{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:YE6YSUHGSLPLWE7BMZBF3S7HEL","short_pith_number":"pith:YE6YSUHG","schema_version":"1.0","canonical_sha256":"c13d8950e692debb13e166425dcbe722c897d795b8e05934e9c9e16f7bf7b297","source":{"kind":"arxiv","id":"1303.3217","version":2},"attestation_state":"computed","paper":{"title":"A note on diastatic entropy and balanced metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Roberto Mossa","submitted_at":"2013-03-13T17:23:19Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1303.3217","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-13T17:23:19Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"38606e31b1c18e64caa9bdccbccfbb1c11630a5fc44ff7fb04730018bfb82f79","abstract_canon_sha256":"341a0898e51bf98fdf3e3511633993f6e6d2f6f5493c0e31eeab6efe7d5a5590"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:12.868266Z","signature_b64":"N3qSWnXhh53NIDFCS238erixklTQ2+fYSCf1zI4L85EvYcvJktsVwj5I4ueei1oS+5DakgMTyuzCparR4pDIBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c13d8950e692debb13e166425dcbe722c897d795b8e05934e9c9e16f7bf7b297","last_reissued_at":"2026-05-18T02:20:12.867799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:12.867799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on diastatic entropy and balanced metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Roberto Mossa","submitted_at":"2013-03-13T17:23:19Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3217","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1303.3217","created_at":"2026-05-18T02:20:12.867876+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.3217v2","created_at":"2026-05-18T02:20:12.867876+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3217","created_at":"2026-05-18T02:20:12.867876+00:00"},{"alias_kind":"pith_short_12","alias_value":"YE6YSUHGSLPL","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"YE6YSUHGSLPLWE7B","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"YE6YSUHG","created_at":"2026-05-18T12:28:06.772260+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YE6YSUHGSLPLWE7BMZBF3S7HEL","json":"https://pith.science/pith/YE6YSUHGSLPLWE7BMZBF3S7HEL.json","graph_json":"https://pith.science/api/pith-number/YE6YSUHGSLPLWE7BMZBF3S7HEL/graph.json","events_json":"https://pith.science/api/pith-number/YE6YSUHGSLPLWE7BMZBF3S7HEL/events.json","paper":"https://pith.science/paper/YE6YSUHG"},"agent_actions":{"view_html":"https://pith.science/pith/YE6YSUHGSLPLWE7BMZBF3S7HEL","download_json":"https://pith.science/pith/YE6YSUHGSLPLWE7BMZBF3S7HEL.json","view_paper":"https://pith.science/paper/YE6YSUHG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.3217&json=true","fetch_graph":"https://pith.science/api/pith-number/YE6YSUHGSLPLWE7BMZBF3S7HEL/graph.json","fetch_events":"https://pith.science/api/pith-number/YE6YSUHGSLPLWE7BMZBF3S7HEL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YE6YSUHGSLPLWE7BMZBF3S7HEL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YE6YSUHGSLPLWE7BMZBF3S7HEL/action/storage_attestation","attest_author":"https://pith.science/pith/YE6YSUHGSLPLWE7BMZBF3S7HEL/action/author_attestation","sign_citation":"https://pith.science/pith/YE6YSUHGSLPLWE7BMZBF3S7HEL/action/citation_signature","submit_replication":"https://pith.science/pith/YE6YSUHGSLPLWE7BMZBF3S7HEL/action/replication_record"}},"created_at":"2026-05-18T02:20:12.867876+00:00","updated_at":"2026-05-18T02:20:12.867876+00:00"}