{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RPVUNOI5CU6GLJO4NCTXSFZ544","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":"3e7b9747640896c4a1cc8bd8b381d911faa7db33180316a012947cf20972e8a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-05-03T17:34:34Z","title_canon_sha256":"5f0eb9e81ec910f3a35938f427ba0634a17fe6d9a4c67829337f06cb7d8a8f9b"},"schema_version":"1.0","source":{"id":"1905.01284","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01284","created_at":"2026-05-17T23:47:06Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01284v1","created_at":"2026-05-17T23:47:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01284","created_at":"2026-05-17T23:47:06Z"},{"alias_kind":"pith_short_12","alias_value":"RPVUNOI5CU6G","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RPVUNOI5CU6GLJO4","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RPVUNOI5","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:100c3345addca927e3009e89f540ffe5b258e3d807ee05d2fe8b22b22586315f","target":"graph","created_at":"2026-05-17T23:47:06Z","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":"Let f:(Y,g)->(X,g_0) be a non zero degree continuous map between compact K\\\"ahler manifolds of dimension greater or equal to 2, where g_0 has constant negative holomorphic sectional curvature. Adapting the Besson-Courtois-Gallot barycentre map techniques to the K\\\"ahler setting, we prove a gap theorem in terms of the degree of f and the diastatic entropies of (Y, g) and (X,g_0), which extends the rigidity result proved by the author in [13].","authors_text":"Roberto Mossa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-05-03T17:34:34Z","title":"On the diastatic entropy and C^1-rigidity of complex hyperbolic manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01284","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:ff129844cb0f20fc38eecd081522a1172312db04fe3ecc8418afa448299cea51","target":"record","created_at":"2026-05-17T23:47:06Z","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":"3e7b9747640896c4a1cc8bd8b381d911faa7db33180316a012947cf20972e8a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-05-03T17:34:34Z","title_canon_sha256":"5f0eb9e81ec910f3a35938f427ba0634a17fe6d9a4c67829337f06cb7d8a8f9b"},"schema_version":"1.0","source":{"id":"1905.01284","kind":"arxiv","version":1}},"canonical_sha256":"8beb46b91d153c65a5dc68a779173de726bf6c78e8d4d6ecac4c9e78ddf62c05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8beb46b91d153c65a5dc68a779173de726bf6c78e8d4d6ecac4c9e78ddf62c05","first_computed_at":"2026-05-17T23:47:06.346511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:06.346511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q+ScyV747Gk5UIN5vahrvJ4DydmeQR6STzFShBSEr6hBUC2T6qCHPjvOCUDcgkXYqx/U6RP5u9Z7d5H7CzEFBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:06.347173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.01284","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff129844cb0f20fc38eecd081522a1172312db04fe3ecc8418afa448299cea51","sha256:100c3345addca927e3009e89f540ffe5b258e3d807ee05d2fe8b22b22586315f"],"state_sha256":"c4d6807be3c0fbceeea48d13cf0a408a92c1055781620b48a96031b198e19c1e"}