{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:DWS6UXDOWPQ5S4QYDHBIZPWIVP","short_pith_number":"pith:DWS6UXDO","canonical_record":{"source":{"id":"hep-th/0608081","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2006-08-12T15:05:47Z","cross_cats_sorted":["gr-qc","math-ph","math.MP","math.QA"],"title_canon_sha256":"17a47af6b09182d01105abe5d99d248e139d391e61a3b3c3ece84afca1c3d792","abstract_canon_sha256":"93a340c227e705d8f14a3f5761ac63914873575b9ea327647760ddbdca0b3695"},"schema_version":"1.0"},"canonical_sha256":"1da5ea5c6eb3e1d9721819c28cbec8abd8844f6e57f46a5b94367bc4995f483b","source":{"kind":"arxiv","id":"hep-th/0608081","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:DWS6UXDOWPQ5S4QYDHBIZPWIVP","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0608081","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2006-08-12T15:05:47Z","cross_cats_sorted":["gr-qc","math-ph","math.MP","math.QA"],"title_canon_sha256":"17a47af6b09182d01105abe5d99d248e139d391e61a3b3c3ece84afca1c3d792","abstract_canon_sha256":"93a340c227e705d8f14a3f5761ac63914873575b9ea327647760ddbdca0b3695"},"schema_version":"1.0"},"canonical_sha256":"1da5ea5c6eb3e1d9721819c28cbec8abd8844f6e57f46a5b94367bc4995f483b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:22:42.701854Z","signature_b64":"tukr2LrzSzEEXOjkOVWs973ig85eUNYjx28Vq5e1XyqHGug50EY4jHUc0sbpVZ4SBD+BidoF0G3x7OexihU9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1da5ea5c6eb3e1d9721819c28cbec8abd8844f6e57f46a5b94367bc4995f483b","last_reissued_at":"2026-07-04T15:22:42.701485Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:22:42.701485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0608081","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:22:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BnOUiLdFtaLYpbHiR5Ao0VYI4uIN57H8oyNrOdyGAFiSIhrRz3wZIejwFDaMhLQTM4e+GHhL24R+L1vJbIYjCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:03:13.556810Z"},"content_sha256":"e5398a6256c3f1e3faff7c0a77004b0de8f8f78883c2172c7e269c578ae45c99","schema_version":"1.0","event_id":"sha256:e5398a6256c3f1e3faff7c0a77004b0de8f8f78883c2172c7e269c578ae45c99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:DWS6UXDOWPQ5S4QYDHBIZPWIVP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deformed Kac-Moody and Virasoro Algebras","license":"","headline":"","cross_cats":["gr-qc","math-ph","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"A. M. Marques, A. P. Balachandran, A. R. Queiroz, P. Teotonio-Sobrinho","submitted_at":"2006-08-12T15:05:47Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0608081","kind":"arxiv","version":3},"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/hep-th/0608081/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:22:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WM1190P5KqEOsrtonTR+mg6skSXACUp94mED3+JwnqbPYkdcygxR++JAbFPa6v5aTZXbI/mi9LRRUmwi1t7MCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:03:13.557163Z"},"content_sha256":"297fd9b28cfdc32658212a904b1cfae14a301225494c160ee8870fab028ba407","schema_version":"1.0","event_id":"sha256:297fd9b28cfdc32658212a904b1cfae14a301225494c160ee8870fab028ba407"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DWS6UXDOWPQ5S4QYDHBIZPWIVP/bundle.json","state_url":"https://pith.science/pith/DWS6UXDOWPQ5S4QYDHBIZPWIVP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DWS6UXDOWPQ5S4QYDHBIZPWIVP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T17:03:13Z","links":{"resolver":"https://pith.science/pith/DWS6UXDOWPQ5S4QYDHBIZPWIVP","bundle":"https://pith.science/pith/DWS6UXDOWPQ5S4QYDHBIZPWIVP/bundle.json","state":"https://pith.science/pith/DWS6UXDOWPQ5S4QYDHBIZPWIVP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DWS6UXDOWPQ5S4QYDHBIZPWIVP/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ICxFGXPXkxBLilVzW+0ueiN2tcNhtjZjZvJ3gAvYGWtAxghHbC2dFLgsO1yxRQTiKJ89Rw0wBmx8sJ0SDDd6Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T17:03:13.560786Z","bundle_sha256":"f1050afc12743ad4c250cb69e76d20b412faef1ba546b5ed77db5371807f3883"}}