{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:53TLIK3OR7NBK27LNU56R4S4PL","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":"2be939141d5b332372aa4608d3365d5474e4da3c1dae023d42300332fe644e97","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-17T12:02:32Z","title_canon_sha256":"4bfcd6a9d34ab425509938d959d10b6c6df0eb63d65c5b481f0f107d7cc988b0"},"schema_version":"1.0","source":{"id":"2607.15886","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.15886","created_at":"2026-07-20T01:19:15Z"},{"alias_kind":"arxiv_version","alias_value":"2607.15886v1","created_at":"2026-07-20T01:19:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.15886","created_at":"2026-07-20T01:19:15Z"},{"alias_kind":"pith_short_12","alias_value":"53TLIK3OR7NB","created_at":"2026-07-20T01:19:15Z"},{"alias_kind":"pith_short_16","alias_value":"53TLIK3OR7NBK27L","created_at":"2026-07-20T01:19:15Z"},{"alias_kind":"pith_short_8","alias_value":"53TLIK3O","created_at":"2026-07-20T01:19:15Z"}],"graph_snapshots":[{"event_id":"sha256:78083b0a7c2fad855b9518fe81cf5fafa3b10dd5c5f84b50a9a0ad37c21a760f","target":"graph","created_at":"2026-07-20T01:19:15Z","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/2607.15886/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Every polynomial with real non-negative coefficients yields a finite probability distribution after normalization. The Ehrhart $h^*$-polynomial of a lattice polytope $P$ is a non-negative integer polynomial that encodes the integer-point counts for positive integer dilations of $P$. We study the corresponding finite distributions, which we call $h^*$-distributions. We determine the mean and variance of these distributions, establish a connection between higher moments and Ehrhart polynomial coefficients, and study their cluster points in the $d$-dimensional probability simplex. We consider the","authors_text":"Andr\\'es R. Vindas-Mel\\'endez, Benjamin Braun, Cesar J. Meza, Max Hlavacek, Santiago Morales","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-17T12:02:32Z","title":"Ehrhart $h^*$-distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.15886","kind":"arxiv","version":1},"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":"sha256:0e5d00f1945b72f4713b3affbe9ed7d6e2b0eee7965d952076768918da79e777","target":"record","created_at":"2026-07-20T01:19:15Z","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":"2be939141d5b332372aa4608d3365d5474e4da3c1dae023d42300332fe644e97","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-17T12:02:32Z","title_canon_sha256":"4bfcd6a9d34ab425509938d959d10b6c6df0eb63d65c5b481f0f107d7cc988b0"},"schema_version":"1.0","source":{"id":"2607.15886","kind":"arxiv","version":1}},"canonical_sha256":"eee6b42b6e8fda156beb6d3be8f25c7ae3cf77bb4ff418eb02b9b31b435ece98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eee6b42b6e8fda156beb6d3be8f25c7ae3cf77bb4ff418eb02b9b31b435ece98","first_computed_at":"2026-07-20T01:19:15.370932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-20T01:19:15.370932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pHKs9UFk0i9MdGebQQpV6ZT+UlBSBOzqauzhiu0omDWYEu6OmKekGCLWqjSGDGtwl06Dd4MMD92RCfhmOX76AQ==","signature_status":"signed_v1","signed_at":"2026-07-20T01:19:15.371749Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.15886","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e5d00f1945b72f4713b3affbe9ed7d6e2b0eee7965d952076768918da79e777","sha256:78083b0a7c2fad855b9518fe81cf5fafa3b10dd5c5f84b50a9a0ad37c21a760f"],"state_sha256":"b6c629cc30975a906dfbfc927c543f58ab2905391a9611abdb1c2ea60c0afd50"}