{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7RFWQWCOCX6EBA3QEHGCPGPHH5","short_pith_number":"pith:7RFWQWCO","canonical_record":{"source":{"id":"1310.1569","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-06T10:11:35Z","cross_cats_sorted":[],"title_canon_sha256":"0dcf2bf585ea5dbfcc028b81a0de919ae398e44f5607c1dea379c24fd3d0f372","abstract_canon_sha256":"a59e3b7d0b096ee13ca75db6150eb4b61c6d6c8591b13cab623e0467c087ee76"},"schema_version":"1.0"},"canonical_sha256":"fc4b68584e15fc40837021cc2799e73f5f69326f4feaad43f0105f09c6b39c72","source":{"kind":"arxiv","id":"1310.1569","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1569","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1569v3","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1569","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"pith_short_12","alias_value":"7RFWQWCOCX6E","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7RFWQWCOCX6EBA3Q","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7RFWQWCO","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7RFWQWCOCX6EBA3QEHGCPGPHH5","target":"record","payload":{"canonical_record":{"source":{"id":"1310.1569","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-06T10:11:35Z","cross_cats_sorted":[],"title_canon_sha256":"0dcf2bf585ea5dbfcc028b81a0de919ae398e44f5607c1dea379c24fd3d0f372","abstract_canon_sha256":"a59e3b7d0b096ee13ca75db6150eb4b61c6d6c8591b13cab623e0467c087ee76"},"schema_version":"1.0"},"canonical_sha256":"fc4b68584e15fc40837021cc2799e73f5f69326f4feaad43f0105f09c6b39c72","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:35.427054Z","signature_b64":"+GQcwSl2c0GoopyGA4jy1f/UPY3nZbX0UtQOXucplRETaBSD6LuBFGZR2IgZuQ+cOWsT9s8IMyKmq6VjnUP+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc4b68584e15fc40837021cc2799e73f5f69326f4feaad43f0105f09c6b39c72","last_reissued_at":"2026-05-18T00:45:35.425861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:35.425861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.1569","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:45:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wSFiHQWX+xonYLL4bGPa2+geWhAmwJL87jLbCr1Ans5f2nEJ1XJXcMgeyekzUDO2YvR7LdkcHQiKKhDz0OntBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:08:18.854897Z"},"content_sha256":"77f41e3712820679c2f4db093ebd049fc2c7c0e96254d48f46da00f58ae3dbea","schema_version":"1.0","event_id":"sha256:77f41e3712820679c2f4db093ebd049fc2c7c0e96254d48f46da00f58ae3dbea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7RFWQWCOCX6EBA3QEHGCPGPHH5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On base sizes for algebraic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Jan Saxl, Robert Guralnick, Timothy Burness","submitted_at":"2013-10-06T10:11:35Z","abstract_excerpt":"Let $G$ be a permutation group on a set $\\Omega$. A subset of $\\Omega$ is a base for $G$ if its pointwise stabilizer is trivial; the base size of $G$ is the minimal cardinality of a base. In this paper we initiate the study of bases for algebraic groups defined over an algebraically closed field. In particular, we calculate the base size for all primitive actions of simple algebraic groups, obtaining the precise value in almost all cases. We also introduce and study two new base measures, which arise naturally in this setting. We give an application concerning the essential dimension of simple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1569","kind":"arxiv","version":3},"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":"2026-05-18T00:45:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7tI/ObEbl4bzHohihu7UmjdkDbdp2VVsro62leavAL+mvYIgHOMx/tuvJa+Wxj/6Zm2L0fyOHAva4Q0kJCWkDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:08:18.855550Z"},"content_sha256":"7918c9bdef46a98f9e274fc5daa784d49988dc7390501c4024b9fef28c49acfe","schema_version":"1.0","event_id":"sha256:7918c9bdef46a98f9e274fc5daa784d49988dc7390501c4024b9fef28c49acfe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RFWQWCOCX6EBA3QEHGCPGPHH5/bundle.json","state_url":"https://pith.science/pith/7RFWQWCOCX6EBA3QEHGCPGPHH5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RFWQWCOCX6EBA3QEHGCPGPHH5/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":"2026-06-06T19:08:18Z","links":{"resolver":"https://pith.science/pith/7RFWQWCOCX6EBA3QEHGCPGPHH5","bundle":"https://pith.science/pith/7RFWQWCOCX6EBA3QEHGCPGPHH5/bundle.json","state":"https://pith.science/pith/7RFWQWCOCX6EBA3QEHGCPGPHH5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RFWQWCOCX6EBA3QEHGCPGPHH5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7RFWQWCOCX6EBA3QEHGCPGPHH5","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":"a59e3b7d0b096ee13ca75db6150eb4b61c6d6c8591b13cab623e0467c087ee76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-06T10:11:35Z","title_canon_sha256":"0dcf2bf585ea5dbfcc028b81a0de919ae398e44f5607c1dea379c24fd3d0f372"},"schema_version":"1.0","source":{"id":"1310.1569","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1569","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1569v3","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1569","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"pith_short_12","alias_value":"7RFWQWCOCX6E","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7RFWQWCOCX6EBA3Q","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7RFWQWCO","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:7918c9bdef46a98f9e274fc5daa784d49988dc7390501c4024b9fef28c49acfe","target":"graph","created_at":"2026-05-18T00:45:35Z","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 permutation group on a set $\\Omega$. A subset of $\\Omega$ is a base for $G$ if its pointwise stabilizer is trivial; the base size of $G$ is the minimal cardinality of a base. In this paper we initiate the study of bases for algebraic groups defined over an algebraically closed field. In particular, we calculate the base size for all primitive actions of simple algebraic groups, obtaining the precise value in almost all cases. We also introduce and study two new base measures, which arise naturally in this setting. We give an application concerning the essential dimension of simple","authors_text":"Jan Saxl, Robert Guralnick, Timothy Burness","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-06T10:11:35Z","title":"On base sizes for algebraic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1569","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":"sha256:77f41e3712820679c2f4db093ebd049fc2c7c0e96254d48f46da00f58ae3dbea","target":"record","created_at":"2026-05-18T00:45:35Z","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":"a59e3b7d0b096ee13ca75db6150eb4b61c6d6c8591b13cab623e0467c087ee76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-06T10:11:35Z","title_canon_sha256":"0dcf2bf585ea5dbfcc028b81a0de919ae398e44f5607c1dea379c24fd3d0f372"},"schema_version":"1.0","source":{"id":"1310.1569","kind":"arxiv","version":3}},"canonical_sha256":"fc4b68584e15fc40837021cc2799e73f5f69326f4feaad43f0105f09c6b39c72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc4b68584e15fc40837021cc2799e73f5f69326f4feaad43f0105f09c6b39c72","first_computed_at":"2026-05-18T00:45:35.425861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:35.425861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+GQcwSl2c0GoopyGA4jy1f/UPY3nZbX0UtQOXucplRETaBSD6LuBFGZR2IgZuQ+cOWsT9s8IMyKmq6VjnUP+BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:35.427054Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1569","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77f41e3712820679c2f4db093ebd049fc2c7c0e96254d48f46da00f58ae3dbea","sha256:7918c9bdef46a98f9e274fc5daa784d49988dc7390501c4024b9fef28c49acfe"],"state_sha256":"7fb75008ebeef285bf3a4dfdb8d288b70077d09303b6847deff5b782dfd6d452"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NYq/EMV596bMXp/b48I9pC/iGUWjE8sSPNGThvrRPQRmQUofSRGLkkfS+5JyCiJLcsx3VsWhYBp7j3vppHBcBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:08:18.858756Z","bundle_sha256":"b91d5f148bf844b918bb173557b9244c48436ea8ccf14b9eeb1a9787269fd968"}}