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From this we conclude that any theory that admits a mixed Alexandrov-Fenchel inequality also admits a generalized Alexandrov-Fenchel inequality involving dually Lorentzian polynomials. As such we deduce generalized Alexandrov-Fenchel inequalities for mixed discriminants, for integrals of K\\\"ahler classes, for mixed"},"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":"2304.08399","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-04-17T16:06:28Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"4d8a365c4917be26e9e0de2c1f699cab8a4cba28a742d5ddb04f73c806eb4b26","abstract_canon_sha256":"a7d518dd66c86ed1ade0921ccef0252fcacf6e3ed1b917a785ad4f6c8b2ce7b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:15:28.891555Z","signature_b64":"DLXA7YUbCO6l/e7Jika2DfOwP9A6i9UXbwiDO4NGh5K29EyRHZSjdztRjmfj+YE8EdPk94yjzqByph74GWOgAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a738e1e7185079afb9039e44a6d97106b9c1343c508bed2f65b249f193822d63","last_reissued_at":"2026-07-05T06:15:28.891195Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:15:28.891195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dually Lorentzian Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Hendrik S\\\"u{\\ss}, Julius Ross, Thomas Wannerer","submitted_at":"2023-04-17T16:06:28Z","abstract_excerpt":"We introduce and study a notion of dually Lorentzian polynomials, and show that if $s$ is non-zero and dually Lorentzian then the operator \\[s(\\partial_{x_1},\\ldots,\\partial_{x_n}):\\mathbb R[x_1,\\ldots,x_n] \\to \\mathbb R[x_1,\\ldots,x_n]\\] preserves (strictly) Lorentzian polynomials. From this we conclude that any theory that admits a mixed Alexandrov-Fenchel inequality also admits a generalized Alexandrov-Fenchel inequality involving dually Lorentzian polynomials. As such we deduce generalized Alexandrov-Fenchel inequalities for mixed discriminants, for integrals of K\\\"ahler classes, for mixed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.08399","kind":"arxiv","version":3},"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/2304.08399/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":"2304.08399","created_at":"2026-07-05T06:15:28.891257+00:00"},{"alias_kind":"arxiv_version","alias_value":"2304.08399v3","created_at":"2026-07-05T06:15:28.891257+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.08399","created_at":"2026-07-05T06:15:28.891257+00:00"},{"alias_kind":"pith_short_12","alias_value":"U44ODZYYKB42","created_at":"2026-07-05T06:15:28.891257+00:00"},{"alias_kind":"pith_short_16","alias_value":"U44ODZYYKB427OID","created_at":"2026-07-05T06:15:28.891257+00:00"},{"alias_kind":"pith_short_8","alias_value":"U44ODZYY","created_at":"2026-07-05T06:15:28.891257+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.13153","citing_title":"Syzygies of polymatroidal ideals","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U44ODZYYKB427OIDTZCKNWLRA2","json":"https://pith.science/pith/U44ODZYYKB427OIDTZCKNWLRA2.json","graph_json":"https://pith.science/api/pith-number/U44ODZYYKB427OIDTZCKNWLRA2/graph.json","events_json":"https://pith.science/api/pith-number/U44ODZYYKB427OIDTZCKNWLRA2/events.json","paper":"https://pith.science/paper/U44ODZYY"},"agent_actions":{"view_html":"https://pith.science/pith/U44ODZYYKB427OIDTZCKNWLRA2","download_json":"https://pith.science/pith/U44ODZYYKB427OIDTZCKNWLRA2.json","view_paper":"https://pith.science/paper/U44ODZYY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2304.08399&json=true","fetch_graph":"https://pith.science/api/pith-number/U44ODZYYKB427OIDTZCKNWLRA2/graph.json","fetch_events":"https://pith.science/api/pith-number/U44ODZYYKB427OIDTZCKNWLRA2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U44ODZYYKB427OIDTZCKNWLRA2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U44ODZYYKB427OIDTZCKNWLRA2/action/storage_attestation","attest_author":"https://pith.science/pith/U44ODZYYKB427OIDTZCKNWLRA2/action/author_attestation","sign_citation":"https://pith.science/pith/U44ODZYYKB427OIDTZCKNWLRA2/action/citation_signature","submit_replication":"https://pith.science/pith/U44ODZYYKB427OIDTZCKNWLRA2/action/replication_record"}},"created_at":"2026-07-05T06:15:28.891257+00:00","updated_at":"2026-07-05T06:15:28.891257+00:00"}