{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CLYS7LWPUOUAAL5MWXDNIEH3BE","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":"843d21273e54c6685ca6ae3f012aeb4521203ce7d66580138a715b984a2fb8d7","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-25T07:36:38Z","title_canon_sha256":"e1ecb3f5785531d8879e17ab21a259e816245b96867265f899e472041a1b9e55"},"schema_version":"1.0","source":{"id":"1509.07608","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07608","created_at":"2026-05-18T01:32:02Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07608v1","created_at":"2026-05-18T01:32:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07608","created_at":"2026-05-18T01:32:02Z"},{"alias_kind":"pith_short_12","alias_value":"CLYS7LWPUOUA","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CLYS7LWPUOUAAL5M","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CLYS7LWP","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:d813accd2cb80c9ac931f72d9e4610ad3147b28ea3ff7479216bfa57bbe63955","target":"graph","created_at":"2026-05-18T01:32:02Z","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":"In this paper we develop a systematic deformation theory for conic constant curvature metrics on a closed surface when all cone angles are less than $2\\pi$; in particular, we define and study the Teichm\\\"uller space $\\mathcal{T}^{\\mathrm{conic}}_{\\gamma,k}$ of conic constant curvature metrics on a surface of genus $\\gamma$ with $k$ conic points. The methods here are adopted from higher dimensional global analysis, generalizing Tromba's approach to the study of the standard Teichm\\\"uller space $\\mathcal{T}_\\gamma$. The main new ingredient is the theory of elliptic conic operators.","authors_text":"Hartmut Weiss, Rafe Mazzeo","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-25T07:36:38Z","title":"Teichm\\\"uller theory for conic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07608","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":"sha256:3fa8adff243a2a9e8ef105fe21ec7f15c9e867b0ce788cdd64f7f4acb14e1b72","target":"record","created_at":"2026-05-18T01:32:02Z","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":"843d21273e54c6685ca6ae3f012aeb4521203ce7d66580138a715b984a2fb8d7","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-25T07:36:38Z","title_canon_sha256":"e1ecb3f5785531d8879e17ab21a259e816245b96867265f899e472041a1b9e55"},"schema_version":"1.0","source":{"id":"1509.07608","kind":"arxiv","version":1}},"canonical_sha256":"12f12faecfa3a8002facb5c6d410fb093ba2bc23e4c0e0caedd2123e61bd8862","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12f12faecfa3a8002facb5c6d410fb093ba2bc23e4c0e0caedd2123e61bd8862","first_computed_at":"2026-05-18T01:32:02.354580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:02.354580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6XQUXW1ymuW/qm/4yAgpCXTFEO0T5E9OpUXLSUU8O1urmkDDQSvBo9EP4kkMaZC7mBGAHQ7ABdtuHRiabaisCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:02.355114Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.07608","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fa8adff243a2a9e8ef105fe21ec7f15c9e867b0ce788cdd64f7f4acb14e1b72","sha256:d813accd2cb80c9ac931f72d9e4610ad3147b28ea3ff7479216bfa57bbe63955"],"state_sha256":"4b207369644c10cb1130c2d83d418a2715346c9d9887c1537a39e52fa22e1220"}