{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HJOB3LWJNL5N4WNKCKFV2XDD5H","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":"4ae14282869590332554e655556a175afc5914b93eaae492bea21156015832e7","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-11T23:00:32Z","title_canon_sha256":"1ca0e0259efe4c37a87e8a0dcbe684e33ea49cf648883c5bfe661acef19452b8"},"schema_version":"1.0","source":{"id":"1111.2880","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2880","created_at":"2026-05-18T04:03:19Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2880v2","created_at":"2026-05-18T04:03:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2880","created_at":"2026-05-18T04:03:19Z"},{"alias_kind":"pith_short_12","alias_value":"HJOB3LWJNL5N","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HJOB3LWJNL5N4WNK","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HJOB3LWJ","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:cb8baed6817c7ec963eba46e260ef3879393809574dfb845aeb2390b836e8fdf","target":"graph","created_at":"2026-05-18T04:03:19Z","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 present a formula for the degree of the discriminant of a smooth projective toric variety associated to a lattice polytope P, in terms of the number of integral points in the interior of dilates of faces of dimension greater or equal than $\\lceil \\frac {\\dim P} 2 \\rceil$.","authors_text":"Alicia Dickenstein, Benjamin Nill, Mich\\`ele Vergne","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-11T23:00:32Z","title":"A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2880","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":"sha256:5f616f39bfbcc78dee9e8a9e6878b40deffd83368e79db4542df52ddecc82e0e","target":"record","created_at":"2026-05-18T04:03:19Z","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":"4ae14282869590332554e655556a175afc5914b93eaae492bea21156015832e7","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-11T23:00:32Z","title_canon_sha256":"1ca0e0259efe4c37a87e8a0dcbe684e33ea49cf648883c5bfe661acef19452b8"},"schema_version":"1.0","source":{"id":"1111.2880","kind":"arxiv","version":2}},"canonical_sha256":"3a5c1daec96afade59aa128b5d5c63e9d94f8afe80ab8e18db794082826ed3b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a5c1daec96afade59aa128b5d5c63e9d94f8afe80ab8e18db794082826ed3b8","first_computed_at":"2026-05-18T04:03:19.042360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:19.042360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0VVRwmjX6tGIignBqrA94JNSbDB3Iyb8ZygCNmIB7lhXjOJhA+dEG4kVXCzkFvOKEn/geO9l74az/J1a8onKDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:19.042964Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.2880","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f616f39bfbcc78dee9e8a9e6878b40deffd83368e79db4542df52ddecc82e0e","sha256:cb8baed6817c7ec963eba46e260ef3879393809574dfb845aeb2390b836e8fdf"],"state_sha256":"1192406b3b203e077a3dba0369239df3881e4c5fc9f544ac22cc2f7a4d96f4f5"}