{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3SVXPDSQ6UGSH6V3LEDLBMPDWN","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":"29f2504bddafa24ea400d10f3b75cc8997b3c2fedcb5969bb1139e989cb1b1d1","cross_cats_sorted":["math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-07-31T15:26:56Z","title_canon_sha256":"093dcf7ff7408e8915e1a8f46342b6d6c69131ea7b5d2c7bd903daaa3127349a"},"schema_version":"1.0","source":{"id":"1207.7290","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.7290","created_at":"2026-05-18T03:49:46Z"},{"alias_kind":"arxiv_version","alias_value":"1207.7290v1","created_at":"2026-05-18T03:49:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.7290","created_at":"2026-05-18T03:49:46Z"},{"alias_kind":"pith_short_12","alias_value":"3SVXPDSQ6UGS","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3SVXPDSQ6UGSH6V3","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3SVXPDSQ","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:0c5656263ba89787f3259e2be03760d74218ba3db5ea4f01d5e6f30adac5a387","target":"graph","created_at":"2026-05-18T03:49:46Z","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":"Analogues of the classical inequalities from the Brunn-Minkowski theory for rotation intertwining additive maps of convex bodies are developed. Analogues are also proved of inequalities from the dual Brunn-Minkowski theory for intertwining additive maps of star bodies. These inequalities provide generalizations of results for projection and intersection bodies. As a corollary, a new Brunn-Minkowski inequality is obtained for the volume of polar projection bodies.","authors_text":"Franz E. Schuster","cross_cats":["math.DG","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-07-31T15:26:56Z","title":"Volume inequalities and additive maps of convex bodies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.7290","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":"sha256:8a01c4bf8302ddb522a1ec2c42ed708624860ff648d0378ece1f2ed393febb17","target":"record","created_at":"2026-05-18T03:49:46Z","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":"29f2504bddafa24ea400d10f3b75cc8997b3c2fedcb5969bb1139e989cb1b1d1","cross_cats_sorted":["math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-07-31T15:26:56Z","title_canon_sha256":"093dcf7ff7408e8915e1a8f46342b6d6c69131ea7b5d2c7bd903daaa3127349a"},"schema_version":"1.0","source":{"id":"1207.7290","kind":"arxiv","version":1}},"canonical_sha256":"dcab778e50f50d23fabb5906b0b1e3b352731a2121ff49fe17f08a166392a78d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcab778e50f50d23fabb5906b0b1e3b352731a2121ff49fe17f08a166392a78d","first_computed_at":"2026-05-18T03:49:46.268474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:46.268474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hbBPGgL8TggsHlXDQPvhelqjDEhKdudRg4BPYJtz0wfERwx6gjWjDQSSy1zmxDeSTOHVfzW8gYFImEdeCO1TDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:46.269042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.7290","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a01c4bf8302ddb522a1ec2c42ed708624860ff648d0378ece1f2ed393febb17","sha256:0c5656263ba89787f3259e2be03760d74218ba3db5ea4f01d5e6f30adac5a387"],"state_sha256":"9f1a3c35599c702cb8e827dfbcca02a0191d6ff6837f38282e1698c7d3ef10d8"}