{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:DWS6UXDOWPQ5S4QYDHBIZPWIVP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"93a340c227e705d8f14a3f5761ac63914873575b9ea327647760ddbdca0b3695","cross_cats_sorted":["gr-qc","math-ph","math.MP","math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"2006-08-12T15:05:47Z","title_canon_sha256":"17a47af6b09182d01105abe5d99d248e139d391e61a3b3c3ece84afca1c3d792"},"schema_version":"1.0","source":{"id":"hep-th/0608081","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0608081","created_at":"2026-07-04T15:22:42Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0608081v3","created_at":"2026-07-04T15:22:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0608081","created_at":"2026-07-04T15:22:42Z"},{"alias_kind":"pith_short_12","alias_value":"DWS6UXDOWPQ5","created_at":"2026-07-04T15:22:42Z"},{"alias_kind":"pith_short_16","alias_value":"DWS6UXDOWPQ5S4QY","created_at":"2026-07-04T15:22:42Z"},{"alias_kind":"pith_short_8","alias_value":"DWS6UXDO","created_at":"2026-07-04T15:22:42Z"}],"graph_snapshots":[{"event_id":"sha256:297fd9b28cfdc32658212a904b1cfae14a301225494c160ee8870fab028ba407","target":"graph","created_at":"2026-07-04T15:22:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-th/0608081/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Whenever the group $\\R^n$ acts on an algebra $\\calA$, there is a method to twist $\\cal A$ to a new algebra $\\calA_\\theta$ which depends on an antisymmetric matrix $\\theta$ ($\\theta^{\\mu \\nu}=-\\theta^{\\nu \\mu}=\\mathrm{constant}$). The Groenewold-Moyal plane $\\calA_\\theta(\\R^{d+1})$ is an example of such a twisted algebra. We give a general construction to realise this twist in terms of $\\calA$ itself and certain ``charge'' operators $Q_\\mu$. For $\\calA_\\theta(\\R^{d+1})$, $Q_\\mu$ are translation generators. This construction is then applied to twist the oscillators realising the Kac-Moody (KM) a","authors_text":"A. M. Marques, A. P. Balachandran, A. R. Queiroz, P. Teotonio-Sobrinho","cross_cats":["gr-qc","math-ph","math.MP","math.QA"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2006-08-12T15:05:47Z","title":"Deformed Kac-Moody and Virasoro Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0608081","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e5398a6256c3f1e3faff7c0a77004b0de8f8f78883c2172c7e269c578ae45c99","target":"record","created_at":"2026-07-04T15:22:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"93a340c227e705d8f14a3f5761ac63914873575b9ea327647760ddbdca0b3695","cross_cats_sorted":["gr-qc","math-ph","math.MP","math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"2006-08-12T15:05:47Z","title_canon_sha256":"17a47af6b09182d01105abe5d99d248e139d391e61a3b3c3ece84afca1c3d792"},"schema_version":"1.0","source":{"id":"hep-th/0608081","kind":"arxiv","version":3}},"canonical_sha256":"1da5ea5c6eb3e1d9721819c28cbec8abd8844f6e57f46a5b94367bc4995f483b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1da5ea5c6eb3e1d9721819c28cbec8abd8844f6e57f46a5b94367bc4995f483b","first_computed_at":"2026-07-04T15:22:42.701485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:22:42.701485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tukr2LrzSzEEXOjkOVWs973ig85eUNYjx28Vq5e1XyqHGug50EY4jHUc0sbpVZ4SBD+BidoF0G3x7OexihU9Bg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:22:42.701854Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0608081","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5398a6256c3f1e3faff7c0a77004b0de8f8f78883c2172c7e269c578ae45c99","sha256:297fd9b28cfdc32658212a904b1cfae14a301225494c160ee8870fab028ba407"],"state_sha256":"27a09252d2af024428c0da0cb3d7c2d5ad588273afb93704376619726d26a96f"}