{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KUL6SOOAGVHOKXIITI3V4HF3KI","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":"d33a021f2efcd3af8fd4e5fed9876b198b3d5c9c385ce011f384b4406e9b3a65","cross_cats_sorted":["math.DG","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-11T09:16:21Z","title_canon_sha256":"574bd25b519d023cb9ea13c9db81b02676baf92d539a3b57fbe95e18b5d02ca5"},"schema_version":"1.0","source":{"id":"1309.2767","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2767","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2767v1","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2767","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"pith_short_12","alias_value":"KUL6SOOAGVHO","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KUL6SOOAGVHOKXII","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KUL6SOOA","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:face1085f8164abc636cac94424284e23f62bb381a2e68a22f0b3437d8e72331","target":"graph","created_at":"2026-05-18T03:13:34Z","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 discuss a certain Riemannian metric, related to the toric Kahler-Einstein equation, that is associated in a linearly-invariant manner with a given log-concave measure in R^n. We use this metric in order to bound the second derivatives of the solution to the toric Kahler-Einstein equation, and in order to obtain spectral-gap estimates similar to those of Payne and Weinberger.","authors_text":"B. Klartag","cross_cats":["math.DG","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-11T09:16:21Z","title":"Logarithmically-concave moment measures I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2767","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":"sha256:2914589e155303fc882c8ad5463cfb97d7f46d7df51d46eedda5060e0f522f60","target":"record","created_at":"2026-05-18T03:13:34Z","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":"d33a021f2efcd3af8fd4e5fed9876b198b3d5c9c385ce011f384b4406e9b3a65","cross_cats_sorted":["math.DG","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-11T09:16:21Z","title_canon_sha256":"574bd25b519d023cb9ea13c9db81b02676baf92d539a3b57fbe95e18b5d02ca5"},"schema_version":"1.0","source":{"id":"1309.2767","kind":"arxiv","version":1}},"canonical_sha256":"5517e939c0354ee55d089a375e1cbb52131585f4226e4acc93e1eb6a55a705df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5517e939c0354ee55d089a375e1cbb52131585f4226e4acc93e1eb6a55a705df","first_computed_at":"2026-05-18T03:13:34.891551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:34.891551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ISApVKg2VBIoYBt7QM7o8H8vmYHbzvFaW3X+JwSAEht6PiJLoycgfnmd8DOYVftVnw+ea7xo33pVKJl7zMP0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:34.892368Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.2767","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2914589e155303fc882c8ad5463cfb97d7f46d7df51d46eedda5060e0f522f60","sha256:face1085f8164abc636cac94424284e23f62bb381a2e68a22f0b3437d8e72331"],"state_sha256":"466cd1382f40c47ef5f0288e252ebd4c72c5c79505dc48a78395f90fee5475ba"}