{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:FVKEH5BUDXARGTXD7GN4SKX5CJ","short_pith_number":"pith:FVKEH5BU","schema_version":"1.0","canonical_sha256":"2d5443f4341dc1134ee3f99bc92afd125c093757be794879629790cb6821189e","source":{"kind":"arxiv","id":"1108.4038","version":1},"attestation_state":"computed","paper":{"title":"Entanglement Entropy of Gapped Phases and Topological Order in Three dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Ari M. Turner, Ashvin Vishwanath, Tarun Grover","submitted_at":"2011-08-19T20:00:27Z","abstract_excerpt":"We discuss entanglement entropy of gapped ground states in different dimensions, obtained on partitioning space into two regions. For trivial phases without topological order, we argue that the entanglement entropy may be obtained by integrating an `entropy density' over the partition boundary that admits a gradient expansion in the curvature of the boundary. This constrains the expansion of entanglement entropy as a function of system size, and points to an even-odd dependence on dimensionality. For example, in contrast to the familiar result in two dimensions, a size independent constant con"},"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":"1108.4038","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2011-08-19T20:00:27Z","cross_cats_sorted":["hep-th","quant-ph"],"title_canon_sha256":"9095ef088a3aa03ffee75d48918f09c2ffe835e7bb3fd103c8ff92b985aac92a","abstract_canon_sha256":"af64f5281e3b779483c014cdae57b10225a75293b6f9cc5f72dafeb602f780de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:44.720132Z","signature_b64":"Vtqv4FwOZKMtVUZJ4qgYwf6eMxQID+SK0T12R/GaNJ4oD00GKRvTf1dhTLfpXEWWpwYXLTvXdLGlaV3wApa2Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d5443f4341dc1134ee3f99bc92afd125c093757be794879629790cb6821189e","last_reissued_at":"2026-05-18T04:06:44.719679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:44.719679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entanglement Entropy of Gapped Phases and Topological Order in Three dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Ari M. Turner, Ashvin Vishwanath, Tarun Grover","submitted_at":"2011-08-19T20:00:27Z","abstract_excerpt":"We discuss entanglement entropy of gapped ground states in different dimensions, obtained on partitioning space into two regions. For trivial phases without topological order, we argue that the entanglement entropy may be obtained by integrating an `entropy density' over the partition boundary that admits a gradient expansion in the curvature of the boundary. This constrains the expansion of entanglement entropy as a function of system size, and points to an even-odd dependence on dimensionality. For example, in contrast to the familiar result in two dimensions, a size independent constant con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4038","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":""},"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":"1108.4038","created_at":"2026-05-18T04:06:44.719746+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.4038v1","created_at":"2026-05-18T04:06:44.719746+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4038","created_at":"2026-05-18T04:06:44.719746+00:00"},{"alias_kind":"pith_short_12","alias_value":"FVKEH5BUDXAR","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"FVKEH5BUDXARGTXD","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"FVKEH5BU","created_at":"2026-05-18T12:26:28.662955+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/FVKEH5BUDXARGTXD7GN4SKX5CJ","json":"https://pith.science/pith/FVKEH5BUDXARGTXD7GN4SKX5CJ.json","graph_json":"https://pith.science/api/pith-number/FVKEH5BUDXARGTXD7GN4SKX5CJ/graph.json","events_json":"https://pith.science/api/pith-number/FVKEH5BUDXARGTXD7GN4SKX5CJ/events.json","paper":"https://pith.science/paper/FVKEH5BU"},"agent_actions":{"view_html":"https://pith.science/pith/FVKEH5BUDXARGTXD7GN4SKX5CJ","download_json":"https://pith.science/pith/FVKEH5BUDXARGTXD7GN4SKX5CJ.json","view_paper":"https://pith.science/paper/FVKEH5BU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.4038&json=true","fetch_graph":"https://pith.science/api/pith-number/FVKEH5BUDXARGTXD7GN4SKX5CJ/graph.json","fetch_events":"https://pith.science/api/pith-number/FVKEH5BUDXARGTXD7GN4SKX5CJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FVKEH5BUDXARGTXD7GN4SKX5CJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FVKEH5BUDXARGTXD7GN4SKX5CJ/action/storage_attestation","attest_author":"https://pith.science/pith/FVKEH5BUDXARGTXD7GN4SKX5CJ/action/author_attestation","sign_citation":"https://pith.science/pith/FVKEH5BUDXARGTXD7GN4SKX5CJ/action/citation_signature","submit_replication":"https://pith.science/pith/FVKEH5BUDXARGTXD7GN4SKX5CJ/action/replication_record"}},"created_at":"2026-05-18T04:06:44.719746+00:00","updated_at":"2026-05-18T04:06:44.719746+00:00"}