{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VPYOP6GYGKMMXNOBS6PQMT4CCA","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":"497a886012f16296ad6cb27edccd52aa8e8a5d98c0b125e8472df62ed10be6bf","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2026-07-27T17:59:11Z","title_canon_sha256":"825c0878f5413bd9105ca607cbe97a4ff3b06a738c4481af26370c6b7b25cafd"},"schema_version":"1.0","source":{"id":"2607.24740","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.24740","created_at":"2026-07-28T02:24:25Z"},{"alias_kind":"arxiv_version","alias_value":"2607.24740v1","created_at":"2026-07-28T02:24:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.24740","created_at":"2026-07-28T02:24:25Z"},{"alias_kind":"pith_short_12","alias_value":"VPYOP6GYGKMM","created_at":"2026-07-28T02:24:25Z"},{"alias_kind":"pith_short_16","alias_value":"VPYOP6GYGKMMXNOB","created_at":"2026-07-28T02:24:25Z"},{"alias_kind":"pith_short_8","alias_value":"VPYOP6GY","created_at":"2026-07-28T02:24:25Z"}],"graph_snapshots":[{"event_id":"sha256:f00805da48efb7028861c7ac9878a24fe1a839d3360242d7ace00dd1ec12e154","target":"graph","created_at":"2026-07-28T02:24:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.24740/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Although anyon condensation is a standard mechanism for relating topological orders, anyon condensation in symmetry-enriched topological (SET) phases is more intricate because the condensate must also be compatible with the global symmetry. We study symmetry-preserving anyon condensation in SET phases described by the enlarged Hu-Geer-Wu (HGW) string-net model with multifusion-category input data. We show that a $G$-preserving condensation is characterized by a compatible grading of the input multifusion category, and that this grading constructs the multifusion-category input of the child SET","authors_text":"Nianrui Fu, Siyuan Wang, Yidun Wan, Yu Zhao","cross_cats":["cond-mat.stat-mech","hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2026-07-27T17:59:11Z","title":"Anyon Condensation In Symmetry-Enriched Topological Phases: $G$-Grading of Multifusion Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24740","kind":"arxiv","version":1},"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":"sha256:49076b4ecdc1efdb2c3c959e2d5c4edba9621a32a1ab23de4eb173fc883a91b0","target":"record","created_at":"2026-07-28T02:24:25Z","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":"497a886012f16296ad6cb27edccd52aa8e8a5d98c0b125e8472df62ed10be6bf","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2026-07-27T17:59:11Z","title_canon_sha256":"825c0878f5413bd9105ca607cbe97a4ff3b06a738c4481af26370c6b7b25cafd"},"schema_version":"1.0","source":{"id":"2607.24740","kind":"arxiv","version":1}},"canonical_sha256":"abf0e7f8d83298cbb5c1979f064f82102d2b2ab98aa0c315c3ac92f2b0eb5c2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abf0e7f8d83298cbb5c1979f064f82102d2b2ab98aa0c315c3ac92f2b0eb5c2a","first_computed_at":"2026-07-28T02:24:25.194265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T02:24:25.194265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8WZmO4kzU1WsB286acOifL0AjAsQDvVlKZaw7fQJDXe2FubIGZ6z7h0f1YBZrg0sKgXYtm3eJGsnLcASQeAcAw==","signature_status":"signed_v1","signed_at":"2026-07-28T02:24:25.195189Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.24740","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49076b4ecdc1efdb2c3c959e2d5c4edba9621a32a1ab23de4eb173fc883a91b0","sha256:f00805da48efb7028861c7ac9878a24fe1a839d3360242d7ace00dd1ec12e154"],"state_sha256":"7a2c87ee183bd003971fb93f60253f223b8a2270d69024b4bb6ae8843f521b18"}