{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:AZKFRF6R2OQEYD244SGKJG4B2Q","short_pith_number":"pith:AZKFRF6R","canonical_record":{"source":{"id":"1309.5584","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-22T10:03:36Z","cross_cats_sorted":[],"title_canon_sha256":"71c66f56af3818175430fc6974c5c7fae52b1da3a3bf8f7f29156b3a3a321799","abstract_canon_sha256":"409e5de59e2313dc766043c431df099514a3d7e29891ec91135d7abaef468274"},"schema_version":"1.0"},"canonical_sha256":"06545897d1d3a04c0f5ce48ca49b81d4352beaf379dad36fc0ab7b046dcb2ee3","source":{"kind":"arxiv","id":"1309.5584","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5584","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5584v2","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5584","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"AZKFRF6R2OQE","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AZKFRF6R2OQEYD24","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AZKFRF6R","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:AZKFRF6R2OQEYD244SGKJG4B2Q","target":"record","payload":{"canonical_record":{"source":{"id":"1309.5584","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-22T10:03:36Z","cross_cats_sorted":[],"title_canon_sha256":"71c66f56af3818175430fc6974c5c7fae52b1da3a3bf8f7f29156b3a3a321799","abstract_canon_sha256":"409e5de59e2313dc766043c431df099514a3d7e29891ec91135d7abaef468274"},"schema_version":"1.0"},"canonical_sha256":"06545897d1d3a04c0f5ce48ca49b81d4352beaf379dad36fc0ab7b046dcb2ee3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:54.315336Z","signature_b64":"RWQMGmstts08AnCh9JjHjFyVE5z9Q0vanTFisQ3GYvIoABtVWqdMVfvdbzSykV04+S2hqmruUHb+yk57UJR2Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06545897d1d3a04c0f5ce48ca49b81d4352beaf379dad36fc0ab7b046dcb2ee3","last_reissued_at":"2026-05-18T03:06:54.314630Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:54.314630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.5584","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:06:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yXfO5fClmqZLFBfN9+X2mY/xDVb4iU5w0KQ22+A7ZQuzCX9/Yh3GvcU5hUZQz+3UwYyR8ZthlEspdgPYAxUyDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:38:31.217695Z"},"content_sha256":"9d862fd2b90835e229d746ec17aabc717ce7537bee1baec0f7e6c0bbcaee4ba8","schema_version":"1.0","event_id":"sha256:9d862fd2b90835e229d746ec17aabc717ce7537bee1baec0f7e6c0bbcaee4ba8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:AZKFRF6R2OQEYD244SGKJG4B2Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Pyber's base size conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"\\'Akos Seress, Timothy Burness","submitted_at":"2013-09-22T10:03:36Z","abstract_excerpt":"Let $G$ be a permutation group on a finite set $\\Omega$. A subset $B \\subseteq \\Omega$ is a base for $G$ if the pointwise stabilizer of $B$ in $G$ is trivial. The base size of $G$, denoted $b(G)$, is the smallest size of a base. A well known conjecture of Pyber from the early 1990s asserts that there exists an absolute constant $c$ such that $b(G) \\le c\\log |G| / \\log n$ for any primitive permutation group $G$ of degree $n$. Some special cases have been verified in recent years, including the almost simple and diagonal cases. In this paper, we prove Pyber's conjecture for all non-affine primit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5584","kind":"arxiv","version":2},"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":"2026-05-18T03:06:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/i7Z34zZ/+5aikJRRoPdwny1JHwOjyTxOaOslCx+RYc6Z6t59ahSiVmkPDi4UCWH/00HKEPbEcHc6w2uKPBFDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:38:31.218374Z"},"content_sha256":"036a36ef149b75ee5013033fa489aee096047d4139d8cbcf7861124ad4021834","schema_version":"1.0","event_id":"sha256:036a36ef149b75ee5013033fa489aee096047d4139d8cbcf7861124ad4021834"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AZKFRF6R2OQEYD244SGKJG4B2Q/bundle.json","state_url":"https://pith.science/pith/AZKFRF6R2OQEYD244SGKJG4B2Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AZKFRF6R2OQEYD244SGKJG4B2Q/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":"2026-06-08T18:38:31Z","links":{"resolver":"https://pith.science/pith/AZKFRF6R2OQEYD244SGKJG4B2Q","bundle":"https://pith.science/pith/AZKFRF6R2OQEYD244SGKJG4B2Q/bundle.json","state":"https://pith.science/pith/AZKFRF6R2OQEYD244SGKJG4B2Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AZKFRF6R2OQEYD244SGKJG4B2Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AZKFRF6R2OQEYD244SGKJG4B2Q","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":"409e5de59e2313dc766043c431df099514a3d7e29891ec91135d7abaef468274","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-22T10:03:36Z","title_canon_sha256":"71c66f56af3818175430fc6974c5c7fae52b1da3a3bf8f7f29156b3a3a321799"},"schema_version":"1.0","source":{"id":"1309.5584","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5584","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5584v2","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5584","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"AZKFRF6R2OQE","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AZKFRF6R2OQEYD24","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AZKFRF6R","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:036a36ef149b75ee5013033fa489aee096047d4139d8cbcf7861124ad4021834","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":"Let $G$ be a permutation group on a finite set $\\Omega$. A subset $B \\subseteq \\Omega$ is a base for $G$ if the pointwise stabilizer of $B$ in $G$ is trivial. The base size of $G$, denoted $b(G)$, is the smallest size of a base. A well known conjecture of Pyber from the early 1990s asserts that there exists an absolute constant $c$ such that $b(G) \\le c\\log |G| / \\log n$ for any primitive permutation group $G$ of degree $n$. Some special cases have been verified in recent years, including the almost simple and diagonal cases. In this paper, we prove Pyber's conjecture for all non-affine primit","authors_text":"\\'Akos Seress, Timothy Burness","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-22T10:03:36Z","title":"On Pyber's base size conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5584","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":"sha256:9d862fd2b90835e229d746ec17aabc717ce7537bee1baec0f7e6c0bbcaee4ba8","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":"409e5de59e2313dc766043c431df099514a3d7e29891ec91135d7abaef468274","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-22T10:03:36Z","title_canon_sha256":"71c66f56af3818175430fc6974c5c7fae52b1da3a3bf8f7f29156b3a3a321799"},"schema_version":"1.0","source":{"id":"1309.5584","kind":"arxiv","version":2}},"canonical_sha256":"06545897d1d3a04c0f5ce48ca49b81d4352beaf379dad36fc0ab7b046dcb2ee3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06545897d1d3a04c0f5ce48ca49b81d4352beaf379dad36fc0ab7b046dcb2ee3","first_computed_at":"2026-05-18T03:06:54.314630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:54.314630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RWQMGmstts08AnCh9JjHjFyVE5z9Q0vanTFisQ3GYvIoABtVWqdMVfvdbzSykV04+S2hqmruUHb+yk57UJR2Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:54.315336Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5584","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d862fd2b90835e229d746ec17aabc717ce7537bee1baec0f7e6c0bbcaee4ba8","sha256:036a36ef149b75ee5013033fa489aee096047d4139d8cbcf7861124ad4021834"],"state_sha256":"af424de2e44bd07de4b5037e4fce5844c1e82d6fd4182a4caa90cf41987bf9e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gk4+HWSxHRh5yvyX7UHo0N8eR+r9AhjFmA/m0QkLC4QO453ic9/TNy/Vt60D43owwrGzkeWQERXYZveQkSzOBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T18:38:31.221938Z","bundle_sha256":"799a2a3ee4a40691237ee4d0b3b04762c1e841a880af66734a704b8303ad5808"}}