{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7YQI5SKXHTRN3TG5CEHTA7V2VC","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":"3af4a037ec75b46194acd8222f82dcbdfb6c12c22959a74a86fe29877d4bc110","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-08-20T16:02:33Z","title_canon_sha256":"ca46ca726a39a20add8cd9b31b0b8da5f9d3336cf276425b675a30833570d9f9"},"schema_version":"1.0","source":{"id":"2408.10969","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.10969","created_at":"2026-07-05T08:57:20Z"},{"alias_kind":"arxiv_version","alias_value":"2408.10969v1","created_at":"2026-07-05T08:57:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.10969","created_at":"2026-07-05T08:57:20Z"},{"alias_kind":"pith_short_12","alias_value":"7YQI5SKXHTRN","created_at":"2026-07-05T08:57:20Z"},{"alias_kind":"pith_short_16","alias_value":"7YQI5SKXHTRN3TG5","created_at":"2026-07-05T08:57:20Z"},{"alias_kind":"pith_short_8","alias_value":"7YQI5SKX","created_at":"2026-07-05T08:57:20Z"}],"graph_snapshots":[{"event_id":"sha256:353b53c29e4ac7ad34b788061cedfca73aaeda87cb74e77ed8172733bfd1fec8","target":"graph","created_at":"2026-07-05T08:57:20Z","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/2408.10969/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show a Springer type theorem for the variety of parabolic subgroups of type $1,2,6$ for all groups of type $E_6$. As far as we know this gives the first example for the validity of the Springer theorem for projective homogeneous varieties of type $^2E_6$ different from varieties of Borel subgroups. The proof combines several topics, notably the Rost invariant, a Tits construction, Cartan's symmetric spaces and indirectly the structure of the Chow motives of projective homogeneous varieties of exceptional type.","authors_text":"Nikita Geldhauser, Victor Petrov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-08-20T16:02:33Z","title":"Tits construction and Rost invariant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.10969","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:c38f3dfcd380de073f30e75e84f8482d9791a9b4833fdde3ec2575ecf2c4cd5a","target":"record","created_at":"2026-07-05T08:57:20Z","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":"3af4a037ec75b46194acd8222f82dcbdfb6c12c22959a74a86fe29877d4bc110","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-08-20T16:02:33Z","title_canon_sha256":"ca46ca726a39a20add8cd9b31b0b8da5f9d3336cf276425b675a30833570d9f9"},"schema_version":"1.0","source":{"id":"2408.10969","kind":"arxiv","version":1}},"canonical_sha256":"fe208ec9573ce2ddccdd110f307ebaa8a02e9a6f4b463fbc42296e14fd43a89c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe208ec9573ce2ddccdd110f307ebaa8a02e9a6f4b463fbc42296e14fd43a89c","first_computed_at":"2026-07-05T08:57:20.394873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:57:20.394873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SUYwxENpNb71lec8HgfcfutQRr652GdfEnIymtjt5y9187ILSqdQ9KR4hhu9JBhu801TvYgP1pZB6hrF/yQzAw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:57:20.395292Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.10969","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c38f3dfcd380de073f30e75e84f8482d9791a9b4833fdde3ec2575ecf2c4cd5a","sha256:353b53c29e4ac7ad34b788061cedfca73aaeda87cb74e77ed8172733bfd1fec8"],"state_sha256":"dcf5e5ea57b5ecc6471d4a976986a5f544518e426342df6c1b2223a351c64a4f"}