{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QXYEN66QVSTHFC4DD62NHLPIYK","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":"2b6688a8c1ca05ebc065a6898814041e36f3ae292d3b779d012d431c56906051","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-26T10:26:10Z","title_canon_sha256":"fd351198ab25c109a4be65ff50f572b0ebb9c9370db025bc2b05497b66b49521"},"schema_version":"1.0","source":{"id":"2607.23584","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23584","created_at":"2026-07-28T01:23:00Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23584v1","created_at":"2026-07-28T01:23:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23584","created_at":"2026-07-28T01:23:00Z"},{"alias_kind":"pith_short_12","alias_value":"QXYEN66QVSTH","created_at":"2026-07-28T01:23:00Z"},{"alias_kind":"pith_short_16","alias_value":"QXYEN66QVSTHFC4D","created_at":"2026-07-28T01:23:00Z"},{"alias_kind":"pith_short_8","alias_value":"QXYEN66Q","created_at":"2026-07-28T01:23:00Z"}],"graph_snapshots":[{"event_id":"sha256:00ba13312aa0164d49858315458de74fbb849c45b8bae72123253843df5280fc","target":"graph","created_at":"2026-07-28T01:23:00Z","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/2607.23584/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study three-dimensional combinatorial Yamabe flows on locally finite infinite triangulations in Euclidean and hyperbolic background geometries. Under suitable non-degeneracy and bounded-degree assumptions, we establish the short-time existence and uniqueness of the original flows. We further introduce the extended flows by using the continuous extension of solid angles, and prove long-time existence for both extended flows under suitable initial assumptions.","authors_text":"Bohao Ji","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-26T10:26:10Z","title":"Infinite Combinatorial Yamabe Flows in Three Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23584","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":"sha256:3c15a7d677dea9ee98e0fd79aed369f2d94563fda1a35efd6a0503d9c74bd9ad","target":"record","created_at":"2026-07-28T01:23:00Z","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":"2b6688a8c1ca05ebc065a6898814041e36f3ae292d3b779d012d431c56906051","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-26T10:26:10Z","title_canon_sha256":"fd351198ab25c109a4be65ff50f572b0ebb9c9370db025bc2b05497b66b49521"},"schema_version":"1.0","source":{"id":"2607.23584","kind":"arxiv","version":1}},"canonical_sha256":"85f046fbd0aca6728b831fb4d3ade8c28f20416d140c0b708c94b88f0f4f81cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85f046fbd0aca6728b831fb4d3ade8c28f20416d140c0b708c94b88f0f4f81cd","first_computed_at":"2026-07-28T01:23:00.565366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T01:23:00.565366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KKlNDFa+KEUuruJaXctbWV+PyY3QtpzhzQdE9zBHGZnXVnvZYxnxnbKAjf003qxPUum2JW5VpupkmlPXMBNxAw==","signature_status":"signed_v1","signed_at":"2026-07-28T01:23:00.566245Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.23584","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c15a7d677dea9ee98e0fd79aed369f2d94563fda1a35efd6a0503d9c74bd9ad","sha256:00ba13312aa0164d49858315458de74fbb849c45b8bae72123253843df5280fc"],"state_sha256":"1465a9e35ba7d602482cc90e89f2f6d40ea455e2043991280d1e2085286c4010"}