{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BPHQDTXLMMSL7JHCF6WEVSAOHF","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":"f8921935b95c8e6168cd2732c9b0b7d664ee2f0a2a125e7af84a750d8153be0f","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GR","submitted_at":"2026-06-28T09:35:28Z","title_canon_sha256":"29caa8c138bcc9f1d4bedbf3917995e04305391cfeef725037384c2312d8afda"},"schema_version":"1.0","source":{"id":"2606.29295","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.29295","created_at":"2026-06-30T01:18:00Z"},{"alias_kind":"arxiv_version","alias_value":"2606.29295v1","created_at":"2026-06-30T01:18:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29295","created_at":"2026-06-30T01:18:00Z"},{"alias_kind":"pith_short_12","alias_value":"BPHQDTXLMMSL","created_at":"2026-06-30T01:18:00Z"},{"alias_kind":"pith_short_16","alias_value":"BPHQDTXLMMSL7JHC","created_at":"2026-06-30T01:18:00Z"},{"alias_kind":"pith_short_8","alias_value":"BPHQDTXL","created_at":"2026-06-30T01:18:00Z"}],"graph_snapshots":[{"event_id":"sha256:d77bb35676504be2d87ce8018721c71875dc365fb5b7b38b9d19a3ac9fd56016","target":"graph","created_at":"2026-06-30T01:18:00Z","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/2606.29295/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a Schur--Zassenhaus theorem for finite skew braces. More precisely, if \\(B\\) is a finite skew brace and \\(I\\) is an ideal of \\(B\\) such that \\(|I|\\) and \\(|B/I|\\) are coprime, then \\(I\\) admits a complement in \\(B\\).","authors_text":"Marco Damele","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GR","submitted_at":"2026-06-28T09:35:28Z","title":"A Schur--Zassenhaus Theorem for Finite Skew Braces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29295","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:f909ec0c40cdf8f3ac27c3100dc5ffd8dccf3863099a193db6f9b4d18ee64667","target":"record","created_at":"2026-06-30T01:18:00Z","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":"f8921935b95c8e6168cd2732c9b0b7d664ee2f0a2a125e7af84a750d8153be0f","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GR","submitted_at":"2026-06-28T09:35:28Z","title_canon_sha256":"29caa8c138bcc9f1d4bedbf3917995e04305391cfeef725037384c2312d8afda"},"schema_version":"1.0","source":{"id":"2606.29295","kind":"arxiv","version":1}},"canonical_sha256":"0bcf01ceeb6324bfa4e22fac4ac80e394cbf226d7aaa832e4bc1fd88b296c094","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bcf01ceeb6324bfa4e22fac4ac80e394cbf226d7aaa832e4bc1fd88b296c094","first_computed_at":"2026-06-30T01:18:00.557557Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T01:18:00.557557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rORlrfT5+8X/34CpvMc1W0K6WyqlKlR6VkicbpCiwxhjg8ZYkzPWb2+BF+2ZCcvAqCWgqPIpWcrbl7UIRmIaCA==","signature_status":"signed_v1","signed_at":"2026-06-30T01:18:00.558033Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.29295","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f909ec0c40cdf8f3ac27c3100dc5ffd8dccf3863099a193db6f9b4d18ee64667","sha256:d77bb35676504be2d87ce8018721c71875dc365fb5b7b38b9d19a3ac9fd56016"],"state_sha256":"77d2618de6bf4e53617e0e50d876ff1a7ae6b19ed1da83ca00c8b5feede24385"}