{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:VRILOZCWPY5AXLFTCE4SITWEJQ","short_pith_number":"pith:VRILOZCW","schema_version":"1.0","canonical_sha256":"ac50b764567e3a0bacb31139244ec44c29c70b6bd091fe7c0027b086168ff793","source":{"kind":"arxiv","id":"1412.8559","version":1},"attestation_state":"computed","paper":{"title":"Elliptic actions on Teichmuller space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Matthew Gentry Durham","submitted_at":"2014-12-30T04:04:52Z","abstract_excerpt":"Let $S$ be an oriented surface of finite type, $\\mathcal{MCG}(S)$ its mapping class group, and $\\mathcal{T}(S)$ its Teichm\\\"uller space with the Teichm\\\"uller metric. Let $H \\leq \\mathcal{MCG}(S)$ be a finite subgroup and consider the subset of $\\mathcal{T}(S)$ fixed by $H$, $\\mathrm{Fix}(H) \\subset \\mathcal{T}(S)$. For any $R>0$, we prove that the set of points whose $H$-orbits have diameter bounded by $R$, $\\mathrm{Fix}_R^T(H)$, lives in a bounded neighborhood of $\\mathrm{Fix}(H)$. As an application, we show that the orbit of any point $X \\in \\mathcal{T}(S)$ under the action of a finite orde"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1412.8559","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-12-30T04:04:52Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"13c309067ef2f94bf5eb9dc987ff00b5bdd6bc6e718c028418899f1876cb6d8a","abstract_canon_sha256":"6a616f22fc5055c2d3f6da4737d9898e6a9c4d35ba362c11543a3e9f30f65ca2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:17.061347Z","signature_b64":"T6Xqiv9sMFbWHT3AGDZC2o2oDtjNohe3QhUlLQwDXet+SVUA+N1WK9rMpjS/ciVyREUeir9LOL+0T17Yt4AJAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac50b764567e3a0bacb31139244ec44c29c70b6bd091fe7c0027b086168ff793","last_reissued_at":"2026-05-18T02:30:17.060897Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:17.060897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Elliptic actions on Teichmuller space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Matthew Gentry Durham","submitted_at":"2014-12-30T04:04:52Z","abstract_excerpt":"Let $S$ be an oriented surface of finite type, $\\mathcal{MCG}(S)$ its mapping class group, and $\\mathcal{T}(S)$ its Teichm\\\"uller space with the Teichm\\\"uller metric. Let $H \\leq \\mathcal{MCG}(S)$ be a finite subgroup and consider the subset of $\\mathcal{T}(S)$ fixed by $H$, $\\mathrm{Fix}(H) \\subset \\mathcal{T}(S)$. For any $R>0$, we prove that the set of points whose $H$-orbits have diameter bounded by $R$, $\\mathrm{Fix}_R^T(H)$, lives in a bounded neighborhood of $\\mathrm{Fix}(H)$. As an application, we show that the orbit of any point $X \\in \\mathcal{T}(S)$ under the action of a finite orde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8559","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1412.8559","created_at":"2026-05-18T02:30:17.060962+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.8559v1","created_at":"2026-05-18T02:30:17.060962+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.8559","created_at":"2026-05-18T02:30:17.060962+00:00"},{"alias_kind":"pith_short_12","alias_value":"VRILOZCWPY5A","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"VRILOZCWPY5AXLFT","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"VRILOZCW","created_at":"2026-05-18T12:28:54.890064+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VRILOZCWPY5AXLFTCE4SITWEJQ","json":"https://pith.science/pith/VRILOZCWPY5AXLFTCE4SITWEJQ.json","graph_json":"https://pith.science/api/pith-number/VRILOZCWPY5AXLFTCE4SITWEJQ/graph.json","events_json":"https://pith.science/api/pith-number/VRILOZCWPY5AXLFTCE4SITWEJQ/events.json","paper":"https://pith.science/paper/VRILOZCW"},"agent_actions":{"view_html":"https://pith.science/pith/VRILOZCWPY5AXLFTCE4SITWEJQ","download_json":"https://pith.science/pith/VRILOZCWPY5AXLFTCE4SITWEJQ.json","view_paper":"https://pith.science/paper/VRILOZCW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.8559&json=true","fetch_graph":"https://pith.science/api/pith-number/VRILOZCWPY5AXLFTCE4SITWEJQ/graph.json","fetch_events":"https://pith.science/api/pith-number/VRILOZCWPY5AXLFTCE4SITWEJQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VRILOZCWPY5AXLFTCE4SITWEJQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VRILOZCWPY5AXLFTCE4SITWEJQ/action/storage_attestation","attest_author":"https://pith.science/pith/VRILOZCWPY5AXLFTCE4SITWEJQ/action/author_attestation","sign_citation":"https://pith.science/pith/VRILOZCWPY5AXLFTCE4SITWEJQ/action/citation_signature","submit_replication":"https://pith.science/pith/VRILOZCWPY5AXLFTCE4SITWEJQ/action/replication_record"}},"created_at":"2026-05-18T02:30:17.060962+00:00","updated_at":"2026-05-18T02:30:17.060962+00:00"}