{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BBJZK4E4K4KVC6HE2OO63SDXZA","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":"ff75ea7b0b4adeaf5d7a2531237b7a01c11abca330b11800362252c28b8dd0b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-10-01T13:41:09Z","title_canon_sha256":"07bbcb82a28b422436bb31badce906d4b6fd1c66a131b38c47fd5b6b575e02e5"},"schema_version":"1.0","source":{"id":"1810.00703","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00703","created_at":"2026-05-18T00:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00703v1","created_at":"2026-05-18T00:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00703","created_at":"2026-05-18T00:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"BBJZK4E4K4KV","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"BBJZK4E4K4KVC6HE","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"BBJZK4E4","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:c741d35d2e20774c09bfa9d8c0a9fcfb6b485f461d506d451bcb0480450920e9","target":"graph","created_at":"2026-05-18T00:04:25Z","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":"This is a short introduction (in Spanish) to the study of growth in finite groups, with SL_2 as an example. Emphasis is put on developments of the decade 2005--2015, originating partly in combinatorics. Little algebraic-geometrical background is assumed, but the proofs are nevertheless presented in a relatively abstract and generalizable way.","authors_text":"Harald Andres Helfgott","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-10-01T13:41:09Z","title":"Crecimiento y expansion en SL_2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00703","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:d7abfb8c27af27423ff02a7351dddb2461d52b41850032c698e515bb64da46cf","target":"record","created_at":"2026-05-18T00:04:25Z","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":"ff75ea7b0b4adeaf5d7a2531237b7a01c11abca330b11800362252c28b8dd0b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-10-01T13:41:09Z","title_canon_sha256":"07bbcb82a28b422436bb31badce906d4b6fd1c66a131b38c47fd5b6b575e02e5"},"schema_version":"1.0","source":{"id":"1810.00703","kind":"arxiv","version":1}},"canonical_sha256":"085395709c57155178e4d39dedc877c83f9628b42194769c7f07833787123c99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"085395709c57155178e4d39dedc877c83f9628b42194769c7f07833787123c99","first_computed_at":"2026-05-18T00:04:25.057400Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:25.057400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KttHiO+e0IUBgZoPJyd/Q0EsGkQ1QdAo8R0iEmN1q7IveOc8xCB6FHSrkOkd7+WCeus13VtbC73MB5mryA3ZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:25.057905Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.00703","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7abfb8c27af27423ff02a7351dddb2461d52b41850032c698e515bb64da46cf","sha256:c741d35d2e20774c09bfa9d8c0a9fcfb6b485f461d506d451bcb0480450920e9"],"state_sha256":"7f1f10443b6e9b6eae7b3cbf7a2913b70a66282bcf9eca6f7c8e2995be1ebeab"}