{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:Y4JQK2M4XYDQ5KBJDUBI7UKXKG","short_pith_number":"pith:Y4JQK2M4","schema_version":"1.0","canonical_sha256":"c71305699cbe070ea8291d028fd1575191916f0966a92e345005c2a48a79af60","source":{"kind":"arxiv","id":"2608.05071","version":1},"attestation_state":"computed","paper":{"title":"Generalized comodule tube algebras for boundary and domain wall defects of (2+1)D topological order","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"Sheng Tan, Zhian Jia","submitted_at":"2026-08-05T17:16:19Z","abstract_excerpt":"The tube algebra, which carries the structure of a $C^*$ weak Hopf algebra, is a fundamental tool for characterizing topological excitations in topological phases. In this work, we generalize the tube algebra framework to codimension-2 defects in $(2+1)$D gapped phases described by Turaev--Viro--Barrett--Westbury TQFTs, with particular emphasis on Levin--Wen string-net models. We show that such codimension-2 defects are described by a \\emph{defect tube algebra}, which naturally carries the structure of a comodule algebra over the weak Hopf tube algebra associated with the topological excitatio"},"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":"2608.05071","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-08-05T17:16:19Z","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP","math.QA"],"title_canon_sha256":"da9b3cd867bcb9f96623f0de933b4ff473e4f1543e06801c41331229fdca9a62","abstract_canon_sha256":"00d7427fd59092c5a5e516fc7d1c89bae5eeab0a08a24fe62ff868bf4c8d6356"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-06T01:48:26.300464Z","signature_b64":"oc2WwHALKvr9kqtZIovkwPKf3JcyfYB0wQukaT5ipi/jYsyX9ka23MwnqDVAcP/5V3V3PtoEVM/3LLW02xVwBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c71305699cbe070ea8291d028fd1575191916f0966a92e345005c2a48a79af60","last_reissued_at":"2026-08-06T01:48:26.299026Z","signature_status":"signed_v1","first_computed_at":"2026-08-06T01:48:26.299026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized comodule tube algebras for boundary and domain wall defects of (2+1)D topological order","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"Sheng Tan, Zhian Jia","submitted_at":"2026-08-05T17:16:19Z","abstract_excerpt":"The tube algebra, which carries the structure of a $C^*$ weak Hopf algebra, is a fundamental tool for characterizing topological excitations in topological phases. In this work, we generalize the tube algebra framework to codimension-2 defects in $(2+1)$D gapped phases described by Turaev--Viro--Barrett--Westbury TQFTs, with particular emphasis on Levin--Wen string-net models. We show that such codimension-2 defects are described by a \\emph{defect tube algebra}, which naturally carries the structure of a comodule algebra over the weak Hopf tube algebra associated with the topological excitatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05071","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.05071/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2608.05071","created_at":"2026-08-06T01:48:26.300866+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.05071v1","created_at":"2026-08-06T01:48:26.300866+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.05071","created_at":"2026-08-06T01:48:26.300866+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y4JQK2M4XYDQ","created_at":"2026-08-06T01:48:26.300866+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y4JQK2M4XYDQ5KBJ","created_at":"2026-08-06T01:48:26.300866+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y4JQK2M4","created_at":"2026-08-06T01:48:26.300866+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/Y4JQK2M4XYDQ5KBJDUBI7UKXKG","json":"https://pith.science/pith/Y4JQK2M4XYDQ5KBJDUBI7UKXKG.json","graph_json":"https://pith.science/api/pith-number/Y4JQK2M4XYDQ5KBJDUBI7UKXKG/graph.json","events_json":"https://pith.science/api/pith-number/Y4JQK2M4XYDQ5KBJDUBI7UKXKG/events.json","paper":"https://pith.science/paper/Y4JQK2M4"},"agent_actions":{"view_html":"https://pith.science/pith/Y4JQK2M4XYDQ5KBJDUBI7UKXKG","download_json":"https://pith.science/pith/Y4JQK2M4XYDQ5KBJDUBI7UKXKG.json","view_paper":"https://pith.science/paper/Y4JQK2M4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.05071&json=true","fetch_graph":"https://pith.science/api/pith-number/Y4JQK2M4XYDQ5KBJDUBI7UKXKG/graph.json","fetch_events":"https://pith.science/api/pith-number/Y4JQK2M4XYDQ5KBJDUBI7UKXKG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y4JQK2M4XYDQ5KBJDUBI7UKXKG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y4JQK2M4XYDQ5KBJDUBI7UKXKG/action/storage_attestation","attest_author":"https://pith.science/pith/Y4JQK2M4XYDQ5KBJDUBI7UKXKG/action/author_attestation","sign_citation":"https://pith.science/pith/Y4JQK2M4XYDQ5KBJDUBI7UKXKG/action/citation_signature","submit_replication":"https://pith.science/pith/Y4JQK2M4XYDQ5KBJDUBI7UKXKG/action/replication_record"}},"created_at":"2026-08-06T01:48:26.300866+00:00","updated_at":"2026-08-06T01:48:26.300866+00:00"}