{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:BGUA7ZOYD4IZGTVXGKAGSVUIUM","short_pith_number":"pith:BGUA7ZOY","canonical_record":{"source":{"id":"1910.03538","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2019-10-08T16:50:40Z","cross_cats_sorted":[],"title_canon_sha256":"42d0fdd2d91df3a1932fdf489bd9160585ebcb1dc6236d4f5aba6b8b26b0288d","abstract_canon_sha256":"5e1801e81f76bc04770496e1d88ed86021c16a609aabea230af18cdef3ca0859"},"schema_version":"1.0"},"canonical_sha256":"09a80fe5d81f11934eb73280695688a31a192d4e87c1dc782bbdca37f6b60869","source":{"kind":"arxiv","id":"1910.03538","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.03538","created_at":"2026-07-05T02:52:56Z"},{"alias_kind":"arxiv_version","alias_value":"1910.03538v2","created_at":"2026-07-05T02:52:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.03538","created_at":"2026-07-05T02:52:56Z"},{"alias_kind":"pith_short_12","alias_value":"BGUA7ZOYD4IZ","created_at":"2026-07-05T02:52:56Z"},{"alias_kind":"pith_short_16","alias_value":"BGUA7ZOYD4IZGTVX","created_at":"2026-07-05T02:52:56Z"},{"alias_kind":"pith_short_8","alias_value":"BGUA7ZOY","created_at":"2026-07-05T02:52:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:BGUA7ZOYD4IZGTVXGKAGSVUIUM","target":"record","payload":{"canonical_record":{"source":{"id":"1910.03538","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2019-10-08T16:50:40Z","cross_cats_sorted":[],"title_canon_sha256":"42d0fdd2d91df3a1932fdf489bd9160585ebcb1dc6236d4f5aba6b8b26b0288d","abstract_canon_sha256":"5e1801e81f76bc04770496e1d88ed86021c16a609aabea230af18cdef3ca0859"},"schema_version":"1.0"},"canonical_sha256":"09a80fe5d81f11934eb73280695688a31a192d4e87c1dc782bbdca37f6b60869","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:52:56.133915Z","signature_b64":"9svIOW9BIan0sYM7V3t0PUpExF1Lm2EobAzSsSKbpe2RK+8jxc0UOe3dmO/JVKF20xZZSZSgSSn4Qrza2Hz1AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09a80fe5d81f11934eb73280695688a31a192d4e87c1dc782bbdca37f6b60869","last_reissued_at":"2026-07-05T02:52:56.133508Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:52:56.133508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1910.03538","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:52:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P1rF5AcCQCJaIvaGlB8jc54zGplcVtBDRMO2KdQNtfffCNH9fCcOumI3CbALnAeYILVPmKqLbCqzHKufgOI+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T09:45:07.641053Z"},"content_sha256":"1830294b8826066994d8fd93d1762d3487aa11ee4e0c63e952ff63f914dca82f","schema_version":"1.0","event_id":"sha256:1830294b8826066994d8fd93d1762d3487aa11ee4e0c63e952ff63f914dca82f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:BGUA7ZOYD4IZGTVXGKAGSVUIUM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Overgroups of Levi subgroups I. The case of abelian unipotent radical","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Pavel Gvozdevsky","submitted_at":"2019-10-08T16:50:40Z","abstract_excerpt":"In the present paper we prove sandwich classification for the overgroups of the subsystem subgroup $E(\\Delta,R)$ of the Chevalley group $G(\\Phi,R)$ for the three types of pair $(\\Phi,\\Delta)$ (the root system and its subsystem) such that the group $G(\\Delta,R)$ is (up to torus) a Levi subgroup of the parabolic subgroup with abelian unipotent radical. Namely we show that for any such an overgroup $H$ there exists a unique pair of ideals $\\sigma$ of the ring $R$ such that $E(\\Phi,\\Delta,R,\\sigma)\\le H\\le N_{G(\\Phi,R)}(E(\\Phi,\\Delta,R,\\sigma))$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.03538","kind":"arxiv","version":2},"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/1910.03538/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":"2026-07-05T02:52:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I25uNUsaBE+TIBCKNMPybNtMZgDf9teJ3I5JE6f4mU0MHgNckpaX5faMFA+hR6IK8+Z08OCnTRpXTcktHpCgDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T09:45:07.642046Z"},"content_sha256":"05013e9c30f4c4300a90e61e00444f72a72134f247f38981949c218d15053040","schema_version":"1.0","event_id":"sha256:05013e9c30f4c4300a90e61e00444f72a72134f247f38981949c218d15053040"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BGUA7ZOYD4IZGTVXGKAGSVUIUM/bundle.json","state_url":"https://pith.science/pith/BGUA7ZOYD4IZGTVXGKAGSVUIUM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BGUA7ZOYD4IZGTVXGKAGSVUIUM/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":"2026-08-11T09:45:07Z","links":{"resolver":"https://pith.science/pith/BGUA7ZOYD4IZGTVXGKAGSVUIUM","bundle":"https://pith.science/pith/BGUA7ZOYD4IZGTVXGKAGSVUIUM/bundle.json","state":"https://pith.science/pith/BGUA7ZOYD4IZGTVXGKAGSVUIUM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BGUA7ZOYD4IZGTVXGKAGSVUIUM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BGUA7ZOYD4IZGTVXGKAGSVUIUM","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":"5e1801e81f76bc04770496e1d88ed86021c16a609aabea230af18cdef3ca0859","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2019-10-08T16:50:40Z","title_canon_sha256":"42d0fdd2d91df3a1932fdf489bd9160585ebcb1dc6236d4f5aba6b8b26b0288d"},"schema_version":"1.0","source":{"id":"1910.03538","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.03538","created_at":"2026-07-05T02:52:56Z"},{"alias_kind":"arxiv_version","alias_value":"1910.03538v2","created_at":"2026-07-05T02:52:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.03538","created_at":"2026-07-05T02:52:56Z"},{"alias_kind":"pith_short_12","alias_value":"BGUA7ZOYD4IZ","created_at":"2026-07-05T02:52:56Z"},{"alias_kind":"pith_short_16","alias_value":"BGUA7ZOYD4IZGTVX","created_at":"2026-07-05T02:52:56Z"},{"alias_kind":"pith_short_8","alias_value":"BGUA7ZOY","created_at":"2026-07-05T02:52:56Z"}],"graph_snapshots":[{"event_id":"sha256:05013e9c30f4c4300a90e61e00444f72a72134f247f38981949c218d15053040","target":"graph","created_at":"2026-07-05T02:52:56Z","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/1910.03538/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the present paper we prove sandwich classification for the overgroups of the subsystem subgroup $E(\\Delta,R)$ of the Chevalley group $G(\\Phi,R)$ for the three types of pair $(\\Phi,\\Delta)$ (the root system and its subsystem) such that the group $G(\\Delta,R)$ is (up to torus) a Levi subgroup of the parabolic subgroup with abelian unipotent radical. Namely we show that for any such an overgroup $H$ there exists a unique pair of ideals $\\sigma$ of the ring $R$ such that $E(\\Phi,\\Delta,R,\\sigma)\\le H\\le N_{G(\\Phi,R)}(E(\\Phi,\\Delta,R,\\sigma))$.","authors_text":"Pavel Gvozdevsky","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2019-10-08T16:50:40Z","title":"Overgroups of Levi subgroups I. The case of abelian unipotent radical"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.03538","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":"sha256:1830294b8826066994d8fd93d1762d3487aa11ee4e0c63e952ff63f914dca82f","target":"record","created_at":"2026-07-05T02:52:56Z","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":"5e1801e81f76bc04770496e1d88ed86021c16a609aabea230af18cdef3ca0859","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2019-10-08T16:50:40Z","title_canon_sha256":"42d0fdd2d91df3a1932fdf489bd9160585ebcb1dc6236d4f5aba6b8b26b0288d"},"schema_version":"1.0","source":{"id":"1910.03538","kind":"arxiv","version":2}},"canonical_sha256":"09a80fe5d81f11934eb73280695688a31a192d4e87c1dc782bbdca37f6b60869","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09a80fe5d81f11934eb73280695688a31a192d4e87c1dc782bbdca37f6b60869","first_computed_at":"2026-07-05T02:52:56.133508Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:52:56.133508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9svIOW9BIan0sYM7V3t0PUpExF1Lm2EobAzSsSKbpe2RK+8jxc0UOe3dmO/JVKF20xZZSZSgSSn4Qrza2Hz1AA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:52:56.133915Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.03538","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1830294b8826066994d8fd93d1762d3487aa11ee4e0c63e952ff63f914dca82f","sha256:05013e9c30f4c4300a90e61e00444f72a72134f247f38981949c218d15053040"],"state_sha256":"c75c970e17628bd65e7d106af6ec2dd3adbf9ea4804ca40106b385c98a1ee397"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aa7QhIOqC6g+tFv/5cbVnxF1wKM5ZtHvbjFB6ddiL5V0DjqK49ViQhL3osZtw68c5TeESPTPVUEl0VwLODThAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T09:45:07.649282Z","bundle_sha256":"32637b7fe5b6e45532cbb066851f30427dd6e4856753fe4d5f14824a1d759125"}}