{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:WWGW7QQ5ESF6GLU6JHYISJKEBS","short_pith_number":"pith:WWGW7QQ5","schema_version":"1.0","canonical_sha256":"b58d6fc21d248be32e9e49f08925440c942bd06f3ef556df75d0b87672a6165f","source":{"kind":"arxiv","id":"0712.0968","version":1},"attestation_state":"computed","paper":{"title":"Projective structures, grafting, and measured laminations","license":"","headline":"","cross_cats":["math.CV","math.GT"],"primary_cat":"math.DG","authors_text":"David Dumas, Michael Wolf","submitted_at":"2007-12-06T15:34:38Z","abstract_excerpt":"We show that grafting any fixed hyperbolic surface defines a homeomorphism from the space of measured laminations to Teichmuller space, complementing a result of Scannell-Wolf on grafting by a fixed lamination. This result is used to study the relationship between the complex-analytic and geometric coordinate systems for the space of complex projective ($\\CP^1$) structures on a surface.\n  We also study the rays in Teichmuller space associated to the grafting coordinates, obtaining estimates for extremal and hyperbolic length functions and their derivatives along these grafting rays."},"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":"0712.0968","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2007-12-06T15:34:38Z","cross_cats_sorted":["math.CV","math.GT"],"title_canon_sha256":"1a830e6385716f5aa64c7b67e24eb1aaadbc5b28e5f8733e4d76e99d2ff8bbe9","abstract_canon_sha256":"5db85cc3a17bcbf073e778f7c0b2b90ea8578661425dc57fda0d5f316842482f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:19.287460Z","signature_b64":"4mP9A7haF1yL7QonXeMvfaCaWKANEVfaq+xlk1i6MEeUeLaOurblq/MRN4iQpekjHJFWtB8RLC9oTURiSQOpAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b58d6fc21d248be32e9e49f08925440c942bd06f3ef556df75d0b87672a6165f","last_reissued_at":"2026-05-18T02:38:19.287006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:19.287006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Projective structures, grafting, and measured laminations","license":"","headline":"","cross_cats":["math.CV","math.GT"],"primary_cat":"math.DG","authors_text":"David Dumas, Michael Wolf","submitted_at":"2007-12-06T15:34:38Z","abstract_excerpt":"We show that grafting any fixed hyperbolic surface defines a homeomorphism from the space of measured laminations to Teichmuller space, complementing a result of Scannell-Wolf on grafting by a fixed lamination. This result is used to study the relationship between the complex-analytic and geometric coordinate systems for the space of complex projective ($\\CP^1$) structures on a surface.\n  We also study the rays in Teichmuller space associated to the grafting coordinates, obtaining estimates for extremal and hyperbolic length functions and their derivatives along these grafting rays."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.0968","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":"0712.0968","created_at":"2026-05-18T02:38:19.287064+00:00"},{"alias_kind":"arxiv_version","alias_value":"0712.0968v1","created_at":"2026-05-18T02:38:19.287064+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.0968","created_at":"2026-05-18T02:38:19.287064+00:00"},{"alias_kind":"pith_short_12","alias_value":"WWGW7QQ5ESF6","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"WWGW7QQ5ESF6GLU6","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"WWGW7QQ5","created_at":"2026-05-18T12:25:56.245647+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/WWGW7QQ5ESF6GLU6JHYISJKEBS","json":"https://pith.science/pith/WWGW7QQ5ESF6GLU6JHYISJKEBS.json","graph_json":"https://pith.science/api/pith-number/WWGW7QQ5ESF6GLU6JHYISJKEBS/graph.json","events_json":"https://pith.science/api/pith-number/WWGW7QQ5ESF6GLU6JHYISJKEBS/events.json","paper":"https://pith.science/paper/WWGW7QQ5"},"agent_actions":{"view_html":"https://pith.science/pith/WWGW7QQ5ESF6GLU6JHYISJKEBS","download_json":"https://pith.science/pith/WWGW7QQ5ESF6GLU6JHYISJKEBS.json","view_paper":"https://pith.science/paper/WWGW7QQ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0712.0968&json=true","fetch_graph":"https://pith.science/api/pith-number/WWGW7QQ5ESF6GLU6JHYISJKEBS/graph.json","fetch_events":"https://pith.science/api/pith-number/WWGW7QQ5ESF6GLU6JHYISJKEBS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WWGW7QQ5ESF6GLU6JHYISJKEBS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WWGW7QQ5ESF6GLU6JHYISJKEBS/action/storage_attestation","attest_author":"https://pith.science/pith/WWGW7QQ5ESF6GLU6JHYISJKEBS/action/author_attestation","sign_citation":"https://pith.science/pith/WWGW7QQ5ESF6GLU6JHYISJKEBS/action/citation_signature","submit_replication":"https://pith.science/pith/WWGW7QQ5ESF6GLU6JHYISJKEBS/action/replication_record"}},"created_at":"2026-05-18T02:38:19.287064+00:00","updated_at":"2026-05-18T02:38:19.287064+00:00"}