{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YE6YSUHGSLPLWE7BMZBF3S7HEL","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":"341a0898e51bf98fdf3e3511633993f6e6d2f6f5493c0e31eeab6efe7d5a5590","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-13T17:23:19Z","title_canon_sha256":"38606e31b1c18e64caa9bdccbccfbb1c11630a5fc44ff7fb04730018bfb82f79"},"schema_version":"1.0","source":{"id":"1303.3217","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3217","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3217v2","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3217","created_at":"2026-05-18T02:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"YE6YSUHGSLPL","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YE6YSUHGSLPLWE7B","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YE6YSUHG","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:9f7eb771e9ab3438a937779f0b17059eec292a1cb516353d2818b9d6f0560f16","target":"graph","created_at":"2026-05-18T02:20:12Z","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 give un upper bound Ent(\\Omega, g)<\\lambda\\ of the diastatic entropy Ent(\\Omega, g) of a complex bounded domain (\\Omega, g) in terms of the balanced condition (in Donaldson terminology) of the Kaehler metric \\lambda g. When (\\Omega, g) is a homogeneous bounded domain we show that the converse holds true, namely if Ent(\\Omega, g)<1 then g is balanced. Moreover, we explcit compute Ent(\\Omega, g) in terms of Piatetski-Shapiro constants.","authors_text":"Roberto Mossa","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-13T17:23:19Z","title":"A note on diastatic entropy and balanced metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3217","kind":"arxiv","version":2},"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":"sha256:9aa404fe25167d610ee29c46b79586506a36c17a798c309677567af81fc85fe0","target":"record","created_at":"2026-05-18T02:20:12Z","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":"341a0898e51bf98fdf3e3511633993f6e6d2f6f5493c0e31eeab6efe7d5a5590","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-13T17:23:19Z","title_canon_sha256":"38606e31b1c18e64caa9bdccbccfbb1c11630a5fc44ff7fb04730018bfb82f79"},"schema_version":"1.0","source":{"id":"1303.3217","kind":"arxiv","version":2}},"canonical_sha256":"c13d8950e692debb13e166425dcbe722c897d795b8e05934e9c9e16f7bf7b297","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c13d8950e692debb13e166425dcbe722c897d795b8e05934e9c9e16f7bf7b297","first_computed_at":"2026-05-18T02:20:12.867799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:12.867799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N3qSWnXhh53NIDFCS238erixklTQ2+fYSCf1zI4L85EvYcvJktsVwj5I4ueei1oS+5DakgMTyuzCparR4pDIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:12.868266Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.3217","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9aa404fe25167d610ee29c46b79586506a36c17a798c309677567af81fc85fe0","sha256:9f7eb771e9ab3438a937779f0b17059eec292a1cb516353d2818b9d6f0560f16"],"state_sha256":"4b6fbca8eeeab9ccd39df2682b263d2ff637068dfee84b2edb3b82077764e080"}