{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7GYBTGK2JDA3APNF5R7DC3DO2D","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":"e22f5996506c4f36d54736a0c81e5478245658d82a8ecba88d191722ab8f5504","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2017-06-02T05:31:20Z","title_canon_sha256":"f3c0e7afee62980ac1ca6e99a42ce6dcaf4a8d0b87bf5f8d07764adfc8cef0e4"},"schema_version":"1.0","source":{"id":"1706.00560","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00560","created_at":"2026-05-18T00:33:17Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00560v1","created_at":"2026-05-18T00:33:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00560","created_at":"2026-05-18T00:33:17Z"},{"alias_kind":"pith_short_12","alias_value":"7GYBTGK2JDA3","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7GYBTGK2JDA3APNF","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7GYBTGK2","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:89e2a38a895d4e753b651293d47da8eefcc41b3642e5ef109afb53b25e758acd","target":"graph","created_at":"2026-05-18T00:33:17Z","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 discuss several bosonic topological phases in (3+1) dimensions enriched by a global $\\mathbb{Z}_2$ symmetry, and gauging the $\\mathbb{Z}_2$ symmetry. More specifically, following the spirit of the bulk-boundary correspondence, expected to hold in topological phases of matter in general, we consider boundary (surface) field theories and their orbifold. From the surface partition functions, we extract the modular $\\mathcal{S}$ and $\\mathcal{T}$ matrices and compare them with $(2+1)$d toplogical phase after dimensional reduction. As a specific example, we discuss topologically ordered phases i","authors_text":"Apoorv Tiwari, Chetan Nayak, Shinsei Ryu, Xiao Chen","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2017-06-02T05:31:20Z","title":"Gauging (3+1)-dimensional topological phases: an approach from surface theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00560","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":"sha256:87d396b06cb1f98aa0d954490145d39549c0f4001422461a9cf643e44b4acf74","target":"record","created_at":"2026-05-18T00:33:17Z","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":"e22f5996506c4f36d54736a0c81e5478245658d82a8ecba88d191722ab8f5504","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2017-06-02T05:31:20Z","title_canon_sha256":"f3c0e7afee62980ac1ca6e99a42ce6dcaf4a8d0b87bf5f8d07764adfc8cef0e4"},"schema_version":"1.0","source":{"id":"1706.00560","kind":"arxiv","version":1}},"canonical_sha256":"f9b019995a48c1b03da5ec7e316c6ed0d5e2d4b77ff609746290a15cdda2c487","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9b019995a48c1b03da5ec7e316c6ed0d5e2d4b77ff609746290a15cdda2c487","first_computed_at":"2026-05-18T00:33:17.760334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:17.760334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DvNLTpY2xsJYrvbhEjE7RYrpDPJrnsqhgjEn/U2pqM+2cr1w2V5PRn2l2+X0PRV7u7WY1/66TOKfGtIoqIKIAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:17.761048Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.00560","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87d396b06cb1f98aa0d954490145d39549c0f4001422461a9cf643e44b4acf74","sha256:89e2a38a895d4e753b651293d47da8eefcc41b3642e5ef109afb53b25e758acd"],"state_sha256":"a7392a8b78cf24f884eefc9d1ee481c539c9d3d65cd91b4582e4337bda55a043"}