{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7FJOGEINVB3RK2MLRC6YVYYSS5","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":"7e23339dc5def27d79de5368e9681c970b4add791ce3a25bdff2d5a5dfcb8d09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-11-13T18:42:38Z","title_canon_sha256":"cfeb98de23c18e80dc1399f2b3b1265e08d9dda4beebfa13251050474fba5597"},"schema_version":"1.0","source":{"id":"2511.10606","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.10606","created_at":"2026-05-22T01:03:49Z"},{"alias_kind":"arxiv_version","alias_value":"2511.10606v2","created_at":"2026-05-22T01:03:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.10606","created_at":"2026-05-22T01:03:49Z"},{"alias_kind":"pith_short_12","alias_value":"7FJOGEINVB3R","created_at":"2026-05-22T01:03:49Z"},{"alias_kind":"pith_short_16","alias_value":"7FJOGEINVB3RK2ML","created_at":"2026-05-22T01:03:49Z"},{"alias_kind":"pith_short_8","alias_value":"7FJOGEIN","created_at":"2026-05-22T01:03:49Z"}],"graph_snapshots":[{"event_id":"sha256:f5976f4514e4e6a359371149565c03fbf99077c01b17776d2863ee34268e5334","target":"graph","created_at":"2026-05-22T01:03:49Z","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/2511.10606/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we provide an explicit construction of continuous paths of $\\mathrm{SL}_2(\\mathbb R)$-representations of the knot groups of $(-2,3,2n+1)$-pretzel knots. As an application, we show that the fundamental group of the $3$-manifold obtained from the $3$-sphere by $\\frac{m}{l}$-surgery along the $(-2,3,2n+1)$-pretzel knot, where $n \\ge 3$ is an integer and $n \\not= 4$, is left-orderable if $\\frac{m}{l}< 2 \\lfloor \\frac{2n+4}{3} \\rfloor$.","authors_text":"Anh T. Tran","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-11-13T18:42:38Z","title":"$\\mathrm{SL}_2(\\mathbb R)$-representations and left-orderable surgeries of $(-2, 3, 2n+1)$-pretzel knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.10606","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":"sha256:5e58db711b45e7477335b2a8e2b64048177bd48b39e99cac8ad830afe155adf9","target":"record","created_at":"2026-05-22T01:03:49Z","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":"7e23339dc5def27d79de5368e9681c970b4add791ce3a25bdff2d5a5dfcb8d09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-11-13T18:42:38Z","title_canon_sha256":"cfeb98de23c18e80dc1399f2b3b1265e08d9dda4beebfa13251050474fba5597"},"schema_version":"1.0","source":{"id":"2511.10606","kind":"arxiv","version":2}},"canonical_sha256":"f952e3110da87715698b88bd8ae312976836cae4d65ba52e27106b6a3c2353bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f952e3110da87715698b88bd8ae312976836cae4d65ba52e27106b6a3c2353bf","first_computed_at":"2026-05-22T01:03:49.595082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:03:49.595082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zVrGovvOwas9zBf4qfp4WGI4zbYOX7AdtOGJaDR66Bt+73ffmcniTgH+w9jMOKp1aLWTe3AY6R1SkTJv+EhMAQ==","signature_status":"signed_v1","signed_at":"2026-05-22T01:03:49.595941Z","signed_message":"canonical_sha256_bytes"},"source_id":"2511.10606","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e58db711b45e7477335b2a8e2b64048177bd48b39e99cac8ad830afe155adf9","sha256:f5976f4514e4e6a359371149565c03fbf99077c01b17776d2863ee34268e5334"],"state_sha256":"c2df64f90a970498d889f9386c5a55367b9a9d1fc5f17728f1d2e20e2c60d27b"}