{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DZGQX6MOEXCOS5IVK6YDX4NYAX","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":"043bab4326948c3e058be9bc78fce927e434b30c1acfda5d503d2ee382489714","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-12-11T19:40:34Z","title_canon_sha256":"698a24c710a04717c63822913b5b1a83108ae3c6988b28e1d501f96c481d61a0"},"schema_version":"1.0","source":{"id":"1012.2482","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2482","created_at":"2026-05-18T00:05:09Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2482v1","created_at":"2026-05-18T00:05:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2482","created_at":"2026-05-18T00:05:09Z"},{"alias_kind":"pith_short_12","alias_value":"DZGQX6MOEXCO","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DZGQX6MOEXCOS5IV","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DZGQX6MO","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:9d32c1847303eb446fd6c7f8c83b430079d4d176de94beb982c6a257245b718b","target":"graph","created_at":"2026-05-18T00:05:09Z","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":"There are several Teichm\\\"uller spaces associated to a surface of infinite topological type, after the choice of a particular basepoint (a complex or a hyperbolic structure on the surface). These spaces include the quasiconformal Teichm\\\"uller space, the length spectrum Teichm\\\"uller space, the Fenchel-Nielsen Teichm\\\"uller space, and there are others. In general, these spaces are set-theoretically different. An important question is therefore to understand relations between these spaces. Each of these spaces is equipped with its own metric, and under some hypotheses, there are inclusions betw","authors_text":"Athanase Papadopoulos (IRMA), Daniele Alessandrini (MPI), Lixin Liu, Weixu Su","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-12-11T19:40:34Z","title":"On local comparison between various metrics on Teichm\\\"uller spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2482","kind":"arxiv","version":1},"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:d04e82f1cfd0564e07cd3a1014e92c3214e58af78084d1a3907d38f381035b1c","target":"record","created_at":"2026-05-18T00:05:09Z","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":"043bab4326948c3e058be9bc78fce927e434b30c1acfda5d503d2ee382489714","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-12-11T19:40:34Z","title_canon_sha256":"698a24c710a04717c63822913b5b1a83108ae3c6988b28e1d501f96c481d61a0"},"schema_version":"1.0","source":{"id":"1012.2482","kind":"arxiv","version":1}},"canonical_sha256":"1e4d0bf98e25c4e9751557b03bf1b805e9742eae52593d4d27c379a9ed29d41b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e4d0bf98e25c4e9751557b03bf1b805e9742eae52593d4d27c379a9ed29d41b","first_computed_at":"2026-05-18T00:05:09.946730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:09.946730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nLNYfJ+GMwVyVaCe/yB5ZJDgB1Z1wqhTVjvSSz4vPuRbZ+7k+NK4S+Xkzbx1QBZ5jkJMdQDrmIdAewv7FqwGAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:09.947286Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.2482","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d04e82f1cfd0564e07cd3a1014e92c3214e58af78084d1a3907d38f381035b1c","sha256:9d32c1847303eb446fd6c7f8c83b430079d4d176de94beb982c6a257245b718b"],"state_sha256":"b28609f7e52017bbd2c4ba152afadce38d53703dde86973b0cbe4960200a07d2"}