{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:WQU7DUZITNXSWFBASBY3HLDPKE","short_pith_number":"pith:WQU7DUZI","schema_version":"1.0","canonical_sha256":"b429f1d3289b6f2b14209071b3ac6f510184bb7d99113b0d8d23b38aa1c9af86","source":{"kind":"arxiv","id":"1506.04774","version":1},"attestation_state":"computed","paper":{"title":"Rigidity of Teichm\\\"uller space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Alex Eskin, Howard Masur, Kasra Rafi","submitted_at":"2015-06-15T21:08:24Z","abstract_excerpt":"We prove that the every quasi-isometry of Teichm\\\"uller space equipped with the Teichm\\\"uller metric is a bounded distance from an isometry of Teichm\\\"uller space. That is, Teichm\\\"uller space is quasi-isometrically rigid."},"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":"1506.04774","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-06-15T21:08:24Z","cross_cats_sorted":[],"title_canon_sha256":"3b771a6bc630994e42b9fe1f6932d5e48deacb90b390c00f041bbf823023511e","abstract_canon_sha256":"412afffba44e2eab736beda1c598a0ff87038354ebda6275aa2b1f828618ceba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:05.970736Z","signature_b64":"z8grhkI9eSe2VpeW2dTrNQr0vL0uIV8bVU/kyG10w5E2xrWrwzyoOAXDDVbQ2/j3Ig6DRRxQ6vLJEIuVRWVNBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b429f1d3289b6f2b14209071b3ac6f510184bb7d99113b0d8d23b38aa1c9af86","last_reissued_at":"2026-05-17T23:58:05.970191Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:05.970191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigidity of Teichm\\\"uller space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Alex Eskin, Howard Masur, Kasra Rafi","submitted_at":"2015-06-15T21:08:24Z","abstract_excerpt":"We prove that the every quasi-isometry of Teichm\\\"uller space equipped with the Teichm\\\"uller metric is a bounded distance from an isometry of Teichm\\\"uller space. That is, Teichm\\\"uller space is quasi-isometrically rigid."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04774","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":"1506.04774","created_at":"2026-05-17T23:58:05.970270+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.04774v1","created_at":"2026-05-17T23:58:05.970270+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04774","created_at":"2026-05-17T23:58:05.970270+00:00"},{"alias_kind":"pith_short_12","alias_value":"WQU7DUZITNXS","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"WQU7DUZITNXSWFBA","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"WQU7DUZI","created_at":"2026-05-18T12:29:47.479230+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/WQU7DUZITNXSWFBASBY3HLDPKE","json":"https://pith.science/pith/WQU7DUZITNXSWFBASBY3HLDPKE.json","graph_json":"https://pith.science/api/pith-number/WQU7DUZITNXSWFBASBY3HLDPKE/graph.json","events_json":"https://pith.science/api/pith-number/WQU7DUZITNXSWFBASBY3HLDPKE/events.json","paper":"https://pith.science/paper/WQU7DUZI"},"agent_actions":{"view_html":"https://pith.science/pith/WQU7DUZITNXSWFBASBY3HLDPKE","download_json":"https://pith.science/pith/WQU7DUZITNXSWFBASBY3HLDPKE.json","view_paper":"https://pith.science/paper/WQU7DUZI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.04774&json=true","fetch_graph":"https://pith.science/api/pith-number/WQU7DUZITNXSWFBASBY3HLDPKE/graph.json","fetch_events":"https://pith.science/api/pith-number/WQU7DUZITNXSWFBASBY3HLDPKE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WQU7DUZITNXSWFBASBY3HLDPKE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WQU7DUZITNXSWFBASBY3HLDPKE/action/storage_attestation","attest_author":"https://pith.science/pith/WQU7DUZITNXSWFBASBY3HLDPKE/action/author_attestation","sign_citation":"https://pith.science/pith/WQU7DUZITNXSWFBASBY3HLDPKE/action/citation_signature","submit_replication":"https://pith.science/pith/WQU7DUZITNXSWFBASBY3HLDPKE/action/replication_record"}},"created_at":"2026-05-17T23:58:05.970270+00:00","updated_at":"2026-05-17T23:58:05.970270+00:00"}