{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OZJDAGNCO77IUVWGH63Y6TCA2M","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":"e19d75a7d014570dfc06c258d0f9baf98eef5bd327c064b69018e06b4f64fd82","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-07-22T00:15:57Z","title_canon_sha256":"d07a7c2ade43f56e1ac5d7effe11646ccfdfde14b7be39004a88b14441fbe8d9"},"schema_version":"1.0","source":{"id":"1407.5697","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5697","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5697v3","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5697","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"pith_short_12","alias_value":"OZJDAGNCO77I","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OZJDAGNCO77IUVWG","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OZJDAGNC","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:6c3ea093fb019e8fffdd01b81bcae4189197ed64c2f59d5aff269d50a69b0b71","target":"graph","created_at":"2026-05-18T00:25:21Z","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 introduce a new product for permutation groups. It takes as input two permutation groups, M and N, and produces an infinite group M [X] N which carries many of the permutational properties of M. Under mild conditions on M and N the group M [X] N is simple.\n  As a permutational product, its most significant property is the following: M [X] N is primitive if and only if M is primitive but not regular, and N is transitive. Despite this remarkable similarity with the wreath product in product action, M [X] N and M Wr N are thoroughly dissimilar. The product provides a general way to build exoti","authors_text":"Simon M. Smith","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-07-22T00:15:57Z","title":"A product for permutation groups and topological groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5697","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:e7dc4e3a03bc80c208daebbc1fac53afab91a4e904986fb72d76b2dee517d55d","target":"record","created_at":"2026-05-18T00:25:21Z","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":"e19d75a7d014570dfc06c258d0f9baf98eef5bd327c064b69018e06b4f64fd82","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-07-22T00:15:57Z","title_canon_sha256":"d07a7c2ade43f56e1ac5d7effe11646ccfdfde14b7be39004a88b14441fbe8d9"},"schema_version":"1.0","source":{"id":"1407.5697","kind":"arxiv","version":3}},"canonical_sha256":"76523019a277fe8a56c63fb78f4c40d31d4c8f364875cc1d3bdf950db518f9f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76523019a277fe8a56c63fb78f4c40d31d4c8f364875cc1d3bdf950db518f9f6","first_computed_at":"2026-05-18T00:25:21.718956Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:21.718956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vHciB+HkHc14zImt+GPLBjXC2HPndj3Pr1vK9S3JD8nKGooY2ZXkDr50C/SSumJEOWTYqvwOp4GEF8Du/iH+CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:21.719536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.5697","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7dc4e3a03bc80c208daebbc1fac53afab91a4e904986fb72d76b2dee517d55d","sha256:6c3ea093fb019e8fffdd01b81bcae4189197ed64c2f59d5aff269d50a69b0b71"],"state_sha256":"66bde87ccdaa0e0bccdebca7994748dd45d24dc62d45eb5580bbf25441ee2ec3"}