{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7264PEM5556GJ7HL354CXE26IV","short_pith_number":"pith:7264PEM5","canonical_record":{"source":{"id":"1403.4083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-17T12:50:42Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"6b112c517f8d178557586811cf2c1278ef672c1b7c8890c8917ab254c864b580","abstract_canon_sha256":"1f9d391632065635c2a5f2736888c302b7a279a9c3d8bfa31bf1a9b187a9ee5b"},"schema_version":"1.0"},"canonical_sha256":"febdc7919def7c64fcebdf782b935e4549ec384d891025beeb7e3823708c103d","source":{"kind":"arxiv","id":"1403.4083","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4083","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4083v1","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4083","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"7264PEM5556G","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7264PEM5556GJ7HL","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7264PEM5","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7264PEM5556GJ7HL354CXE26IV","target":"record","payload":{"canonical_record":{"source":{"id":"1403.4083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-17T12:50:42Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"6b112c517f8d178557586811cf2c1278ef672c1b7c8890c8917ab254c864b580","abstract_canon_sha256":"1f9d391632065635c2a5f2736888c302b7a279a9c3d8bfa31bf1a9b187a9ee5b"},"schema_version":"1.0"},"canonical_sha256":"febdc7919def7c64fcebdf782b935e4549ec384d891025beeb7e3823708c103d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:12.211240Z","signature_b64":"U/d2A3EZU0yKOYWGyyDB6U80RwEyqx7QQk3Wz2H+oUHfts3YkTgaxiGQ2daGN2oP4rV36fxhW5KN/YQ5qllBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"febdc7919def7c64fcebdf782b935e4549ec384d891025beeb7e3823708c103d","last_reissued_at":"2026-05-18T02:56:12.210838Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:12.210838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.4083","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":"2026-05-18T02:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zc7VDtlDT2BIaaf63k3EGa654Odsq1yynwig7yD6Q1AQM6G96O1/ADGKA8oFPj3y/Za2MTCGjk9npsxoFKR3Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:10:28.632010Z"},"content_sha256":"670630edef02cc5a8e5f81ae85820de8d39fc7d36f996bbe88b5f130df67ec66","schema_version":"1.0","event_id":"sha256:670630edef02cc5a8e5f81ae85820de8d39fc7d36f996bbe88b5f130df67ec66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7264PEM5556GJ7HL354CXE26IV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Total cohomology of solvable Lie algebras and linear deformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Leandro Cagliero, Paulo Tirao","submitted_at":"2014-03-17T12:50:42Z","abstract_excerpt":"Given a finite dimensional Lie algebra $\\mathfrak{g}$, let $\\Gamma_\\circ(\\mathfrak{g})$ be the set of irreducible $\\mathfrak{g}$-modules with non-vanishing cohomology. We prove that a $\\mathfrak{g}$-module $V$ belongs to $\\Gamma_\\circ(\\mathfrak{g})$ only if $V$ is contained in the exterior algebra of the solvable radical $\\mathfrak{s}$ of $\\mathfrak{g}$, showing in particular that $\\Gamma_\\circ(\\mathfrak{g})$ is a finite set and we deduce that $H^*(\\mathfrak{g},V)$ is an $L$-module, where $L$ is a fixed subgroup of the connected component of $\\operatorname{Aut}(\\mathfrak{g})$ which contains a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4083","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":"2026-05-18T02:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1hJ4x8wKHPiLoGgd2K/BkmFILKBrtR0hkspARRqnZsd/5ui9jTsI8qmXjhqHyslJ2Ux0a+C2/lE66lmJWs+3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:10:28.632368Z"},"content_sha256":"bb2c0834c17254e9746bd954f775159bb225cf1091a924f7808f30e133e33fb0","schema_version":"1.0","event_id":"sha256:bb2c0834c17254e9746bd954f775159bb225cf1091a924f7808f30e133e33fb0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7264PEM5556GJ7HL354CXE26IV/bundle.json","state_url":"https://pith.science/pith/7264PEM5556GJ7HL354CXE26IV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7264PEM5556GJ7HL354CXE26IV/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":"2026-06-25T05:10:28Z","links":{"resolver":"https://pith.science/pith/7264PEM5556GJ7HL354CXE26IV","bundle":"https://pith.science/pith/7264PEM5556GJ7HL354CXE26IV/bundle.json","state":"https://pith.science/pith/7264PEM5556GJ7HL354CXE26IV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7264PEM5556GJ7HL354CXE26IV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7264PEM5556GJ7HL354CXE26IV","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":"1f9d391632065635c2a5f2736888c302b7a279a9c3d8bfa31bf1a9b187a9ee5b","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-17T12:50:42Z","title_canon_sha256":"6b112c517f8d178557586811cf2c1278ef672c1b7c8890c8917ab254c864b580"},"schema_version":"1.0","source":{"id":"1403.4083","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4083","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4083v1","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4083","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"7264PEM5556G","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7264PEM5556GJ7HL","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7264PEM5","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:bb2c0834c17254e9746bd954f775159bb225cf1091a924f7808f30e133e33fb0","target":"graph","created_at":"2026-05-18T02:56:12Z","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":"Given a finite dimensional Lie algebra $\\mathfrak{g}$, let $\\Gamma_\\circ(\\mathfrak{g})$ be the set of irreducible $\\mathfrak{g}$-modules with non-vanishing cohomology. We prove that a $\\mathfrak{g}$-module $V$ belongs to $\\Gamma_\\circ(\\mathfrak{g})$ only if $V$ is contained in the exterior algebra of the solvable radical $\\mathfrak{s}$ of $\\mathfrak{g}$, showing in particular that $\\Gamma_\\circ(\\mathfrak{g})$ is a finite set and we deduce that $H^*(\\mathfrak{g},V)$ is an $L$-module, where $L$ is a fixed subgroup of the connected component of $\\operatorname{Aut}(\\mathfrak{g})$ which contains a ","authors_text":"Leandro Cagliero, Paulo Tirao","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-17T12:50:42Z","title":"Total cohomology of solvable Lie algebras and linear deformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4083","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":"sha256:670630edef02cc5a8e5f81ae85820de8d39fc7d36f996bbe88b5f130df67ec66","target":"record","created_at":"2026-05-18T02:56:12Z","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":"1f9d391632065635c2a5f2736888c302b7a279a9c3d8bfa31bf1a9b187a9ee5b","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-17T12:50:42Z","title_canon_sha256":"6b112c517f8d178557586811cf2c1278ef672c1b7c8890c8917ab254c864b580"},"schema_version":"1.0","source":{"id":"1403.4083","kind":"arxiv","version":1}},"canonical_sha256":"febdc7919def7c64fcebdf782b935e4549ec384d891025beeb7e3823708c103d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"febdc7919def7c64fcebdf782b935e4549ec384d891025beeb7e3823708c103d","first_computed_at":"2026-05-18T02:56:12.210838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:12.210838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U/d2A3EZU0yKOYWGyyDB6U80RwEyqx7QQk3Wz2H+oUHfts3YkTgaxiGQ2daGN2oP4rV36fxhW5KN/YQ5qllBAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:12.211240Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.4083","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:670630edef02cc5a8e5f81ae85820de8d39fc7d36f996bbe88b5f130df67ec66","sha256:bb2c0834c17254e9746bd954f775159bb225cf1091a924f7808f30e133e33fb0"],"state_sha256":"5e8b9edd930a7882dcdf02a17733d437c4d36d2d61acc0108a0cae888332b5ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DGNGoD5vYhJMDcIDsurapvcd8fASQElBBFgdTxxGwtt0TM8fpgfnHMqKdjZI5KctEHf/cVRAdsebc5hCP3rMCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T05:10:28.634328Z","bundle_sha256":"fdafb50a33c03b43ba1e50863bd1ffac022ecf63036f26b0762e33fa896c159c"}}