{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:7Y6EGQR3BRD26BYURZLLW4FPGH","short_pith_number":"pith:7Y6EGQR3","schema_version":"1.0","canonical_sha256":"fe3c43423b0c47af07148e56bb70af31d1ca0451b3822874d0945d5b543ed792","source":{"kind":"arxiv","id":"2112.12828","version":5},"attestation_state":"computed","paper":{"title":"Gravity and the Crossed Product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Edward Witten","submitted_at":"2021-12-23T20:27:03Z","abstract_excerpt":"Recently Leutheusser and Liu [1,2] identified an emergent algebra of Type III$_1$ in the operator algebra of ${\\mathcal N}=4$ super Yang-Mills theory for large $N$. Here we describe some $1/N$ corrections to this picture and show that the emergent Type III$_1$ algebra becomes an algebra of Type II$_\\infty$. The Type II$_\\infty$ algebra is the crossed product of the Type III$_1$ algebra by its modular automorphism group. In the context of the emergent Type II$_\\infty$ algebra, the entropy of a black hole state is well-defined up to an additive constant, independent of the state. This is somewha"},"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":"2112.12828","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-12-23T20:27:03Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"dc0e7c2112e94536d9f49031f1092909fa198c380ea2c0f732c0ef283598f03c","abstract_canon_sha256":"83bef5490b35e53a05dcbf4d2e01f7c658fc67f19f801ff8e805e2f8f93e5157"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:07:37.577691Z","signature_b64":"60uLbgGCuTVfCIpwEX8KGxBVrEcWryMJaD463ffoiA5vbTCT1hxEPKdPeadE3eZXXU9tgOlk0dCF+gC26+1/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe3c43423b0c47af07148e56bb70af31d1ca0451b3822874d0945d5b543ed792","last_reissued_at":"2026-07-05T05:07:37.577276Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:07:37.577276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gravity and the Crossed Product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Edward Witten","submitted_at":"2021-12-23T20:27:03Z","abstract_excerpt":"Recently Leutheusser and Liu [1,2] identified an emergent algebra of Type III$_1$ in the operator algebra of ${\\mathcal N}=4$ super Yang-Mills theory for large $N$. Here we describe some $1/N$ corrections to this picture and show that the emergent Type III$_1$ algebra becomes an algebra of Type II$_\\infty$. The Type II$_\\infty$ algebra is the crossed product of the Type III$_1$ algebra by its modular automorphism group. In the context of the emergent Type II$_\\infty$ algebra, the entropy of a black hole state is well-defined up to an additive constant, independent of the state. This is somewha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.12828","kind":"arxiv","version":5},"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/2112.12828/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":"2112.12828","created_at":"2026-07-05T05:07:37.577341+00:00"},{"alias_kind":"arxiv_version","alias_value":"2112.12828v5","created_at":"2026-07-05T05:07:37.577341+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.12828","created_at":"2026-07-05T05:07:37.577341+00:00"},{"alias_kind":"pith_short_12","alias_value":"7Y6EGQR3BRD2","created_at":"2026-07-05T05:07:37.577341+00:00"},{"alias_kind":"pith_short_16","alias_value":"7Y6EGQR3BRD26BYU","created_at":"2026-07-05T05:07:37.577341+00:00"},{"alias_kind":"pith_short_8","alias_value":"7Y6EGQR3","created_at":"2026-07-05T05:07:37.577341+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":27,"internal_anchor_count":3,"sample":[{"citing_arxiv_id":"2607.07785","citing_title":"Quantization of Gravity on Null Hypersurfaces","ref_index":70,"is_internal_anchor":true},{"citing_arxiv_id":"2607.07799","citing_title":"No off-diagonal quantum focusing for R\\'enyi divergences","ref_index":11,"is_internal_anchor":true},{"citing_arxiv_id":"2607.08737","citing_title":"The mini-Page Curve in Cosmology","ref_index":32,"is_internal_anchor":true},{"citing_arxiv_id":"2607.01351","citing_title":"Wigner negativity in Krylov space and emergent semiclassicality","ref_index":83,"is_internal_anchor":false},{"citing_arxiv_id":"2606.10924","citing_title":"Spacetime from Operator Algebras","ref_index":17,"is_internal_anchor":false},{"citing_arxiv_id":"2606.09344","citing_title":"Quantum Reference Fields Transformations in Linearized Quantum Gravity","ref_index":97,"is_internal_anchor":false},{"citing_arxiv_id":"2605.13956","citing_title":"q-Askey Deformations of Double-Scaled SYK","ref_index":87,"is_internal_anchor":false},{"citing_arxiv_id":"2605.30423","citing_title":"Spectral Admissibility of Real Observers in Euclidean de Sitter Gravity","ref_index":31,"is_internal_anchor":false},{"citing_arxiv_id":"2403.09021","citing_title":"Von Neumann Algebras in Double-Scaled SYK","ref_index":68,"is_internal_anchor":false},{"citing_arxiv_id":"2503.19342","citing_title":"Timelike entanglement entropy Revisited","ref_index":24,"is_internal_anchor":false},{"citing_arxiv_id":"2507.20983","citing_title":"Fiducial observers and the thermal atmosphere in the black hole quantum throat","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2508.13283","citing_title":"Algebraic traversable wormholes","ref_index":6,"is_internal_anchor":false},{"citing_arxiv_id":"2509.01458","citing_title":"Quantum reference frames for spacetime symmetries and large gauge transformations","ref_index":20,"is_internal_anchor":false},{"citing_arxiv_id":"2510.20902","citing_title":"Searching for emergent spacetime in spin glasses","ref_index":40,"is_internal_anchor":false},{"citing_arxiv_id":"2206.10780","citing_title":"An Algebra of Observables for de Sitter Space","ref_index":26,"is_internal_anchor":false},{"citing_arxiv_id":"2511.01978","citing_title":"Single-Sided Black Holes in Double-Scaled SYK Model and No Man's Island","ref_index":24,"is_internal_anchor":false},{"citing_arxiv_id":"2511.03779","citing_title":"Cosmological Entanglement Entropy from the von Neumann Algebra of Double-Scaled SYK & Its Connection with Krylov Complexity","ref_index":141,"is_internal_anchor":false},{"citing_arxiv_id":"2512.11754","citing_title":"Modular Witten Diagrams and Quantum Extremality","ref_index":10,"is_internal_anchor":false},{"citing_arxiv_id":"2512.10101","citing_title":"The von Neumann algebraic quantum group $\\mathrm{SU}_q(1,1)\\rtimes \\mathbb{Z}_2$ and the DSSYK model","ref_index":6,"is_internal_anchor":false},{"citing_arxiv_id":"2602.06113","citing_title":"Deforming the Double-Scaled SYK & Reaching the Stretched Horizon From Finite Cutoff Holography","ref_index":209,"is_internal_anchor":false},{"citing_arxiv_id":"2605.13956","citing_title":"q-Askey Deformations of Double-Scaled SYK","ref_index":87,"is_internal_anchor":false},{"citing_arxiv_id":"2603.25990","citing_title":"Implication of dressed form of relational observable on von Neumann algebra","ref_index":62,"is_internal_anchor":false},{"citing_arxiv_id":"2605.13576","citing_title":"Semiclassical algebraic reconstruction for type III algebras","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2604.02228","citing_title":"Gravitational null rays: Covariant Quantization and the Dressing Time","ref_index":49,"is_internal_anchor":false},{"citing_arxiv_id":"2605.02792","citing_title":"Albertian Channel Memory in Black-Hole Evaporation","ref_index":29,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7Y6EGQR3BRD26BYURZLLW4FPGH","json":"https://pith.science/pith/7Y6EGQR3BRD26BYURZLLW4FPGH.json","graph_json":"https://pith.science/api/pith-number/7Y6EGQR3BRD26BYURZLLW4FPGH/graph.json","events_json":"https://pith.science/api/pith-number/7Y6EGQR3BRD26BYURZLLW4FPGH/events.json","paper":"https://pith.science/paper/7Y6EGQR3"},"agent_actions":{"view_html":"https://pith.science/pith/7Y6EGQR3BRD26BYURZLLW4FPGH","download_json":"https://pith.science/pith/7Y6EGQR3BRD26BYURZLLW4FPGH.json","view_paper":"https://pith.science/paper/7Y6EGQR3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2112.12828&json=true","fetch_graph":"https://pith.science/api/pith-number/7Y6EGQR3BRD26BYURZLLW4FPGH/graph.json","fetch_events":"https://pith.science/api/pith-number/7Y6EGQR3BRD26BYURZLLW4FPGH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7Y6EGQR3BRD26BYURZLLW4FPGH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7Y6EGQR3BRD26BYURZLLW4FPGH/action/storage_attestation","attest_author":"https://pith.science/pith/7Y6EGQR3BRD26BYURZLLW4FPGH/action/author_attestation","sign_citation":"https://pith.science/pith/7Y6EGQR3BRD26BYURZLLW4FPGH/action/citation_signature","submit_replication":"https://pith.science/pith/7Y6EGQR3BRD26BYURZLLW4FPGH/action/replication_record"}},"created_at":"2026-07-05T05:07:37.577341+00:00","updated_at":"2026-07-05T05:07:37.577341+00:00"}