{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:53VPV4HQG7F44HSFWOXFJPOJZP","short_pith_number":"pith:53VPV4HQ","schema_version":"1.0","canonical_sha256":"eeeafaf0f037cbce1e45b3ae54bdc9cbeb7fb26da52b09487e75f73c419d0261","source":{"kind":"arxiv","id":"1712.05670","version":2},"attestation_state":"computed","paper":{"title":"Constructive Matrix Theory for Higher Order Interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Thomas Krajewski, Vasily Sazonov, Vincent Rivasseau","submitted_at":"2017-12-15T13:47:36Z","abstract_excerpt":"This paper provides an extension of the constructive loop vertex expansion to stable matrix models with interactions of arbitrarily high order. We introduce a new representation for such models, then perform a forest expansion on this representation. It allows to prove that the perturbation series of the free energy for such models is analytic in a domain uniform in the size N of the matrix. Our method applies to complex (rectangular) matrices. The extension to Hermitian square matrices, which was claimed wrongly in the first arXiv version of this paper, is postponed to a future study."},"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":"1712.05670","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-12-15T13:47:36Z","cross_cats_sorted":["hep-th","math.CO","math.MP"],"title_canon_sha256":"5a93bc6b706aa7b160120261f10f15957f3e49209ea56db7c213b73db2cb9c48","abstract_canon_sha256":"c367454438a5438e1d8b984aff39bad3a5fa924c90a71336b0a0d2b760ee17c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:49.595947Z","signature_b64":"uH5Vb4qC/ivNNnOAYNkIXB3LtMMhS7szzbf2Gk4nFG2MuASThYl1SzRUMn/x+wg4L5ULRcdIy21zn0WJ8w3bBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eeeafaf0f037cbce1e45b3ae54bdc9cbeb7fb26da52b09487e75f73c419d0261","last_reissued_at":"2026-05-17T23:51:49.595284Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:49.595284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constructive Matrix Theory for Higher Order Interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Thomas Krajewski, Vasily Sazonov, Vincent Rivasseau","submitted_at":"2017-12-15T13:47:36Z","abstract_excerpt":"This paper provides an extension of the constructive loop vertex expansion to stable matrix models with interactions of arbitrarily high order. We introduce a new representation for such models, then perform a forest expansion on this representation. It allows to prove that the perturbation series of the free energy for such models is analytic in a domain uniform in the size N of the matrix. Our method applies to complex (rectangular) matrices. The extension to Hermitian square matrices, which was claimed wrongly in the first arXiv version of this paper, is postponed to a future study."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05670","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":"1712.05670","created_at":"2026-05-17T23:51:49.595389+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.05670v2","created_at":"2026-05-17T23:51:49.595389+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05670","created_at":"2026-05-17T23:51:49.595389+00:00"},{"alias_kind":"pith_short_12","alias_value":"53VPV4HQG7F4","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"53VPV4HQG7F44HSF","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"53VPV4HQ","created_at":"2026-05-18T12:31:00.734936+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1907.03531","citing_title":"Notes on Tensor Models and Tensor Field Theories","ref_index":20,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/53VPV4HQG7F44HSFWOXFJPOJZP","json":"https://pith.science/pith/53VPV4HQG7F44HSFWOXFJPOJZP.json","graph_json":"https://pith.science/api/pith-number/53VPV4HQG7F44HSFWOXFJPOJZP/graph.json","events_json":"https://pith.science/api/pith-number/53VPV4HQG7F44HSFWOXFJPOJZP/events.json","paper":"https://pith.science/paper/53VPV4HQ"},"agent_actions":{"view_html":"https://pith.science/pith/53VPV4HQG7F44HSFWOXFJPOJZP","download_json":"https://pith.science/pith/53VPV4HQG7F44HSFWOXFJPOJZP.json","view_paper":"https://pith.science/paper/53VPV4HQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.05670&json=true","fetch_graph":"https://pith.science/api/pith-number/53VPV4HQG7F44HSFWOXFJPOJZP/graph.json","fetch_events":"https://pith.science/api/pith-number/53VPV4HQG7F44HSFWOXFJPOJZP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/53VPV4HQG7F44HSFWOXFJPOJZP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/53VPV4HQG7F44HSFWOXFJPOJZP/action/storage_attestation","attest_author":"https://pith.science/pith/53VPV4HQG7F44HSFWOXFJPOJZP/action/author_attestation","sign_citation":"https://pith.science/pith/53VPV4HQG7F44HSFWOXFJPOJZP/action/citation_signature","submit_replication":"https://pith.science/pith/53VPV4HQG7F44HSFWOXFJPOJZP/action/replication_record"}},"created_at":"2026-05-17T23:51:49.595389+00:00","updated_at":"2026-05-17T23:51:49.595389+00:00"}