{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YI72ZOX4FXHJQRWHU7BMSLBYWP","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":"245fa0fc56a1016a64e6517a2e9bbbbc000ac31b5ed3c919c18f1d5dbd5b3691","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-01-21T15:13:28Z","title_canon_sha256":"c1d86ae7f29cee5d927cde1d1705d8c213cab594795b1ecd638a0573fd6e065b"},"schema_version":"1.0","source":{"id":"1701.06037","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06037","created_at":"2026-05-17T23:51:26Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06037v3","created_at":"2026-05-17T23:51:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06037","created_at":"2026-05-17T23:51:26Z"},{"alias_kind":"pith_short_12","alias_value":"YI72ZOX4FXHJ","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YI72ZOX4FXHJQRWH","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YI72ZOX4","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:f3203d0ccb008810152d62c4fd0f72bdd2854c67885daeae4bbba89d45c54d04","target":"graph","created_at":"2026-05-17T23:51:26Z","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 compute the Hessian of quantized Ding functionals and give an elementary proof for the convexity of quantized Ding functionals along Bergman geodesics from the view point of projective geometry. We study also the asymptotic behavior of the Hessian using the Berezin-Toeplitz quantization.","authors_text":"Ryosuke Takahashi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-01-21T15:13:28Z","title":"The Hessian of quantized Ding functionals and its asymptotic behavior"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06037","kind":"arxiv","version":3},"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":"sha256:532a2d612e1087ff9b43dc6d4c2093b667ac7865d94885de366241609ed0cda2","target":"record","created_at":"2026-05-17T23:51:26Z","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":"245fa0fc56a1016a64e6517a2e9bbbbc000ac31b5ed3c919c18f1d5dbd5b3691","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-01-21T15:13:28Z","title_canon_sha256":"c1d86ae7f29cee5d927cde1d1705d8c213cab594795b1ecd638a0573fd6e065b"},"schema_version":"1.0","source":{"id":"1701.06037","kind":"arxiv","version":3}},"canonical_sha256":"c23facbafc2dce9846c7a7c2c92c38b3ce369f253d6eebfb735b0dacda09bdd6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c23facbafc2dce9846c7a7c2c92c38b3ce369f253d6eebfb735b0dacda09bdd6","first_computed_at":"2026-05-17T23:51:26.274811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:26.274811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"toZ4W9+q9vaF8Rn8+eTzp7ZGzQqVjTVz8hjQ7w1dzJLZrBvdc4jS0//0Z1X0/VPvKdvxVLcMX9D/T+PHETrsCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:26.275467Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06037","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:532a2d612e1087ff9b43dc6d4c2093b667ac7865d94885de366241609ed0cda2","sha256:f3203d0ccb008810152d62c4fd0f72bdd2854c67885daeae4bbba89d45c54d04"],"state_sha256":"474ec4aa56de87d6f71e0c73720bfd345c23066ef62fab1fec62e507f9b65af3"}