{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SGWC7Y7PBMNUYIK2ASE675J3QD","short_pith_number":"pith:SGWC7Y7P","canonical_record":{"source":{"id":"1611.08233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-11-24T16:06:35Z","cross_cats_sorted":[],"title_canon_sha256":"078e2820a2bfcc04702c7cfaba2257882ea22f22350a15d24561e92d2f57c2e2","abstract_canon_sha256":"4e8305ac3674071e3cac2dfda981141dd36db59dd77e631bee2794e8b477445a"},"schema_version":"1.0"},"canonical_sha256":"91ac2fe3ef0b1b4c215a0489eff53b80f825eaff300ed52d8e944fef54d9a927","source":{"kind":"arxiv","id":"1611.08233","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08233","created_at":"2026-05-18T00:56:39Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08233v1","created_at":"2026-05-18T00:56:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08233","created_at":"2026-05-18T00:56:39Z"},{"alias_kind":"pith_short_12","alias_value":"SGWC7Y7PBMNU","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SGWC7Y7PBMNUYIK2","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SGWC7Y7P","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SGWC7Y7PBMNUYIK2ASE675J3QD","target":"record","payload":{"canonical_record":{"source":{"id":"1611.08233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-11-24T16:06:35Z","cross_cats_sorted":[],"title_canon_sha256":"078e2820a2bfcc04702c7cfaba2257882ea22f22350a15d24561e92d2f57c2e2","abstract_canon_sha256":"4e8305ac3674071e3cac2dfda981141dd36db59dd77e631bee2794e8b477445a"},"schema_version":"1.0"},"canonical_sha256":"91ac2fe3ef0b1b4c215a0489eff53b80f825eaff300ed52d8e944fef54d9a927","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:39.807142Z","signature_b64":"Jd6Cyp53cRPWezNYTikAlhEa0mEphBuDiairX2j70A62HiYSxGBe6sg+0pOVVivu3O6BcTiNzDpCEQZ6U1/xDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91ac2fe3ef0b1b4c215a0489eff53b80f825eaff300ed52d8e944fef54d9a927","last_reissued_at":"2026-05-18T00:56:39.806487Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:39.806487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.08233","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ypfVFe2jmZ+EZuZBqtrIxcUFrqqjst+G67wQPR/WTrSBamhuzQA7EcyN1C6Jk1LsHYPqcT/NH1VinHBXAMXFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:17:27.908989Z"},"content_sha256":"10064dc5b624290bce81d05998ccc5063fa29fb6f054290fc5153d74a6a949d8","schema_version":"1.0","event_id":"sha256:10064dc5b624290bce81d05998ccc5063fa29fb6f054290fc5153d74a6a949d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SGWC7Y7PBMNUYIK2ASE675J3QD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Primitive groups, road closures, and idempotent generation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Jo\\~ao Ara\\'ujo, Peter J. Cameron","submitted_at":"2016-11-24T16:06:35Z","abstract_excerpt":"We are interested in semigroups of the form $\\langle G,a\\rangle\\setminus G$, where $G$ is a permutation group of degree $n$ and $a$ a non-permutation on the domain of $G$. A theorem of the first author, Mitchell and Schneider shows that, if this semigroup is idempotent-generated for all possible choices of $a$, then $G$ is the symmetric or alternating group of degree $n$, with three exceptions (having $n=5$ or $n=6$). Our purpose here is to prove stronger results where we assume that $\\langle G,a\\rangle\\setminus G$ is idempotent-generated for all maps of fixed rank $k$. For $k\\ge6$ and $n\\ge2k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08233","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"maBDRGn5DtBFClk4oj6GGk8fJoro9pPSE6gVGRvVYQ/ijCtuOYtDHANRG0hh8vMU5oqPPcEx8gzFQg8/HSfyCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:17:27.909692Z"},"content_sha256":"612ed6f87e1e577ff2e29e9b0c79fa5bdfdeda5fd665d82afcba8a4274add50a","schema_version":"1.0","event_id":"sha256:612ed6f87e1e577ff2e29e9b0c79fa5bdfdeda5fd665d82afcba8a4274add50a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SGWC7Y7PBMNUYIK2ASE675J3QD/bundle.json","state_url":"https://pith.science/pith/SGWC7Y7PBMNUYIK2ASE675J3QD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SGWC7Y7PBMNUYIK2ASE675J3QD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T09:17:27Z","links":{"resolver":"https://pith.science/pith/SGWC7Y7PBMNUYIK2ASE675J3QD","bundle":"https://pith.science/pith/SGWC7Y7PBMNUYIK2ASE675J3QD/bundle.json","state":"https://pith.science/pith/SGWC7Y7PBMNUYIK2ASE675J3QD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SGWC7Y7PBMNUYIK2ASE675J3QD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SGWC7Y7PBMNUYIK2ASE675J3QD","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":"4e8305ac3674071e3cac2dfda981141dd36db59dd77e631bee2794e8b477445a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-11-24T16:06:35Z","title_canon_sha256":"078e2820a2bfcc04702c7cfaba2257882ea22f22350a15d24561e92d2f57c2e2"},"schema_version":"1.0","source":{"id":"1611.08233","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08233","created_at":"2026-05-18T00:56:39Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08233v1","created_at":"2026-05-18T00:56:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08233","created_at":"2026-05-18T00:56:39Z"},{"alias_kind":"pith_short_12","alias_value":"SGWC7Y7PBMNU","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SGWC7Y7PBMNUYIK2","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SGWC7Y7P","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:612ed6f87e1e577ff2e29e9b0c79fa5bdfdeda5fd665d82afcba8a4274add50a","target":"graph","created_at":"2026-05-18T00:56:39Z","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 are interested in semigroups of the form $\\langle G,a\\rangle\\setminus G$, where $G$ is a permutation group of degree $n$ and $a$ a non-permutation on the domain of $G$. A theorem of the first author, Mitchell and Schneider shows that, if this semigroup is idempotent-generated for all possible choices of $a$, then $G$ is the symmetric or alternating group of degree $n$, with three exceptions (having $n=5$ or $n=6$). Our purpose here is to prove stronger results where we assume that $\\langle G,a\\rangle\\setminus G$ is idempotent-generated for all maps of fixed rank $k$. For $k\\ge6$ and $n\\ge2k","authors_text":"Jo\\~ao Ara\\'ujo, Peter J. Cameron","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-11-24T16:06:35Z","title":"Primitive groups, road closures, and idempotent generation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08233","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":"sha256:10064dc5b624290bce81d05998ccc5063fa29fb6f054290fc5153d74a6a949d8","target":"record","created_at":"2026-05-18T00:56:39Z","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":"4e8305ac3674071e3cac2dfda981141dd36db59dd77e631bee2794e8b477445a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-11-24T16:06:35Z","title_canon_sha256":"078e2820a2bfcc04702c7cfaba2257882ea22f22350a15d24561e92d2f57c2e2"},"schema_version":"1.0","source":{"id":"1611.08233","kind":"arxiv","version":1}},"canonical_sha256":"91ac2fe3ef0b1b4c215a0489eff53b80f825eaff300ed52d8e944fef54d9a927","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91ac2fe3ef0b1b4c215a0489eff53b80f825eaff300ed52d8e944fef54d9a927","first_computed_at":"2026-05-18T00:56:39.806487Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:39.806487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jd6Cyp53cRPWezNYTikAlhEa0mEphBuDiairX2j70A62HiYSxGBe6sg+0pOVVivu3O6BcTiNzDpCEQZ6U1/xDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:39.807142Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.08233","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10064dc5b624290bce81d05998ccc5063fa29fb6f054290fc5153d74a6a949d8","sha256:612ed6f87e1e577ff2e29e9b0c79fa5bdfdeda5fd665d82afcba8a4274add50a"],"state_sha256":"afc66ffc4c7cc0baa5075bae7dfe3a296794455747a19f95fc55019d59fcbaeb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vCwLj9VN1REPTbRFH/H46VApUjwV9ilwpSpAnQcZvkW0C3cn9GoeyMU7pwqMe2uCU1RXokLoFEZxcKiD9EjWDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T09:17:27.913885Z","bundle_sha256":"a5d2e7e0f2cb3597aa79a46f42b42e5305f20b4f4362f01bc3469d183d094502"}}