{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QFS26YBG6PA3YVSPCKETWY5TOR","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":"12fa8fd257265cb2d6f1ea659df3cc5da37c2cf9166f32b80f6abf38fabe12ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-08-13T09:57:21Z","title_canon_sha256":"9f05286e4f0957899b19d7072fb5ed49717b8d5f201ad223b6cb574bf9ea944b"},"schema_version":"1.0","source":{"id":"1208.2538","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2538","created_at":"2026-05-18T03:48:57Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2538v1","created_at":"2026-05-18T03:48:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2538","created_at":"2026-05-18T03:48:57Z"},{"alias_kind":"pith_short_12","alias_value":"QFS26YBG6PA3","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QFS26YBG6PA3YVSP","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QFS26YBG","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:9051b719ac49e4629a5491ec07a3082bb1a3a42ecb810f6c5151105d3682065f","target":"graph","created_at":"2026-05-18T03:48:57Z","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 give a description of non-growing subsets in linear groups, which extends the Product theorem for simple groups of Lie type. We also give an account of various related aspects of growth in linear groups.","authors_text":"Endre Szab\\'o, L\\'aszl\\'o Pyber","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-08-13T09:57:21Z","title":"Growth in linear groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2538","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:dfa0c8fa3a0db230747e37832fb28f0c6da71c7fc4620bc583a1015bf2914385","target":"record","created_at":"2026-05-18T03:48:57Z","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":"12fa8fd257265cb2d6f1ea659df3cc5da37c2cf9166f32b80f6abf38fabe12ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-08-13T09:57:21Z","title_canon_sha256":"9f05286e4f0957899b19d7072fb5ed49717b8d5f201ad223b6cb574bf9ea944b"},"schema_version":"1.0","source":{"id":"1208.2538","kind":"arxiv","version":1}},"canonical_sha256":"8165af6026f3c1bc564f12893b63b3745cea790a5e5991d2864917324b3990b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8165af6026f3c1bc564f12893b63b3745cea790a5e5991d2864917324b3990b1","first_computed_at":"2026-05-18T03:48:57.590667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:57.590667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SD01WMyJbuRMQOGxRltglyiAooXKJ72XMtoS5o5TiopvknM2uaQXengXiDaugQD8FH1TUIBm+ngrltdN1qP8AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:57.591369Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2538","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfa0c8fa3a0db230747e37832fb28f0c6da71c7fc4620bc583a1015bf2914385","sha256:9051b719ac49e4629a5491ec07a3082bb1a3a42ecb810f6c5151105d3682065f"],"state_sha256":"e93c1324f6299f44b3330c76f32bc622ff4742675d4e8e9d49a1df36d546c553"}