{"paper":{"title":"From Baby Universes to Narain Moduli: Topological Boundary Averaging in SymTFTs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Ensemble averaging in low-dimensional holography arises from averaging over topological boundary conditions at one end of a fixed SymTFT slab while holding the physical boundary fixed.","cross_cats":[],"primary_cat":"hep-th","authors_text":"Xingyang Yu","submitted_at":"2026-05-07T17:56:48Z","abstract_excerpt":"Building on the viewpoint that ensemble averages in TQFT gravity can be organized by topological boundary data, we develop a SymTFT interpretation of ensemble averaging in low-dimensional holography. The central operation is to keep fixed both the SymTFT and the physical boundary condition, while averaging over topological boundary conditions at the other end of the SymTFT slab. Each such boundary condition gives an absolute completion of the same relative theory, so the ensemble is interpreted as an average over topological completions rather than over arbitrary local dynamics. We formulate t"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We propose a SymTFT interpretation of ensemble averaging in low-dimensional holography. The central operation is to keep fixed both the SymTFT and the physical boundary condition, while averaging over topological boundary conditions at the other end of the SymTFT slab.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the groupoid or Haar-type measures on topological boundary conditions naturally reproduce the physically relevant ensemble measures (Poisson/Bell polynomials and Zamolodchikov) without additional fitting or selection rules.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Ensemble averaging in low-dimensional holography is reinterpreted as averaging over topological boundary conditions in a fixed SymTFT slab, reproducing Poisson moments in the Marolf-Maxfield model and Zamolodchikov measure in the Narain case.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Ensemble averaging in low-dimensional holography arises from averaging over topological boundary conditions at one end of a fixed SymTFT slab while holding the physical boundary fixed.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f0a13c2debc866f45a1f767a9bc4edb84642d2be849d925f919d90cdbc22e5f4"},"source":{"id":"2605.06653","kind":"arxiv","version":2},"verdict":{"id":"a47b7b6f-319a-43d5-9c09-01b450f50097","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T07:35:39.402572Z","strongest_claim":"We propose a SymTFT interpretation of ensemble averaging in low-dimensional holography. The central operation is to keep fixed both the SymTFT and the physical boundary condition, while averaging over topological boundary conditions at the other end of the SymTFT slab.","one_line_summary":"Ensemble averaging in low-dimensional holography is reinterpreted as averaging over topological boundary conditions in a fixed SymTFT slab, reproducing Poisson moments in the Marolf-Maxfield model and Zamolodchikov measure in the Narain case.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the groupoid or Haar-type measures on topological boundary conditions naturally reproduce the physically relevant ensemble measures (Poisson/Bell polynomials and Zamolodchikov) without additional fitting or selection rules.","pith_extraction_headline":"Ensemble averaging in low-dimensional holography arises from averaging over topological boundary conditions at one end of a fixed SymTFT slab while holding the physical boundary fixed."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.06653/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T12:02:03.888593Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-20T07:36:51.783056Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T18:01:19.163781Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T12:31:17.166085Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"f0c632397495f8244408225f5eeeeca0250ddd19ce075272e0da63075d7edaa9"},"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"}