{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:67D2GIWUYFKAE5TFBZ22TCYWDK","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":"c44188ae71a5a06b09ae581994555c0e4db80e5aa737abf1e24538b1a28f049c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-12T19:39:42Z","title_canon_sha256":"5c6f8086cc43ad356139ee3d613e3aee92ca7868606a09fe7764b8552b71769a"},"schema_version":"1.0","source":{"id":"1709.04041","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04041","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04041v3","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04041","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"pith_short_12","alias_value":"67D2GIWUYFKA","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"67D2GIWUYFKAE5TF","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"67D2GIWU","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:46b0af2931244a8cad49049e9a007f7b2021d70fe4ecc1f651119a2a1a2ad560","target":"graph","created_at":"2026-05-17T23:56:30Z","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":"Makeenko and Migdal (1979) gave heuristic identities involving the expectation of the product of two Wilson loop functionals associated to splitting a single loop at a self-intersection point. Kazakov and I. K. Kostov (1980) reformulated the Makeenko--Migdal equations in the plane case into a form which made rigorous sense. Nevertheless, the first rigorous proof of these equations (and their generalizations) was not given until the fundamental paper of T. L\\'{e}vy (2011). Subsequently Driver, Kemp, and Hall (2017) gave a simplified proof of L\\'{e}vy's result and then with F. Gabriel (2017) we ","authors_text":"Bruce K. Driver","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-12T19:39:42Z","title":"A Functional Integral Approaches to the Makeenko-Migdal Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04041","kind":"arxiv","version":3},"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":"sha256:7134b55746659e38fcf655a96612fb1e03f0c6cf8549ea0de990f53e207f7429","target":"record","created_at":"2026-05-17T23:56:30Z","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":"c44188ae71a5a06b09ae581994555c0e4db80e5aa737abf1e24538b1a28f049c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-12T19:39:42Z","title_canon_sha256":"5c6f8086cc43ad356139ee3d613e3aee92ca7868606a09fe7764b8552b71769a"},"schema_version":"1.0","source":{"id":"1709.04041","kind":"arxiv","version":3}},"canonical_sha256":"f7c7a322d4c1540276650e75a98b161aae4b01ca892eaf7d17c6b8fde78f0920","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7c7a322d4c1540276650e75a98b161aae4b01ca892eaf7d17c6b8fde78f0920","first_computed_at":"2026-05-17T23:56:30.221299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:30.221299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1E4ankca8y0MbW21eBO6upvMwtRYneGP0/sXwj2754/dsaGkrzNjZk0o3tgXdC5hYVtvEPa8Dj3/KZJx6pslAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:30.221785Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04041","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7134b55746659e38fcf655a96612fb1e03f0c6cf8549ea0de990f53e207f7429","sha256:46b0af2931244a8cad49049e9a007f7b2021d70fe4ecc1f651119a2a1a2ad560"],"state_sha256":"28311cc64ed7525b800ae0d117019d9511e032c123c0a314157cf20b3c6b504b"}