{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:OWVGH3GDMJSMVZXO2RX6MUVODT","short_pith_number":"pith:OWVGH3GD","schema_version":"1.0","canonical_sha256":"75aa63ecc36264cae6eed46fe652ae1cfb687ab17f7f8f92778290c66942c9f2","source":{"kind":"arxiv","id":"2103.02476","version":2},"attestation_state":"computed","paper":{"title":"Tensor hierarchy algebra extensions of over-extended Kac--Moody algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.RT","authors_text":"Jakob Palmkvist, Martin Cederwall","submitted_at":"2021-03-03T15:38:07Z","abstract_excerpt":"Tensor hierarchy algebras are infinite-dimensional generalisations of Cartan-type Lie superalgebras. They are not contragredient, exhibiting an asymmetry between positive and negative levels. These superalgebras have been a focus of attention due to the fundamental role they play for extended geometry. In the present paper, we examine tensor hierarchy algebras which are super-extensions of over-extended (often, hyperbolic) Kac--Moody algebras. They contain novel algebraic structures. Of particular interest is the extension of a over-extended algebra by its fundamental module, an extension that"},"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":"2103.02476","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-03-03T15:38:07Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"b184ee0f04ccdd1af9bb1ac5495ad2042eee2ee3ab6a5db9879dd9c07ff0b898","abstract_canon_sha256":"dd12051f4acf7f3dc16e9bb289626d54d46331b3e4c5c702c49011615dca2975"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:42:40.395549Z","signature_b64":"P6HJbkdyFyqvHKPh/zbeeEdQpfw/LdquYEro/ZBKMAJaSgh6kS3XaqLE5bZb6mFcSavRRVcnKxS8PAu6SaPqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75aa63ecc36264cae6eed46fe652ae1cfb687ab17f7f8f92778290c66942c9f2","last_reissued_at":"2026-07-05T03:42:40.395110Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:42:40.395110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tensor hierarchy algebra extensions of over-extended Kac--Moody algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.RT","authors_text":"Jakob Palmkvist, Martin Cederwall","submitted_at":"2021-03-03T15:38:07Z","abstract_excerpt":"Tensor hierarchy algebras are infinite-dimensional generalisations of Cartan-type Lie superalgebras. They are not contragredient, exhibiting an asymmetry between positive and negative levels. These superalgebras have been a focus of attention due to the fundamental role they play for extended geometry. In the present paper, we examine tensor hierarchy algebras which are super-extensions of over-extended (often, hyperbolic) Kac--Moody algebras. They contain novel algebraic structures. Of particular interest is the extension of a over-extended algebra by its fundamental module, an extension that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.02476","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/2103.02476/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":"2103.02476","created_at":"2026-07-05T03:42:40.395166+00:00"},{"alias_kind":"arxiv_version","alias_value":"2103.02476v2","created_at":"2026-07-05T03:42:40.395166+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.02476","created_at":"2026-07-05T03:42:40.395166+00:00"},{"alias_kind":"pith_short_12","alias_value":"OWVGH3GDMJSM","created_at":"2026-07-05T03:42:40.395166+00:00"},{"alias_kind":"pith_short_16","alias_value":"OWVGH3GDMJSMVZXO","created_at":"2026-07-05T03:42:40.395166+00:00"},{"alias_kind":"pith_short_8","alias_value":"OWVGH3GD","created_at":"2026-07-05T03:42:40.395166+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.04595","citing_title":"Gauged Extended Field Theory and Generalised Cartan Geometry","ref_index":101,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OWVGH3GDMJSMVZXO2RX6MUVODT","json":"https://pith.science/pith/OWVGH3GDMJSMVZXO2RX6MUVODT.json","graph_json":"https://pith.science/api/pith-number/OWVGH3GDMJSMVZXO2RX6MUVODT/graph.json","events_json":"https://pith.science/api/pith-number/OWVGH3GDMJSMVZXO2RX6MUVODT/events.json","paper":"https://pith.science/paper/OWVGH3GD"},"agent_actions":{"view_html":"https://pith.science/pith/OWVGH3GDMJSMVZXO2RX6MUVODT","download_json":"https://pith.science/pith/OWVGH3GDMJSMVZXO2RX6MUVODT.json","view_paper":"https://pith.science/paper/OWVGH3GD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2103.02476&json=true","fetch_graph":"https://pith.science/api/pith-number/OWVGH3GDMJSMVZXO2RX6MUVODT/graph.json","fetch_events":"https://pith.science/api/pith-number/OWVGH3GDMJSMVZXO2RX6MUVODT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OWVGH3GDMJSMVZXO2RX6MUVODT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OWVGH3GDMJSMVZXO2RX6MUVODT/action/storage_attestation","attest_author":"https://pith.science/pith/OWVGH3GDMJSMVZXO2RX6MUVODT/action/author_attestation","sign_citation":"https://pith.science/pith/OWVGH3GDMJSMVZXO2RX6MUVODT/action/citation_signature","submit_replication":"https://pith.science/pith/OWVGH3GDMJSMVZXO2RX6MUVODT/action/replication_record"}},"created_at":"2026-07-05T03:42:40.395166+00:00","updated_at":"2026-07-05T03:42:40.395166+00:00"}