{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VWU34RJYPIKCG3LLHF3OG64M5U","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":"4a505da3f3bf80a1f8f0fb8bcdd74e9b35177025b5a7f9a4c99923f77443c98a","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-12-10T11:32:27Z","title_canon_sha256":"9f7d6bab7c39499822adbc9a8a575a57b7318371f03d6f8307fd31b556321cc5"},"schema_version":"1.0","source":{"id":"1412.3263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3263","created_at":"2026-05-18T02:17:33Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3263v2","created_at":"2026-05-18T02:17:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3263","created_at":"2026-05-18T02:17:33Z"},{"alias_kind":"pith_short_12","alias_value":"VWU34RJYPIKC","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VWU34RJYPIKCG3LL","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VWU34RJY","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:d38a868732e45886d34e3e880edd3cda4008068dc680167f709f6b7bd3a5cf39","target":"graph","created_at":"2026-05-18T02:17:33Z","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 give a sharp upper bound for the entries of the representations of a rational number as a sum of Egyptian fractions.","authors_text":"Florin Ambro, Mugurel Barcau","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-12-10T11:32:27Z","title":"On representations by Egyptian fractions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3263","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:f17f46baef45d5a7d7f8a992914b66c61f15ad2dbf8b09e4fca6ad9b334c7f3c","target":"record","created_at":"2026-05-18T02:17:33Z","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":"4a505da3f3bf80a1f8f0fb8bcdd74e9b35177025b5a7f9a4c99923f77443c98a","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-12-10T11:32:27Z","title_canon_sha256":"9f7d6bab7c39499822adbc9a8a575a57b7318371f03d6f8307fd31b556321cc5"},"schema_version":"1.0","source":{"id":"1412.3263","kind":"arxiv","version":2}},"canonical_sha256":"ada9be45387a14236d6b3976e37b8ced2c9271fdd767033e442939ecb503dfb7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ada9be45387a14236d6b3976e37b8ced2c9271fdd767033e442939ecb503dfb7","first_computed_at":"2026-05-18T02:17:33.361490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:33.361490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I8jjp0NpYby6UJl9TR+/PUcSBH4bW/4HKEKx5RvVdLCl3hampwP8wLtgPtfhboJstJHukruSthLAdMowMjVtDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:33.362286Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f17f46baef45d5a7d7f8a992914b66c61f15ad2dbf8b09e4fca6ad9b334c7f3c","sha256:d38a868732e45886d34e3e880edd3cda4008068dc680167f709f6b7bd3a5cf39"],"state_sha256":"4da51c0b848a646b9db1584d3ed3618abe87f222ba9194570d4e9e58e2ad6ecb"}