{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:LRFAPEGQV6U24HD2D3HER73LTT","short_pith_number":"pith:LRFAPEGQ","schema_version":"1.0","canonical_sha256":"5c4a0790d0afa9ae1c7a1ece48ff6b9cff37147ccdd2f30b82085fc0c5a427b1","source":{"kind":"arxiv","id":"2605.20905","version":1},"attestation_state":"computed","paper":{"title":"Horizontal miniatures and normal-sized miniatures of convex lattice polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Takashi Hirotsu","submitted_at":"2026-05-20T08:49:13Z","abstract_excerpt":"Let $d$ be a nonnegative integer, and let $P \\subset \\mathbb R^d$ be a $d$-dimensional convex lattice polytope. In this article, we prove that the ratio of the volume of a normal-sized miniature of $P$ to that of $P$ is $1:\\binom{2d+1}{d},$ which generalizes the known results for the unit hypercube and lattice simplices provided by the author. This theorem is proven by establishing that the number of horizontal miniatures of $P$ with resolution $t$ is a polynomial of degree $d+1$ in $t$ whose leading coefficient is $\\mathrm{vol}\\,(P)/(d+1),$ which is derived from Ehrhart theory."},"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":"2605.20905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-20T08:49:13Z","cross_cats_sorted":[],"title_canon_sha256":"4174386ea694116cadc93318df44ff3ea53b4980cdf68ff8cb34d273d8173d3f","abstract_canon_sha256":"606b37bf6822fa1c15b89f48b1a69f5ad310196659bcdce168da0865d4b2b1e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:27.325649Z","signature_b64":"14DYOe2w4+HaqNq8W9sPsPjgsKyfR63fTIOqfGbH7MlQYCUyRCuDIwb4nNIQDrjwCLpbUlNSXVjrm9i8REQoDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c4a0790d0afa9ae1c7a1ece48ff6b9cff37147ccdd2f30b82085fc0c5a427b1","last_reissued_at":"2026-05-21T01:05:27.325051Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:27.325051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Horizontal miniatures and normal-sized miniatures of convex lattice polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Takashi Hirotsu","submitted_at":"2026-05-20T08:49:13Z","abstract_excerpt":"Let $d$ be a nonnegative integer, and let $P \\subset \\mathbb R^d$ be a $d$-dimensional convex lattice polytope. In this article, we prove that the ratio of the volume of a normal-sized miniature of $P$ to that of $P$ is $1:\\binom{2d+1}{d},$ which generalizes the known results for the unit hypercube and lattice simplices provided by the author. This theorem is proven by establishing that the number of horizontal miniatures of $P$ with resolution $t$ is a polynomial of degree $d+1$ in $t$ whose leading coefficient is $\\mathrm{vol}\\,(P)/(d+1),$ which is derived from Ehrhart theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20905","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/2605.20905/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":"2605.20905","created_at":"2026-05-21T01:05:27.325135+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.20905v1","created_at":"2026-05-21T01:05:27.325135+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20905","created_at":"2026-05-21T01:05:27.325135+00:00"},{"alias_kind":"pith_short_12","alias_value":"LRFAPEGQV6U2","created_at":"2026-05-21T01:05:27.325135+00:00"},{"alias_kind":"pith_short_16","alias_value":"LRFAPEGQV6U24HD2","created_at":"2026-05-21T01:05:27.325135+00:00"},{"alias_kind":"pith_short_8","alias_value":"LRFAPEGQ","created_at":"2026-05-21T01:05:27.325135+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/LRFAPEGQV6U24HD2D3HER73LTT","json":"https://pith.science/pith/LRFAPEGQV6U24HD2D3HER73LTT.json","graph_json":"https://pith.science/api/pith-number/LRFAPEGQV6U24HD2D3HER73LTT/graph.json","events_json":"https://pith.science/api/pith-number/LRFAPEGQV6U24HD2D3HER73LTT/events.json","paper":"https://pith.science/paper/LRFAPEGQ"},"agent_actions":{"view_html":"https://pith.science/pith/LRFAPEGQV6U24HD2D3HER73LTT","download_json":"https://pith.science/pith/LRFAPEGQV6U24HD2D3HER73LTT.json","view_paper":"https://pith.science/paper/LRFAPEGQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.20905&json=true","fetch_graph":"https://pith.science/api/pith-number/LRFAPEGQV6U24HD2D3HER73LTT/graph.json","fetch_events":"https://pith.science/api/pith-number/LRFAPEGQV6U24HD2D3HER73LTT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LRFAPEGQV6U24HD2D3HER73LTT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LRFAPEGQV6U24HD2D3HER73LTT/action/storage_attestation","attest_author":"https://pith.science/pith/LRFAPEGQV6U24HD2D3HER73LTT/action/author_attestation","sign_citation":"https://pith.science/pith/LRFAPEGQV6U24HD2D3HER73LTT/action/citation_signature","submit_replication":"https://pith.science/pith/LRFAPEGQV6U24HD2D3HER73LTT/action/replication_record"}},"created_at":"2026-05-21T01:05:27.325135+00:00","updated_at":"2026-05-21T01:05:27.325135+00:00"}