{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5EX4RYNFOJ3WXS64FEQXWU33C7","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":"d938f287c49e26e0a8eb40379ea391ba00c004e9791826841fc30e9cf8a8f0c0","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-09T22:14:01Z","title_canon_sha256":"6311ca639de6eab5531af0c11c902e22efca03810b6e5d6290809b1ebb50da09"},"schema_version":"1.0","source":{"id":"1307.2612","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2612","created_at":"2026-05-18T03:18:50Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2612v1","created_at":"2026-05-18T03:18:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2612","created_at":"2026-05-18T03:18:50Z"},{"alias_kind":"pith_short_12","alias_value":"5EX4RYNFOJ3W","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5EX4RYNFOJ3WXS64","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5EX4RYNF","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:73aaeeeda9ecfbd5b51ef87b420e17b382bf6c8cf71a26ea0259cfc9c0f6bb2c","target":"graph","created_at":"2026-05-18T03:18:50Z","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 main purpose of this paper is to define representations and a cohomology of color Hom-Lie algebras and to study some key constructions and properties. We describe Hartwig-Larsson-Silvestrov Theorem in the case of $\\Gamma$-graded algebras, study one-parameter formal deformations, discuss $\\alpha^{k}$-generalized derivation and provide examples.","authors_text":"A. Makhlouf, F. Ammar, K. Abdaoui","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-09T22:14:01Z","title":"Constructions and Cohomology of color Hom-Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2612","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":"sha256:7c565ce77b5bf91042fcf4f6bea0e72de30624c68d8cd6d790a79cf9047b7236","target":"record","created_at":"2026-05-18T03:18:50Z","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":"d938f287c49e26e0a8eb40379ea391ba00c004e9791826841fc30e9cf8a8f0c0","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-09T22:14:01Z","title_canon_sha256":"6311ca639de6eab5531af0c11c902e22efca03810b6e5d6290809b1ebb50da09"},"schema_version":"1.0","source":{"id":"1307.2612","kind":"arxiv","version":1}},"canonical_sha256":"e92fc8e1a572776bcbdc29217b537b17ed35ca605030b0879ecebd1d056327d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e92fc8e1a572776bcbdc29217b537b17ed35ca605030b0879ecebd1d056327d6","first_computed_at":"2026-05-18T03:18:50.934992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:50.934992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DaW849VVHPxrwME95df2hXBUQyTYWy2UUjMGfKv/6pyG1nL3Kw7pzMnu/L7aHQkmHJjIR+igdoDUajzUQjVxCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:50.935736Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2612","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c565ce77b5bf91042fcf4f6bea0e72de30624c68d8cd6d790a79cf9047b7236","sha256:73aaeeeda9ecfbd5b51ef87b420e17b382bf6c8cf71a26ea0259cfc9c0f6bb2c"],"state_sha256":"c0d362abc7dad96ed8946eadce6c8c5b227de33a27d81388fba4c3c4ac07ffdc"}