{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:XVPPBD5PDPQYTHEASQ6VOUUJQW","short_pith_number":"pith:XVPPBD5P","schema_version":"1.0","canonical_sha256":"bd5ef08faf1be1899c80943d57528985b05a7b3ab4bd3e79fcd3b77a0b9cb6c7","source":{"kind":"arxiv","id":"1006.4871","version":1},"attestation_state":"computed","paper":{"title":"Topological order in an exactly solvable 3D spin model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Barbara M. Terhal, Bernhard Leemhuis, Sergey Bravyi","submitted_at":"2010-06-24T20:20:05Z","abstract_excerpt":"We study a 3D generalization of the toric code model introduced recently by Chamon. This is an exactly solvable spin model with six-qubit nearest neighbor interactions on an FCC lattice whose ground space exhibits topological quantum order. The elementary excitations of this model which we call monopoles can be geometrically described as the corners of rectangular-shaped membranes. We prove that the creation of an isolated monopole separated from other monopoles by a distance R requires an operator acting on at least R^2 qubits. Composite particles that consist of two monopoles (dipoles) and f"},"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":"1006.4871","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-06-24T20:20:05Z","cross_cats_sorted":[],"title_canon_sha256":"0cc88c498aaf6852ae8416dee6796f4005fe985b494674153c63653d3a10abfb","abstract_canon_sha256":"c56dffe50aaf9f643d0637c74176612e58ebc16c0f2db52b49ec9c559d208ef8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:06:42.610735Z","signature_b64":"DWK9sEYjKHbV/3R5FVDPJnVBvaRA5ojgmNACCm4DjFlKvr5LAEQy+hZjAd7RD8auOO0HQM0b9WUKkVSkXNkrAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd5ef08faf1be1899c80943d57528985b05a7b3ab4bd3e79fcd3b77a0b9cb6c7","last_reissued_at":"2026-05-18T02:06:42.609879Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:06:42.609879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological order in an exactly solvable 3D spin model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Barbara M. Terhal, Bernhard Leemhuis, Sergey Bravyi","submitted_at":"2010-06-24T20:20:05Z","abstract_excerpt":"We study a 3D generalization of the toric code model introduced recently by Chamon. This is an exactly solvable spin model with six-qubit nearest neighbor interactions on an FCC lattice whose ground space exhibits topological quantum order. The elementary excitations of this model which we call monopoles can be geometrically described as the corners of rectangular-shaped membranes. We prove that the creation of an isolated monopole separated from other monopoles by a distance R requires an operator acting on at least R^2 qubits. Composite particles that consist of two monopoles (dipoles) and f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4871","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":"1006.4871","created_at":"2026-05-18T02:06:42.610020+00:00"},{"alias_kind":"arxiv_version","alias_value":"1006.4871v1","created_at":"2026-05-18T02:06:42.610020+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.4871","created_at":"2026-05-18T02:06:42.610020+00:00"},{"alias_kind":"pith_short_12","alias_value":"XVPPBD5PDPQY","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"XVPPBD5PDPQYTHEA","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"XVPPBD5P","created_at":"2026-05-18T12:26:17.028572+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2406.07334","citing_title":"Fractonic solids","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XVPPBD5PDPQYTHEASQ6VOUUJQW","json":"https://pith.science/pith/XVPPBD5PDPQYTHEASQ6VOUUJQW.json","graph_json":"https://pith.science/api/pith-number/XVPPBD5PDPQYTHEASQ6VOUUJQW/graph.json","events_json":"https://pith.science/api/pith-number/XVPPBD5PDPQYTHEASQ6VOUUJQW/events.json","paper":"https://pith.science/paper/XVPPBD5P"},"agent_actions":{"view_html":"https://pith.science/pith/XVPPBD5PDPQYTHEASQ6VOUUJQW","download_json":"https://pith.science/pith/XVPPBD5PDPQYTHEASQ6VOUUJQW.json","view_paper":"https://pith.science/paper/XVPPBD5P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1006.4871&json=true","fetch_graph":"https://pith.science/api/pith-number/XVPPBD5PDPQYTHEASQ6VOUUJQW/graph.json","fetch_events":"https://pith.science/api/pith-number/XVPPBD5PDPQYTHEASQ6VOUUJQW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XVPPBD5PDPQYTHEASQ6VOUUJQW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XVPPBD5PDPQYTHEASQ6VOUUJQW/action/storage_attestation","attest_author":"https://pith.science/pith/XVPPBD5PDPQYTHEASQ6VOUUJQW/action/author_attestation","sign_citation":"https://pith.science/pith/XVPPBD5PDPQYTHEASQ6VOUUJQW/action/citation_signature","submit_replication":"https://pith.science/pith/XVPPBD5PDPQYTHEASQ6VOUUJQW/action/replication_record"}},"created_at":"2026-05-18T02:06:42.610020+00:00","updated_at":"2026-05-18T02:06:42.610020+00:00"}