{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7EWWHWPMEAQD4E3SDTFR3OLXIS","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":"6086ae745fbef351732b67917ed08dfe3635d36eee594a44f8e36bf3264741a4","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-19T21:03:46Z","title_canon_sha256":"ee4b91deb27da0137cf6b31f879250ab2435b90b6316c7a571cde70ad20cee83"},"schema_version":"1.0","source":{"id":"1703.06510","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06510","created_at":"2026-05-17T23:51:14Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06510v2","created_at":"2026-05-17T23:51:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06510","created_at":"2026-05-17T23:51:14Z"},{"alias_kind":"pith_short_12","alias_value":"7EWWHWPMEAQD","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7EWWHWPMEAQD4E3S","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7EWWHWPM","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:c901bc57446d1f359aa42a0b35a5aac991b0e32ee52f78ce0168dd9c3e99a30f","target":"graph","created_at":"2026-05-17T23:51:14Z","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 continue our constructive study of tensor field theory through the next natural model, namely the rank four tensor theory with quartic melonic interactions and propagator inverse of the Laplacian on $U(1)^4$. This superrenormalizable tensor field theory has a power counting quite similar to ordinary $\\phi^4_3$. We control the model via a multiscale loop vertex expansion which has to be pushed quite beyond the one of the $T^4_3$ model and we establish its Borel summability in the coupling constant. This paper is also a step to prepare the constructive treatment of just renormalizable models,","authors_text":"Fabien Vignes-Tourneret, Vincent Rivasseau","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-19T21:03:46Z","title":"Constructive tensor field theory: The $T^{4}_{4}$ model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06510","kind":"arxiv","version":2},"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":"sha256:6d92c45c3da74f2dfcad710918076477c5cf7eefa8ccdd698f1b0f8089f61593","target":"record","created_at":"2026-05-17T23:51:14Z","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":"6086ae745fbef351732b67917ed08dfe3635d36eee594a44f8e36bf3264741a4","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-19T21:03:46Z","title_canon_sha256":"ee4b91deb27da0137cf6b31f879250ab2435b90b6316c7a571cde70ad20cee83"},"schema_version":"1.0","source":{"id":"1703.06510","kind":"arxiv","version":2}},"canonical_sha256":"f92d63d9ec20203e13721ccb1db977448656bd58c2d0be0a145e70c646f3d90f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f92d63d9ec20203e13721ccb1db977448656bd58c2d0be0a145e70c646f3d90f","first_computed_at":"2026-05-17T23:51:14.903485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:14.903485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5VQHqTfpRKoboP83/jz/8lSYurLsfG/2SLxlZ33uZ9eIcw3QsUH75kvu2ghVBnAgZq06c0cYEmnd4/VJpanGBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:14.904056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.06510","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d92c45c3da74f2dfcad710918076477c5cf7eefa8ccdd698f1b0f8089f61593","sha256:c901bc57446d1f359aa42a0b35a5aac991b0e32ee52f78ce0168dd9c3e99a30f"],"state_sha256":"0b17c5082051c62dcaa399b66a3aa29ca72152438e687d9995515a1020d5f7fb"}