{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:YAWLEQRRWMY4VVLZHRZOSIJ3OM","short_pith_number":"pith:YAWLEQRR","schema_version":"1.0","canonical_sha256":"c02cb24231b331cad5793c72e9213b73294e1ec9610cb754ef671378ae21fc83","source":{"kind":"arxiv","id":"1702.04237","version":1},"attestation_state":"computed","paper":{"title":"Minkowski additive operators under volume constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Andrea Colesanti, Eugenia Saor\\'in G\\'omez, Judit Abardia-Ev\\'equoz","submitted_at":"2017-02-14T14:40:26Z","abstract_excerpt":"We investigate Minkowski additive, continuous, and translation invariant operators $\\Phi:\\mathcal{K}^n\\to\\mathcal{K}^n$ defined on the family of convex bodies such that the volume of the image $\\Phi(K)$ is bounded from above and below by multiples of the volume of the convex body $K$, uniformly in $K$. We obtain a representation result for an infinite subcone contained in the cone formed by this type of operators. Under the additional assumption of monotonicity or $SO(n)$-equivariance, we obtain new characterization results for the difference body operator."},"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":"1702.04237","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-02-14T14:40:26Z","cross_cats_sorted":[],"title_canon_sha256":"bbba2a54ae8a5f6d8a1f5605f223b231369845367ad55b6f161651de4913418d","abstract_canon_sha256":"f999d6ac7836f90c324f3436e32e6636220e749a1527848b12351a6393cfd44d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:48.656407Z","signature_b64":"vKCOuMibH+6o0Wwr+C9Aih8Byj2aT3wLyh/8hmfxXWk1hmtWGpd9jH3OfnxLWwBTuLHX0CJwJUFKiZI+CQE7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c02cb24231b331cad5793c72e9213b73294e1ec9610cb754ef671378ae21fc83","last_reissued_at":"2026-05-18T00:50:48.655761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:48.655761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minkowski additive operators under volume constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Andrea Colesanti, Eugenia Saor\\'in G\\'omez, Judit Abardia-Ev\\'equoz","submitted_at":"2017-02-14T14:40:26Z","abstract_excerpt":"We investigate Minkowski additive, continuous, and translation invariant operators $\\Phi:\\mathcal{K}^n\\to\\mathcal{K}^n$ defined on the family of convex bodies such that the volume of the image $\\Phi(K)$ is bounded from above and below by multiples of the volume of the convex body $K$, uniformly in $K$. We obtain a representation result for an infinite subcone contained in the cone formed by this type of operators. Under the additional assumption of monotonicity or $SO(n)$-equivariance, we obtain new characterization results for the difference body operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04237","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":"1702.04237","created_at":"2026-05-18T00:50:48.655858+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.04237v1","created_at":"2026-05-18T00:50:48.655858+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04237","created_at":"2026-05-18T00:50:48.655858+00:00"},{"alias_kind":"pith_short_12","alias_value":"YAWLEQRRWMY4","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"YAWLEQRRWMY4VVLZ","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"YAWLEQRR","created_at":"2026-05-18T12:31:56.362134+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/YAWLEQRRWMY4VVLZHRZOSIJ3OM","json":"https://pith.science/pith/YAWLEQRRWMY4VVLZHRZOSIJ3OM.json","graph_json":"https://pith.science/api/pith-number/YAWLEQRRWMY4VVLZHRZOSIJ3OM/graph.json","events_json":"https://pith.science/api/pith-number/YAWLEQRRWMY4VVLZHRZOSIJ3OM/events.json","paper":"https://pith.science/paper/YAWLEQRR"},"agent_actions":{"view_html":"https://pith.science/pith/YAWLEQRRWMY4VVLZHRZOSIJ3OM","download_json":"https://pith.science/pith/YAWLEQRRWMY4VVLZHRZOSIJ3OM.json","view_paper":"https://pith.science/paper/YAWLEQRR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.04237&json=true","fetch_graph":"https://pith.science/api/pith-number/YAWLEQRRWMY4VVLZHRZOSIJ3OM/graph.json","fetch_events":"https://pith.science/api/pith-number/YAWLEQRRWMY4VVLZHRZOSIJ3OM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YAWLEQRRWMY4VVLZHRZOSIJ3OM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YAWLEQRRWMY4VVLZHRZOSIJ3OM/action/storage_attestation","attest_author":"https://pith.science/pith/YAWLEQRRWMY4VVLZHRZOSIJ3OM/action/author_attestation","sign_citation":"https://pith.science/pith/YAWLEQRRWMY4VVLZHRZOSIJ3OM/action/citation_signature","submit_replication":"https://pith.science/pith/YAWLEQRRWMY4VVLZHRZOSIJ3OM/action/replication_record"}},"created_at":"2026-05-18T00:50:48.655858+00:00","updated_at":"2026-05-18T00:50:48.655858+00:00"}