{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NJ6T3G7NAMMOLSMZE7QLQMDXKN","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":"0f4ec6732db27e535eada849882d81f8243d053b63cfb67047567ee9c8af43ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-01-08T11:09:42Z","title_canon_sha256":"29b96573d17e77c23628998ffc6070946a200b01868c8a3992528b2e2883ab89"},"schema_version":"1.0","source":{"id":"1601.01832","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01832","created_at":"2026-05-18T01:21:21Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01832v2","created_at":"2026-05-18T01:21:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01832","created_at":"2026-05-18T01:21:21Z"},{"alias_kind":"pith_short_12","alias_value":"NJ6T3G7NAMMO","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NJ6T3G7NAMMOLSMZ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NJ6T3G7N","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:bfba3017f53e0dd2209672fb59fa6b06c82cd948959fa1c0919f6daac16addf3","target":"graph","created_at":"2026-05-18T01:21:21Z","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":"We study evolution algebras of arbitrary dimension. We analyze in deep the notions of evolution subalgebras, ideals and non-degeneracy and describe the ideals generated by one element and characterize the simple evolution algebras. We also prove the existence and unicity of a direct sum decomposition into irreducible components for every non-degenerate evolution algebra. When the algebra is degenerate, the uniqueness cannot be assured.\n  The graph associated to an evolution algebra (relative to a natural basis) will play a fundamental role to describe the structure of the algebra. Concretely, ","authors_text":"Mercedes Siles Molina, M. Victoria Velasco, Yolanda Cabrera Casado","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-01-08T11:09:42Z","title":"Evolution algebras of arbitrary dimension and their decompositions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01832","kind":"arxiv","version":2},"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":"sha256:3b8feadf321806c221a481a5d346dc23100eed9c381e5b4aa254357a1cbb64a5","target":"record","created_at":"2026-05-18T01:21:21Z","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":"0f4ec6732db27e535eada849882d81f8243d053b63cfb67047567ee9c8af43ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-01-08T11:09:42Z","title_canon_sha256":"29b96573d17e77c23628998ffc6070946a200b01868c8a3992528b2e2883ab89"},"schema_version":"1.0","source":{"id":"1601.01832","kind":"arxiv","version":2}},"canonical_sha256":"6a7d3d9bed0318e5c99927e0b83077537292b750342206680fa1ad838c6c011c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a7d3d9bed0318e5c99927e0b83077537292b750342206680fa1ad838c6c011c","first_computed_at":"2026-05-18T01:21:21.094556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:21.094556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xmUC06RqHoObcZ3R79O+ff0jaCdFwfr+yUGOgM7dqyk8p8hXMty2KfXH9g6Qb7/ptQtQNyV3p2rrTzb6BHIjBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:21.095036Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.01832","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b8feadf321806c221a481a5d346dc23100eed9c381e5b4aa254357a1cbb64a5","sha256:bfba3017f53e0dd2209672fb59fa6b06c82cd948959fa1c0919f6daac16addf3"],"state_sha256":"53f39ebc8b98189ff11241251a2643cd08f86a8b015817dec8c37ebea7198356"}