{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4XD5QKD5YDIPLB7IZYMCWM3MLN","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":"36182977c0aec380c3eb35913ff992e62c11ffec38854c20571b464b28e1c2fc","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-01-18T12:51:48Z","title_canon_sha256":"8befae455b7ecdb815bdbca46d56f5f1010723445b69112d42abf23ecff664ff"},"schema_version":"1.0","source":{"id":"1301.4369","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4369","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4369v1","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4369","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"pith_short_12","alias_value":"4XD5QKD5YDIP","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4XD5QKD5YDIPLB7I","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4XD5QKD5","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:60958908aba02d9dbb6e0c421fe6332959f12b62499d0e60363ccee21cdc1104","target":"graph","created_at":"2026-05-18T01:22:25Z","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":"We prove that if $M \\longrightarrow P$ is a small cover of a compact right-angled hyperbolic polyhedron $P$ then $M$ admits a cofinal tower of finite sheeted covers with positive rank gradient. As a corollary, if $\\pi_1(M)$ is commensurable with the reflection group of $P$, then $M$ admits a cofinal tower of finite sheeted covers with positive rank gradient.","authors_text":"Darlan Gir\\~ao","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-01-18T12:51:48Z","title":"Rank gradient of small covers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4369","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":"sha256:495866927fc57f7fa783c2b5f560ef6d364dbb372331271b1cce265edb672539","target":"record","created_at":"2026-05-18T01:22:25Z","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":"36182977c0aec380c3eb35913ff992e62c11ffec38854c20571b464b28e1c2fc","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-01-18T12:51:48Z","title_canon_sha256":"8befae455b7ecdb815bdbca46d56f5f1010723445b69112d42abf23ecff664ff"},"schema_version":"1.0","source":{"id":"1301.4369","kind":"arxiv","version":1}},"canonical_sha256":"e5c7d8287dc0d0f587e8ce182b336c5b7206ab96c7f803b192db0863822a92f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5c7d8287dc0d0f587e8ce182b336c5b7206ab96c7f803b192db0863822a92f9","first_computed_at":"2026-05-18T01:22:25.801079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:25.801079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PxukU5M0Dqiy6fq1PjPNFmL8aB+sMsXIarHVbEuaOeFt1nkgKLRHaRzU4OikRG2uVNcw2EQ8t6K5ENWjqeoLAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:25.801774Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.4369","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:495866927fc57f7fa783c2b5f560ef6d364dbb372331271b1cce265edb672539","sha256:60958908aba02d9dbb6e0c421fe6332959f12b62499d0e60363ccee21cdc1104"],"state_sha256":"7ce52bf94d8f7fdf43fbe720c493c31126eb818e555b5205908b85f937015bbc"}