{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:PEHF2LGQGPEEJBJ4N7ZSIDKOZB","short_pith_number":"pith:PEHF2LGQ","schema_version":"1.0","canonical_sha256":"790e5d2cd033c844853c6ff3240d4ec85b6a166307d4b96b77c7eebc684b9dbb","source":{"kind":"arxiv","id":"2606.25641","version":1},"attestation_state":"computed","paper":{"title":"Towards Hodge-Riemann relations for non-Archimedean analogs of valuations on convex sets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Semyon Alesker","submitted_at":"2026-06-24T09:50:05Z","abstract_excerpt":"In [8], a non-Archimedean analogue of the space of translation-invariant even valuations on convex sets was introduced. In [7], motivated by a further analogy with the classical theory, this space was equipped with two multiplicative structures, the product and the convolution. Both structures satisfy Poincare duality and the (non-mixed) hard Lefschetz theorem. In this paper, we formulate a conjecture concerning a more general mixed versions of the hard Lefschetz theorem and the Hodge-Riemann relations. We prove the non-mixed Hodge-Riemann relations in degree 1 for the product and, equivalentl"},"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":"2606.25641","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2026-06-24T09:50:05Z","cross_cats_sorted":[],"title_canon_sha256":"a4a1b70b96ef6c4515a959ff4a50ff3a1d370c6471cff79be28829e8934b19c3","abstract_canon_sha256":"2ddfb0d73aed6afd34dd4847ce661efda32e6832539cd2a324cc6d377820937c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T01:18:11.451234Z","signature_b64":"CHSPbQdWe/uPKeCcKE8y+sRCzlX8dIpDPT5OyA5cmhMrht0XkucQLzQJIspH9zP8WLIh8vHafomIrRcEYtSWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"790e5d2cd033c844853c6ff3240d4ec85b6a166307d4b96b77c7eebc684b9dbb","last_reissued_at":"2026-06-25T01:18:11.450834Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T01:18:11.450834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards Hodge-Riemann relations for non-Archimedean analogs of valuations on convex sets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Semyon Alesker","submitted_at":"2026-06-24T09:50:05Z","abstract_excerpt":"In [8], a non-Archimedean analogue of the space of translation-invariant even valuations on convex sets was introduced. In [7], motivated by a further analogy with the classical theory, this space was equipped with two multiplicative structures, the product and the convolution. Both structures satisfy Poincare duality and the (non-mixed) hard Lefschetz theorem. In this paper, we formulate a conjecture concerning a more general mixed versions of the hard Lefschetz theorem and the Hodge-Riemann relations. We prove the non-mixed Hodge-Riemann relations in degree 1 for the product and, equivalentl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25641","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/2606.25641/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":"2606.25641","created_at":"2026-06-25T01:18:11.450894+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.25641v1","created_at":"2026-06-25T01:18:11.450894+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.25641","created_at":"2026-06-25T01:18:11.450894+00:00"},{"alias_kind":"pith_short_12","alias_value":"PEHF2LGQGPEE","created_at":"2026-06-25T01:18:11.450894+00:00"},{"alias_kind":"pith_short_16","alias_value":"PEHF2LGQGPEEJBJ4","created_at":"2026-06-25T01:18:11.450894+00:00"},{"alias_kind":"pith_short_8","alias_value":"PEHF2LGQ","created_at":"2026-06-25T01:18:11.450894+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/PEHF2LGQGPEEJBJ4N7ZSIDKOZB","json":"https://pith.science/pith/PEHF2LGQGPEEJBJ4N7ZSIDKOZB.json","graph_json":"https://pith.science/api/pith-number/PEHF2LGQGPEEJBJ4N7ZSIDKOZB/graph.json","events_json":"https://pith.science/api/pith-number/PEHF2LGQGPEEJBJ4N7ZSIDKOZB/events.json","paper":"https://pith.science/paper/PEHF2LGQ"},"agent_actions":{"view_html":"https://pith.science/pith/PEHF2LGQGPEEJBJ4N7ZSIDKOZB","download_json":"https://pith.science/pith/PEHF2LGQGPEEJBJ4N7ZSIDKOZB.json","view_paper":"https://pith.science/paper/PEHF2LGQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.25641&json=true","fetch_graph":"https://pith.science/api/pith-number/PEHF2LGQGPEEJBJ4N7ZSIDKOZB/graph.json","fetch_events":"https://pith.science/api/pith-number/PEHF2LGQGPEEJBJ4N7ZSIDKOZB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PEHF2LGQGPEEJBJ4N7ZSIDKOZB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PEHF2LGQGPEEJBJ4N7ZSIDKOZB/action/storage_attestation","attest_author":"https://pith.science/pith/PEHF2LGQGPEEJBJ4N7ZSIDKOZB/action/author_attestation","sign_citation":"https://pith.science/pith/PEHF2LGQGPEEJBJ4N7ZSIDKOZB/action/citation_signature","submit_replication":"https://pith.science/pith/PEHF2LGQGPEEJBJ4N7ZSIDKOZB/action/replication_record"}},"created_at":"2026-06-25T01:18:11.450894+00:00","updated_at":"2026-06-25T01:18:11.450894+00:00"}