{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5BGAE2WHWFT5EAG7WDGYDRYFK3","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":"3da4f559a522eb0278b9d8f73d925f066b48c6e20efed6487e0799c272a1423b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-17T15:55:02Z","title_canon_sha256":"28c3605e7e6899895ec9519ec103d5a16f88dbd4266e2b70ca9afb8e52f19744"},"schema_version":"1.0","source":{"id":"1312.4834","kind":"arxiv","version":9}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4834","created_at":"2026-05-18T02:17:12Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4834v9","created_at":"2026-05-18T02:17:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4834","created_at":"2026-05-18T02:17:12Z"},{"alias_kind":"pith_short_12","alias_value":"5BGAE2WHWFT5","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5BGAE2WHWFT5EAG7","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5BGAE2WH","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:8aa28b0af9b68e8ab4a6659dac30ea1c4cda47e24d8ed8a2a702b8fed850df39","target":"graph","created_at":"2026-05-18T02:17:12Z","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":"In [Centro-affine invariants for smooth convex bodies, Int. Math. Res. Notices. doi: 10.1093/imrn/rnr110, 2011] Stancu introduced a family of centro-affine normal flows, $p$-flow, for $1\\leq p<\\infty.$ Here we investigate the asymptotic behavior of the planar $p$-flow for $p=\\infty$ in the class of smooth, origin-symmetric convex bodies. First, we prove that the $\\infty$-flow evolves suitably normalized origin-symmetric solutions to the unit disk in the Hausdorff metric, modulo $SL(2).$ Second, using the $\\infty$-flow and a Harnack estimate for this flow, we prove a stability version of the pl","authors_text":"Mohammad N. Ivaki","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-17T15:55:02Z","title":"The planar Busemann-Petty centroid inequality and its stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4834","kind":"arxiv","version":9},"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:fb31e1ee0df1e9b57515c9934d275f85f89884928b2642615d81c2e11529080a","target":"record","created_at":"2026-05-18T02:17:12Z","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":"3da4f559a522eb0278b9d8f73d925f066b48c6e20efed6487e0799c272a1423b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-17T15:55:02Z","title_canon_sha256":"28c3605e7e6899895ec9519ec103d5a16f88dbd4266e2b70ca9afb8e52f19744"},"schema_version":"1.0","source":{"id":"1312.4834","kind":"arxiv","version":9}},"canonical_sha256":"e84c026ac7b167d200dfb0cd81c70556dca20466bbc055bc8bafcd3ef6a6ffe9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e84c026ac7b167d200dfb0cd81c70556dca20466bbc055bc8bafcd3ef6a6ffe9","first_computed_at":"2026-05-18T02:17:12.424568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:12.424568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PiM6AUbvNOLPNIflacZXNFUC397j4SVr3paWoaqQfAtfh2e58xyLFaCZ/gsUIw1ERGbDAnqoTOoxdlZ4cysJAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:12.425204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.4834","source_kind":"arxiv","source_version":9}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb31e1ee0df1e9b57515c9934d275f85f89884928b2642615d81c2e11529080a","sha256:8aa28b0af9b68e8ab4a6659dac30ea1c4cda47e24d8ed8a2a702b8fed850df39"],"state_sha256":"a10eb62f4ce4d97ced2284d8c16e649cea40790b2881698e02cdda5db2033600"}