{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PFVKN3TCIQ2RQ3W3G5WM6NNYEI","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":"d2cc6039e2a55aeb614dc00b8b9f075406e904557fdc77f44bf642c4909ae553","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-29T09:17:45Z","title_canon_sha256":"d0b96ea6a8d907baca0c8357e0dae050875a7f48ce3fd986e092c6fc0d40a72f"},"schema_version":"1.0","source":{"id":"1908.11114","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.11114","created_at":"2026-07-05T00:42:52Z"},{"alias_kind":"arxiv_version","alias_value":"1908.11114v3","created_at":"2026-07-05T00:42:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.11114","created_at":"2026-07-05T00:42:52Z"},{"alias_kind":"pith_short_12","alias_value":"PFVKN3TCIQ2R","created_at":"2026-07-05T00:42:52Z"},{"alias_kind":"pith_short_16","alias_value":"PFVKN3TCIQ2RQ3W3","created_at":"2026-07-05T00:42:52Z"},{"alias_kind":"pith_short_8","alias_value":"PFVKN3TC","created_at":"2026-07-05T00:42:52Z"}],"graph_snapshots":[{"event_id":"sha256:d14300fedcf7323bac1c9a353ab1898e5a7e6ee941e136a37a4a506e8d6c4abf","target":"graph","created_at":"2026-07-05T00:42:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.11114/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a practical algorithm which, given a non-archimedean local field $K$ and any two elements $A,B\\in {\\rm SL_2}(K)$, determines after finitely many steps whether or not the subgroup $\\langle A, B \\rangle\\le {\\rm SL_2}(K)$ is discrete and free of rank two. This makes use of the Ping Pong Lemma applied to the action of ${\\rm SL_2}(K)$ by isometries on its Bruhat-Tits tree. The algorithm itself can also be used for two-generated subgroups of the isometry group of any locally finite simplicial tree, and has applications to the constructive membership problem. In an appendix joint with Fr\\'","authors_text":"Matthew J. Conder","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-29T09:17:45Z","title":"Discrete and free two-generated subgroups of ${\\rm SL_2}$ over non-archimedean local fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.11114","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":"sha256:7c05a736cc1f414c9fbca7f2a569f697127439d6a861092417baef0175bf5b45","target":"record","created_at":"2026-07-05T00:42:52Z","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":"d2cc6039e2a55aeb614dc00b8b9f075406e904557fdc77f44bf642c4909ae553","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-29T09:17:45Z","title_canon_sha256":"d0b96ea6a8d907baca0c8357e0dae050875a7f48ce3fd986e092c6fc0d40a72f"},"schema_version":"1.0","source":{"id":"1908.11114","kind":"arxiv","version":3}},"canonical_sha256":"796aa6ee624435186edb376ccf35b8223b8e6cb9338feaf3198099d287f29431","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"796aa6ee624435186edb376ccf35b8223b8e6cb9338feaf3198099d287f29431","first_computed_at":"2026-07-05T00:42:52.837840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:42:52.837840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zg3HDW/xYk9KroffqbxVkxaZQL6xe16Ki8FH6CtfqVLZ2zYm92t0DAg0NgS/Kdnx1DJUVByiaB+fkTrVsITHDA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:42:52.838293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.11114","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c05a736cc1f414c9fbca7f2a569f697127439d6a861092417baef0175bf5b45","sha256:d14300fedcf7323bac1c9a353ab1898e5a7e6ee941e136a37a4a506e8d6c4abf"],"state_sha256":"9faf7aee705c12c8164ee09e6a9e0b7b031b66ccd44849bbc67d50b315b3eb06"}