{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:V56F5FGXHFE7P3DOP2RL2TJM7F","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":"d0cda13d6a5b72d88b7570ffbb284ad0d6862badb0696add59cd0b0b41e64ce4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-06T15:10:25Z","title_canon_sha256":"5f81f0cbf4d8038d08e9929e32a5a1715f7b1f8b4f95254e8a270dab57141793"},"schema_version":"1.0","source":{"id":"1806.02236","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02236","created_at":"2026-05-17T23:40:36Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02236v2","created_at":"2026-05-17T23:40:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02236","created_at":"2026-05-17T23:40:36Z"},{"alias_kind":"pith_short_12","alias_value":"V56F5FGXHFE7","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"V56F5FGXHFE7P3DO","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"V56F5FGX","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:cf10e607cfd620243f80d99301c578a1b7fa2f6a4d840b42747e3057eec15dae","target":"graph","created_at":"2026-05-17T23:40:36Z","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":"K3 polytopes appear in complements of tropical quartic surfaces. They are dual to regular unimodular central triangulations of reflexive polytopes in the fourth dilation of the standard tetrahedron. Exploring these combinatorial objects, we classify K3 polytopes with up to $30$ vertices. Their number is $36\\,297\\,333$. We study the singular loci of quartic surfaces that tropicalize to K3 polytopes. These surfaces are stable in the sense of Geometric Invariant Theory.","authors_text":"Bernd Sturmfels, Gabriele Balletti, Marta Panizzut","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-06T15:10:25Z","title":"K3 Polytopes and their Quartic Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02236","kind":"arxiv","version":2},"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":"sha256:69642082b2cd658f1e42f0b1b4234f658ef9df23a10cb04549f0c4e0f3294d5b","target":"record","created_at":"2026-05-17T23:40:36Z","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":"d0cda13d6a5b72d88b7570ffbb284ad0d6862badb0696add59cd0b0b41e64ce4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-06T15:10:25Z","title_canon_sha256":"5f81f0cbf4d8038d08e9929e32a5a1715f7b1f8b4f95254e8a270dab57141793"},"schema_version":"1.0","source":{"id":"1806.02236","kind":"arxiv","version":2}},"canonical_sha256":"af7c5e94d73949f7ec6e7ea2bd4d2cf955ecbc0f016faf684111d6c7066cac09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af7c5e94d73949f7ec6e7ea2bd4d2cf955ecbc0f016faf684111d6c7066cac09","first_computed_at":"2026-05-17T23:40:36.435688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:36.435688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NOvXpqQTkDP7ONDF4i1cAxEzmwL62JHHyiLEOiDxsmURBLAXSwp+lN6Xp6tFmq8nib2+nhtdyST48Km5zQjlBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:36.436161Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.02236","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69642082b2cd658f1e42f0b1b4234f658ef9df23a10cb04549f0c4e0f3294d5b","sha256:cf10e607cfd620243f80d99301c578a1b7fa2f6a4d840b42747e3057eec15dae"],"state_sha256":"d6f3e5d4eb8dd249c15ae94f9df8d84bd5a250d3e18d69bc9b8447ed21ff0016"}