{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ERS2JSGPA4K7HIABAJVHVE7Y3M","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":"7db2328c17f2cda6b9e117401b97083222c0e4e038f57746ae1638fac0c263ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-23T19:23:24Z","title_canon_sha256":"9293bc6cee233d4c5556a76502f337423a9667d14cda9b1dbb83f883fc3a1608"},"schema_version":"1.0","source":{"id":"1512.07594","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07594","created_at":"2026-05-18T00:02:46Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07594v3","created_at":"2026-05-18T00:02:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07594","created_at":"2026-05-18T00:02:46Z"},{"alias_kind":"pith_short_12","alias_value":"ERS2JSGPA4K7","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"ERS2JSGPA4K7HIAB","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"ERS2JSGP","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:79a3905c026c749df397e0a68c0aeb9464ff74414e6d17af9d6fd03bd2ec4c70","target":"graph","created_at":"2026-05-18T00:02:46Z","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":"Let $G$ be a group. The orbits of the natural action of $\\mbox{Aut}(G)$ on $G$ are called \"automorphism orbits\" of $G$, and the number of automorphism orbits of $G$ is denoted by $\\omega(G)$. In this paper the finite nonsolvable groups $G$ with $\\omega(G) \\leq 6$ are classified - this solves a problem posed by Markus Stroppel - and it is proved that there are infinitely many finite nonsolvable groups $G$ with $\\omega(G)=7$. Moreover it is proved that for a given number $n$ there are only finitely many finite groups $G$ without nontrivial abelian normal subgroups and such that $\\omega(G) \\leq n","authors_text":"Alex Carrazedo Dantas, Martino Garonzi, Raimundo Bastos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-23T19:23:24Z","title":"Finite Groups with 6 or 7 Automorphism Orbits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07594","kind":"arxiv","version":3},"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":"sha256:9e74f4296e66aa9171e014fbdd35fca1eff9d771349bd51e670869b2d0681dd1","target":"record","created_at":"2026-05-18T00:02:46Z","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":"7db2328c17f2cda6b9e117401b97083222c0e4e038f57746ae1638fac0c263ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-23T19:23:24Z","title_canon_sha256":"9293bc6cee233d4c5556a76502f337423a9667d14cda9b1dbb83f883fc3a1608"},"schema_version":"1.0","source":{"id":"1512.07594","kind":"arxiv","version":3}},"canonical_sha256":"2465a4c8cf0715f3a001026a7a93f8db30b89fe4e12e35798f3edfe9389952d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2465a4c8cf0715f3a001026a7a93f8db30b89fe4e12e35798f3edfe9389952d7","first_computed_at":"2026-05-18T00:02:46.022434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:46.022434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zBgIKDzzP07EWizya0QhqLj2bB+4jS6yORdEjQ0CLhWM/PogsS2dqOBiAXvfjooV0KUXPfz4FPlni3UKgmwNCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:46.022837Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.07594","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e74f4296e66aa9171e014fbdd35fca1eff9d771349bd51e670869b2d0681dd1","sha256:79a3905c026c749df397e0a68c0aeb9464ff74414e6d17af9d6fd03bd2ec4c70"],"state_sha256":"466fdab533ebac094949e64cc6f268ac4ead3703e4593309918a12d318b31df0"}