{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:X2VZJNGTU6VMFUN37YM7PM2WZO","short_pith_number":"pith:X2VZJNGT","schema_version":"1.0","canonical_sha256":"beab94b4d3a7aac2d1bbfe19f7b356cbb6275599981208946e723ec2d4c5a451","source":{"kind":"arxiv","id":"1409.3216","version":2},"attestation_state":"computed","paper":{"title":"Twisted Gauge Theory Model of Topological Phases in Three Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"cond-mat.str-el","authors_text":"Huan He, Juven Wang, Yidun Wan","submitted_at":"2014-09-10T19:58:03Z","abstract_excerpt":"We propose an exactly solvable lattice Hamiltonian model of topological phases in $3+1$ dimensions, based on a generic finite group $G$ and a $4$-cocycle $\\omega$ over $G$. We show that our model has topologically protected degenerate ground states and obtain the formula of its ground state degeneracy on the $3$-torus. In particular, the ground state spectrum implies the existence of purely three-dimensional looplike quasi-excitations specified by two nontrivial flux indices and one charge index. We also construct other nontrivial topological observables of the model, namely the $SL(3,\\mathbb{"},"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":"1409.3216","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2014-09-10T19:58:03Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"e7b3945e0fd0ca5d4dfffc3b10a43f8f63c63c51a2677455c2e18834f090fe76","abstract_canon_sha256":"d8ad119f2482c4b6e3d3d3422effcb7148375b0740f5113ca06fe103769716c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:29.955871Z","signature_b64":"PCXuK/tr1WOEQ/LmpWyI+NsfymR106d487fyF8bO5czkXC5c/QDNLGCWy4EnEV1XojC9vjr8FX2V5YDuI8eKAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"beab94b4d3a7aac2d1bbfe19f7b356cbb6275599981208946e723ec2d4c5a451","last_reissued_at":"2026-05-18T01:37:29.955279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:29.955279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Twisted Gauge Theory Model of Topological Phases in Three Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"cond-mat.str-el","authors_text":"Huan He, Juven Wang, Yidun Wan","submitted_at":"2014-09-10T19:58:03Z","abstract_excerpt":"We propose an exactly solvable lattice Hamiltonian model of topological phases in $3+1$ dimensions, based on a generic finite group $G$ and a $4$-cocycle $\\omega$ over $G$. We show that our model has topologically protected degenerate ground states and obtain the formula of its ground state degeneracy on the $3$-torus. In particular, the ground state spectrum implies the existence of purely three-dimensional looplike quasi-excitations specified by two nontrivial flux indices and one charge index. We also construct other nontrivial topological observables of the model, namely the $SL(3,\\mathbb{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3216","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1409.3216","created_at":"2026-05-18T01:37:29.955354+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.3216v2","created_at":"2026-05-18T01:37:29.955354+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3216","created_at":"2026-05-18T01:37:29.955354+00:00"},{"alias_kind":"pith_short_12","alias_value":"X2VZJNGTU6VM","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"X2VZJNGTU6VMFUN3","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"X2VZJNGT","created_at":"2026-05-18T12:28:54.890064+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.03708","citing_title":"Twisted quantum doubles are sign problem-free","ref_index":29,"is_internal_anchor":true},{"citing_arxiv_id":"2604.02414","citing_title":"On Lagrangians of Non-abelian Dijkgraaf-Witten Theories","ref_index":14,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X2VZJNGTU6VMFUN37YM7PM2WZO","json":"https://pith.science/pith/X2VZJNGTU6VMFUN37YM7PM2WZO.json","graph_json":"https://pith.science/api/pith-number/X2VZJNGTU6VMFUN37YM7PM2WZO/graph.json","events_json":"https://pith.science/api/pith-number/X2VZJNGTU6VMFUN37YM7PM2WZO/events.json","paper":"https://pith.science/paper/X2VZJNGT"},"agent_actions":{"view_html":"https://pith.science/pith/X2VZJNGTU6VMFUN37YM7PM2WZO","download_json":"https://pith.science/pith/X2VZJNGTU6VMFUN37YM7PM2WZO.json","view_paper":"https://pith.science/paper/X2VZJNGT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.3216&json=true","fetch_graph":"https://pith.science/api/pith-number/X2VZJNGTU6VMFUN37YM7PM2WZO/graph.json","fetch_events":"https://pith.science/api/pith-number/X2VZJNGTU6VMFUN37YM7PM2WZO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X2VZJNGTU6VMFUN37YM7PM2WZO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X2VZJNGTU6VMFUN37YM7PM2WZO/action/storage_attestation","attest_author":"https://pith.science/pith/X2VZJNGTU6VMFUN37YM7PM2WZO/action/author_attestation","sign_citation":"https://pith.science/pith/X2VZJNGTU6VMFUN37YM7PM2WZO/action/citation_signature","submit_replication":"https://pith.science/pith/X2VZJNGTU6VMFUN37YM7PM2WZO/action/replication_record"}},"created_at":"2026-05-18T01:37:29.955354+00:00","updated_at":"2026-05-18T01:37:29.955354+00:00"}