{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:T6WIARFHRZX2DPVKQ363INCQJ2","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":"a540bc6042370343b9336be8366718620f3a5e70db9c2209c9966a418f6b1aab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-05-17T13:38:11Z","title_canon_sha256":"09818d0d32d0f7499908047748a9ec39538d473b4625b30b43db1ba2861fa5bd"},"schema_version":"1.0","source":{"id":"1705.06154","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06154","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06154v1","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06154","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"pith_short_12","alias_value":"T6WIARFHRZX2","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T6WIARFHRZX2DPVK","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T6WIARFH","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:03ab57be3df873fc8847dfc4a6a43f087984b308c19f058dc3b89f0fe9ee9678","target":"graph","created_at":"2026-05-18T00:44:18Z","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 will prove a reverse Rogers-Shephard inequality for log-concave functions. In some particular cases, the method used for general log-concave functions can be slightly improved, allowing us to prove volume estimates for polars of $\\ell_p$-diferences of convex bodies whose polar bodies under some condition on the barycenter of their polar bodies.","authors_text":"David Alonso-Guti\\'errez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-05-17T13:38:11Z","title":"A reverse Rogers-Shephard inequality for log-concave functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06154","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":"sha256:60452aaa91217fb2cc49ba70eff6e21a1d05dddcead0247bea57f0c09d9e89b5","target":"record","created_at":"2026-05-18T00:44:18Z","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":"a540bc6042370343b9336be8366718620f3a5e70db9c2209c9966a418f6b1aab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-05-17T13:38:11Z","title_canon_sha256":"09818d0d32d0f7499908047748a9ec39538d473b4625b30b43db1ba2861fa5bd"},"schema_version":"1.0","source":{"id":"1705.06154","kind":"arxiv","version":1}},"canonical_sha256":"9fac8044a78e6fa1beaa86fdb434504e9db545317794ddc40f596836847842b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fac8044a78e6fa1beaa86fdb434504e9db545317794ddc40f596836847842b1","first_computed_at":"2026-05-18T00:44:18.521407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:18.521407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Y2OTCxFXYd10cC9althLi5MtKv8Gl8xiC+ckoa9YoWS7aNPrlEnykYDG9iJaLVEBn7amMe+Mk8lfPqkG/rvCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:18.522006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.06154","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60452aaa91217fb2cc49ba70eff6e21a1d05dddcead0247bea57f0c09d9e89b5","sha256:03ab57be3df873fc8847dfc4a6a43f087984b308c19f058dc3b89f0fe9ee9678"],"state_sha256":"880ebf524aa03e7e296d322b350c2b87d2349e140ef3ee8dfd077f241ec5def1"}