{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IOGZTS4MOL3GINXOC7I2CQX24T","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":"ddd6fcae49cf88dc2376454e1f4ac762fc3369b02bcd44bff4283de61e5c3101","cross_cats_sorted":["math.DG","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-07T02:36:08Z","title_canon_sha256":"b81c8702899327880ad04d087e563abdecf906bda47e0b1ca9f0f487a37d3e33"},"schema_version":"1.0","source":{"id":"1205.1270","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1270","created_at":"2026-05-18T03:33:26Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1270v2","created_at":"2026-05-18T03:33:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1270","created_at":"2026-05-18T03:33:26Z"},{"alias_kind":"pith_short_12","alias_value":"IOGZTS4MOL3G","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IOGZTS4MOL3GINXO","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IOGZTS4M","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:0ec99deb145daf037fd8e0e9c3ee2b98449da126e9468ce1e0e8bb34321b2af0","target":"graph","created_at":"2026-05-18T03:33:26Z","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":"Ehrhart's conjecture proposes a sharp upper bound on the volume of a convex body whose barycenter is its only interior lattice point. Recently, Berman and Berndtsson proved this conjecture for a class of rational polytopes including reflexive polytopes. In particular, they showed that the complex projective space has the maximal anticanonical degree among all toric Kaehler-Einstein Fano manifolds. In this note, we prove that projective space is the only such toric manifold with maximal degree by proving its corresponding convex-geometric statement. We also discuss a generalized version of Ehrh","authors_text":"Andreas Paffenholz, Benjamin Nill","cross_cats":["math.DG","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-07T02:36:08Z","title":"On the equality case in Ehrhart's volume conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1270","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:a992d122ec16ebc696eba44c3164b145a967d626dd0fcd7171136af0509ca24d","target":"record","created_at":"2026-05-18T03:33:26Z","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":"ddd6fcae49cf88dc2376454e1f4ac762fc3369b02bcd44bff4283de61e5c3101","cross_cats_sorted":["math.DG","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-07T02:36:08Z","title_canon_sha256":"b81c8702899327880ad04d087e563abdecf906bda47e0b1ca9f0f487a37d3e33"},"schema_version":"1.0","source":{"id":"1205.1270","kind":"arxiv","version":2}},"canonical_sha256":"438d99cb8c72f66436ee17d1a142fae4efeefaf68865537ef283171dc6990027","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"438d99cb8c72f66436ee17d1a142fae4efeefaf68865537ef283171dc6990027","first_computed_at":"2026-05-18T03:33:26.047002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:26.047002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RVG7GL1L6UvEK2IpnsZc7i/kRr/ZvsY4olHBaxjx0kW/dDqaP4kuH974jycV+dDo6nTf8fNiAUlNr217Rj9ZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:26.047780Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1270","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a992d122ec16ebc696eba44c3164b145a967d626dd0fcd7171136af0509ca24d","sha256:0ec99deb145daf037fd8e0e9c3ee2b98449da126e9468ce1e0e8bb34321b2af0"],"state_sha256":"f7525cffc1e4c1bc6d54a874e77d4d84c6b4495ebc03f6fddaf4197a97bd00ba"}