{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6W5RZA7IZHHVDG7YVVPZIPAVUM","short_pith_number":"pith:6W5RZA7I","schema_version":"1.0","canonical_sha256":"f5bb1c83e8c9cf519bf8ad5f943c15a317030191356c8fe4645e48ed7988d7e8","source":{"kind":"arxiv","id":"1710.10708","version":4},"attestation_state":"computed","paper":{"title":"A note on the quantitative local version of the log-Brunn-Minkowski inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrea Colesanti, Galyna V. Livshyts","submitted_at":"2017-10-29T22:36:04Z","abstract_excerpt":"We prove that the log-Brunn-Minkowski inequality \\begin{equation*} |\\lambda K+_0 (1-\\lambda)L|\\geq |K|^{\\lambda}|L|^{1-\\lambda} \\end{equation*} (where $|\\cdot|$ is the Lebesgue measure and $+_0$ is the so-called log-addition) holds when $K\\subset\\mathbb{R}^n$ is a ball and $L$ is a symmetric convex body in a suitable $C^2$ neighborhood of $K$."},"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":"1710.10708","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-29T22:36:04Z","cross_cats_sorted":[],"title_canon_sha256":"47f364d68466eb05447df777b9be04d1b0f7dedc0de28702b9fc3d0f3b232d68","abstract_canon_sha256":"3391a501d1533d419e79414476bd196ff6544af5ba6d620f57660e35948eabd9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:15.919522Z","signature_b64":"w+8Ok7Em3ffJKAPX4mFHS7Ranzo06GwepRGl9q7A2r9EjPjzEvKhQ/c6cOnScqFGth0AWhstOxmm59h3ipnsBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5bb1c83e8c9cf519bf8ad5f943c15a317030191356c8fe4645e48ed7988d7e8","last_reissued_at":"2026-05-18T00:22:15.918932Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:15.918932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the quantitative local version of the log-Brunn-Minkowski inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrea Colesanti, Galyna V. Livshyts","submitted_at":"2017-10-29T22:36:04Z","abstract_excerpt":"We prove that the log-Brunn-Minkowski inequality \\begin{equation*} |\\lambda K+_0 (1-\\lambda)L|\\geq |K|^{\\lambda}|L|^{1-\\lambda} \\end{equation*} (where $|\\cdot|$ is the Lebesgue measure and $+_0$ is the so-called log-addition) holds when $K\\subset\\mathbb{R}^n$ is a ball and $L$ is a symmetric convex body in a suitable $C^2$ neighborhood of $K$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10708","kind":"arxiv","version":4},"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":"1710.10708","created_at":"2026-05-18T00:22:15.919024+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.10708v4","created_at":"2026-05-18T00:22:15.919024+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10708","created_at":"2026-05-18T00:22:15.919024+00:00"},{"alias_kind":"pith_short_12","alias_value":"6W5RZA7IZHHV","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6W5RZA7IZHHVDG7Y","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6W5RZA7I","created_at":"2026-05-18T12:31:03.183658+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/6W5RZA7IZHHVDG7YVVPZIPAVUM","json":"https://pith.science/pith/6W5RZA7IZHHVDG7YVVPZIPAVUM.json","graph_json":"https://pith.science/api/pith-number/6W5RZA7IZHHVDG7YVVPZIPAVUM/graph.json","events_json":"https://pith.science/api/pith-number/6W5RZA7IZHHVDG7YVVPZIPAVUM/events.json","paper":"https://pith.science/paper/6W5RZA7I"},"agent_actions":{"view_html":"https://pith.science/pith/6W5RZA7IZHHVDG7YVVPZIPAVUM","download_json":"https://pith.science/pith/6W5RZA7IZHHVDG7YVVPZIPAVUM.json","view_paper":"https://pith.science/paper/6W5RZA7I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.10708&json=true","fetch_graph":"https://pith.science/api/pith-number/6W5RZA7IZHHVDG7YVVPZIPAVUM/graph.json","fetch_events":"https://pith.science/api/pith-number/6W5RZA7IZHHVDG7YVVPZIPAVUM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6W5RZA7IZHHVDG7YVVPZIPAVUM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6W5RZA7IZHHVDG7YVVPZIPAVUM/action/storage_attestation","attest_author":"https://pith.science/pith/6W5RZA7IZHHVDG7YVVPZIPAVUM/action/author_attestation","sign_citation":"https://pith.science/pith/6W5RZA7IZHHVDG7YVVPZIPAVUM/action/citation_signature","submit_replication":"https://pith.science/pith/6W5RZA7IZHHVDG7YVVPZIPAVUM/action/replication_record"}},"created_at":"2026-05-18T00:22:15.919024+00:00","updated_at":"2026-05-18T00:22:15.919024+00:00"}