{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:RH23NLCOHW2SPZFE5XERFGJ3BY","short_pith_number":"pith:RH23NLCO","schema_version":"1.0","canonical_sha256":"89f5b6ac4e3db527e4a4edc912993b0e13061237974f54c470bbdfdc5f9efa5f","source":{"kind":"arxiv","id":"2108.10324","version":2},"attestation_state":"computed","paper":{"title":"Hilbert Space Fragmentation and Commutant Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.MP","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Olexei I. Motrunich, Sanjay Moudgalya","submitted_at":"2021-08-23T18:00:01Z","abstract_excerpt":"We study the phenomenon of Hilbert space fragmentation in isolated Hamiltonian and Floquet quantum systems using the language of commutant algebras, the algebra of all operators that commute with each term of the Hamiltonian or each gate of the circuit. We provide a precise definition of Hilbert space fragmentation in this formalism as the case where the dimension of the commutant algebra grows exponentially with the system size. Fragmentation can hence be distinguished from systems with conventional symmetries such as $U(1)$ or $SU(2)$, where the dimension of the commutant algebra grows polyn"},"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":"2108.10324","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2021-08-23T18:00:01Z","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP","quant-ph"],"title_canon_sha256":"3c9ae8afa34a6e712051623b1f4d26a7d06281cbc1aa9a8f124dbde264e01447","abstract_canon_sha256":"4b72ace487099e752074bbc034f6855e079b898092756d72fe757ad8f1a21541"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:08:39.978126Z","signature_b64":"PNaaaiPSQPO0TURAS5hrfoz9rWm4PFYh56IQpnVBWNOauryOJI8HKvrgyituh9rrpphOOs28BDfjX0/9+hH8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89f5b6ac4e3db527e4a4edc912993b0e13061237974f54c470bbdfdc5f9efa5f","last_reissued_at":"2026-07-05T04:08:39.977703Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:08:39.977703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hilbert Space Fragmentation and Commutant Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.MP","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Olexei I. Motrunich, Sanjay Moudgalya","submitted_at":"2021-08-23T18:00:01Z","abstract_excerpt":"We study the phenomenon of Hilbert space fragmentation in isolated Hamiltonian and Floquet quantum systems using the language of commutant algebras, the algebra of all operators that commute with each term of the Hamiltonian or each gate of the circuit. We provide a precise definition of Hilbert space fragmentation in this formalism as the case where the dimension of the commutant algebra grows exponentially with the system size. Fragmentation can hence be distinguished from systems with conventional symmetries such as $U(1)$ or $SU(2)$, where the dimension of the commutant algebra grows polyn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.10324","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.10324/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":"2108.10324","created_at":"2026-07-05T04:08:39.977758+00:00"},{"alias_kind":"arxiv_version","alias_value":"2108.10324v2","created_at":"2026-07-05T04:08:39.977758+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.10324","created_at":"2026-07-05T04:08:39.977758+00:00"},{"alias_kind":"pith_short_12","alias_value":"RH23NLCOHW2S","created_at":"2026-07-05T04:08:39.977758+00:00"},{"alias_kind":"pith_short_16","alias_value":"RH23NLCOHW2SPZFE","created_at":"2026-07-05T04:08:39.977758+00:00"},{"alias_kind":"pith_short_8","alias_value":"RH23NLCO","created_at":"2026-07-05T04:08:39.977758+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.08655","citing_title":"Temperature Beyond Equilibrium in Isolated Quantum Many-Body Systems and Their Subsystems","ref_index":79,"is_internal_anchor":true},{"citing_arxiv_id":"2606.20850","citing_title":"Hydrodynamic tails in chaotic spin chains with quantum group symmetry","ref_index":35,"is_internal_anchor":false},{"citing_arxiv_id":"2604.10519","citing_title":"Energy-momentum and dark energy in $\\boldsymbol{SU(\\infty)}$-QGR quantum gravity","ref_index":80,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RH23NLCOHW2SPZFE5XERFGJ3BY","json":"https://pith.science/pith/RH23NLCOHW2SPZFE5XERFGJ3BY.json","graph_json":"https://pith.science/api/pith-number/RH23NLCOHW2SPZFE5XERFGJ3BY/graph.json","events_json":"https://pith.science/api/pith-number/RH23NLCOHW2SPZFE5XERFGJ3BY/events.json","paper":"https://pith.science/paper/RH23NLCO"},"agent_actions":{"view_html":"https://pith.science/pith/RH23NLCOHW2SPZFE5XERFGJ3BY","download_json":"https://pith.science/pith/RH23NLCOHW2SPZFE5XERFGJ3BY.json","view_paper":"https://pith.science/paper/RH23NLCO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2108.10324&json=true","fetch_graph":"https://pith.science/api/pith-number/RH23NLCOHW2SPZFE5XERFGJ3BY/graph.json","fetch_events":"https://pith.science/api/pith-number/RH23NLCOHW2SPZFE5XERFGJ3BY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RH23NLCOHW2SPZFE5XERFGJ3BY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RH23NLCOHW2SPZFE5XERFGJ3BY/action/storage_attestation","attest_author":"https://pith.science/pith/RH23NLCOHW2SPZFE5XERFGJ3BY/action/author_attestation","sign_citation":"https://pith.science/pith/RH23NLCOHW2SPZFE5XERFGJ3BY/action/citation_signature","submit_replication":"https://pith.science/pith/RH23NLCOHW2SPZFE5XERFGJ3BY/action/replication_record"}},"created_at":"2026-07-05T04:08:39.977758+00:00","updated_at":"2026-07-05T04:08:39.977758+00:00"}