{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NORLYVCLX3MNW64WFHHURTJQQ4","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":"4450020e899ad31f6a3032aa2c42dad0f20cfb67826a7bcb573a90ef644563f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-25T16:36:56Z","title_canon_sha256":"b135433ab82078d1e0427d4e91de1698f0da305370eb80a47b45aaceda7411af"},"schema_version":"1.0","source":{"id":"1310.6973","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6973","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6973v2","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6973","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"NORLYVCLX3MN","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NORLYVCLX3MNW64W","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NORLYVCL","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:f0a83a466baa8d46bc6fa779a19e3d9dbe12e3c47d607bc346afe7ffff2b5189","target":"graph","created_at":"2026-05-18T03:06:54Z","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":"We work with a finite relational vocabulary with at least one relation symbol with arity at least 2. Fix any integer $m > 1$. For almost all finite structures (labelled or unlabelled) such that at least $m$ elements are moved by some automorphisms, the automorphism group is $(Z_2)^i$ for some $i \\leq (m+1)/2$; and if some relation symbol has arity at least 3, then the automorphism group is almost always $Z_2$.","authors_text":"Vera Koponen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-25T16:36:56Z","title":"Typical automorphism groups of finite nonrigid structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6973","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:a591005b5882a8f5672ec801072710d9c02ea8d1ff165881cb8574a45bf82fcb","target":"record","created_at":"2026-05-18T03:06:54Z","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":"4450020e899ad31f6a3032aa2c42dad0f20cfb67826a7bcb573a90ef644563f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-25T16:36:56Z","title_canon_sha256":"b135433ab82078d1e0427d4e91de1698f0da305370eb80a47b45aaceda7411af"},"schema_version":"1.0","source":{"id":"1310.6973","kind":"arxiv","version":2}},"canonical_sha256":"6ba2bc544bbed8db7b9629cf48cd30873382699201e64e78b333b901d1bbcc3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ba2bc544bbed8db7b9629cf48cd30873382699201e64e78b333b901d1bbcc3f","first_computed_at":"2026-05-18T03:06:54.210499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:54.210499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hFYj1XuCvSB/oszzTNVUpofOuVzSEyNpEq11LVWk6+gM4JL2795X40YkWsO2W4gdSOwG8y4Rlrl9XS3Kj7SCAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:54.211164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.6973","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a591005b5882a8f5672ec801072710d9c02ea8d1ff165881cb8574a45bf82fcb","sha256:f0a83a466baa8d46bc6fa779a19e3d9dbe12e3c47d607bc346afe7ffff2b5189"],"state_sha256":"3fe84de469ca0e147f5158e1bd1d3d22fa704fcb0bad3e423f3c043a8353da9e"}