{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:LA3NM6KX7WIWNLPOBKQKSHFAZM","short_pith_number":"pith:LA3NM6KX","schema_version":"1.0","canonical_sha256":"5836d67957fd9166adee0aa0a91ca0cb39d5ad4c2021df7959ba3bc8987a093e","source":{"kind":"arxiv","id":"1301.1346","version":1},"attestation_state":"computed","paper":{"title":"Oxidizing Borcherds symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"hep-th","authors_text":"Axel Kleinschmidt, Jakob Palmkvist","submitted_at":"2013-01-07T21:00:11Z","abstract_excerpt":"The tensor hierarchy of maximal supergravity in D dimensions is known to be closely related to a Borcherds (super)algebra that is constructed from the global symmetry group E(11-D). We here explain how the Borcherds algebras in different dimensions are embedded into each other and can be constructed from a unifying Borcherds algebra. The construction also has a natural physical explanation in terms of oxidation. We then go on to show that the Hodge duality that is present in the tensor hierarchy has an algebraic counterpart. For D>8 the Borcherds algebras we find differ from the ones existing "},"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":"1301.1346","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-01-07T21:00:11Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"f64bb8cc919a2e79cd234eb35ee6137393e87ec8e772adf1122d46e68e729c5e","abstract_canon_sha256":"a59660407e74944fa1916ee46cc2d4b07aa05656dffe9133f9bae27262a29305"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:52:20.871629Z","signature_b64":"BuX4aH/SRL8oVkpcMfq4WAChsDDeYIZ59VXFVV75kDLqsbNTUHuV9Mw9wmPbllamWhQ5Nof7SGL9wwYsBEMfDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5836d67957fd9166adee0aa0a91ca0cb39d5ad4c2021df7959ba3bc8987a093e","last_reissued_at":"2026-05-18T01:52:20.871262Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:52:20.871262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Oxidizing Borcherds symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"hep-th","authors_text":"Axel Kleinschmidt, Jakob Palmkvist","submitted_at":"2013-01-07T21:00:11Z","abstract_excerpt":"The tensor hierarchy of maximal supergravity in D dimensions is known to be closely related to a Borcherds (super)algebra that is constructed from the global symmetry group E(11-D). We here explain how the Borcherds algebras in different dimensions are embedded into each other and can be constructed from a unifying Borcherds algebra. The construction also has a natural physical explanation in terms of oxidation. We then go on to show that the Hodge duality that is present in the tensor hierarchy has an algebraic counterpart. For D>8 the Borcherds algebras we find differ from the ones existing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1346","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1301.1346","created_at":"2026-05-18T01:52:20.871321+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.1346v1","created_at":"2026-05-18T01:52:20.871321+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1346","created_at":"2026-05-18T01:52:20.871321+00:00"},{"alias_kind":"pith_short_12","alias_value":"LA3NM6KX7WIW","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LA3NM6KX7WIWNLPO","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LA3NM6KX","created_at":"2026-05-18T12:27:51.066281+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LA3NM6KX7WIWNLPOBKQKSHFAZM","json":"https://pith.science/pith/LA3NM6KX7WIWNLPOBKQKSHFAZM.json","graph_json":"https://pith.science/api/pith-number/LA3NM6KX7WIWNLPOBKQKSHFAZM/graph.json","events_json":"https://pith.science/api/pith-number/LA3NM6KX7WIWNLPOBKQKSHFAZM/events.json","paper":"https://pith.science/paper/LA3NM6KX"},"agent_actions":{"view_html":"https://pith.science/pith/LA3NM6KX7WIWNLPOBKQKSHFAZM","download_json":"https://pith.science/pith/LA3NM6KX7WIWNLPOBKQKSHFAZM.json","view_paper":"https://pith.science/paper/LA3NM6KX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.1346&json=true","fetch_graph":"https://pith.science/api/pith-number/LA3NM6KX7WIWNLPOBKQKSHFAZM/graph.json","fetch_events":"https://pith.science/api/pith-number/LA3NM6KX7WIWNLPOBKQKSHFAZM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LA3NM6KX7WIWNLPOBKQKSHFAZM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LA3NM6KX7WIWNLPOBKQKSHFAZM/action/storage_attestation","attest_author":"https://pith.science/pith/LA3NM6KX7WIWNLPOBKQKSHFAZM/action/author_attestation","sign_citation":"https://pith.science/pith/LA3NM6KX7WIWNLPOBKQKSHFAZM/action/citation_signature","submit_replication":"https://pith.science/pith/LA3NM6KX7WIWNLPOBKQKSHFAZM/action/replication_record"}},"created_at":"2026-05-18T01:52:20.871321+00:00","updated_at":"2026-05-18T01:52:20.871321+00:00"}