{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FIRNKQFBV5DWOAEYSPCWLRGUGI","short_pith_number":"pith:FIRNKQFB","schema_version":"1.0","canonical_sha256":"2a22d540a1af4767009893c565c4d4320cd1c4fcf5fd6f974a6bb7aa9c80ed96","source":{"kind":"arxiv","id":"1610.00526","version":2},"attestation_state":"computed","paper":{"title":"Exact solution of matricial $\\Phi^3_2$ quantum field theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Akifumi Sako (Tokyo), Harald Grosse (Vienna), Raimar Wulkenhaar (M\\\"unster)","submitted_at":"2016-10-03T12:58:45Z","abstract_excerpt":"We apply a recently developed method to exactly solve the $\\Phi^3$ matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a multi-punctured 2-sphere. We show how Ward-Takahashi identities and Schwinger-Dyson equations lead in a special large-$\\mathcal{N}$ limit to integral equations that we solve exactly for all correlation functions. Remarkably, these functions are analytic in the $\\Phi^3$ coupling constant, although bounds on individual graphs justify only Borel summability.\n  The solved "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.00526","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-10-03T12:58:45Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"45fdb72e1be48653d288dea7b76221fc1b228e3727f01ea7f213bc378ed395a7","abstract_canon_sha256":"791dae00b38ae3d35ea165e13f34f7a0523a549cb77272dfe581b48b65e721c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:29.172854Z","signature_b64":"fdWxB6oNCS3+uHU19NTAjH5oBzIUj92XqjMAFqtd37sxhZIigOsUjym9sarUxRSOkIt1nfSWFR+aBh4zft5XDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a22d540a1af4767009893c565c4d4320cd1c4fcf5fd6f974a6bb7aa9c80ed96","last_reissued_at":"2026-05-18T00:21:29.172285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:29.172285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact solution of matricial $\\Phi^3_2$ quantum field theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Akifumi Sako (Tokyo), Harald Grosse (Vienna), Raimar Wulkenhaar (M\\\"unster)","submitted_at":"2016-10-03T12:58:45Z","abstract_excerpt":"We apply a recently developed method to exactly solve the $\\Phi^3$ matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a multi-punctured 2-sphere. We show how Ward-Takahashi identities and Schwinger-Dyson equations lead in a special large-$\\mathcal{N}$ limit to integral equations that we solve exactly for all correlation functions. Remarkably, these functions are analytic in the $\\Phi^3$ coupling constant, although bounds on individual graphs justify only Borel summability.\n  The solved "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00526","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.00526","created_at":"2026-05-18T00:21:29.172373+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.00526v2","created_at":"2026-05-18T00:21:29.172373+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00526","created_at":"2026-05-18T00:21:29.172373+00:00"},{"alias_kind":"pith_short_12","alias_value":"FIRNKQFBV5DW","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FIRNKQFBV5DWOAEY","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FIRNKQFB","created_at":"2026-05-18T12:30:15.759754+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FIRNKQFBV5DWOAEYSPCWLRGUGI","json":"https://pith.science/pith/FIRNKQFBV5DWOAEYSPCWLRGUGI.json","graph_json":"https://pith.science/api/pith-number/FIRNKQFBV5DWOAEYSPCWLRGUGI/graph.json","events_json":"https://pith.science/api/pith-number/FIRNKQFBV5DWOAEYSPCWLRGUGI/events.json","paper":"https://pith.science/paper/FIRNKQFB"},"agent_actions":{"view_html":"https://pith.science/pith/FIRNKQFBV5DWOAEYSPCWLRGUGI","download_json":"https://pith.science/pith/FIRNKQFBV5DWOAEYSPCWLRGUGI.json","view_paper":"https://pith.science/paper/FIRNKQFB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.00526&json=true","fetch_graph":"https://pith.science/api/pith-number/FIRNKQFBV5DWOAEYSPCWLRGUGI/graph.json","fetch_events":"https://pith.science/api/pith-number/FIRNKQFBV5DWOAEYSPCWLRGUGI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FIRNKQFBV5DWOAEYSPCWLRGUGI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FIRNKQFBV5DWOAEYSPCWLRGUGI/action/storage_attestation","attest_author":"https://pith.science/pith/FIRNKQFBV5DWOAEYSPCWLRGUGI/action/author_attestation","sign_citation":"https://pith.science/pith/FIRNKQFBV5DWOAEYSPCWLRGUGI/action/citation_signature","submit_replication":"https://pith.science/pith/FIRNKQFBV5DWOAEYSPCWLRGUGI/action/replication_record"}},"created_at":"2026-05-18T00:21:29.172373+00:00","updated_at":"2026-05-18T00:21:29.172373+00:00"}