{"paper":{"title":"Pro-Tensor Network","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Pro-tensor networks categorify tensor networks to study many-many-body theories without semisimplicity or finiteness.","cross_cats":["hep-th","math-ph","math.CT","math.MP","math.QA"],"primary_cat":"cond-mat.str-el","authors_text":"Ansi Bai, Gen Yue, Linqian Wu, Tian Lan","submitted_at":"2026-05-07T17:58:40Z","abstract_excerpt":"We introduce the pro-tensor network, a categorification of the tensor network, as a fully rigorous yet graphically transparent framework for studying the collection of many many-body theories, which we dub many-many-body theory. We provide a comprehensive toolbox for the graphical calculations using pro-tensor networks. As applications, we recover the Levin-Wen model as a \"uniform\" pro-tensor network and generalize a result of Kitaev and Kong by characterizing particles as modules over promonads. One can also interpret the string-net pro-tensor network as the space of symmetric tensor networks"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We introduce the pro-tensor network, a categorification of the tensor network, as a fully rigorous yet graphically transparent framework for studying the collection of many many-body theories, which we dub many-many-body theory.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That a well-defined pro-tensor network can be constructed and used for physical calculations while dispensing with the assumptions of semisimplicity, finiteness, and rigidity.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Pro-tensor networks form a categorified framework for many-many-body theories that recovers the Levin-Wen model and characterizes particles as modules over promonads without requiring semisimplicity, finiteness or rigidity.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Pro-tensor networks categorify tensor networks to study many-many-body theories without semisimplicity or finiteness.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c4dbbf18f67997fb96761f1975d8a26111c10872e2798ff6b3933de6409bedc9"},"source":{"id":"2605.06661","kind":"arxiv","version":2},"verdict":{"id":"6009f93a-b338-46d3-8e19-f3f325dae0de","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T05:29:00.531655Z","strongest_claim":"We introduce the pro-tensor network, a categorification of the tensor network, as a fully rigorous yet graphically transparent framework for studying the collection of many many-body theories, which we dub many-many-body theory.","one_line_summary":"Pro-tensor networks form a categorified framework for many-many-body theories that recovers the Levin-Wen model and characterizes particles as modules over promonads without requiring semisimplicity, finiteness or rigidity.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That a well-defined pro-tensor network can be constructed and used for physical calculations while dispensing with the assumptions of semisimplicity, finiteness, and rigidity.","pith_extraction_headline":"Pro-tensor networks categorify tensor networks to study many-many-body theories without semisimplicity or finiteness."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.06661/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T18:01:19.114331Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T12:29:56.084827Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"a7621981fab139558597985ae80d0eefc71c9bb98ae6e504a706eae857a8bc7b"},"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"}