{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FFW62UOB6P3SVOJGK56DWLVJNC","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":"b611220017126d6d111d5d5115696bc45a9a67167b454c47066bec6b8709ef88","cross_cats_sorted":["math.AC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-27T18:16:42Z","title_canon_sha256":"d415121c881cc1fa9101789662470658d7272c0ef1c225a0a8db744ada703b4b"},"schema_version":"1.0","source":{"id":"1605.08739","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08739","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08739v2","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08739","created_at":"2026-05-17T23:56:00Z"},{"alias_kind":"pith_short_12","alias_value":"FFW62UOB6P3S","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FFW62UOB6P3SVOJG","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FFW62UOB","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:763ba81bb3b49e2dc8fe15f73ff3ce3bc5ce263b4dbe0a8c83913e07dd9dccda","target":"graph","created_at":"2026-05-17T23:56:00Z","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 notion of a random toric surface modeled on a notion of a random graph. We then study some threshold phenomena related to the smoothness of the resulting surfaces.","authors_text":"Jay Yang","cross_cats":["math.AC","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-27T18:16:42Z","title":"Random Toric Surfaces and a Threshold for Smoothness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08739","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":"sha256:10b6c3c17314967258ef7dc78908f8152d83c377bd9f907d4727dbd9b337d14a","target":"record","created_at":"2026-05-17T23:56:00Z","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":"b611220017126d6d111d5d5115696bc45a9a67167b454c47066bec6b8709ef88","cross_cats_sorted":["math.AC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-27T18:16:42Z","title_canon_sha256":"d415121c881cc1fa9101789662470658d7272c0ef1c225a0a8db744ada703b4b"},"schema_version":"1.0","source":{"id":"1605.08739","kind":"arxiv","version":2}},"canonical_sha256":"296ded51c1f3f72ab926577c3b2ea968b312165a30e20df20fbdd759b5953216","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"296ded51c1f3f72ab926577c3b2ea968b312165a30e20df20fbdd759b5953216","first_computed_at":"2026-05-17T23:56:00.785040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:00.785040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+GG3sA1mA/LBHuJY9yTBI5aZ7FXxzGxe65BnjpzEXaM1ql89nTzy9KlVZO9LVCdp1AkXqjccyaUvS9NysfH2AA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:00.785759Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.08739","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10b6c3c17314967258ef7dc78908f8152d83c377bd9f907d4727dbd9b337d14a","sha256:763ba81bb3b49e2dc8fe15f73ff3ce3bc5ce263b4dbe0a8c83913e07dd9dccda"],"state_sha256":"dcda55838156593a734fec38747bad78e5502e3c2f25b033007e2cbf3527af7b"}