{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:2MKZTT5RLG3R6UQ6AWRYLHZOIE","short_pith_number":"pith:2MKZTT5R","canonical_record":{"source":{"id":"2507.01935","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2025-07-02T17:46:19Z","cross_cats_sorted":[],"title_canon_sha256":"c22ade684fceba240d05714f08d41db24f56fb617d0bb4cc0ffc03928519ed4c","abstract_canon_sha256":"2b47e97ba3c3340f5e68d984803be3fa57a1998f1169fc7902ae8db3fb461889"},"schema_version":"1.0"},"canonical_sha256":"d31599cfb159b71f521e05a3859f2e413203134cd38d80709ff3616fc1705587","source":{"kind":"arxiv","id":"2507.01935","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.01935","created_at":"2026-07-05T11:30:58Z"},{"alias_kind":"arxiv_version","alias_value":"2507.01935v1","created_at":"2026-07-05T11:30:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.01935","created_at":"2026-07-05T11:30:58Z"},{"alias_kind":"pith_short_12","alias_value":"2MKZTT5RLG3R","created_at":"2026-07-05T11:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"2MKZTT5RLG3R6UQ6","created_at":"2026-07-05T11:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"2MKZTT5R","created_at":"2026-07-05T11:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:2MKZTT5RLG3R6UQ6AWRYLHZOIE","target":"record","payload":{"canonical_record":{"source":{"id":"2507.01935","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2025-07-02T17:46:19Z","cross_cats_sorted":[],"title_canon_sha256":"c22ade684fceba240d05714f08d41db24f56fb617d0bb4cc0ffc03928519ed4c","abstract_canon_sha256":"2b47e97ba3c3340f5e68d984803be3fa57a1998f1169fc7902ae8db3fb461889"},"schema_version":"1.0"},"canonical_sha256":"d31599cfb159b71f521e05a3859f2e413203134cd38d80709ff3616fc1705587","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:30:58.471594Z","signature_b64":"03FXGshor/Z4FuR1rMDDuyvnVZYmRbD6fjtBbVjsue4FF/1ltC5299yLoB/eY0dJGTQQnEPF8VRkAklWq3JpAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d31599cfb159b71f521e05a3859f2e413203134cd38d80709ff3616fc1705587","last_reissued_at":"2026-07-05T11:30:58.470919Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:30:58.470919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.01935","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":"2026-07-05T11:30:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hHhS/0Eynj/rTTGfZEpchoIUtpTJRb5YAmwhDZoWCQgYDwJXwEDQgmfw2Rlgyv9GE2OmHNE6EjX30CnbtOUzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T18:34:42.227056Z"},"content_sha256":"819a60d52846e3218226207a76690b00273ab2530253f1d4418afd96eb4184fe","schema_version":"1.0","event_id":"sha256:819a60d52846e3218226207a76690b00273ab2530253f1d4418afd96eb4184fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:2MKZTT5RLG3R6UQ6AWRYLHZOIE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Frattini theory for evolution algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Andr\\'es P\\'erez-Rodr\\'iguez, Manuel Ladra","submitted_at":"2025-07-02T17:46:19Z","abstract_excerpt":"This paper develops a Frattini theory for evolution algebras defining the Frattini subalgebra as the intersection of all maximal subalgebras, and the Frattini ideal as the largest ideal contained in it. To this end, we revisit the notion of nilradical, whose classical definition is not directly applicable in this setting, and propose the supersolvable nilradical as a suitable alternative. This leads to necessary and sufficient conditions for the triviality of the Frattini subalgebra and ideal. Finally, we also briefly examine the relevance of the Frattini ideal in the study of dually atomistic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.01935","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.01935/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":"2026-07-05T11:30:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IwvIGFR8ONjz1K6pM4dUKAWlefqOdgS/NLq9DgSYhRn3N12vOathpbrwW+Jze1Uh8eVrI2j5iM1tOv91BTqNCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T18:34:42.227694Z"},"content_sha256":"7141dd1044529566218d61ebccffd81a87e1e2bb831213d92be7beaa772d4947","schema_version":"1.0","event_id":"sha256:7141dd1044529566218d61ebccffd81a87e1e2bb831213d92be7beaa772d4947"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2MKZTT5RLG3R6UQ6AWRYLHZOIE/bundle.json","state_url":"https://pith.science/pith/2MKZTT5RLG3R6UQ6AWRYLHZOIE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2MKZTT5RLG3R6UQ6AWRYLHZOIE/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":"2026-08-06T18:34:42Z","links":{"resolver":"https://pith.science/pith/2MKZTT5RLG3R6UQ6AWRYLHZOIE","bundle":"https://pith.science/pith/2MKZTT5RLG3R6UQ6AWRYLHZOIE/bundle.json","state":"https://pith.science/pith/2MKZTT5RLG3R6UQ6AWRYLHZOIE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2MKZTT5RLG3R6UQ6AWRYLHZOIE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2MKZTT5RLG3R6UQ6AWRYLHZOIE","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":"2b47e97ba3c3340f5e68d984803be3fa57a1998f1169fc7902ae8db3fb461889","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2025-07-02T17:46:19Z","title_canon_sha256":"c22ade684fceba240d05714f08d41db24f56fb617d0bb4cc0ffc03928519ed4c"},"schema_version":"1.0","source":{"id":"2507.01935","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.01935","created_at":"2026-07-05T11:30:58Z"},{"alias_kind":"arxiv_version","alias_value":"2507.01935v1","created_at":"2026-07-05T11:30:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.01935","created_at":"2026-07-05T11:30:58Z"},{"alias_kind":"pith_short_12","alias_value":"2MKZTT5RLG3R","created_at":"2026-07-05T11:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"2MKZTT5RLG3R6UQ6","created_at":"2026-07-05T11:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"2MKZTT5R","created_at":"2026-07-05T11:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:7141dd1044529566218d61ebccffd81a87e1e2bb831213d92be7beaa772d4947","target":"graph","created_at":"2026-07-05T11:30:58Z","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/2507.01935/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper develops a Frattini theory for evolution algebras defining the Frattini subalgebra as the intersection of all maximal subalgebras, and the Frattini ideal as the largest ideal contained in it. To this end, we revisit the notion of nilradical, whose classical definition is not directly applicable in this setting, and propose the supersolvable nilradical as a suitable alternative. This leads to necessary and sufficient conditions for the triviality of the Frattini subalgebra and ideal. Finally, we also briefly examine the relevance of the Frattini ideal in the study of dually atomistic","authors_text":"Andr\\'es P\\'erez-Rodr\\'iguez, Manuel Ladra","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2025-07-02T17:46:19Z","title":"A Frattini theory for evolution algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.01935","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":"sha256:819a60d52846e3218226207a76690b00273ab2530253f1d4418afd96eb4184fe","target":"record","created_at":"2026-07-05T11:30:58Z","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":"2b47e97ba3c3340f5e68d984803be3fa57a1998f1169fc7902ae8db3fb461889","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2025-07-02T17:46:19Z","title_canon_sha256":"c22ade684fceba240d05714f08d41db24f56fb617d0bb4cc0ffc03928519ed4c"},"schema_version":"1.0","source":{"id":"2507.01935","kind":"arxiv","version":1}},"canonical_sha256":"d31599cfb159b71f521e05a3859f2e413203134cd38d80709ff3616fc1705587","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d31599cfb159b71f521e05a3859f2e413203134cd38d80709ff3616fc1705587","first_computed_at":"2026-07-05T11:30:58.470919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:30:58.470919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"03FXGshor/Z4FuR1rMDDuyvnVZYmRbD6fjtBbVjsue4FF/1ltC5299yLoB/eY0dJGTQQnEPF8VRkAklWq3JpAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:30:58.471594Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.01935","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:819a60d52846e3218226207a76690b00273ab2530253f1d4418afd96eb4184fe","sha256:7141dd1044529566218d61ebccffd81a87e1e2bb831213d92be7beaa772d4947"],"state_sha256":"0ae258b834b9825613749f9f5dbd48f967198a267cf13083a06c5e26fff762eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ODHrZmDdcIxz+wGcAoiKWdxCFG696OY/aJLoklXnEXxOyMWJ7xSDaDnL7yo0fKXYIx+Ywh3ZSFn1Z5kDk6gAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T18:34:42.235297Z","bundle_sha256":"4d60008bf5846f8e245d7dd0708beaeabbf8d9896690f2d104ff27f18fb84315"}}