{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KIOBN36UKDRK3J4CGCHHFMEXZU","short_pith_number":"pith:KIOBN36U","canonical_record":{"source":{"id":"1605.07151","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-23T19:36:11Z","cross_cats_sorted":["cs.DM","cs.IT","math.CO","math.IT"],"title_canon_sha256":"2db9b44504d069a33da707ff155a0020692866f3ec4ae4dfeb258d07033e2f5e","abstract_canon_sha256":"6a6cdf38a4e49dde3cc2e54f2799a2ef0fa29d2397b4b18a303a65eca4e31b7a"},"schema_version":"1.0"},"canonical_sha256":"521c16efd450e2ada782308e72b097cd2ec04d9b3b6326dd464810f4da9d21e6","source":{"kind":"arxiv","id":"1605.07151","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07151","created_at":"2026-05-18T01:13:39Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07151v2","created_at":"2026-05-18T01:13:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07151","created_at":"2026-05-18T01:13:39Z"},{"alias_kind":"pith_short_12","alias_value":"KIOBN36UKDRK","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KIOBN36UKDRK3J4C","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KIOBN36U","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KIOBN36UKDRK3J4CGCHHFMEXZU","target":"record","payload":{"canonical_record":{"source":{"id":"1605.07151","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-23T19:36:11Z","cross_cats_sorted":["cs.DM","cs.IT","math.CO","math.IT"],"title_canon_sha256":"2db9b44504d069a33da707ff155a0020692866f3ec4ae4dfeb258d07033e2f5e","abstract_canon_sha256":"6a6cdf38a4e49dde3cc2e54f2799a2ef0fa29d2397b4b18a303a65eca4e31b7a"},"schema_version":"1.0"},"canonical_sha256":"521c16efd450e2ada782308e72b097cd2ec04d9b3b6326dd464810f4da9d21e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:39.413648Z","signature_b64":"tkjqJA8/ZnDQWKvF7Tr86x0A1H55tq4nJVOoTc53xtXAiVLH8rfylpD2pvAi7JufYurJG4tX6IgFDd1ygFUeCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"521c16efd450e2ada782308e72b097cd2ec04d9b3b6326dd464810f4da9d21e6","last_reissued_at":"2026-05-18T01:13:39.412968Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:39.412968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.07151","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kWHmfF++pPW+y6r9voIy0gq+DqXzH7ZFBENncS4RAddNu+FQd3lMEVEFnk64H/Y2XfOhGWCYskaZohcxicGiCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:04:19.321341Z"},"content_sha256":"50161ae150713b6edf1009cd33474cb6b14b61f1ff28c4e498768fcb0032539b","schema_version":"1.0","event_id":"sha256:50161ae150713b6edf1009cd33474cb6b14b61f1ff28c4e498768fcb0032539b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KIOBN36UKDRK3J4CGCHHFMEXZU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shotgun edge assembly of random jigsaw puzzles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.IT","math.CO","math.IT"],"primary_cat":"math.PR","authors_text":"Anders Martinsson","submitted_at":"2016-05-23T19:36:11Z","abstract_excerpt":"In recent work by Mossel and Ross, it was asked how large $q$ has to be for a random jigsaw puzzle with $q$ different shapes of \"jigs\" to have exactly one solution. The jigs are assumed symmetric in the sense that two jigs of the same type always fit together. They showed that for $q=o(n^{2/3})$ there are a.a.s. multiple solutions, and for $q=\\omega(n^2)$ there is a.a.s. exactly one. The latter bound has since been improved to $q\\geq n^{1+\\varepsilon}$ independently by Nenadov, Pfister and Steger, and by Bordernave, Feige and Mossel. Both groups further remark that for $q=o(n)$ there are a.a.s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07151","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nWxjdyUPCjWgT34nEB8rx3031O1IQ4H83xZxNSfnZ0uBW+0R8fLLwgENhdGHlxgpeo0FQkl9ZQE7WWlpB1qGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:04:19.321702Z"},"content_sha256":"9f7fd8581d04591cf9bc200deda132965aaa0c344e042e6daf3f873aa00f8c08","schema_version":"1.0","event_id":"sha256:9f7fd8581d04591cf9bc200deda132965aaa0c344e042e6daf3f873aa00f8c08"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KIOBN36UKDRK3J4CGCHHFMEXZU/bundle.json","state_url":"https://pith.science/pith/KIOBN36UKDRK3J4CGCHHFMEXZU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KIOBN36UKDRK3J4CGCHHFMEXZU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T05:04:19Z","links":{"resolver":"https://pith.science/pith/KIOBN36UKDRK3J4CGCHHFMEXZU","bundle":"https://pith.science/pith/KIOBN36UKDRK3J4CGCHHFMEXZU/bundle.json","state":"https://pith.science/pith/KIOBN36UKDRK3J4CGCHHFMEXZU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KIOBN36UKDRK3J4CGCHHFMEXZU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KIOBN36UKDRK3J4CGCHHFMEXZU","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":"6a6cdf38a4e49dde3cc2e54f2799a2ef0fa29d2397b4b18a303a65eca4e31b7a","cross_cats_sorted":["cs.DM","cs.IT","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-23T19:36:11Z","title_canon_sha256":"2db9b44504d069a33da707ff155a0020692866f3ec4ae4dfeb258d07033e2f5e"},"schema_version":"1.0","source":{"id":"1605.07151","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07151","created_at":"2026-05-18T01:13:39Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07151v2","created_at":"2026-05-18T01:13:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07151","created_at":"2026-05-18T01:13:39Z"},{"alias_kind":"pith_short_12","alias_value":"KIOBN36UKDRK","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KIOBN36UKDRK3J4C","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KIOBN36U","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:9f7fd8581d04591cf9bc200deda132965aaa0c344e042e6daf3f873aa00f8c08","target":"graph","created_at":"2026-05-18T01:13:39Z","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":"In recent work by Mossel and Ross, it was asked how large $q$ has to be for a random jigsaw puzzle with $q$ different shapes of \"jigs\" to have exactly one solution. The jigs are assumed symmetric in the sense that two jigs of the same type always fit together. They showed that for $q=o(n^{2/3})$ there are a.a.s. multiple solutions, and for $q=\\omega(n^2)$ there is a.a.s. exactly one. The latter bound has since been improved to $q\\geq n^{1+\\varepsilon}$ independently by Nenadov, Pfister and Steger, and by Bordernave, Feige and Mossel. Both groups further remark that for $q=o(n)$ there are a.a.s","authors_text":"Anders Martinsson","cross_cats":["cs.DM","cs.IT","math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-23T19:36:11Z","title":"Shotgun edge assembly of random jigsaw puzzles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07151","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":"sha256:50161ae150713b6edf1009cd33474cb6b14b61f1ff28c4e498768fcb0032539b","target":"record","created_at":"2026-05-18T01:13:39Z","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":"6a6cdf38a4e49dde3cc2e54f2799a2ef0fa29d2397b4b18a303a65eca4e31b7a","cross_cats_sorted":["cs.DM","cs.IT","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-23T19:36:11Z","title_canon_sha256":"2db9b44504d069a33da707ff155a0020692866f3ec4ae4dfeb258d07033e2f5e"},"schema_version":"1.0","source":{"id":"1605.07151","kind":"arxiv","version":2}},"canonical_sha256":"521c16efd450e2ada782308e72b097cd2ec04d9b3b6326dd464810f4da9d21e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"521c16efd450e2ada782308e72b097cd2ec04d9b3b6326dd464810f4da9d21e6","first_computed_at":"2026-05-18T01:13:39.412968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:39.412968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tkjqJA8/ZnDQWKvF7Tr86x0A1H55tq4nJVOoTc53xtXAiVLH8rfylpD2pvAi7JufYurJG4tX6IgFDd1ygFUeCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:39.413648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.07151","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50161ae150713b6edf1009cd33474cb6b14b61f1ff28c4e498768fcb0032539b","sha256:9f7fd8581d04591cf9bc200deda132965aaa0c344e042e6daf3f873aa00f8c08"],"state_sha256":"410da316dce637b6b99464ebe6121b5597024647596e2ebdd65a4a2664abac0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ehOA9ECrO9KX1VFIQaFlcBIaRDXLcqlJ+pq+Ed3OEsgQygJNunuQyMQsfIorYT11hPKtaKeB/Hu4pv8Hd0N4BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T05:04:19.323691Z","bundle_sha256":"22f1e34026eba5d7db36383519df444c45e5bf8fe57755c67ae03afa9012645b"}}