{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:N3OQEWC3FAQQRKUSK3XIZH33GY","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":"34daf53805be99f12d35ecca1dba90adb5bedce198a6f1aece71acbe7f875ec7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-12-13T23:47:24Z","title_canon_sha256":"3a0939b5b017ecd80c91893fc61c86b63b78fca8e4b20825b28d7ec52864df3f"},"schema_version":"1.0","source":{"id":"1112.3073","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3073","created_at":"2026-05-18T04:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3073v1","created_at":"2026-05-18T04:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3073","created_at":"2026-05-18T04:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"N3OQEWC3FAQQ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"N3OQEWC3FAQQRKUS","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"N3OQEWC3","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:26c5511aa251cb959a004530ed325b72f7c105461ff2cec95bc4e8b77823a88e","target":"graph","created_at":"2026-05-18T04:06:20Z","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 present proofs of the reverse Santal\\'{o} inequality, the existence of M-ellipsoids and the reverse Brunn-Minkowski inequality, using purely convex geometric tools. Our approach is based on properties of the isotropic position.","authors_text":"Apostolos Giannopoulos, Beatrice-Helen Vritsiou, Grigoris Paouris","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-12-13T23:47:24Z","title":"The isotropic position and the reverse Santal\\'{o} inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3073","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:cf7837f1da4a61d94f7ee66178b3deb5a6788dcc5dbf64aacc33386632c45777","target":"record","created_at":"2026-05-18T04:06:20Z","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":"34daf53805be99f12d35ecca1dba90adb5bedce198a6f1aece71acbe7f875ec7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-12-13T23:47:24Z","title_canon_sha256":"3a0939b5b017ecd80c91893fc61c86b63b78fca8e4b20825b28d7ec52864df3f"},"schema_version":"1.0","source":{"id":"1112.3073","kind":"arxiv","version":1}},"canonical_sha256":"6edd02585b282108aa9256ee8c9f7b36248e2a06678a0e018948be747f665ccf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6edd02585b282108aa9256ee8c9f7b36248e2a06678a0e018948be747f665ccf","first_computed_at":"2026-05-18T04:06:20.260165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:20.260165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NHpEdh0obNxyMsria5pxMW7Er6OooSDa+fOkwV+ujXJVUSLRQtiKd1wsX9Xh612vCRXnm8wFnwEvkdXYs6wHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:20.260853Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.3073","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf7837f1da4a61d94f7ee66178b3deb5a6788dcc5dbf64aacc33386632c45777","sha256:26c5511aa251cb959a004530ed325b72f7c105461ff2cec95bc4e8b77823a88e"],"state_sha256":"8ad56046724361b64e2c799be98e39848779098d8dcd786ab6903a636bc70b6d"}