{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SBDCN4ABXL54MUEDKV7K22HORV","short_pith_number":"pith:SBDCN4AB","canonical_record":{"source":{"id":"1606.06586","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-06-18T17:06:31Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"2c02fc87c621f0dbfe6ba82b7f653c78af25713a614426b9c54ad1bee6dd7b78","abstract_canon_sha256":"90e5e3b504a08a2887e3b6b074d655864f2bacc103f818c64c6df2bab82ac330"},"schema_version":"1.0"},"canonical_sha256":"904626f001bafbc65083557ead68ee8d65d9d3713e7e525137a1f765ce963824","source":{"kind":"arxiv","id":"1606.06586","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06586","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06586v4","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06586","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"SBDCN4ABXL54","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SBDCN4ABXL54MUED","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SBDCN4AB","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SBDCN4ABXL54MUEDKV7K22HORV","target":"record","payload":{"canonical_record":{"source":{"id":"1606.06586","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-06-18T17:06:31Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"2c02fc87c621f0dbfe6ba82b7f653c78af25713a614426b9c54ad1bee6dd7b78","abstract_canon_sha256":"90e5e3b504a08a2887e3b6b074d655864f2bacc103f818c64c6df2bab82ac330"},"schema_version":"1.0"},"canonical_sha256":"904626f001bafbc65083557ead68ee8d65d9d3713e7e525137a1f765ce963824","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:31.894216Z","signature_b64":"eqtoIXGXBgIS/GGGru8Ee+5wPkj+fff7S6LRBP3MEYWftb68kQS8Ytpd4Bo3iGtWIyWxR894VlIr94pd4+BkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"904626f001bafbc65083557ead68ee8d65d9d3713e7e525137a1f765ce963824","last_reissued_at":"2026-05-17T23:47:31.893573Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:31.893573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.06586","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xsjy3igDCLAn6DwqhG2VuoAbJHmI0lzbEkJJqNNA9oStO1L0/hqJDARMBqqmIZDGY+hthZvbanNmOKIL+F5YBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:29:02.084222Z"},"content_sha256":"85919da4251d8680a825120d08b60508d0ff1839377e8e80bc2df5cdbdf4897a","schema_version":"1.0","event_id":"sha256:85919da4251d8680a825120d08b60508d0ff1839377e8e80bc2df5cdbdf4897a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SBDCN4ABXL54MUEDKV7K22HORV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the stability of Brunn-Minkowski type inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Andrea Colesanti, Arnaud Marsiglietti, Galyna V. Livshyts","submitted_at":"2016-06-18T17:06:31Z","abstract_excerpt":"Log-Brunn-Minkowski inequality was conjectured by Bor\\\"oczky, Lutwak, Yang and Zhang \\cite{BLYZ}, and it states that a certain strengthening of the classical Brunn-Minkowski inequality is admissible in the case of symmetric convex sets. It was recently shown by Nayar, Zvavitch, the second and the third authors \\cite{LMNZ}, that Log-Brunn-Minkowski inequality implies a certain dimensional Brunn-Minkowski inequality for log-concave measures, which in the case of Gaussian measure was conjectured by Gardner and Zvavitch \\cite{GZ}.\n  In this note, we obtain stability results for both Log-Brunn-Mink"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06586","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aJK8O/KNZtG6GxKnLQyLQQdQpUhXPJQR8vEfWk1yyNp8/WI0k61N5U00QvPv9xeW3ZL9zxFsTR/08WO5hFBbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:29:02.084875Z"},"content_sha256":"66fa017a92f3600351f5483aac8659d629de6ed42dff1811ff404ab63116e8da","schema_version":"1.0","event_id":"sha256:66fa017a92f3600351f5483aac8659d629de6ed42dff1811ff404ab63116e8da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SBDCN4ABXL54MUEDKV7K22HORV/bundle.json","state_url":"https://pith.science/pith/SBDCN4ABXL54MUEDKV7K22HORV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SBDCN4ABXL54MUEDKV7K22HORV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T07:29:02Z","links":{"resolver":"https://pith.science/pith/SBDCN4ABXL54MUEDKV7K22HORV","bundle":"https://pith.science/pith/SBDCN4ABXL54MUEDKV7K22HORV/bundle.json","state":"https://pith.science/pith/SBDCN4ABXL54MUEDKV7K22HORV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SBDCN4ABXL54MUEDKV7K22HORV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SBDCN4ABXL54MUEDKV7K22HORV","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":"90e5e3b504a08a2887e3b6b074d655864f2bacc103f818c64c6df2bab82ac330","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-06-18T17:06:31Z","title_canon_sha256":"2c02fc87c621f0dbfe6ba82b7f653c78af25713a614426b9c54ad1bee6dd7b78"},"schema_version":"1.0","source":{"id":"1606.06586","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06586","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06586v4","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06586","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"SBDCN4ABXL54","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SBDCN4ABXL54MUED","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SBDCN4AB","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:66fa017a92f3600351f5483aac8659d629de6ed42dff1811ff404ab63116e8da","target":"graph","created_at":"2026-05-17T23:47:31Z","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":"Log-Brunn-Minkowski inequality was conjectured by Bor\\\"oczky, Lutwak, Yang and Zhang \\cite{BLYZ}, and it states that a certain strengthening of the classical Brunn-Minkowski inequality is admissible in the case of symmetric convex sets. It was recently shown by Nayar, Zvavitch, the second and the third authors \\cite{LMNZ}, that Log-Brunn-Minkowski inequality implies a certain dimensional Brunn-Minkowski inequality for log-concave measures, which in the case of Gaussian measure was conjectured by Gardner and Zvavitch \\cite{GZ}.\n  In this note, we obtain stability results for both Log-Brunn-Mink","authors_text":"Andrea Colesanti, Arnaud Marsiglietti, Galyna V. Livshyts","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-06-18T17:06:31Z","title":"On the stability of Brunn-Minkowski type inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06586","kind":"arxiv","version":4},"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":"sha256:85919da4251d8680a825120d08b60508d0ff1839377e8e80bc2df5cdbdf4897a","target":"record","created_at":"2026-05-17T23:47:31Z","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":"90e5e3b504a08a2887e3b6b074d655864f2bacc103f818c64c6df2bab82ac330","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-06-18T17:06:31Z","title_canon_sha256":"2c02fc87c621f0dbfe6ba82b7f653c78af25713a614426b9c54ad1bee6dd7b78"},"schema_version":"1.0","source":{"id":"1606.06586","kind":"arxiv","version":4}},"canonical_sha256":"904626f001bafbc65083557ead68ee8d65d9d3713e7e525137a1f765ce963824","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"904626f001bafbc65083557ead68ee8d65d9d3713e7e525137a1f765ce963824","first_computed_at":"2026-05-17T23:47:31.893573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:31.893573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eqtoIXGXBgIS/GGGru8Ee+5wPkj+fff7S6LRBP3MEYWftb68kQS8Ytpd4Bo3iGtWIyWxR894VlIr94pd4+BkCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:31.894216Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.06586","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85919da4251d8680a825120d08b60508d0ff1839377e8e80bc2df5cdbdf4897a","sha256:66fa017a92f3600351f5483aac8659d629de6ed42dff1811ff404ab63116e8da"],"state_sha256":"7c1f1638d80c233270de47abbd443e3b06de4dcf2c86665b2cf468b2f10405e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6O5ETrpirsbZ1c0nPslACZx0RS+oXgOScw6QjYzMwO1la5TT8LekCi9QRp9/BWcUrpmjr0iirDmEIAyqEkKMCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T07:29:02.087947Z","bundle_sha256":"ca8c0d332c5269f2da7d78d1507532a742ba7029db56df2bd8b22710f4b0ee2b"}}