{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WKWKYBDNTGF3Y3U7VRMLFFL3ZM","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":"f5ddcc8a005a88e347feb3e38f6d9e02bb63ab44517efb10c7498e1d742d06cc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-05-04T07:32:34Z","title_canon_sha256":"792d5a7f0dc95e99de004ec12765910667ad051f382fb4316bc84c5c71eb4b74"},"schema_version":"1.0","source":{"id":"2305.02609","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.02609","created_at":"2026-07-05T08:56:55Z"},{"alias_kind":"arxiv_version","alias_value":"2305.02609v2","created_at":"2026-07-05T08:56:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.02609","created_at":"2026-07-05T08:56:55Z"},{"alias_kind":"pith_short_12","alias_value":"WKWKYBDNTGF3","created_at":"2026-07-05T08:56:55Z"},{"alias_kind":"pith_short_16","alias_value":"WKWKYBDNTGF3Y3U7","created_at":"2026-07-05T08:56:55Z"},{"alias_kind":"pith_short_8","alias_value":"WKWKYBDN","created_at":"2026-07-05T08:56:55Z"}],"graph_snapshots":[{"event_id":"sha256:1be25db5f6dd741bf35258f95c4606c70ae95b141c4ab37911c7efe0915ea1ae","target":"graph","created_at":"2026-07-05T08:56:55Z","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/2305.02609/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We proved a rigidity result for Delaunay triangulations of the plane under Luo's discrete conformal change, extending previous results on hexagonal triangulations. Our result is a discrete analogue of the conformal rigidity of the plane. We followed Zhengxu He's analytical approach in his work on the rigidity of disk patterns, and developed a discrete Schwarz lemma and a discrete Liouville theorem. The main tools include conformal modulus, discrete extremal length, and maximum principles in discrete conformal geometry.","authors_text":"Song Dai, Tianqi Wu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-05-04T07:32:34Z","title":"Rigidity of the Delaunay triangulations of the plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.02609","kind":"arxiv","version":2},"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:b3a44daf8fb9c1b6fe0623dce674b0fa73b855a1de60cd6d02908b3d731a930b","target":"record","created_at":"2026-07-05T08:56:55Z","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":"f5ddcc8a005a88e347feb3e38f6d9e02bb63ab44517efb10c7498e1d742d06cc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2023-05-04T07:32:34Z","title_canon_sha256":"792d5a7f0dc95e99de004ec12765910667ad051f382fb4316bc84c5c71eb4b74"},"schema_version":"1.0","source":{"id":"2305.02609","kind":"arxiv","version":2}},"canonical_sha256":"b2acac046d998bbc6e9fac58b2957bcb3eedf13d81f7735bc3d341a13b01f303","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2acac046d998bbc6e9fac58b2957bcb3eedf13d81f7735bc3d341a13b01f303","first_computed_at":"2026-07-05T08:56:55.703371Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:56:55.703371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V+mGLyzIAO1ueDZiInPWoemiykfq6Hzwk87eYA/WRF+ubkuRMRvrGx9DK+HxLqoABO/3Un9CFo7oadqVb4bZCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:56:55.703964Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.02609","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3a44daf8fb9c1b6fe0623dce674b0fa73b855a1de60cd6d02908b3d731a930b","sha256:1be25db5f6dd741bf35258f95c4606c70ae95b141c4ab37911c7efe0915ea1ae"],"state_sha256":"dd5b3a344d6838d8a23bb11278ac9d60a0de0e69077afc651323394fbc0256a6"}