{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WCNJYF7TL54EM46E2DIG445QI6","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":"42b9e46ec981d6135b3955b4eac2807e5baec3a69f59155dd615ca837cde5b8b","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-10-05T05:51:26Z","title_canon_sha256":"049ba71f168dfd65cf7b3da680804362fa8b1b8cc6761aa6dfa1a379834560e6"},"schema_version":"1.0","source":{"id":"1910.02215","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.02215","created_at":"2026-07-05T04:15:06Z"},{"alias_kind":"arxiv_version","alias_value":"1910.02215v3","created_at":"2026-07-05T04:15:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.02215","created_at":"2026-07-05T04:15:06Z"},{"alias_kind":"pith_short_12","alias_value":"WCNJYF7TL54E","created_at":"2026-07-05T04:15:06Z"},{"alias_kind":"pith_short_16","alias_value":"WCNJYF7TL54EM46E","created_at":"2026-07-05T04:15:06Z"},{"alias_kind":"pith_short_8","alias_value":"WCNJYF7T","created_at":"2026-07-05T04:15:06Z"}],"graph_snapshots":[{"event_id":"sha256:731b7b7a61c0fb8b2175fc2f9b646522d2621e948181a136396645f221a31708","target":"graph","created_at":"2026-07-05T04:15:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1910.02215/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we define a new metric structure on the shape space of a high genus surface. We introduce a rigorous definition of a shape of a surface and construct a metric based on two energies measuring the area distortion and the angle distortion of a quasiconformal homeomorphism. We show that the energy minimizer in a fixed homotopy class is achieved by a quasiconformal homeomorphism by the lower semicontinuity property of these two energies.","authors_text":"Yanwen Luo","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-10-05T05:51:26Z","title":"Comparing shapes of high genus surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.02215","kind":"arxiv","version":3},"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":"sha256:690e6297f1923d7ed4875f0e8004018e8d443e376025d7b530f070291ec75ee5","target":"record","created_at":"2026-07-05T04:15:06Z","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":"42b9e46ec981d6135b3955b4eac2807e5baec3a69f59155dd615ca837cde5b8b","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-10-05T05:51:26Z","title_canon_sha256":"049ba71f168dfd65cf7b3da680804362fa8b1b8cc6761aa6dfa1a379834560e6"},"schema_version":"1.0","source":{"id":"1910.02215","kind":"arxiv","version":3}},"canonical_sha256":"b09a9c17f35f784673c4d0d06e73b0479bb0478cda74d4a750f6703ad807a005","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b09a9c17f35f784673c4d0d06e73b0479bb0478cda74d4a750f6703ad807a005","first_computed_at":"2026-07-05T04:15:06.321873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:15:06.321873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2HUDCX0t+UukYJih9PhMgp0FqzBbpSpxYv6YgvIGtilSLh6PF5GK+mZ7n0PWiE0gXGwkhtH7WoAP9xR8favvDA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:15:06.322263Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.02215","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:690e6297f1923d7ed4875f0e8004018e8d443e376025d7b530f070291ec75ee5","sha256:731b7b7a61c0fb8b2175fc2f9b646522d2621e948181a136396645f221a31708"],"state_sha256":"0220cb5b36b40921cf052c36c64e47707773f802fdedfc1e7b95930d50630022"}