{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:C4ASMN4JYU43EJLATAKZ6L2XGU","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":"47959f08add4b4a2edbee3c6f9d4d23080ccccfe3410eb62b5d38a1f15d9e7c7","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-06-16T09:03:45Z","title_canon_sha256":"861eb6da5b0bfc3181e9db15716afc96d22810ceffaab96a6b04f618ef2a3279"},"schema_version":"1.0","source":{"id":"1706.05187","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.05187","created_at":"2026-05-18T00:42:14Z"},{"alias_kind":"arxiv_version","alias_value":"1706.05187v1","created_at":"2026-05-18T00:42:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.05187","created_at":"2026-05-18T00:42:14Z"},{"alias_kind":"pith_short_12","alias_value":"C4ASMN4JYU43","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"C4ASMN4JYU43EJLA","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"C4ASMN4J","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:dd6c58ea3b1c7d50394cae894317550913fbf1bd181fe8b805c0440bb3a0532e","target":"graph","created_at":"2026-05-18T00:42:14Z","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 finite group acting orthogonally on a pair (S^d,\\Gamma) where \\Gamma is a finite, connected graph of genus g>1 embedded in the sphere S^d. The 3-dimensional case d=3 has recently been considered in a paper by C. Wang, S. Wang, Y. Zhang and the present author where for each genus g>1 the maximum order of a G-action on a pair (S^3,\\Gamma) is determined and the corresponding graphs \\Gamma are classified. In the present paper we consider arbitrary dimensions d and prove that the order of G is bounded above by a polynomial of degree d/2 in g if d is even, and of degree (d+1)/2 if d is od","authors_text":"Bruno P. Zimmermann","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-06-16T09:03:45Z","title":"On large groups of symmetries of finite graphs embedded in spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05187","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":"sha256:596fcffb6b7e319768abfdc8e3971b0c85c1be9f84a0dfc28f23f5e7b9e8cda0","target":"record","created_at":"2026-05-18T00:42:14Z","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":"47959f08add4b4a2edbee3c6f9d4d23080ccccfe3410eb62b5d38a1f15d9e7c7","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-06-16T09:03:45Z","title_canon_sha256":"861eb6da5b0bfc3181e9db15716afc96d22810ceffaab96a6b04f618ef2a3279"},"schema_version":"1.0","source":{"id":"1706.05187","kind":"arxiv","version":1}},"canonical_sha256":"1701263789c539b2256098159f2f5735341961e259a6a30f44362821ffe53ae5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1701263789c539b2256098159f2f5735341961e259a6a30f44362821ffe53ae5","first_computed_at":"2026-05-18T00:42:14.506635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:14.506635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KyFogPZtClVuYiKXnKzV+EK1EhkgwoHZJyE7p6WkJqDIFr/QgQ4gMTHY4Xbz2pa77acEEb4zXXjAsy3mh8++BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:14.507244Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.05187","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:596fcffb6b7e319768abfdc8e3971b0c85c1be9f84a0dfc28f23f5e7b9e8cda0","sha256:dd6c58ea3b1c7d50394cae894317550913fbf1bd181fe8b805c0440bb3a0532e"],"state_sha256":"d88d9c53ecc7929e9e501c2edee2cba904bed20f99a614d29344350166849e97"}