{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PHCNGFASH6X6UUQSAWT3Z4K3GR","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":"9d2da80cbe7a31817d0ef71848e0ead5e58e166fc2613c1c6d7bf052e2682861","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-07-16T06:08:47Z","title_canon_sha256":"fa062234c547c44957a900adccf39cea60d6bb50bcc9a71dda8e803b9deb2067"},"schema_version":"1.0","source":{"id":"2607.14603","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.14603","created_at":"2026-07-17T01:21:20Z"},{"alias_kind":"arxiv_version","alias_value":"2607.14603v1","created_at":"2026-07-17T01:21:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.14603","created_at":"2026-07-17T01:21:20Z"},{"alias_kind":"pith_short_12","alias_value":"PHCNGFASH6X6","created_at":"2026-07-17T01:21:20Z"},{"alias_kind":"pith_short_16","alias_value":"PHCNGFASH6X6UUQS","created_at":"2026-07-17T01:21:20Z"},{"alias_kind":"pith_short_8","alias_value":"PHCNGFAS","created_at":"2026-07-17T01:21:20Z"}],"graph_snapshots":[{"event_id":"sha256:5f948490c066239041669535d0bd02740c277bab0435a1f673e94b2204579840","target":"graph","created_at":"2026-07-17T01:21:20Z","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/2607.14603/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the primitive actions of almost simple groups with socle \\(E_7(q)\\) or \\(E_8(q)\\) on an \\(s\\)-arc-transitive digraph. Our motivation goes back to the question of whether \\(s\\) is bounded above for finite connected \\(G\\)-vertex-primitive \\(s\\)-arc-transitive digraphs that are not directed cycles. The question has been reduced by Giudici and Xia to the case where \\(G\\) is almost simple. This work succeeds our 2025 paper (Yin and Chen), which addressed \\({}^3\\!D_4(q)\\), \\(G_2(q)\\), \\({}^2\\!F_4(q)'\\), \\(F_4(q)\\), \\(E_6(q)\\), and \\({}^2\\!E_6(q)\\). Together with Chen, Giudici","authors_text":"Fu-Gang Yin, Lei Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-07-16T06:08:47Z","title":"Exceptional groups and the s-arc-transitivity of vertex-primitive digraphs, II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14603","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":"sha256:7a48cfe20052248588079bddc1230a6140f2bb6b553cce9f1655d5f53704ff17","target":"record","created_at":"2026-07-17T01:21:20Z","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":"9d2da80cbe7a31817d0ef71848e0ead5e58e166fc2613c1c6d7bf052e2682861","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-07-16T06:08:47Z","title_canon_sha256":"fa062234c547c44957a900adccf39cea60d6bb50bcc9a71dda8e803b9deb2067"},"schema_version":"1.0","source":{"id":"2607.14603","kind":"arxiv","version":1}},"canonical_sha256":"79c4d314123fafea521205a7bcf15b347c3dba2db47c138c58931071c5339a9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79c4d314123fafea521205a7bcf15b347c3dba2db47c138c58931071c5339a9f","first_computed_at":"2026-07-17T01:21:20.351027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-17T01:21:20.351027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j0Nzrt+0zFluEHralJY3dwjLXhXrCZOjqUVoiSHnc2QE8oGb5QFIP6AvisGXfMSwEE4TWhI7ddnlqZ0ZzN76BA==","signature_status":"signed_v1","signed_at":"2026-07-17T01:21:20.351847Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.14603","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a48cfe20052248588079bddc1230a6140f2bb6b553cce9f1655d5f53704ff17","sha256:5f948490c066239041669535d0bd02740c277bab0435a1f673e94b2204579840"],"state_sha256":"f7b687bb2a1101def8b8d707c1679c8ebd4841dc4b16ae4153c9ca19f44defe6"}