha256":"d976a7ee7795213a952899093c6571b44b1a1e62c6eae2faeebfbcf428172831"},"schema_version":"1.0"},"canonical_sha256":"20f22ee00aa31d44401d156c984049859cb0f018b1cd8208b551cd71eea7db41","source":{"kind":"arxiv","id":"0710.5652","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.5652","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"arxiv_version","alias_value":"0710.5652v1","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.5652","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"pith_short_12","alias_value":"EDZC5YAKUMOU","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"EDZC5YAKUMOUIQA5","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"EDZC5YAK","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:EDZC5YAKUMOUIQA5CVWJQQCJQW","target":"record","payload":{"canonical_record":{"source":{"id":"0710.5652","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2007-10-30T14:04:46Z","cross_cats_sorted":[],"title_canon_sha256":"2a6284c9d421188afd2250e441046e67c107c834cb38a35fb895de4c4d28c73e","abstract_canon_sha256":"d976a7ee7795213a952899093c6571b44b1a1e62c6eae2faeebfbcf428172831"},"schema_version":"1.0"},"canonical_sha256":"20f22ee00aa31d44401d156c984049859cb0f018b1cd8208b551cd71eea7db41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:04.067662Z","signature_b64":"kVk/FuWpwvSNPk2l58vGics0vgRacu4eAK1MuwDsinbqAO7/tKYTx3VSxDhxVPNSmmIFNCTRDdZL3oIrkmH8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20f22ee00aa31d44401d156c984049859cb0f018b1cd8208b551cd71eea7db41","last_reissued_at":"2026-05-18T04:41:04.067252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:04.067252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0710.5652","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:41:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JH23RPDYyX9obJ5hDyQu85HDsLjFx5s05djJCAKhhyB0bzCXjEEFslu69BCp8aze82lJxNYHzG4w8tr3YP1CCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:52:52.889278Z"},"content_sha256":"1c9d74fe06b1d36877a75e44bd086b17e6c9944a0a08e7cd76e0de2ba9e72df8","schema_version":"1.0","event_id":"sha256:1c9d74fe06b1d36877a75e44bd086b17e6c9944a0a08e7cd76e0de2ba9e72df8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:EDZC5YAKUMOUIQA5CVWJQQCJQW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The structure of Green functions in quantum field theory with a general state","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Christian Brouder (IMPMC)","submitted_at":"2007-10-30T14:04:46Z","abstract_excerpt":"In quantum field theory, the Green function is usually calculated as the expectation value of the time-ordered product of fields over the vacuum. In some cases, especially in degenerate systems, expectation values over general states are required. The corresponding Green functions are essentially more complex than in the vacuum, because they cannot be written in terms of standard Feynman diagrams. Here, a method is proposed to determine the structure of these Green functions and to derive nonperturbative equations for them. The main idea is to transform the cumulants describing correlations in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.5652","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:41:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lAny44mf5lCijaFE39E7MCfS5wBY5JbWX/vSuwUo8wkgFZZpdxWcLphXiD/SXRKxDGv/jlbudztO0hOIK+1VBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:52:52.889989Z"},"content_sha256":"b09582d7afa759c6c2283e634ac7ce03b5e0f53a5511892dba271113f5c5febf","schema_version":"1.0","event_id":"sha256:b09582d7afa759c6c2283e634ac7ce03b5e0f53a5511892dba271113f5c5febf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EDZC5YAKUMOUIQA5CVWJQQCJQW/bundle.json","state_url":"https://pith.science/pith/EDZC5YAKUMOUIQA5CVWJQQCJQW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EDZC5YAKUMOUIQA5CVWJQQCJQW/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":"2026-06-07T16:52:52Z","links":{"resolver":"https://pith.science/pith/EDZC5YAKUMOUIQA5CVWJQQCJQW","bundle":"https://pith.science/pith/EDZC5YAKUMOUIQA5CVWJQQCJQW/bundle.json","state":"https://pith.science/pith/EDZC5YAKUMOUIQA5CVWJQQCJQW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EDZC5YAKUMOUIQA5CVWJQQCJQW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:EDZC5YAKUMOUIQA5CVWJQQCJQW","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":"d976a7ee7795213a952899093c6571b44b1a1e62c6eae2faeebfbcf428172831","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2007-10-30T14:04:46Z","title_canon_sha256":"2a6284c9d421188afd2250e441046e67c107c834cb38a35fb895de4c4d28c73e"},"schema_version":"1.0","source":{"id":"0710.5652","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.5652","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"arxiv_version","alias_value":"0710.5652v1","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.5652","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"pith_short_12","alias_value":"EDZC5YAKUMOU","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"EDZC5YAKUMOUIQA5","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"EDZC5YAK","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:b09582d7afa759c6c2283e634ac7ce03b5e0f53a5511892dba271113f5c5febf","target":"graph","created_at":"2026-05-18T04:41:04Z","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":"In quantum field theory, the Green function is usually calculated as the expectation value of the time-ordered product of fields over the vacuum. In some cases, especially in degenerate systems, expectation values over general states are required. The corresponding Green functions are essentially more complex than in the vacuum, because they cannot be written in terms of standard Feynman diagrams. Here, a method is proposed to determine the structure of these Green functions and to derive nonperturbative equations for them. The main idea is to transform the cumulants describing correlations in","authors_text":"Christian Brouder (IMPMC)","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2007-10-30T14:04:46Z","title":"The structure of Green functions in quantum field theory with a general state"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.5652","kind":"arxiv","version":1},"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":"sha256:1c9d74fe06b1d36877a75e44bd086b17e6c9944a0a08e7cd76e0de2ba9e72df8","target":"record","created_at":"2026-05-18T04:41:04Z","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":"d976a7ee7795213a952899093c6571b44b1a1e62c6eae2faeebfbcf428172831","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2007-10-30T14:04:46Z","title_canon_sha256":"2a6284c9d421188afd2250e441046e67c107c834cb38a35fb895de4c4d28c73e"},"schema_version":"1.0","source":{"id":"0710.5652","kind":"arxiv","version":1}},"canonical_sha256":"20f22ee00aa31d44401d156c984049859cb0f018b1cd8208b551cd71eea7db41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20f22ee00aa31d44401d156c984049859cb0f018b1cd8208b551cd71eea7db41","first_computed_at":"2026-05-18T04:41:04.067252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:04.067252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kVk/FuWpwvSNPk2l58vGics0vgRacu4eAK1MuwDsinbqAO7/tKYTx3VSxDhxVPNSmmIFNCTRDdZL3oIrkmH8Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:04.067662Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.5652","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c9d74fe06b1d36877a75e44bd086b17e6c9944a0a08e7cd76e0de2ba9e72df8","sha256:b09582d7afa759c6c2283e634ac7ce03b5e0f53a5511892dba271113f5c5febf"],"state_sha256":"df23f54628171e7ae42351fc2acbd9feb2e5c8c9f65cff8fddbf02575aa34127"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q9706Vr3uOP5D6p6tHQNMTRHz4LjJ/PpwuO8ZIlPTxar8XsEXgEHVDBtRVnYqJhL8yVPf0RLT8fprdtBjHVECA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:52:52.894305Z","bundle_sha256":"b31a14d56770e752769f5b4cc4ada69756f5d1b6ce0e1291b38d04f94febd63e"}}