{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EHPKVMDDR6OLQEW4R2SFQ27SPE","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":"979b3ee3b4cb50a48cf51ee686eefe89ca8c39ce0e45fd1164311f3ecc23ee74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-10T15:33:34Z","title_canon_sha256":"e548ab523f3226ab3171615f8c444ade9786dbb9e9b977c7b971133e398ad120"},"schema_version":"1.0","source":{"id":"1412.3340","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3340","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3340v1","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3340","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"pith_short_12","alias_value":"EHPKVMDDR6OL","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EHPKVMDDR6OLQEW4","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EHPKVMDD","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:5bc3df3dc946bfbb85fc4b3d78270f8ca74e0841441f82d5a6e538428e381517","target":"graph","created_at":"2026-05-18T02:31:36Z","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":"We introduce a new version of a curvature-dimension inequality for non-negative curvature. We use this inequality to prove a logarithmic Li-Yau inequality on finite graphs. To formulate this inequality, we introduce a non-linear variant of the calculus of Bakry and \\'Emery. In the case of manifolds, the new calculus and the new curvature-dimension inequality coincide with the common ones. In the case of graphs, they coincide in a limit. In this sense, the new curvature-dimension inequality gives a more general concept of curvature on graphs and on manifolds. We show that Ricci-flat graphs have","authors_text":"Florentin M\\\"unch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-10T15:33:34Z","title":"Li-Yau inequality on finite graphs via non-linear curvature dimension conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3340","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":"sha256:6fd26e6108d9acb121a54eb20b6db82744f8edfe5c0e07154edd55abff7f73b8","target":"record","created_at":"2026-05-18T02:31:36Z","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":"979b3ee3b4cb50a48cf51ee686eefe89ca8c39ce0e45fd1164311f3ecc23ee74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-10T15:33:34Z","title_canon_sha256":"e548ab523f3226ab3171615f8c444ade9786dbb9e9b977c7b971133e398ad120"},"schema_version":"1.0","source":{"id":"1412.3340","kind":"arxiv","version":1}},"canonical_sha256":"21deaab0638f9cb812dc8ea4586bf27908e33b2887b72baf1cddce03d334169d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21deaab0638f9cb812dc8ea4586bf27908e33b2887b72baf1cddce03d334169d","first_computed_at":"2026-05-18T02:31:36.918386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:36.918386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dLMN79xZfcoiEaZdDs3qatFISzFB1Y9HyW0u+3Sm3oLdHVpwkxr7XMpWTFNgxzi8MWloWqWjO/M4Va3mskMqDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:36.919060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3340","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fd26e6108d9acb121a54eb20b6db82744f8edfe5c0e07154edd55abff7f73b8","sha256:5bc3df3dc946bfbb85fc4b3d78270f8ca74e0841441f82d5a6e538428e381517"],"state_sha256":"5c585fc40a7e9d27f9016b6404285a87b05bb8a1cb07e9424fab35e48a6038c8"}