{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HLVJKOQ35F47WUVW2XUDAIFSP2","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":"59ddd2df8d73ee9d3f528463b472ad85fdc5e61233ff50fd01111c6a2a734f0f","cross_cats_sorted":["math.DG","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-07-04T23:40:35Z","title_canon_sha256":"a6fe75ef892bec8883fdb15f35b34f08ee75b4edf1191dfc4240bd970ee36e63"},"schema_version":"1.0","source":{"id":"1207.1142","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1142","created_at":"2026-05-18T02:50:34Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1142v1","created_at":"2026-05-18T02:50:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1142","created_at":"2026-05-18T02:50:34Z"},{"alias_kind":"pith_short_12","alias_value":"HLVJKOQ35F47","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HLVJKOQ35F47WUVW","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HLVJKOQ3","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:ea4b667e5c59aa3f88c9053a3efd51895ffe4f3433acd463ff84a76fbbf20991","target":"graph","created_at":"2026-05-18T02:50:34Z","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"},"paper":{"abstract_excerpt":"We prove that the metric balls of a Hilbert geometry admit a volume growth at least polynomial of degree their dimension. We also characterise the convex polytopes as those having exactly polynomial volume growth of degree their dimension.","authors_text":"Constantin Vernicos","cross_cats":["math.DG","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-07-04T23:40:35Z","title":"Asymptotic volume in Hilbert Geometries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1142","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":"sha256:04c4c7af49e13d1fd7e303c94bc52747c58a4a5b20e96eefa9847fb12d8ab0f3","target":"record","created_at":"2026-05-18T02:50:34Z","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":"59ddd2df8d73ee9d3f528463b472ad85fdc5e61233ff50fd01111c6a2a734f0f","cross_cats_sorted":["math.DG","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-07-04T23:40:35Z","title_canon_sha256":"a6fe75ef892bec8883fdb15f35b34f08ee75b4edf1191dfc4240bd970ee36e63"},"schema_version":"1.0","source":{"id":"1207.1142","kind":"arxiv","version":1}},"canonical_sha256":"3aea953a1be979fb52b6d5e83020b27eba496212853376f2f9e8095ed367b0e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3aea953a1be979fb52b6d5e83020b27eba496212853376f2f9e8095ed367b0e4","first_computed_at":"2026-05-18T02:50:34.237825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:34.237825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SeWGFCvspO2z6w7f/8Nlnq+1Fn2n8vj0CZPGQX9ugo73vYuD9U4f84bH/dOM4FdP3tmOi7CcroCd/JWgp8T3Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:34.238452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1142","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04c4c7af49e13d1fd7e303c94bc52747c58a4a5b20e96eefa9847fb12d8ab0f3","sha256:ea4b667e5c59aa3f88c9053a3efd51895ffe4f3433acd463ff84a76fbbf20991"],"state_sha256":"fbb889f45a8f6db70b9fbb9fc9545f5d2f9aefa6c9885cc647a5f5852195c0b4"}