{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TO64EC2EOW22WNCPZUSSIJNFTZ","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":"cd8c5590a8238138d590820084d71f3bed3183295a267abe6928826a2d4bf72e","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-03-08T16:55:39Z","title_canon_sha256":"c8970b7f688182ccdc9d7f294ee4cb67dd6f419ed5e6f5d6bd82e0979c3df933"},"schema_version":"1.0","source":{"id":"1003.1672","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.1672","created_at":"2026-05-18T04:32:43Z"},{"alias_kind":"arxiv_version","alias_value":"1003.1672v2","created_at":"2026-05-18T04:32:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.1672","created_at":"2026-05-18T04:32:43Z"},{"alias_kind":"pith_short_12","alias_value":"TO64EC2EOW22","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TO64EC2EOW22WNCP","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TO64EC2E","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:d9439b6a09c7bf6b27eb30cd0b24a5dceec19308c7e52b11ddff975dd4907a93","target":"graph","created_at":"2026-05-18T04:32:43Z","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 characterize subgroups of the mapping class group that stabilize a Teichmueller disk in terms of ellipses and strips that are immersed in the associated translation surface. In particular, we show that the space of immersed ellipses/strips that meet at least three cone points is naturally a (non-manifold) 2-dimensional cell complex. The topology of this complex and the geometry of its 0-cells determine the translation surface and its affine diffeomorphism group (up to the kernel of the differential).","authors_text":"Chris Judge, S. Allen Broughton","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-03-08T16:55:39Z","title":"Ellipses in translation surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1672","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":"sha256:6fe828567a001e5e560620f0f0af0a00c4b96b00290e3c87f2900633a9be6009","target":"record","created_at":"2026-05-18T04:32:43Z","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":"cd8c5590a8238138d590820084d71f3bed3183295a267abe6928826a2d4bf72e","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-03-08T16:55:39Z","title_canon_sha256":"c8970b7f688182ccdc9d7f294ee4cb67dd6f419ed5e6f5d6bd82e0979c3df933"},"schema_version":"1.0","source":{"id":"1003.1672","kind":"arxiv","version":2}},"canonical_sha256":"9bbdc20b4475b5ab344fcd252425a59e5617fd950333ab21b1e3b2366e73eccd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bbdc20b4475b5ab344fcd252425a59e5617fd950333ab21b1e3b2366e73eccd","first_computed_at":"2026-05-18T04:32:43.580250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:43.580250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2/z8eXQMlxBS4BoYHLJeHtr0nxAq1lBt27TLZ1H/x33QiURncn+voojT6sM2AJvy1tCCfhL/kAiWSdQQi+QfAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:43.580923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.1672","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fe828567a001e5e560620f0f0af0a00c4b96b00290e3c87f2900633a9be6009","sha256:d9439b6a09c7bf6b27eb30cd0b24a5dceec19308c7e52b11ddff975dd4907a93"],"state_sha256":"549499a27a27b2792d636d46e6dfc73932736db1af57ff8137e431fdc6c1fa4e"}