{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:OVKRWYGGHKJZFLXN42OLQGLYDQ","short_pith_number":"pith:OVKRWYGG","canonical_record":{"source":{"id":"hep-th/0306133","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2003-06-13T22:21:09Z","cross_cats_sorted":[],"title_canon_sha256":"8e06081ca13a9e2a0e3c6206f5655f9fbb166081285797ec6b7502201578c0cb","abstract_canon_sha256":"8916130d947c97a4728ba612ed2bd5155a68db1b1edfbc7e1b96fef0dc95f83f"},"schema_version":"1.0"},"canonical_sha256":"75551b60c63a9392aeede69cb819781c3d229067d0d3e85caaf4076f213fe07e","source":{"kind":"arxiv","id":"hep-th/0306133","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0306133","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0306133v1","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0306133","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"pith_short_12","alias_value":"OVKRWYGGHKJZ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"OVKRWYGGHKJZFLXN","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"OVKRWYGG","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:OVKRWYGGHKJZFLXN42OLQGLYDQ","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0306133","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2003-06-13T22:21:09Z","cross_cats_sorted":[],"title_canon_sha256":"8e06081ca13a9e2a0e3c6206f5655f9fbb166081285797ec6b7502201578c0cb","abstract_canon_sha256":"8916130d947c97a4728ba612ed2bd5155a68db1b1edfbc7e1b96fef0dc95f83f"},"schema_version":"1.0"},"canonical_sha256":"75551b60c63a9392aeede69cb819781c3d229067d0d3e85caaf4076f213fe07e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:10.833856Z","signature_b64":"rhi7vspBkj7XjXp/ulTubHnjvweEwkJ7R7fI98wd3VgsjIBDjlWbfXA+/X7/cYW8Wlg7GevdeEquiHKTJMtxBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75551b60c63a9392aeede69cb819781c3d229067d0d3e85caaf4076f213fe07e","last_reissued_at":"2026-05-18T04:34:10.833329Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:10.833329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0306133","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":"2026-05-18T04:34:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qpvh6/SNS0k42D8mTJWK2o0Ybg3cLSi+3yXRXvkLQcvN3QWtnKoZ5pBbyeRwFgjlKX3cic4j6KO0/2stCYfPAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:16:53.261936Z"},"content_sha256":"455444f0187144ef37a196d843622c1140d6b16cb3d706ad11e31cc183f90a09","schema_version":"1.0","event_id":"sha256:455444f0187144ef37a196d843622c1140d6b16cb3d706ad11e31cc183f90a09"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:OVKRWYGGHKJZFLXN42OLQGLYDQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Field Theory in the Large N Limit: a review","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Jean Zinn-Justin, Moshe Moshe","submitted_at":"2003-06-13T22:21:09Z","abstract_excerpt":"We review the solutions of O(N) and U(N) quantum field theories in the large $N$ limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large $N$, the method relies on constructing effective field theories for composite fields after integration over the original degrees of freedom. We first solve a general scalar $U(\\phib^2)$ field theory for $N$ large and discuss various non-perturbative physical issues such as critical behaviour. We show how large $N$ results can also be obtained from variational calculations.We illust"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0306133","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":"2026-05-18T04:34:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uq3uB+0JMmHjFpmuyY/JlFP1AB1R4ohQ8mVqzYRxtIcwqgbRhZ3DyszGUO/J0XDHsovV6zQGmLC2mxFoMgj/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:16:53.262628Z"},"content_sha256":"2287067bbea0568ece5db027c86309efc3967248d388a7e310c7b7cbbca1080a","schema_version":"1.0","event_id":"sha256:2287067bbea0568ece5db027c86309efc3967248d388a7e310c7b7cbbca1080a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OVKRWYGGHKJZFLXN42OLQGLYDQ/bundle.json","state_url":"https://pith.science/pith/OVKRWYGGHKJZFLXN42OLQGLYDQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OVKRWYGGHKJZFLXN42OLQGLYDQ/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":"2026-05-31T19:16:53Z","links":{"resolver":"https://pith.science/pith/OVKRWYGGHKJZFLXN42OLQGLYDQ","bundle":"https://pith.science/pith/OVKRWYGGHKJZFLXN42OLQGLYDQ/bundle.json","state":"https://pith.science/pith/OVKRWYGGHKJZFLXN42OLQGLYDQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OVKRWYGGHKJZFLXN42OLQGLYDQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:OVKRWYGGHKJZFLXN42OLQGLYDQ","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":"8916130d947c97a4728ba612ed2bd5155a68db1b1edfbc7e1b96fef0dc95f83f","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2003-06-13T22:21:09Z","title_canon_sha256":"8e06081ca13a9e2a0e3c6206f5655f9fbb166081285797ec6b7502201578c0cb"},"schema_version":"1.0","source":{"id":"hep-th/0306133","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0306133","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0306133v1","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0306133","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"pith_short_12","alias_value":"OVKRWYGGHKJZ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"OVKRWYGGHKJZFLXN","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"OVKRWYGG","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:2287067bbea0568ece5db027c86309efc3967248d388a7e310c7b7cbbca1080a","target":"graph","created_at":"2026-05-18T04:34:10Z","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":"We review the solutions of O(N) and U(N) quantum field theories in the large $N$ limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large $N$, the method relies on constructing effective field theories for composite fields after integration over the original degrees of freedom. We first solve a general scalar $U(\\phib^2)$ field theory for $N$ large and discuss various non-perturbative physical issues such as critical behaviour. We show how large $N$ results can also be obtained from variational calculations.We illust","authors_text":"Jean Zinn-Justin, Moshe Moshe","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2003-06-13T22:21:09Z","title":"Quantum Field Theory in the Large N Limit: a review"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0306133","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":"sha256:455444f0187144ef37a196d843622c1140d6b16cb3d706ad11e31cc183f90a09","target":"record","created_at":"2026-05-18T04:34:10Z","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":"8916130d947c97a4728ba612ed2bd5155a68db1b1edfbc7e1b96fef0dc95f83f","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2003-06-13T22:21:09Z","title_canon_sha256":"8e06081ca13a9e2a0e3c6206f5655f9fbb166081285797ec6b7502201578c0cb"},"schema_version":"1.0","source":{"id":"hep-th/0306133","kind":"arxiv","version":1}},"canonical_sha256":"75551b60c63a9392aeede69cb819781c3d229067d0d3e85caaf4076f213fe07e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75551b60c63a9392aeede69cb819781c3d229067d0d3e85caaf4076f213fe07e","first_computed_at":"2026-05-18T04:34:10.833329Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:10.833329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rhi7vspBkj7XjXp/ulTubHnjvweEwkJ7R7fI98wd3VgsjIBDjlWbfXA+/X7/cYW8Wlg7GevdeEquiHKTJMtxBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:10.833856Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0306133","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:455444f0187144ef37a196d843622c1140d6b16cb3d706ad11e31cc183f90a09","sha256:2287067bbea0568ece5db027c86309efc3967248d388a7e310c7b7cbbca1080a"],"state_sha256":"ecdb282e436179b26e02f006240bbfb96eeea39c52fc3ec3c33f6aeeea6400d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BFjm7oxV7Qx9JqEBr2ZbU0PDQSmpeAVwmh+3Ga+sm8A0Pl7x2d/lopPZgwuOhdzqHI7f3O3myzA8SE+czdVGDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T19:16:53.267023Z","bundle_sha256":"8113e66203cc25fad83f8d130e4ed330af6fca1b78791f2fdbe425e4714a1e58"}}