{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:SBN3V3W72RD2G5IRRNVALZGCGP","short_pith_number":"pith:SBN3V3W7","schema_version":"1.0","canonical_sha256":"905bbaeedfd447a375118b6a05e4c233d68d51957bc71586cfe2f7b933e5f6fd","source":{"kind":"arxiv","id":"2304.00068","version":3},"attestation_state":"computed","paper":{"title":"DHR bimodules of quasi-local algebras and symmetric quantum cellular automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.OA","math.QA","quant-ph"],"primary_cat":"math-ph","authors_text":"Corey Jones","submitted_at":"2023-03-31T18:33:07Z","abstract_excerpt":"For a net of C*-algebras on a discrete metric space, we introduce a bimodule version of the DHR tensor category and show it is an invariant of quasi-local algebras under isomorphisms with bounded spread. For abstract spin systems on a lattice $L\\subseteq \\mathbb{R}^{n}$ satisfying a weak version of Haag duality, we construct a braiding on these categories. Applying the general theory to quasi-local algebras $A$ of operators on a lattice invariant under a (categorical) symmetry, we obtain a homomorphism from the group of symmetric quantum cellular automata (QCA) to $\\textbf{Aut}_{br}(\\textbf{DH"},"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":"2304.00068","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-03-31T18:33:07Z","cross_cats_sorted":["math.MP","math.OA","math.QA","quant-ph"],"title_canon_sha256":"df73a367241ffd62d90dd73efd3f315fb3778f04d0ec7f4620df5290514d06ea","abstract_canon_sha256":"582dca6a764162e459780cad0613165f72c335162b28c9b75e28a854c1c411b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:46:17.010290Z","signature_b64":"8R2w7jbT8xlM2dsuGWcuLz+2oMwBKSza8rTWPtAshZBrJdcR0yIBxmRDn71hDozcw/0u/b4mKrwLQKAo+ZT8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"905bbaeedfd447a375118b6a05e4c233d68d51957bc71586cfe2f7b933e5f6fd","last_reissued_at":"2026-07-05T07:46:17.009895Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:46:17.009895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"DHR bimodules of quasi-local algebras and symmetric quantum cellular automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.OA","math.QA","quant-ph"],"primary_cat":"math-ph","authors_text":"Corey Jones","submitted_at":"2023-03-31T18:33:07Z","abstract_excerpt":"For a net of C*-algebras on a discrete metric space, we introduce a bimodule version of the DHR tensor category and show it is an invariant of quasi-local algebras under isomorphisms with bounded spread. For abstract spin systems on a lattice $L\\subseteq \\mathbb{R}^{n}$ satisfying a weak version of Haag duality, we construct a braiding on these categories. Applying the general theory to quasi-local algebras $A$ of operators on a lattice invariant under a (categorical) symmetry, we obtain a homomorphism from the group of symmetric quantum cellular automata (QCA) to $\\textbf{Aut}_{br}(\\textbf{DH"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.00068","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.00068/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2304.00068","created_at":"2026-07-05T07:46:17.009967+00:00"},{"alias_kind":"arxiv_version","alias_value":"2304.00068v3","created_at":"2026-07-05T07:46:17.009967+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.00068","created_at":"2026-07-05T07:46:17.009967+00:00"},{"alias_kind":"pith_short_12","alias_value":"SBN3V3W72RD2","created_at":"2026-07-05T07:46:17.009967+00:00"},{"alias_kind":"pith_short_16","alias_value":"SBN3V3W72RD2G5IR","created_at":"2026-07-05T07:46:17.009967+00:00"},{"alias_kind":"pith_short_8","alias_value":"SBN3V3W7","created_at":"2026-07-05T07:46:17.009967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.06661","citing_title":"Pro-Tensor Network","ref_index":24,"is_internal_anchor":false},{"citing_arxiv_id":"2509.22051","citing_title":"From gauging to duality in one-dimensional quantum lattice models","ref_index":41,"is_internal_anchor":false},{"citing_arxiv_id":"2605.03891","citing_title":"Parameterized Families of Toric Code Phase: $em$-duality family and higher-order anyon pumping","ref_index":63,"is_internal_anchor":false},{"citing_arxiv_id":"2605.06661","citing_title":"Pro-Tensor Network","ref_index":24,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SBN3V3W72RD2G5IRRNVALZGCGP","json":"https://pith.science/pith/SBN3V3W72RD2G5IRRNVALZGCGP.json","graph_json":"https://pith.science/api/pith-number/SBN3V3W72RD2G5IRRNVALZGCGP/graph.json","events_json":"https://pith.science/api/pith-number/SBN3V3W72RD2G5IRRNVALZGCGP/events.json","paper":"https://pith.science/paper/SBN3V3W7"},"agent_actions":{"view_html":"https://pith.science/pith/SBN3V3W72RD2G5IRRNVALZGCGP","download_json":"https://pith.science/pith/SBN3V3W72RD2G5IRRNVALZGCGP.json","view_paper":"https://pith.science/paper/SBN3V3W7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2304.00068&json=true","fetch_graph":"https://pith.science/api/pith-number/SBN3V3W72RD2G5IRRNVALZGCGP/graph.json","fetch_events":"https://pith.science/api/pith-number/SBN3V3W72RD2G5IRRNVALZGCGP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SBN3V3W72RD2G5IRRNVALZGCGP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SBN3V3W72RD2G5IRRNVALZGCGP/action/storage_attestation","attest_author":"https://pith.science/pith/SBN3V3W72RD2G5IRRNVALZGCGP/action/author_attestation","sign_citation":"https://pith.science/pith/SBN3V3W72RD2G5IRRNVALZGCGP/action/citation_signature","submit_replication":"https://pith.science/pith/SBN3V3W72RD2G5IRRNVALZGCGP/action/replication_record"}},"created_at":"2026-07-05T07:46:17.009967+00:00","updated_at":"2026-07-05T07:46:17.009967+00:00"}