{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2NIC2HSORA3RGETRE52J2GOQUX","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":"7d0deced60c82b2a7cc072002141e3bb857bdb5439af912171b1fb498cb1b617","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-16T22:32:22Z","title_canon_sha256":"5995b1c573717b3a8f73f51fd39a7d96d576329ae25c2d9b154f37c7b46648b6"},"schema_version":"1.0","source":{"id":"1510.05039","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05039","created_at":"2026-05-18T01:11:21Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05039v2","created_at":"2026-05-18T01:11:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05039","created_at":"2026-05-18T01:11:21Z"},{"alias_kind":"pith_short_12","alias_value":"2NIC2HSORA3R","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2NIC2HSORA3RGETR","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2NIC2HSO","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:433c298626f54517dd54a6cb7833412f970712eb04da938ee6758dd1916c87a7","target":"graph","created_at":"2026-05-18T01:11:21Z","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":"Let $G = \\langle A,B \\rangle$ be a non-elementary two generator subgroup of the isometry group of $\\mathbb{H}^2$, the hyperbolic plane. If $G$ is discrete and free and geometrically finite, its quotient is a pair of pants and in prior work we produced a formula for the number of essential self intersections (ESIs) of any primitive geodesic on the quotient. An ESI is a point where the geodesic has a self-intersection on a seam. Self-intersections of geodesics on arbitrary hyperbolic surfaces have recently been studied by Basmajian and Chas. Here we extend our results to two generator subgroups ","authors_text":"Jane Gilman, Linda Keen","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-16T22:32:22Z","title":"Winding and Unwinding and Essential Intersections in $\\mathbb{H}^3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05039","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":"sha256:2664ba1900d6553a9622cfd8f59cac79050312524fac331c2ce180302fa53e05","target":"record","created_at":"2026-05-18T01:11:21Z","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":"7d0deced60c82b2a7cc072002141e3bb857bdb5439af912171b1fb498cb1b617","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-16T22:32:22Z","title_canon_sha256":"5995b1c573717b3a8f73f51fd39a7d96d576329ae25c2d9b154f37c7b46648b6"},"schema_version":"1.0","source":{"id":"1510.05039","kind":"arxiv","version":2}},"canonical_sha256":"d3502d1e4e883713127127749d19d0a5d0f75725d92f0898522a52d57ae00417","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3502d1e4e883713127127749d19d0a5d0f75725d92f0898522a52d57ae00417","first_computed_at":"2026-05-18T01:11:21.693952Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:21.693952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iGfbHqMO/E9T2V3xuyIdREqWx5sf6EVXD2QMXk08wggUOlsxADredWgrATUSYavO2RXoLPRs7d2FdxjzKHnqDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:21.694511Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.05039","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2664ba1900d6553a9622cfd8f59cac79050312524fac331c2ce180302fa53e05","sha256:433c298626f54517dd54a6cb7833412f970712eb04da938ee6758dd1916c87a7"],"state_sha256":"e33e4f628c12c1be33749828b6c0964577703963f1df798e668a2d9b9cc4f9c9"}