{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RY4ANMW7KKTUQ26Z2WP22JCZC2","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":"85e3cec29c3ba97bb98e390cbf7851ea9acc21b02db842b67cec3571ac3e489d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-03T06:32:32Z","title_canon_sha256":"623278d2bc793b5b52304f5e016e18f210cf5a4437770e0311cd6dd481f146c3"},"schema_version":"1.0","source":{"id":"2606.04501","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04501","created_at":"2026-06-04T01:09:14Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04501v1","created_at":"2026-06-04T01:09:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04501","created_at":"2026-06-04T01:09:14Z"},{"alias_kind":"pith_short_12","alias_value":"RY4ANMW7KKTU","created_at":"2026-06-04T01:09:14Z"},{"alias_kind":"pith_short_16","alias_value":"RY4ANMW7KKTUQ26Z","created_at":"2026-06-04T01:09:14Z"},{"alias_kind":"pith_short_8","alias_value":"RY4ANMW7","created_at":"2026-06-04T01:09:14Z"}],"graph_snapshots":[{"event_id":"sha256:59e3146f78ebd152c7c9dd651f80e96c410e1eac7f910e19d8419d02b5d3d6c8","target":"graph","created_at":"2026-06-04T01:09:14Z","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/2606.04501/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For compact K\\\"ahler manifolds $(M,g,J)$ with negative scalar curvature we study the existence problem for non-trivial Einstein deformations of $g$, that is small time curves $g_t$ of Einstein metrics with $g_0=g$. No asssumption on the complex structure $J$ is made; also we do not assume that the metrics $g_t$ are K\\\"ahler w.r.t. $J$. We determine explicitly the obstruction to third order Einstein deformation for $g$; that is we fully solve the equations $(\\Ric^{g_t})^{(k)}(0)=0$ for $1 \\leq k \\le 3$ in terms of the Taylor expansion $g^{-1}g_t=\\id+th_1+\\tfrac{t^2}{2!}h_2+\\tfrac{t^3}{3!}h_3+o(","authors_text":"Paul-Andi Nagy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-03T06:32:32Z","title":"Third order Einstein deformations for Kaehler-Einstein metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04501","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":"sha256:705dd324410689d68c9b3c8e18c6a0d5dd5a18d971aeded37b6f878b28d07915","target":"record","created_at":"2026-06-04T01:09:14Z","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":"85e3cec29c3ba97bb98e390cbf7851ea9acc21b02db842b67cec3571ac3e489d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-03T06:32:32Z","title_canon_sha256":"623278d2bc793b5b52304f5e016e18f210cf5a4437770e0311cd6dd481f146c3"},"schema_version":"1.0","source":{"id":"2606.04501","kind":"arxiv","version":1}},"canonical_sha256":"8e3806b2df52a7486bd9d59fad24591692e1f8f9d02ac29ec296ab6955dc1923","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e3806b2df52a7486bd9d59fad24591692e1f8f9d02ac29ec296ab6955dc1923","first_computed_at":"2026-06-04T01:09:14.560980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T01:09:14.560980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y/bR33ZeKIhWjbX9zlz4v2R1y4x9oRr56twFV/vKw35HuNqiKbPVJ8Ki4SqZC6yyzfDskrG1qR9j56iSejowDg==","signature_status":"signed_v1","signed_at":"2026-06-04T01:09:14.561786Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.04501","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:705dd324410689d68c9b3c8e18c6a0d5dd5a18d971aeded37b6f878b28d07915","sha256:59e3146f78ebd152c7c9dd651f80e96c410e1eac7f910e19d8419d02b5d3d6c8"],"state_sha256":"c2773d9893ef7ff451d663f61e8f89d05accddec019ca44cc96646ba725bb47b"}