{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:YR6XYIT75BBQUTW4GAPPOTNFP5","short_pith_number":"pith:YR6XYIT7","schema_version":"1.0","canonical_sha256":"c47d7c227fe8430a4edc301ef74da57f567f35da81bf75d4f077d0f7590dd65b","source":{"kind":"arxiv","id":"1908.02213","version":1},"attestation_state":"computed","paper":{"title":"A Universality Theorem for Nested Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","cs.DS","math.CO"],"primary_cat":"cs.CG","authors_text":"Andreas Holmsen, Michael G. Dobbins, Tillmann Miltzow","submitted_at":"2019-08-06T15:31:43Z","abstract_excerpt":"In a nutshell, we show that polynomials and nested polytopes are topological, algebraic and algorithmically equivalent. Given two polytops $A\\subseteq B$ and a number $k$, the Nested Polytope Problem (NPP) asks, if there exists a polytope $X$ on $k$ vertices such that $A\\subseteq X \\subseteq B$. The polytope $A$ is given by a set of vertices and the polytope $B$ is given by the defining hyperplanes. We show a universality theorem for NPP. Given an instance $I$ of the NPP, we define the solutions set of $I$ as $$ V'(I) = \\{(x_1,\\ldots,x_k)\\in \\mathbb{R}^{k\\cdot n} : A\\subseteq \\text{conv}(x_1,\\"},"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":"1908.02213","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-08-06T15:31:43Z","cross_cats_sorted":["cs.CC","cs.DM","cs.DS","math.CO"],"title_canon_sha256":"5fe818d90faddaf63eb4d198726c24633d7229427c44738ff3dc319a7737dcb4","abstract_canon_sha256":"05e557b9e46df2b388f2b8e54a959d724ffd6b6d659d52a6d26d7f2586f75a8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:51:52.140556Z","signature_b64":"S+A3y8ZBhkI1RunuAk/dR8Ld9oYrHhtQrhgWrW1a20ux0vrADoGQjd31C5STYrJVxxpZ/72uWdUeC2NFFvKLCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c47d7c227fe8430a4edc301ef74da57f567f35da81bf75d4f077d0f7590dd65b","last_reissued_at":"2026-07-04T23:51:52.140163Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:51:52.140163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Universality Theorem for Nested Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","cs.DS","math.CO"],"primary_cat":"cs.CG","authors_text":"Andreas Holmsen, Michael G. Dobbins, Tillmann Miltzow","submitted_at":"2019-08-06T15:31:43Z","abstract_excerpt":"In a nutshell, we show that polynomials and nested polytopes are topological, algebraic and algorithmically equivalent. Given two polytops $A\\subseteq B$ and a number $k$, the Nested Polytope Problem (NPP) asks, if there exists a polytope $X$ on $k$ vertices such that $A\\subseteq X \\subseteq B$. The polytope $A$ is given by a set of vertices and the polytope $B$ is given by the defining hyperplanes. We show a universality theorem for NPP. Given an instance $I$ of the NPP, we define the solutions set of $I$ as $$ V'(I) = \\{(x_1,\\ldots,x_k)\\in \\mathbb{R}^{k\\cdot n} : A\\subseteq \\text{conv}(x_1,\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02213","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.02213/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.02213","created_at":"2026-07-04T23:51:52.140219+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.02213v1","created_at":"2026-07-04T23:51:52.140219+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02213","created_at":"2026-07-04T23:51:52.140219+00:00"},{"alias_kind":"pith_short_12","alias_value":"YR6XYIT75BBQ","created_at":"2026-07-04T23:51:52.140219+00:00"},{"alias_kind":"pith_short_16","alias_value":"YR6XYIT75BBQUTW4","created_at":"2026-07-04T23:51:52.140219+00:00"},{"alias_kind":"pith_short_8","alias_value":"YR6XYIT7","created_at":"2026-07-04T23:51:52.140219+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.26749","citing_title":"The Nesting Bird Box Problem is ER-complete: Sharp Hardness Results for the Hidden Set Problem","ref_index":11,"is_internal_anchor":false},{"citing_arxiv_id":"2604.26749","citing_title":"The Nesting Bird Box Problem is ER-complete: Sharp Hardness Results for the Hidden Set Problem","ref_index":11,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YR6XYIT75BBQUTW4GAPPOTNFP5","json":"https://pith.science/pith/YR6XYIT75BBQUTW4GAPPOTNFP5.json","graph_json":"https://pith.science/api/pith-number/YR6XYIT75BBQUTW4GAPPOTNFP5/graph.json","events_json":"https://pith.science/api/pith-number/YR6XYIT75BBQUTW4GAPPOTNFP5/events.json","paper":"https://pith.science/paper/YR6XYIT7"},"agent_actions":{"view_html":"https://pith.science/pith/YR6XYIT75BBQUTW4GAPPOTNFP5","download_json":"https://pith.science/pith/YR6XYIT75BBQUTW4GAPPOTNFP5.json","view_paper":"https://pith.science/paper/YR6XYIT7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.02213&json=true","fetch_graph":"https://pith.science/api/pith-number/YR6XYIT75BBQUTW4GAPPOTNFP5/graph.json","fetch_events":"https://pith.science/api/pith-number/YR6XYIT75BBQUTW4GAPPOTNFP5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YR6XYIT75BBQUTW4GAPPOTNFP5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YR6XYIT75BBQUTW4GAPPOTNFP5/action/storage_attestation","attest_author":"https://pith.science/pith/YR6XYIT75BBQUTW4GAPPOTNFP5/action/author_attestation","sign_citation":"https://pith.science/pith/YR6XYIT75BBQUTW4GAPPOTNFP5/action/citation_signature","submit_replication":"https://pith.science/pith/YR6XYIT75BBQUTW4GAPPOTNFP5/action/replication_record"}},"created_at":"2026-07-04T23:51:52.140219+00:00","updated_at":"2026-07-04T23:51:52.140219+00:00"}