{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NPPZICDSJQFSCVARKK2GWYKE4O","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":"b12e25fb56182868877e0491cd7980513a77031f6bb520270866650ec59914d7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2025-06-18T11:36:58Z","title_canon_sha256":"90658c750e1745cab2044b7f189df6f1af1823e42d1387d74f68c6f8b13ce089"},"schema_version":"1.0","source":{"id":"2506.15370","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.15370","created_at":"2026-06-19T16:12:46Z"},{"alias_kind":"arxiv_version","alias_value":"2506.15370v2","created_at":"2026-06-19T16:12:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.15370","created_at":"2026-06-19T16:12:46Z"},{"alias_kind":"pith_short_12","alias_value":"NPPZICDSJQFS","created_at":"2026-06-19T16:12:46Z"},{"alias_kind":"pith_short_16","alias_value":"NPPZICDSJQFSCVAR","created_at":"2026-06-19T16:12:46Z"},{"alias_kind":"pith_short_8","alias_value":"NPPZICDS","created_at":"2026-06-19T16:12:46Z"}],"graph_snapshots":[{"event_id":"sha256:b72ec15991f21b4dd03eac57e3ad986f4242787044d56ef3a9f110fd0d5ecc01","target":"graph","created_at":"2026-06-19T16:12:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.15370/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by the discrete logarithmic Minkowski problem we study for a given matrix $U\\in\\mathbb{R}^{n\\times m}$ its cone-volume set $C_{\\tt cv}(U)$ consisting of all the cone-volume vectors of polytopes $P(U,b)=\\{ x\\in\\mathbb{R}^n : U^\\intercal x\\leq b\\}$, $b\\in\\mathbb{R}^n_{\\geq 0}$. We will show that $C_{\\tt cv}(U)$ is a path-connected semialgebraic set which extends former results in the planar case or for particular polytopes. Moreover, we define a subspace concentration polytope $P_{\\tt scc}(U)$ which represents geometrically the subspace concentration conditions for a finite discrete Bo","authors_text":"Martin Henk, Tom Baumbach","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2025-06-18T11:36:58Z","title":"On polynomial inequalities for cone-volumes of polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.15370","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":"sha256:6d6eed1c5e4dafdbfbcc658c8b4413d0eaddbfcdc23583073563542b706f0abc","target":"record","created_at":"2026-06-19T16:12:46Z","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":"b12e25fb56182868877e0491cd7980513a77031f6bb520270866650ec59914d7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2025-06-18T11:36:58Z","title_canon_sha256":"90658c750e1745cab2044b7f189df6f1af1823e42d1387d74f68c6f8b13ce089"},"schema_version":"1.0","source":{"id":"2506.15370","kind":"arxiv","version":2}},"canonical_sha256":"6bdf9408724c0b21541152b46b6144e3b257585db341b9d905bd1d5e9afe1765","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bdf9408724c0b21541152b46b6144e3b257585db341b9d905bd1d5e9afe1765","first_computed_at":"2026-06-19T16:12:46.322568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:46.322568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g5VjuH99uMZ54F1h9izkmGJ5cesawUJRJhe7dg0oxwtjqjXrkXw/q51mUyGT/2Zgk3RkEi+jXe57DDhZ4CYhCg==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:46.323030Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.15370","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d6eed1c5e4dafdbfbcc658c8b4413d0eaddbfcdc23583073563542b706f0abc","sha256:b72ec15991f21b4dd03eac57e3ad986f4242787044d56ef3a9f110fd0d5ecc01"],"state_sha256":"015a415833227ee10bb24ae98a2fd958c5456da5ff4d65c693a0a52a00b73f4c"}