{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ISMRAENN3P4VD4EFKIUY3YKHL2","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":"bdd3087dd366721b911bcafda56025a719b85968b795c112b45ecaa6d1d6dfe7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-05-22T21:00:50Z","title_canon_sha256":"d3ad8856b1e8d93838cf40d28cd0496a48983d3308770efd17f064dc2a3bd6f2"},"schema_version":"1.0","source":{"id":"1505.06224","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06224","created_at":"2026-05-18T02:02:07Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06224v2","created_at":"2026-05-18T02:02:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06224","created_at":"2026-05-18T02:02:07Z"},{"alias_kind":"pith_short_12","alias_value":"ISMRAENN3P4V","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"ISMRAENN3P4VD4EF","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"ISMRAENN","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:dcaed23ff9e15254b77b969e19fb7adbf3bac3b581b1fb7feac086e6b28d8935","target":"graph","created_at":"2026-05-18T02:02:07Z","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 consider $14$ medial-like balanced functional equations with four object variables for a pair $(f, g)$ of binary quasigroup operations. Then, we prove that every algebra $(B; f, g)$ with quasigroup operations satisfying a medial-like balanced functional equation has a linear representation on an abelian group $(B; +)$.","authors_text":"Aleksandar Krape\\v{z}, Amir Ehsani, Yuri Movsisyan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-05-22T21:00:50Z","title":"Algebras with Medial-like Functional Equations on Quasigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06224","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:e809f2f2ea723b38196b58eb2db5960ed80e1e22c2a955ab278e69ef74fe30aa","target":"record","created_at":"2026-05-18T02:02:07Z","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":"bdd3087dd366721b911bcafda56025a719b85968b795c112b45ecaa6d1d6dfe7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-05-22T21:00:50Z","title_canon_sha256":"d3ad8856b1e8d93838cf40d28cd0496a48983d3308770efd17f064dc2a3bd6f2"},"schema_version":"1.0","source":{"id":"1505.06224","kind":"arxiv","version":2}},"canonical_sha256":"44991011addbf951f08552298de1475ebcee0ba05fa492ad5b67f37fe0ed9dd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44991011addbf951f08552298de1475ebcee0ba05fa492ad5b67f37fe0ed9dd0","first_computed_at":"2026-05-18T02:02:07.540604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:02:07.540604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A3jD7yeFUIAQNaqzGqksnztP7ZlfYjVuWiXIqbXPmWZhNS7YweKpNjb9yF0RfCo4YK5LSUXprlTq4Y8xLFI0AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:02:07.541511Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06224","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e809f2f2ea723b38196b58eb2db5960ed80e1e22c2a955ab278e69ef74fe30aa","sha256:dcaed23ff9e15254b77b969e19fb7adbf3bac3b581b1fb7feac086e6b28d8935"],"state_sha256":"f2371751182b650f724b7764b8aef0e10cc3e0b4467bc9a1af82ef9c7ac84cfe"}