{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MKJRQTHEGCYGHPIY5L25D3C5YI","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":"5029eb0b5d9e1645d410834cbc71e1087061a18cebb15e72367cfcfb15b1166c","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-15T12:20:46Z","title_canon_sha256":"692ef551c8c581abecd8ecc43b9bad95aad656453790fb71225d2b0361372223"},"schema_version":"1.0","source":{"id":"1707.04730","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.04730","created_at":"2026-05-18T00:40:12Z"},{"alias_kind":"arxiv_version","alias_value":"1707.04730v1","created_at":"2026-05-18T00:40:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04730","created_at":"2026-05-18T00:40:12Z"},{"alias_kind":"pith_short_12","alias_value":"MKJRQTHEGCYG","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MKJRQTHEGCYGHPIY","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MKJRQTHE","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:c0499695d1160e64c8caa1757c0a74c4f8bead3455b908966f0af45a904aa9d0","target":"graph","created_at":"2026-05-18T00:40:12Z","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":"A colouring of the edges of an $n \\times n$ grid is said to be \\emph{reconstructible} if the colouring is uniquely determined by the multiset of its $n^2$ \\emph{tiles}, where the tile corresponding to a vertex of the grid specifies the colours of the edges incident to that vertex in some fixed order. In 2015, Mossel and Ross asked the following question: if the edges of an $n \\times n$ grid are coloured independently and uniformly at random using $q=q(n)$ different colours, then is the resulting colouring reconstructible with high probability? From below, Mossel and Ross showed that such a col","authors_text":"B\\'ela Bollob\\'as, Bhargav Narayanan, Paul Balister","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-15T12:20:46Z","title":"Reconstructing random jigsaws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04730","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":"sha256:14b1e9eedd0b949eed94f8d51f312e2d11622a8619c81cc15946c2714a746f85","target":"record","created_at":"2026-05-18T00:40:12Z","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":"5029eb0b5d9e1645d410834cbc71e1087061a18cebb15e72367cfcfb15b1166c","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-15T12:20:46Z","title_canon_sha256":"692ef551c8c581abecd8ecc43b9bad95aad656453790fb71225d2b0361372223"},"schema_version":"1.0","source":{"id":"1707.04730","kind":"arxiv","version":1}},"canonical_sha256":"6293184ce430b063bd18eaf5d1ec5dc232e1fb3cf4c13aff792da2e5d6579493","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6293184ce430b063bd18eaf5d1ec5dc232e1fb3cf4c13aff792da2e5d6579493","first_computed_at":"2026-05-18T00:40:12.444007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:12.444007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oLsFyQzzrXqn57PYYSbqaSoVTc9BGjZ5HN0MmhJcrl74NGm2DOixMLBlYLO22jkT6CbI/SQsPT/17Rkl38D4DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:12.444518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.04730","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14b1e9eedd0b949eed94f8d51f312e2d11622a8619c81cc15946c2714a746f85","sha256:c0499695d1160e64c8caa1757c0a74c4f8bead3455b908966f0af45a904aa9d0"],"state_sha256":"aa998179c83d73fe469a03b1e0f55fbcfb2580d9b6497b40b0253ad3c4818fce"}