{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DSKNXOVICSHD4HLQZ5O6L2UYTG","short_pith_number":"pith:DSKNXOVI","canonical_record":{"source":{"id":"1801.07918","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-24T10:58:48Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"c5ee15dda16a55ba5f38bd9abc55e282d551d7b6bc7010a84c6aadce04088b0c","abstract_canon_sha256":"d128be5b4e336390801e432a03e3246981d5511136098e50a4a5e5a02e3e6c94"},"schema_version":"1.0"},"canonical_sha256":"1c94dbbaa8148e3e1d70cf5de5ea98998083d4cc1cbee3bef37b1f8ad7c287ee","source":{"kind":"arxiv","id":"1801.07918","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.07918","created_at":"2026-05-18T00:10:28Z"},{"alias_kind":"arxiv_version","alias_value":"1801.07918v2","created_at":"2026-05-18T00:10:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07918","created_at":"2026-05-18T00:10:28Z"},{"alias_kind":"pith_short_12","alias_value":"DSKNXOVICSHD","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DSKNXOVICSHD4HLQ","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DSKNXOVI","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DSKNXOVICSHD4HLQZ5O6L2UYTG","target":"record","payload":{"canonical_record":{"source":{"id":"1801.07918","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-24T10:58:48Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"c5ee15dda16a55ba5f38bd9abc55e282d551d7b6bc7010a84c6aadce04088b0c","abstract_canon_sha256":"d128be5b4e336390801e432a03e3246981d5511136098e50a4a5e5a02e3e6c94"},"schema_version":"1.0"},"canonical_sha256":"1c94dbbaa8148e3e1d70cf5de5ea98998083d4cc1cbee3bef37b1f8ad7c287ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:28.203803Z","signature_b64":"cZGrAJZijkCinG1fC55PzixrtRRWaYRVFn7o9Nt+eJvUK9hFqDGI4gwqFJ6qeppffRVK6GwJy2alFFyMu46dAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c94dbbaa8148e3e1d70cf5de5ea98998083d4cc1cbee3bef37b1f8ad7c287ee","last_reissued_at":"2026-05-18T00:10:28.203255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:28.203255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.07918","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":"2026-05-18T00:10:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+eVZp6eREqrkQyV4MNLcgYW5R0J09pef07TakyAX5s57Qb5Hv7eMbChiP1K7YlYDIQsJUFVfHPZqYRcA42H/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:07:36.377552Z"},"content_sha256":"c17abbae7363eb03b2b3267266d1e23ae9424926f56093d55274b4b542f1767c","schema_version":"1.0","event_id":"sha256:c17abbae7363eb03b2b3267266d1e23ae9424926f56093d55274b4b542f1767c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DSKNXOVICSHD4HLQZ5O6L2UYTG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Overgroups of exterior powers of an elementary group. I. Levels and normalizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Ilia Nekrasov, Roman Lubkov","submitted_at":"2018-01-24T10:58:48Z","abstract_excerpt":"In the present paper, we prove the first part in the standard description of groups $H$ lying between $m$-th exterior power of elementary group $E(n,R)$ and the general linear group $GL_{\\binom{n}{m}}(R)$. We study structure of the exterior power of elementary group and its relative analog $E\\left(\\binom{n}{m},R,A\\right)$. In the considering case $n \\geq 3m$, the description is explained by the classical notion of level: for every such $H$ we find unique ideal $A$ of the ring $R$. Motivated by the problem, we prove the coincidence of the following groups: normalizer of the exterior power of el"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07918","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":""},"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":"2026-05-18T00:10:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T2GemlXGV4a7j7qBKMRYQohewLo8IHPzjAeHPS4IIXiP5MLvab0XKm6LzPdX5C+LesDTDB4vyMbYWHkN6ZXIDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:07:36.378221Z"},"content_sha256":"cc080124c8f9dabd3b0a80a7656898d0319f635b0343b090571d89d24fd9f826","schema_version":"1.0","event_id":"sha256:cc080124c8f9dabd3b0a80a7656898d0319f635b0343b090571d89d24fd9f826"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DSKNXOVICSHD4HLQZ5O6L2UYTG/bundle.json","state_url":"https://pith.science/pith/DSKNXOVICSHD4HLQZ5O6L2UYTG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DSKNXOVICSHD4HLQZ5O6L2UYTG/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":"2026-06-11T00:07:36Z","links":{"resolver":"https://pith.science/pith/DSKNXOVICSHD4HLQZ5O6L2UYTG","bundle":"https://pith.science/pith/DSKNXOVICSHD4HLQZ5O6L2UYTG/bundle.json","state":"https://pith.science/pith/DSKNXOVICSHD4HLQZ5O6L2UYTG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DSKNXOVICSHD4HLQZ5O6L2UYTG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DSKNXOVICSHD4HLQZ5O6L2UYTG","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":"d128be5b4e336390801e432a03e3246981d5511136098e50a4a5e5a02e3e6c94","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-24T10:58:48Z","title_canon_sha256":"c5ee15dda16a55ba5f38bd9abc55e282d551d7b6bc7010a84c6aadce04088b0c"},"schema_version":"1.0","source":{"id":"1801.07918","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.07918","created_at":"2026-05-18T00:10:28Z"},{"alias_kind":"arxiv_version","alias_value":"1801.07918v2","created_at":"2026-05-18T00:10:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07918","created_at":"2026-05-18T00:10:28Z"},{"alias_kind":"pith_short_12","alias_value":"DSKNXOVICSHD","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DSKNXOVICSHD4HLQ","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DSKNXOVI","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:cc080124c8f9dabd3b0a80a7656898d0319f635b0343b090571d89d24fd9f826","target":"graph","created_at":"2026-05-18T00:10:28Z","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":"In the present paper, we prove the first part in the standard description of groups $H$ lying between $m$-th exterior power of elementary group $E(n,R)$ and the general linear group $GL_{\\binom{n}{m}}(R)$. We study structure of the exterior power of elementary group and its relative analog $E\\left(\\binom{n}{m},R,A\\right)$. In the considering case $n \\geq 3m$, the description is explained by the classical notion of level: for every such $H$ we find unique ideal $A$ of the ring $R$. Motivated by the problem, we prove the coincidence of the following groups: normalizer of the exterior power of el","authors_text":"Ilia Nekrasov, Roman Lubkov","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-24T10:58:48Z","title":"Overgroups of exterior powers of an elementary group. I. Levels and normalizers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07918","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:c17abbae7363eb03b2b3267266d1e23ae9424926f56093d55274b4b542f1767c","target":"record","created_at":"2026-05-18T00:10:28Z","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":"d128be5b4e336390801e432a03e3246981d5511136098e50a4a5e5a02e3e6c94","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-24T10:58:48Z","title_canon_sha256":"c5ee15dda16a55ba5f38bd9abc55e282d551d7b6bc7010a84c6aadce04088b0c"},"schema_version":"1.0","source":{"id":"1801.07918","kind":"arxiv","version":2}},"canonical_sha256":"1c94dbbaa8148e3e1d70cf5de5ea98998083d4cc1cbee3bef37b1f8ad7c287ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c94dbbaa8148e3e1d70cf5de5ea98998083d4cc1cbee3bef37b1f8ad7c287ee","first_computed_at":"2026-05-18T00:10:28.203255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:28.203255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cZGrAJZijkCinG1fC55PzixrtRRWaYRVFn7o9Nt+eJvUK9hFqDGI4gwqFJ6qeppffRVK6GwJy2alFFyMu46dAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:28.203803Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.07918","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c17abbae7363eb03b2b3267266d1e23ae9424926f56093d55274b4b542f1767c","sha256:cc080124c8f9dabd3b0a80a7656898d0319f635b0343b090571d89d24fd9f826"],"state_sha256":"8e164319fa44e75795394bf533a59b72137299a6543bdae0b533a76948c49e31"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2qZEzmgrZFfKbKnfhlZMue0ezNRilnAxce5AO8wfD2P4PaL7TNsTKzXANH5dII+XABJgR4tMcXU2auwwcVaVCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T00:07:36.381867Z","bundle_sha256":"bfe90d5a2bc97ca6d5712f2e0ee404c7adbde82984f03b325ae6ac51b3e5f05a"}}