{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:G5S7GPVOGPLDSUYAUBMWXFDUDW","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":"90b4d4b3dbef4f3ec58d603c12909d54108e5a76abe38d1d63ed3aa7c09c9bc7","cross_cats_sorted":["math.AG","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-05-22T08:09:05Z","title_canon_sha256":"64142e81a44d5b8e58f25f429c6abcbaa0cdad3bb15cf98eab58fe0301a72ff5"},"schema_version":"1.0","source":{"id":"1705.07599","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07599","created_at":"2026-05-18T00:44:05Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07599v1","created_at":"2026-05-18T00:44:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07599","created_at":"2026-05-18T00:44:05Z"},{"alias_kind":"pith_short_12","alias_value":"G5S7GPVOGPLD","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"G5S7GPVOGPLDSUYA","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"G5S7GPVO","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:ad3a98022663ba6b05d49fe7fc5029e27ad6398a8b4c4c6fbff1b226b6e1b47d","target":"graph","created_at":"2026-05-18T00:44:05Z","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 establish a natural and geometric 1-1 correspondence between projective toric varieties of dimension $n$ and horofunction compactifications of $\\mathbb{R}^n$ with respect to rational polyhedral norms. For this purpose, we explain a topological model of toric varieties. Consequently, toric varieties in algebraic geometry, normed spaces in convex analysis, and horofunction compactifications in metric geometry are directly and explicitly related.","authors_text":"Anna-Sofie Schilling, Lizhen Ji","cross_cats":["math.AG","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-05-22T08:09:05Z","title":"Toric Varieties vs. Horofunction Compactifications of Polyhedral Norms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07599","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":"sha256:4a9e2a9ccb9b2c04e7100d72b51890c156ebaac1bad96f84424b48f2186db503","target":"record","created_at":"2026-05-18T00:44:05Z","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":"90b4d4b3dbef4f3ec58d603c12909d54108e5a76abe38d1d63ed3aa7c09c9bc7","cross_cats_sorted":["math.AG","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-05-22T08:09:05Z","title_canon_sha256":"64142e81a44d5b8e58f25f429c6abcbaa0cdad3bb15cf98eab58fe0301a72ff5"},"schema_version":"1.0","source":{"id":"1705.07599","kind":"arxiv","version":1}},"canonical_sha256":"3765f33eae33d6395300a0596b94741d9560d9ab195000332512ee75f66675cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3765f33eae33d6395300a0596b94741d9560d9ab195000332512ee75f66675cf","first_computed_at":"2026-05-18T00:44:05.082628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:05.082628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bH6lBaBtQxGtmwmS1FID3nLFmmwAiIKIO9t390rMkC/vuDtVco8vj8NgHpv6ccBtj/6O1GolGL3dgE0dyeA2CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:05.083132Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.07599","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a9e2a9ccb9b2c04e7100d72b51890c156ebaac1bad96f84424b48f2186db503","sha256:ad3a98022663ba6b05d49fe7fc5029e27ad6398a8b4c4c6fbff1b226b6e1b47d"],"state_sha256":"11e9f20abaa6f76eedcd472d320bea5d99f36f43c37e59314fb67c03d212e6a8"}