{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MRICVDV2P7RBKDSUFC37KT67FX","short_pith_number":"pith:MRICVDV2","canonical_record":{"source":{"id":"1809.04051","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-09-11T17:32:57Z","cross_cats_sorted":[],"title_canon_sha256":"5b01758c82a9f7411b96fbb1f2bedbbf73b01418f84f7bb617ae0ed00866f4aa","abstract_canon_sha256":"63f194056cfd7fb3eb675be7ea2184a672c8a38c71ba8c69459e9635ee16ad6a"},"schema_version":"1.0"},"canonical_sha256":"64502a8eba7fe2150e5428b7f54fdf2dc5403615ea01b421a84cbeb7dd0e818a","source":{"kind":"arxiv","id":"1809.04051","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.04051","created_at":"2026-05-17T23:57:31Z"},{"alias_kind":"arxiv_version","alias_value":"1809.04051v2","created_at":"2026-05-17T23:57:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.04051","created_at":"2026-05-17T23:57:31Z"},{"alias_kind":"pith_short_12","alias_value":"MRICVDV2P7RB","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MRICVDV2P7RBKDSU","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MRICVDV2","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MRICVDV2P7RBKDSUFC37KT67FX","target":"record","payload":{"canonical_record":{"source":{"id":"1809.04051","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-09-11T17:32:57Z","cross_cats_sorted":[],"title_canon_sha256":"5b01758c82a9f7411b96fbb1f2bedbbf73b01418f84f7bb617ae0ed00866f4aa","abstract_canon_sha256":"63f194056cfd7fb3eb675be7ea2184a672c8a38c71ba8c69459e9635ee16ad6a"},"schema_version":"1.0"},"canonical_sha256":"64502a8eba7fe2150e5428b7f54fdf2dc5403615ea01b421a84cbeb7dd0e818a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:31.343091Z","signature_b64":"4TU7LEDIiZ0kkTFFJmCSZR93l+LBvMe+i+1/dHsfWMxxKWMDLf3pBJU40+WccqE3YH5wBCfpkwjHQD8RQ+T9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64502a8eba7fe2150e5428b7f54fdf2dc5403615ea01b421a84cbeb7dd0e818a","last_reissued_at":"2026-05-17T23:57:31.342501Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:31.342501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.04051","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JbFfKcWYjneeiLpTZw9rTPiCF6e3HPSeZ8YX4X01TKeyyV90DFqJPkxZXJja3QoLjCUIn99KYTlfrQmxQHmOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:11:25.939837Z"},"content_sha256":"c0413903eb8606ccd6fd43380ec206a4ea37cd491ba5b0db5f92d78c207cc6a9","schema_version":"1.0","event_id":"sha256:c0413903eb8606ccd6fd43380ec206a4ea37cd491ba5b0db5f92d78c207cc6a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MRICVDV2P7RBKDSUFC37KT67FX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Rogers-Shephard type inequalities for general measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Artem Zvavitch, David Alonso-Guti\\'errez, Jes\\'us Yepes Nicol\\'as, Mar\\'ia A. Hern\\'andez Cifre, Michael Roysdon","submitted_at":"2018-09-11T17:32:57Z","abstract_excerpt":"In this paper we prove a series of Rogers-Shephard type inequalities for convex bodies when dealing with measures on the Euclidean space with either radially decreasing densities, or quasi-concave densities attaining their maximum at the origin. Functional versions of classical Rogers-Shephard inequalities are also derived as consequences of our approach."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04051","kind":"arxiv","version":2},"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":"2026-05-17T23:57:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wKwFVJlFWKoi3PFs+m/qDJVMEP3O5IIuwoR6VwAWtDfl0YW00dCji8oFkABuqAdxwsGi6rMu6F2TzWd5JcmuCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:11:25.940541Z"},"content_sha256":"4fdd94e4d85821ee9fa69c3f32656f55f433b90bbb97dcaa237a0fb8fee0e46f","schema_version":"1.0","event_id":"sha256:4fdd94e4d85821ee9fa69c3f32656f55f433b90bbb97dcaa237a0fb8fee0e46f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MRICVDV2P7RBKDSUFC37KT67FX/bundle.json","state_url":"https://pith.science/pith/MRICVDV2P7RBKDSUFC37KT67FX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MRICVDV2P7RBKDSUFC37KT67FX/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":"2026-05-31T00:11:25Z","links":{"resolver":"https://pith.science/pith/MRICVDV2P7RBKDSUFC37KT67FX","bundle":"https://pith.science/pith/MRICVDV2P7RBKDSUFC37KT67FX/bundle.json","state":"https://pith.science/pith/MRICVDV2P7RBKDSUFC37KT67FX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MRICVDV2P7RBKDSUFC37KT67FX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MRICVDV2P7RBKDSUFC37KT67FX","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":"63f194056cfd7fb3eb675be7ea2184a672c8a38c71ba8c69459e9635ee16ad6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-09-11T17:32:57Z","title_canon_sha256":"5b01758c82a9f7411b96fbb1f2bedbbf73b01418f84f7bb617ae0ed00866f4aa"},"schema_version":"1.0","source":{"id":"1809.04051","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.04051","created_at":"2026-05-17T23:57:31Z"},{"alias_kind":"arxiv_version","alias_value":"1809.04051v2","created_at":"2026-05-17T23:57:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.04051","created_at":"2026-05-17T23:57:31Z"},{"alias_kind":"pith_short_12","alias_value":"MRICVDV2P7RB","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MRICVDV2P7RBKDSU","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MRICVDV2","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:4fdd94e4d85821ee9fa69c3f32656f55f433b90bbb97dcaa237a0fb8fee0e46f","target":"graph","created_at":"2026-05-17T23:57:31Z","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":"In this paper we prove a series of Rogers-Shephard type inequalities for convex bodies when dealing with measures on the Euclidean space with either radially decreasing densities, or quasi-concave densities attaining their maximum at the origin. Functional versions of classical Rogers-Shephard inequalities are also derived as consequences of our approach.","authors_text":"Artem Zvavitch, David Alonso-Guti\\'errez, Jes\\'us Yepes Nicol\\'as, Mar\\'ia A. Hern\\'andez Cifre, Michael Roysdon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-09-11T17:32:57Z","title":"On Rogers-Shephard type inequalities for general measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04051","kind":"arxiv","version":2},"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:c0413903eb8606ccd6fd43380ec206a4ea37cd491ba5b0db5f92d78c207cc6a9","target":"record","created_at":"2026-05-17T23:57:31Z","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":"63f194056cfd7fb3eb675be7ea2184a672c8a38c71ba8c69459e9635ee16ad6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-09-11T17:32:57Z","title_canon_sha256":"5b01758c82a9f7411b96fbb1f2bedbbf73b01418f84f7bb617ae0ed00866f4aa"},"schema_version":"1.0","source":{"id":"1809.04051","kind":"arxiv","version":2}},"canonical_sha256":"64502a8eba7fe2150e5428b7f54fdf2dc5403615ea01b421a84cbeb7dd0e818a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64502a8eba7fe2150e5428b7f54fdf2dc5403615ea01b421a84cbeb7dd0e818a","first_computed_at":"2026-05-17T23:57:31.342501Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:31.342501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4TU7LEDIiZ0kkTFFJmCSZR93l+LBvMe+i+1/dHsfWMxxKWMDLf3pBJU40+WccqE3YH5wBCfpkwjHQD8RQ+T9AA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:31.343091Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.04051","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0413903eb8606ccd6fd43380ec206a4ea37cd491ba5b0db5f92d78c207cc6a9","sha256:4fdd94e4d85821ee9fa69c3f32656f55f433b90bbb97dcaa237a0fb8fee0e46f"],"state_sha256":"d50e3ef358c692d8cea4d9c91de3762f00ee589201072cb475c3fc58690ad46f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y+p4VpezALS5rw5i/bBqaavedideJKdBit8aELvJ1H/sfusuaojeyzcDub4AkyVcTo2tWog+f2foSvPSU4ufAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T00:11:25.944122Z","bundle_sha256":"5f3bc40fb870e2548a2f7b4ae7f5c5818cd0c511a6d61adf4aaefb9cd34959d4"}}