{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WBTWD5H55G77AX5POE67IAR463","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":"dd52ab00c972a58db97a0abd1dcf407ab2e4e4bcf0d856ba79cb576933033197","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2025-05-30T10:10:53Z","title_canon_sha256":"99bbb1cd85b8c1ccefc865d604fdad3bc6b9ac7d1127c609bef6736dd1107daa"},"schema_version":"1.0","source":{"id":"2505.24430","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.24430","created_at":"2026-07-05T11:12:49Z"},{"alias_kind":"arxiv_version","alias_value":"2505.24430v1","created_at":"2026-07-05T11:12:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24430","created_at":"2026-07-05T11:12:49Z"},{"alias_kind":"pith_short_12","alias_value":"WBTWD5H55G77","created_at":"2026-07-05T11:12:49Z"},{"alias_kind":"pith_short_16","alias_value":"WBTWD5H55G77AX5P","created_at":"2026-07-05T11:12:49Z"},{"alias_kind":"pith_short_8","alias_value":"WBTWD5H5","created_at":"2026-07-05T11:12:49Z"}],"graph_snapshots":[{"event_id":"sha256:0de72c45d18e60dab561f9f28c8fd1854c28cfa15e476d02b622215b111d7aff","target":"graph","created_at":"2026-07-05T11:12:49Z","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/2505.24430/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This thesis investigates certain structural properties of twisted Chevalley groups over commutative rings, focusing on three key problems.\n  Let $R$ be a commutative ring satisfying mild conditions. Let $G_{\\pi,\\sigma} (\\Phi, R)$ denote a twisted Chevalley group over $R$, and let $E'_{\\pi, \\sigma} (\\Phi, R)$ denote its elementary subgroup. The first problem concerns the normality of $E'_{\\pi, \\sigma} (\\Phi, R, J)$, the relative elementary subgroups at level $J$, in the group $G_{\\pi, \\sigma} (\\Phi, R)$. The second problem addresses the classification of the subgroups of $G_{\\pi, \\sigma}(\\Phi, ","authors_text":"Deep H. Makadiya","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2025-05-30T10:10:53Z","title":"Some Properties of Twisted Chevalley Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24430","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":"sha256:01429ff9e32e81db83ea0bc7b71dc300af869b360ea125382aea74d94e8c3498","target":"record","created_at":"2026-07-05T11:12:49Z","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":"dd52ab00c972a58db97a0abd1dcf407ab2e4e4bcf0d856ba79cb576933033197","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2025-05-30T10:10:53Z","title_canon_sha256":"99bbb1cd85b8c1ccefc865d604fdad3bc6b9ac7d1127c609bef6736dd1107daa"},"schema_version":"1.0","source":{"id":"2505.24430","kind":"arxiv","version":1}},"canonical_sha256":"b06761f4fde9bff05faf713df4023cf6dfec84244d97fc62c18e0a29f6bed95a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b06761f4fde9bff05faf713df4023cf6dfec84244d97fc62c18e0a29f6bed95a","first_computed_at":"2026-07-05T11:12:49.577512Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:12:49.577512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"onNdWYn7VmMiAlb7bsq+Xv9K9avw7x0x2Oh7uutjfjfGu3KWkgSKIfabhT/57QK6NwE7enSqx6sWPopjcG59DA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:12:49.578041Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.24430","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01429ff9e32e81db83ea0bc7b71dc300af869b360ea125382aea74d94e8c3498","sha256:0de72c45d18e60dab561f9f28c8fd1854c28cfa15e476d02b622215b111d7aff"],"state_sha256":"0529a12f1a5eee99a104c14233b91254c5abfb742b2482218a91ea32ed51fb18"}