{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JGQVV2FU5EUFBDYUVQTHUZAQRO","short_pith_number":"pith:JGQVV2FU","schema_version":"1.0","canonical_sha256":"49a15ae8b4e928508f14ac267a64108baa159d43ace4417201da6f7e6afe7d1c","source":{"kind":"arxiv","id":"1608.03435","version":1},"attestation_state":"computed","paper":{"title":"Volume difference inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Alexander Koldobsky, Apostolos Giannopoulos","submitted_at":"2016-08-11T12:36:30Z","abstract_excerpt":"We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these bodies. We also provide extensions in which volume is replaced by an arbitrary measure."},"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":"1608.03435","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-08-11T12:36:30Z","cross_cats_sorted":[],"title_canon_sha256":"0b5fa3139ff75454415c96405c646726b200db1bbae1b3c0ad47cb538b1eafc4","abstract_canon_sha256":"cd7eea39e363d42d505a944e050716bf04a8d2a321d97dbc3805626363a2265e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:28.933932Z","signature_b64":"qm91oFT5clhsfBtZtScTz3UifknDXxrJXcTZm7mkkRtuzBAUHqL7+jlzHU/VmTzb4wKKoyylHu8Em07j6wTSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49a15ae8b4e928508f14ac267a64108baa159d43ace4417201da6f7e6afe7d1c","last_reissued_at":"2026-05-18T01:09:28.933453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:28.933453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Volume difference inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Alexander Koldobsky, Apostolos Giannopoulos","submitted_at":"2016-08-11T12:36:30Z","abstract_excerpt":"We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these bodies. We also provide extensions in which volume is replaced by an arbitrary measure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03435","kind":"arxiv","version":1},"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":"1608.03435","created_at":"2026-05-18T01:09:28.933527+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.03435v1","created_at":"2026-05-18T01:09:28.933527+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03435","created_at":"2026-05-18T01:09:28.933527+00:00"},{"alias_kind":"pith_short_12","alias_value":"JGQVV2FU5EUF","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JGQVV2FU5EUFBDYU","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JGQVV2FU","created_at":"2026-05-18T12:30:25.849896+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/JGQVV2FU5EUFBDYUVQTHUZAQRO","json":"https://pith.science/pith/JGQVV2FU5EUFBDYUVQTHUZAQRO.json","graph_json":"https://pith.science/api/pith-number/JGQVV2FU5EUFBDYUVQTHUZAQRO/graph.json","events_json":"https://pith.science/api/pith-number/JGQVV2FU5EUFBDYUVQTHUZAQRO/events.json","paper":"https://pith.science/paper/JGQVV2FU"},"agent_actions":{"view_html":"https://pith.science/pith/JGQVV2FU5EUFBDYUVQTHUZAQRO","download_json":"https://pith.science/pith/JGQVV2FU5EUFBDYUVQTHUZAQRO.json","view_paper":"https://pith.science/paper/JGQVV2FU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.03435&json=true","fetch_graph":"https://pith.science/api/pith-number/JGQVV2FU5EUFBDYUVQTHUZAQRO/graph.json","fetch_events":"https://pith.science/api/pith-number/JGQVV2FU5EUFBDYUVQTHUZAQRO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JGQVV2FU5EUFBDYUVQTHUZAQRO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JGQVV2FU5EUFBDYUVQTHUZAQRO/action/storage_attestation","attest_author":"https://pith.science/pith/JGQVV2FU5EUFBDYUVQTHUZAQRO/action/author_attestation","sign_citation":"https://pith.science/pith/JGQVV2FU5EUFBDYUVQTHUZAQRO/action/citation_signature","submit_replication":"https://pith.science/pith/JGQVV2FU5EUFBDYUVQTHUZAQRO/action/replication_record"}},"created_at":"2026-05-18T01:09:28.933527+00:00","updated_at":"2026-05-18T01:09:28.933527+00:00"}