{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:L7URNI3U3QDLVVK6YEND4A4ODF","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":"ca6d97a89c3c1960a9c5a29a0224db6901427c010f0bb88dc28ae2e11c4d4220","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-16T04:42:15Z","title_canon_sha256":"1591dc45b9a5707347b6862ecb20576b2fef3433cedaaed81f99870be0fcc76a"},"schema_version":"1.0","source":{"id":"1805.06127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06127","created_at":"2026-05-18T00:15:48Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06127v1","created_at":"2026-05-18T00:15:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06127","created_at":"2026-05-18T00:15:48Z"},{"alias_kind":"pith_short_12","alias_value":"L7URNI3U3QDL","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L7URNI3U3QDLVVK6","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L7URNI3U","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:fc9f78d05dfbb0a1705fa4f12b440bb86a446d4beb575b5141ab5d555b53d60b","target":"graph","created_at":"2026-05-18T00:15:48Z","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":"This is an appendix to arXiv:1610.04888, \"Quantitative null-cobordism\", which improves one of the main results of that paper to a near-sharp one. It is not a self-contained paper.","authors_text":"Fedor Manin, Shmuel Weinberger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-16T04:42:15Z","title":"The Gromov--Guth--Whitney embedding theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06127","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:ef51a7083a97e9d73974df36e8aa7eea78637b8b5f1d221f4598c17976d1bb00","target":"record","created_at":"2026-05-18T00:15:48Z","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":"ca6d97a89c3c1960a9c5a29a0224db6901427c010f0bb88dc28ae2e11c4d4220","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-16T04:42:15Z","title_canon_sha256":"1591dc45b9a5707347b6862ecb20576b2fef3433cedaaed81f99870be0fcc76a"},"schema_version":"1.0","source":{"id":"1805.06127","kind":"arxiv","version":1}},"canonical_sha256":"5fe916a374dc06bad55ec11a3e038e19787ab318e5b2ffe1aff40f9762647cb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fe916a374dc06bad55ec11a3e038e19787ab318e5b2ffe1aff40f9762647cb3","first_computed_at":"2026-05-18T00:15:48.803343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:48.803343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GvaroAuJohqhTnUReRgJiKHztP1d4nXZsVr59wxFqpR2VFM99YDUh5doJvkEecrmd3zYbry7lTznkehiM/zQCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:48.804073Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.06127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef51a7083a97e9d73974df36e8aa7eea78637b8b5f1d221f4598c17976d1bb00","sha256:fc9f78d05dfbb0a1705fa4f12b440bb86a446d4beb575b5141ab5d555b53d60b"],"state_sha256":"c63a4cc0b024b5a473915a17128322dc4d4ce8dca6f24ab7ebc9d8db9be0ff7c"}