{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RLF2QLECCJP62SCQPJKXVHGS2M","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":"27d6f48dd4ab911a85275354bc7a47c5ec5f4dcbce05834820fb8463c310b21c","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-19T16:38:39Z","title_canon_sha256":"607a48281f962455ef3306a8d64225bb552b8ecd85e2a2ffe57987d9f3cfadf6"},"schema_version":"1.0","source":{"id":"1505.05076","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05076","created_at":"2026-05-18T02:05:22Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05076v1","created_at":"2026-05-18T02:05:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05076","created_at":"2026-05-18T02:05:22Z"},{"alias_kind":"pith_short_12","alias_value":"RLF2QLECCJP6","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RLF2QLECCJP62SCQ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RLF2QLEC","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:8a2b66ba9c8846355c04dd50fda7f839381c323ab92965518bb350d5b313ad51","target":"graph","created_at":"2026-05-18T02:05:22Z","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 generalize our results in \\cite{GX3} to triangulated surfaces in hyperbolic background geometry, which means that all triangles can be embedded in the standard hyperbolic space. We introduce a new discrete Gaussian curvature by dividing the classical discrete Gauss curvature by an area element, which could be taken as the area of the hyperbolic disk packed at each vertex. We prove that the corresponding discrete Ricci flow converges if and only if there exists a circle packing metric with zero curvature. We also prove that the flow converges if the initial curvatures are all ","authors_text":"Huabin Ge, Xu Xu","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-19T16:38:39Z","title":"A Discrete Ricci Flow on Surfaces in Hyperbolic Background Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05076","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":"sha256:406884cf986d14263b949c5a95a0d5117423ef7c746749f6594aed7f552fe556","target":"record","created_at":"2026-05-18T02:05:22Z","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":"27d6f48dd4ab911a85275354bc7a47c5ec5f4dcbce05834820fb8463c310b21c","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-19T16:38:39Z","title_canon_sha256":"607a48281f962455ef3306a8d64225bb552b8ecd85e2a2ffe57987d9f3cfadf6"},"schema_version":"1.0","source":{"id":"1505.05076","kind":"arxiv","version":1}},"canonical_sha256":"8acba82c82125fed48507a557a9cd2d3010b1705110741962275eff48e200ed4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8acba82c82125fed48507a557a9cd2d3010b1705110741962275eff48e200ed4","first_computed_at":"2026-05-18T02:05:22.264396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:22.264396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8ofKzED3Z5T6IwQ7bUscbda9Kf56ekfhh+f2kk6YheLmZklJkWltN2na06OA9XG3ddODQY+pors7y1oXcdGTCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:22.265176Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.05076","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:406884cf986d14263b949c5a95a0d5117423ef7c746749f6594aed7f552fe556","sha256:8a2b66ba9c8846355c04dd50fda7f839381c323ab92965518bb350d5b313ad51"],"state_sha256":"3ef64b8b3ad70e68a370e34e97122ebb097221a73cc409755861a82fd11f29ce"}