{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:W3TEQWJXZ4DPIU6FRCFUECW4X6","short_pith_number":"pith:W3TEQWJX","schema_version":"1.0","canonical_sha256":"b6e6485937cf06f453c5888b420adcbfb9f8b8ca985de55a549cc08de6d81656","source":{"kind":"arxiv","id":"1509.02254","version":2},"attestation_state":"computed","paper":{"title":"Mixed Ehrhart polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Christian Haase, Martina Juhnke-Kubitzke, Raman Sanyal, Thorsten Theobald","submitted_at":"2015-09-08T05:22:23Z","abstract_excerpt":"For lattice polytopes $P_1,\\ldots, P_k \\subseteq \\mathbb{R}^d$, Bihan (2014) introduced the discrete mixed volume $\\mathrm{DMV}(P_1,\\dots,P_k)$ in analogy to the classical mixed volume. In this note we initiate the study of the associated mixed Ehrhart polynomial $\\mathrm{ME}_{P_1,\\dots,P_k}(n) = \\mathrm{DMV}(nP_1,\\dots,nP_k)$. We study properties of this polynomial and we give interpretations for some of its coefficients in terms of (discrete) mixed volumes. Bihan (2014) showed that the discrete mixed volume is always non-negative. Our investigations yield simpler proofs for certain special c"},"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":"1509.02254","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-08T05:22:23Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"0bf0d4eed3ab90391dc38603dc6da83ebd2796e3c280ac65c15278ccdcecbe30","abstract_canon_sha256":"8b967de9ea513779de1c93071f456d5369db20adfe3890e1df600275dfeef9ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:12.557189Z","signature_b64":"toi8MoWR7dYmlwlduOFtipnkTbhe4Oqb07hSorvOqNq8s+CTk1Hf2fkCMgEkHz65QazTkPo+94RMeFrKCVFJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6e6485937cf06f453c5888b420adcbfb9f8b8ca985de55a549cc08de6d81656","last_reissued_at":"2026-05-18T00:53:12.556671Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:12.556671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mixed Ehrhart polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Christian Haase, Martina Juhnke-Kubitzke, Raman Sanyal, Thorsten Theobald","submitted_at":"2015-09-08T05:22:23Z","abstract_excerpt":"For lattice polytopes $P_1,\\ldots, P_k \\subseteq \\mathbb{R}^d$, Bihan (2014) introduced the discrete mixed volume $\\mathrm{DMV}(P_1,\\dots,P_k)$ in analogy to the classical mixed volume. In this note we initiate the study of the associated mixed Ehrhart polynomial $\\mathrm{ME}_{P_1,\\dots,P_k}(n) = \\mathrm{DMV}(nP_1,\\dots,nP_k)$. We study properties of this polynomial and we give interpretations for some of its coefficients in terms of (discrete) mixed volumes. Bihan (2014) showed that the discrete mixed volume is always non-negative. Our investigations yield simpler proofs for certain special c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02254","kind":"arxiv","version":2},"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":"1509.02254","created_at":"2026-05-18T00:53:12.556733+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.02254v2","created_at":"2026-05-18T00:53:12.556733+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02254","created_at":"2026-05-18T00:53:12.556733+00:00"},{"alias_kind":"pith_short_12","alias_value":"W3TEQWJXZ4DP","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"W3TEQWJXZ4DPIU6F","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"W3TEQWJX","created_at":"2026-05-18T12:29:47.479230+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/W3TEQWJXZ4DPIU6FRCFUECW4X6","json":"https://pith.science/pith/W3TEQWJXZ4DPIU6FRCFUECW4X6.json","graph_json":"https://pith.science/api/pith-number/W3TEQWJXZ4DPIU6FRCFUECW4X6/graph.json","events_json":"https://pith.science/api/pith-number/W3TEQWJXZ4DPIU6FRCFUECW4X6/events.json","paper":"https://pith.science/paper/W3TEQWJX"},"agent_actions":{"view_html":"https://pith.science/pith/W3TEQWJXZ4DPIU6FRCFUECW4X6","download_json":"https://pith.science/pith/W3TEQWJXZ4DPIU6FRCFUECW4X6.json","view_paper":"https://pith.science/paper/W3TEQWJX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.02254&json=true","fetch_graph":"https://pith.science/api/pith-number/W3TEQWJXZ4DPIU6FRCFUECW4X6/graph.json","fetch_events":"https://pith.science/api/pith-number/W3TEQWJXZ4DPIU6FRCFUECW4X6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W3TEQWJXZ4DPIU6FRCFUECW4X6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W3TEQWJXZ4DPIU6FRCFUECW4X6/action/storage_attestation","attest_author":"https://pith.science/pith/W3TEQWJXZ4DPIU6FRCFUECW4X6/action/author_attestation","sign_citation":"https://pith.science/pith/W3TEQWJXZ4DPIU6FRCFUECW4X6/action/citation_signature","submit_replication":"https://pith.science/pith/W3TEQWJXZ4DPIU6FRCFUECW4X6/action/replication_record"}},"created_at":"2026-05-18T00:53:12.556733+00:00","updated_at":"2026-05-18T00:53:12.556733+00:00"}