{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:MGLDGJJWI6OBAFE6YIXD22Z5QW","short_pith_number":"pith:MGLDGJJW","schema_version":"1.0","canonical_sha256":"6196332536479c10149ec22e3d6b3d85bbffa63389a9df5d8b66e2cccdac7d1f","source":{"kind":"arxiv","id":"2303.07431","version":2},"attestation_state":"computed","paper":{"title":"Homotopical Foundations of Parametrized Quantum Spin Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","math.AT","math.FA","math.MP","math.OA"],"primary_cat":"math-ph","authors_text":"Agnes Beaudry, Daniel Spiegel, Juan Moreno, Markus Pflaum, Marvin Qi, Michael Hermele","submitted_at":"2023-03-13T19:14:26Z","abstract_excerpt":"In this paper, we present a homotopical framework for studying invertible gapped phases of matter from the point of view of infinite spin lattice systems, using the framework of algebraic quantum mechanics. We define the notion of quantum state types. These are certain lax-monoidal functors from the category of finite dimensional Hilbert spaces to the category of topological spaces. The universal example takes a finite dimensional Hilbert space to the pure state space of the quasi-local algebra of the quantum spin system with this Hilbert space at each site of a specified lattice. The lax-mono"},"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":"2303.07431","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-03-13T19:14:26Z","cross_cats_sorted":["cond-mat.str-el","math.AT","math.FA","math.MP","math.OA"],"title_canon_sha256":"e9671c30916abbe9958b7408219bd2d5c89e13064a62c19a4b3e4300b034c4c0","abstract_canon_sha256":"c71c5e65fc574995d96c96191e5b8e858435aea3851c7ae3f1665c083a8a8a46"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:47:24.725734Z","signature_b64":"A5Gh7FtsK4L6uQMHa9SKCgtLSUos1EK3qlX7/fnv9Y+oIdw80rbbU9QdQVDV/JErM6mOEUNj6HC4exRb70hsCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6196332536479c10149ec22e3d6b3d85bbffa63389a9df5d8b66e2cccdac7d1f","last_reissued_at":"2026-07-05T07:47:24.725242Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:47:24.725242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homotopical Foundations of Parametrized Quantum Spin Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","math.AT","math.FA","math.MP","math.OA"],"primary_cat":"math-ph","authors_text":"Agnes Beaudry, Daniel Spiegel, Juan Moreno, Markus Pflaum, Marvin Qi, Michael Hermele","submitted_at":"2023-03-13T19:14:26Z","abstract_excerpt":"In this paper, we present a homotopical framework for studying invertible gapped phases of matter from the point of view of infinite spin lattice systems, using the framework of algebraic quantum mechanics. We define the notion of quantum state types. These are certain lax-monoidal functors from the category of finite dimensional Hilbert spaces to the category of topological spaces. The universal example takes a finite dimensional Hilbert space to the pure state space of the quasi-local algebra of the quantum spin system with this Hilbert space at each site of a specified lattice. The lax-mono"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.07431","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/2303.07431/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":"2303.07431","created_at":"2026-07-05T07:47:24.725298+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.07431v2","created_at":"2026-07-05T07:47:24.725298+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.07431","created_at":"2026-07-05T07:47:24.725298+00:00"},{"alias_kind":"pith_short_12","alias_value":"MGLDGJJWI6OB","created_at":"2026-07-05T07:47:24.725298+00:00"},{"alias_kind":"pith_short_16","alias_value":"MGLDGJJWI6OBAFE6","created_at":"2026-07-05T07:47:24.725298+00:00"},{"alias_kind":"pith_short_8","alias_value":"MGLDGJJW","created_at":"2026-07-05T07:47:24.725298+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2410.16250","citing_title":"Cups and Gates I: Cohomology invariants and logical quantum operations","ref_index":51,"is_internal_anchor":false},{"citing_arxiv_id":"2602.13627","citing_title":"Higher Connection in Open String Field Theory","ref_index":55,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MGLDGJJWI6OBAFE6YIXD22Z5QW","json":"https://pith.science/pith/MGLDGJJWI6OBAFE6YIXD22Z5QW.json","graph_json":"https://pith.science/api/pith-number/MGLDGJJWI6OBAFE6YIXD22Z5QW/graph.json","events_json":"https://pith.science/api/pith-number/MGLDGJJWI6OBAFE6YIXD22Z5QW/events.json","paper":"https://pith.science/paper/MGLDGJJW"},"agent_actions":{"view_html":"https://pith.science/pith/MGLDGJJWI6OBAFE6YIXD22Z5QW","download_json":"https://pith.science/pith/MGLDGJJWI6OBAFE6YIXD22Z5QW.json","view_paper":"https://pith.science/paper/MGLDGJJW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.07431&json=true","fetch_graph":"https://pith.science/api/pith-number/MGLDGJJWI6OBAFE6YIXD22Z5QW/graph.json","fetch_events":"https://pith.science/api/pith-number/MGLDGJJWI6OBAFE6YIXD22Z5QW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MGLDGJJWI6OBAFE6YIXD22Z5QW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MGLDGJJWI6OBAFE6YIXD22Z5QW/action/storage_attestation","attest_author":"https://pith.science/pith/MGLDGJJWI6OBAFE6YIXD22Z5QW/action/author_attestation","sign_citation":"https://pith.science/pith/MGLDGJJWI6OBAFE6YIXD22Z5QW/action/citation_signature","submit_replication":"https://pith.science/pith/MGLDGJJWI6OBAFE6YIXD22Z5QW/action/replication_record"}},"created_at":"2026-07-05T07:47:24.725298+00:00","updated_at":"2026-07-05T07:47:24.725298+00:00"}