{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:EJLXG4NMFTLJ2SHKC5ZRRH5DAH","short_pith_number":"pith:EJLXG4NM","canonical_record":{"source":{"id":"0903.4712","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-03-26T22:33:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4663e99fe4c895cd5056afe9625d79db5ea3029c1943590a8b79cb71333ed2c9","abstract_canon_sha256":"4c792c0cc52d9345afe2959a005080938e9c18c2c9d5bb6db5dc3bac8f8b2bf6"},"schema_version":"1.0"},"canonical_sha256":"22577371ac2cd69d48ea1773189fa301d7932e13f1fd88ad76e1fd2e663fae51","source":{"kind":"arxiv","id":"0903.4712","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.4712","created_at":"2026-05-18T02:14:19Z"},{"alias_kind":"arxiv_version","alias_value":"0903.4712v1","created_at":"2026-05-18T02:14:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.4712","created_at":"2026-05-18T02:14:19Z"},{"alias_kind":"pith_short_12","alias_value":"EJLXG4NMFTLJ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EJLXG4NMFTLJ2SHK","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EJLXG4NM","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:EJLXG4NMFTLJ2SHKC5ZRRH5DAH","target":"record","payload":{"canonical_record":{"source":{"id":"0903.4712","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-03-26T22:33:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4663e99fe4c895cd5056afe9625d79db5ea3029c1943590a8b79cb71333ed2c9","abstract_canon_sha256":"4c792c0cc52d9345afe2959a005080938e9c18c2c9d5bb6db5dc3bac8f8b2bf6"},"schema_version":"1.0"},"canonical_sha256":"22577371ac2cd69d48ea1773189fa301d7932e13f1fd88ad76e1fd2e663fae51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:19.227347Z","signature_b64":"4TEy9ZTY+ZJkL57hxAozOchjJXP23wyt1mPZnLDQxV3MUElmzfU7xuIOna/ITWV/ulqCWvhib0wvgu4TEzqhAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22577371ac2cd69d48ea1773189fa301d7932e13f1fd88ad76e1fd2e663fae51","last_reissued_at":"2026-05-18T02:14:19.226827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:19.226827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0903.4712","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:14:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TVzIfU1HMsf8jsRJJFZvM5bhgc7IOre+J/h1E1esLJZ6W0Ad9vIr2IAYMC+GQ+QKzy/fCimB4K3E0267NuxJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:02:21.923744Z"},"content_sha256":"63c0e681b43fed0395635c828ffaa2c9fdf23001c7c54f158efd5ce1e4963d74","schema_version":"1.0","event_id":"sha256:63c0e681b43fed0395635c828ffaa2c9fdf23001c7c54f158efd5ce1e4963d74"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:EJLXG4NMFTLJ2SHKC5ZRRH5DAH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dual Formulation of the Lie Algebra S-expansion Procedure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Alfredo P\\'erez, Eduardo Rodr\\'iguez, Fernando Izaurieta, Patricio Salgado","submitted_at":"2009-03-26T22:33:04Z","abstract_excerpt":"The expansion of a Lie algebra entails finding a new, bigger algebra G, through a series of well-defined steps, from an original Lie algebra g. One incarnation of the method, the so-called S-expansion, involves the use of a finite abelian semigroup S to accomplish this task. In this paper we put forward a dual formulation of the S-expansion method which is based on the dual picture of a Lie algebra given by the Maurer-Cartan forms. The dual version of the method is useful in finding a generalization to the case of a gauge free differential algebra, which in turn is relevant for physical applic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4712","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:14:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ExH1CYket6dAks9RHA6EcgAhBcZA9cMKwBe+R4gXbreXh8gzZhWvrE/MTlG97TAjsc4Xm+qSw3K1E2H11ItYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:02:21.924491Z"},"content_sha256":"77dcfeda2b59d4dd7c51c25379d25696290330bbcda76f8f9eb771da1bb792aa","schema_version":"1.0","event_id":"sha256:77dcfeda2b59d4dd7c51c25379d25696290330bbcda76f8f9eb771da1bb792aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EJLXG4NMFTLJ2SHKC5ZRRH5DAH/bundle.json","state_url":"https://pith.science/pith/EJLXG4NMFTLJ2SHKC5ZRRH5DAH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EJLXG4NMFTLJ2SHKC5ZRRH5DAH/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":"2026-05-25T17:02:21Z","links":{"resolver":"https://pith.science/pith/EJLXG4NMFTLJ2SHKC5ZRRH5DAH","bundle":"https://pith.science/pith/EJLXG4NMFTLJ2SHKC5ZRRH5DAH/bundle.json","state":"https://pith.science/pith/EJLXG4NMFTLJ2SHKC5ZRRH5DAH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EJLXG4NMFTLJ2SHKC5ZRRH5DAH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:EJLXG4NMFTLJ2SHKC5ZRRH5DAH","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":"4c792c0cc52d9345afe2959a005080938e9c18c2c9d5bb6db5dc3bac8f8b2bf6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-03-26T22:33:04Z","title_canon_sha256":"4663e99fe4c895cd5056afe9625d79db5ea3029c1943590a8b79cb71333ed2c9"},"schema_version":"1.0","source":{"id":"0903.4712","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.4712","created_at":"2026-05-18T02:14:19Z"},{"alias_kind":"arxiv_version","alias_value":"0903.4712v1","created_at":"2026-05-18T02:14:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.4712","created_at":"2026-05-18T02:14:19Z"},{"alias_kind":"pith_short_12","alias_value":"EJLXG4NMFTLJ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EJLXG4NMFTLJ2SHK","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EJLXG4NM","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:77dcfeda2b59d4dd7c51c25379d25696290330bbcda76f8f9eb771da1bb792aa","target":"graph","created_at":"2026-05-18T02:14:19Z","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"},"paper":{"abstract_excerpt":"The expansion of a Lie algebra entails finding a new, bigger algebra G, through a series of well-defined steps, from an original Lie algebra g. One incarnation of the method, the so-called S-expansion, involves the use of a finite abelian semigroup S to accomplish this task. In this paper we put forward a dual formulation of the S-expansion method which is based on the dual picture of a Lie algebra given by the Maurer-Cartan forms. The dual version of the method is useful in finding a generalization to the case of a gauge free differential algebra, which in turn is relevant for physical applic","authors_text":"Alfredo P\\'erez, Eduardo Rodr\\'iguez, Fernando Izaurieta, Patricio Salgado","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-03-26T22:33:04Z","title":"Dual Formulation of the Lie Algebra S-expansion Procedure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4712","kind":"arxiv","version":1},"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":"sha256:63c0e681b43fed0395635c828ffaa2c9fdf23001c7c54f158efd5ce1e4963d74","target":"record","created_at":"2026-05-18T02:14:19Z","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":"4c792c0cc52d9345afe2959a005080938e9c18c2c9d5bb6db5dc3bac8f8b2bf6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-03-26T22:33:04Z","title_canon_sha256":"4663e99fe4c895cd5056afe9625d79db5ea3029c1943590a8b79cb71333ed2c9"},"schema_version":"1.0","source":{"id":"0903.4712","kind":"arxiv","version":1}},"canonical_sha256":"22577371ac2cd69d48ea1773189fa301d7932e13f1fd88ad76e1fd2e663fae51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22577371ac2cd69d48ea1773189fa301d7932e13f1fd88ad76e1fd2e663fae51","first_computed_at":"2026-05-18T02:14:19.226827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:19.226827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4TEy9ZTY+ZJkL57hxAozOchjJXP23wyt1mPZnLDQxV3MUElmzfU7xuIOna/ITWV/ulqCWvhib0wvgu4TEzqhAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:19.227347Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.4712","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63c0e681b43fed0395635c828ffaa2c9fdf23001c7c54f158efd5ce1e4963d74","sha256:77dcfeda2b59d4dd7c51c25379d25696290330bbcda76f8f9eb771da1bb792aa"],"state_sha256":"d024c347cffb9b481e7909344d5402872939687a2e63681851d94eed4c6235ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2zXN/NU6UtPicGMSg+91eVsqdrWLwdhW+UjCgiUhCYRvgksYEs5xdYlhgOxhOFuGPvWt70pGssFXizmlaqn+AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T17:02:21.929487Z","bundle_sha256":"4b2a1b6ba1099c48787ddef70445408429c2e2a6329bd18de35136f921e7783f"}}