{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1998:4T4N3KDYTPITXLLLECB3KESYMP","short_pith_number":"pith:4T4N3KDY","schema_version":"1.0","canonical_sha256":"e4f8dda8789bd13bad6b2083b5125863e96feb6d8263c6ab2b914982d1b2a7c7","source":{"kind":"arxiv","id":"math/9801039","version":1},"attestation_state":"computed","paper":{"title":"Minimal stretch maps between hyperbolic surfaces","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"William P. Thurston","submitted_at":"1998-01-09T18:15:11Z","abstract_excerpt":"This paper develops a theory of Lipschitz comparisons of hyperbolic surfaces analogous to the theory of quasi-conformal comparisons. Extremal Lipschitz maps (minimal stretch maps) and geodesics for the `Lipschitz metric' are constructed. The extremal Lipschitz constant equals the maximum ratio of lengths of measured laminations, which is attained with probability one on a simple closed curve. Cataclysms are introduced, generalizing earthquakes by permitting more violent shearing in both directions along a fault. Cataclysms provide useful coordinates for Teichmuller space that are convenient fo"},"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":"math/9801039","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"1998-01-09T18:15:11Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"ddb3edbd108f13d3128c76929e18acc1123cde3c3d22a6d24f99511ff480c563","abstract_canon_sha256":"ff8ad6c76f05254d2d17802e395c6e78de32382284408cc796b9adfbb741f498"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:40:24.947332Z","signature_b64":"gFj9AVjSdfxHx3uKXlKjukRNGBsTwtVKQxAg38gaCqao3ntvme6s7zXZ0fNTuHk5YbFJoRC/PZzlbHCkPEUoDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4f8dda8789bd13bad6b2083b5125863e96feb6d8263c6ab2b914982d1b2a7c7","last_reissued_at":"2026-07-04T14:40:24.946904Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:40:24.946904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal stretch maps between hyperbolic surfaces","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"William P. Thurston","submitted_at":"1998-01-09T18:15:11Z","abstract_excerpt":"This paper develops a theory of Lipschitz comparisons of hyperbolic surfaces analogous to the theory of quasi-conformal comparisons. Extremal Lipschitz maps (minimal stretch maps) and geodesics for the `Lipschitz metric' are constructed. The extremal Lipschitz constant equals the maximum ratio of lengths of measured laminations, which is attained with probability one on a simple closed curve. Cataclysms are introduced, generalizing earthquakes by permitting more violent shearing in both directions along a fault. Cataclysms provide useful coordinates for Teichmuller space that are convenient fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9801039","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/9801039/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math/9801039","created_at":"2026-07-04T14:40:24.946963+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9801039v1","created_at":"2026-07-04T14:40:24.946963+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9801039","created_at":"2026-07-04T14:40:24.946963+00:00"},{"alias_kind":"pith_short_12","alias_value":"4T4N3KDYTPIT","created_at":"2026-07-04T14:40:24.946963+00:00"},{"alias_kind":"pith_short_16","alias_value":"4T4N3KDYTPITXLLL","created_at":"2026-07-04T14:40:24.946963+00:00"},{"alias_kind":"pith_short_8","alias_value":"4T4N3KDY","created_at":"2026-07-04T14:40:24.946963+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2607.07150","citing_title":"On 4-dimensional convex projective domains invariant by a lattice of $\\mathrm{SL}_2 (\\mathbb{R})$","ref_index":196,"is_internal_anchor":true},{"citing_arxiv_id":"2606.10897","citing_title":"A characterisation of $\\infty$-harmonic maps in terms of $1$-currents","ref_index":48,"is_internal_anchor":true},{"citing_arxiv_id":"2605.04614","citing_title":"Counting Minimal Lagrangians Via Mirzakhani Functions","ref_index":40,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4T4N3KDYTPITXLLLECB3KESYMP","json":"https://pith.science/pith/4T4N3KDYTPITXLLLECB3KESYMP.json","graph_json":"https://pith.science/api/pith-number/4T4N3KDYTPITXLLLECB3KESYMP/graph.json","events_json":"https://pith.science/api/pith-number/4T4N3KDYTPITXLLLECB3KESYMP/events.json","paper":"https://pith.science/paper/4T4N3KDY"},"agent_actions":{"view_html":"https://pith.science/pith/4T4N3KDYTPITXLLLECB3KESYMP","download_json":"https://pith.science/pith/4T4N3KDYTPITXLLLECB3KESYMP.json","view_paper":"https://pith.science/paper/4T4N3KDY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9801039&json=true","fetch_graph":"https://pith.science/api/pith-number/4T4N3KDYTPITXLLLECB3KESYMP/graph.json","fetch_events":"https://pith.science/api/pith-number/4T4N3KDYTPITXLLLECB3KESYMP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4T4N3KDYTPITXLLLECB3KESYMP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4T4N3KDYTPITXLLLECB3KESYMP/action/storage_attestation","attest_author":"https://pith.science/pith/4T4N3KDYTPITXLLLECB3KESYMP/action/author_attestation","sign_citation":"https://pith.science/pith/4T4N3KDYTPITXLLLECB3KESYMP/action/citation_signature","submit_replication":"https://pith.science/pith/4T4N3KDYTPITXLLLECB3KESYMP/action/replication_record"}},"created_at":"2026-07-04T14:40:24.946963+00:00","updated_at":"2026-07-04T14:40:24.946963+00:00"}