{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6CRZBLUTHHBPN5DLEVBFS7PNZJ","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":"b529c15ed762479cfcbf3011617ce9c1edacb15e4ae0cd2875bc009a5a0fe91c","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-11-27T14:47:31Z","title_canon_sha256":"f9c4f7549c07e9c6a7da2c47b865b75569b7ab5078574684d9d45e2dcdec8e9c"},"schema_version":"1.0","source":{"id":"1711.09717","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.09717","created_at":"2026-05-18T00:29:34Z"},{"alias_kind":"arxiv_version","alias_value":"1711.09717v1","created_at":"2026-05-18T00:29:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.09717","created_at":"2026-05-18T00:29:34Z"},{"alias_kind":"pith_short_12","alias_value":"6CRZBLUTHHBP","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6CRZBLUTHHBPN5DL","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6CRZBLUT","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:b2b4c1056a379b29ce09869c4cf49dccfad4cf4ec6980fbea16af4a0f5093233","target":"graph","created_at":"2026-05-18T00:29:34Z","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":"There are two parts of this paper. First, we discovered an explicit formula for the complex Hessian of the weighted log-Bergman kernel on a parallelogram domain, and utilised this formula to give a new proof about the strict convexity of the Mabuchi functional along a smooth geodesic. Second, when a C^{1,1}-geodesic connects two non-degenerate energy minimizers, we also proved this strict convexity, by showing that such a geodesic must be non-degenerate and smooth.","authors_text":"Long Li","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-11-27T14:47:31Z","title":"Strict convexity of the Mabuchi functional for energy minimizers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09717","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":"sha256:714cf858b1d4690741a60c18f07727cfc6e0edbdaf5d72a3c8bb47d43353dfcc","target":"record","created_at":"2026-05-18T00:29:34Z","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":"b529c15ed762479cfcbf3011617ce9c1edacb15e4ae0cd2875bc009a5a0fe91c","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-11-27T14:47:31Z","title_canon_sha256":"f9c4f7549c07e9c6a7da2c47b865b75569b7ab5078574684d9d45e2dcdec8e9c"},"schema_version":"1.0","source":{"id":"1711.09717","kind":"arxiv","version":1}},"canonical_sha256":"f0a390ae9339c2f6f46b2542597dedca5f48ac3c6747586f8b8f38016ada128d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0a390ae9339c2f6f46b2542597dedca5f48ac3c6747586f8b8f38016ada128d","first_computed_at":"2026-05-18T00:29:34.723859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:34.723859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QMDKL/B+p30KH4DAjTVV1xuKrE12u7IWxz+4MeyG8F45AOEUCsrBpkQxNKqxQtbr5Eg+dnoyjwlXFc0mVl3WCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:34.724345Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.09717","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:714cf858b1d4690741a60c18f07727cfc6e0edbdaf5d72a3c8bb47d43353dfcc","sha256:b2b4c1056a379b29ce09869c4cf49dccfad4cf4ec6980fbea16af4a0f5093233"],"state_sha256":"384f878d31559dd82ce5276dbc93c69c4c0c1d742ff0bb9aae2157714fafd384"}