{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:J2EC7UTWGB6ESSNMTHPGMKFDTQ","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":"7aec1701f79092632004f6a7dfd1b3032971fa2cd470df7be014d98937c874d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-12-22T08:54:49Z","title_canon_sha256":"a726f6ed0929e17e31acb6b715e1eb49ce4530c3eb5393edb433ded418dac9b9"},"schema_version":"1.0","source":{"id":"1612.07491","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07491","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07491v1","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07491","created_at":"2026-05-18T00:54:09Z"},{"alias_kind":"pith_short_12","alias_value":"J2EC7UTWGB6E","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"J2EC7UTWGB6ESSNM","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"J2EC7UTW","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:c1660c9d9b94d3da65033e0b7e90f812f4a6ab57e19d4ff90ba79685fd7addec","target":"graph","created_at":"2026-05-18T00:54:09Z","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 revisit the Raz-Safra plane-vs.-plane test and study the closely related cube vs. cube test. In this test the tester has access to a \"cubes table\" which assigns to every cube a low degree polynomial. The tester randomly selects two cubes (affine sub-spaces of dimension $3$) that intersect on a point $x\\in \\mathbf{F}^m$, and checks that the assignments to the cubes agree with each other on the point $x$.\n  Our main result is a new combinatorial proof for a low degree test that comes closer to the soundness limit, as it works for all $\\epsilon \\ge poly(d)/{\\mathbf{F}}^{1/2}$, where $d$ is the","authors_text":"Amey Bhangale, Inbal Livni Navon, Irit Dinur","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-12-22T08:54:49Z","title":"Cube vs. Cube Low Degree Test"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07491","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:ca65e08b8097b894f0af837c5a07e8ab3aaafdf653003070939136a641ae6ddb","target":"record","created_at":"2026-05-18T00:54:09Z","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":"7aec1701f79092632004f6a7dfd1b3032971fa2cd470df7be014d98937c874d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-12-22T08:54:49Z","title_canon_sha256":"a726f6ed0929e17e31acb6b715e1eb49ce4530c3eb5393edb433ded418dac9b9"},"schema_version":"1.0","source":{"id":"1612.07491","kind":"arxiv","version":1}},"canonical_sha256":"4e882fd276307c4949ac99de6628a39c2db0c04c40248458959f5ac26dcb0a81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e882fd276307c4949ac99de6628a39c2db0c04c40248458959f5ac26dcb0a81","first_computed_at":"2026-05-18T00:54:09.912527Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:09.912527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bwx4xf4WUyEEi7jridQdaN0+wdCltUlqmd6u+/6g6PVJW57QGbxwY6o8zS+94i0i/GAqPjOI/2GdfzgX/riGAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:09.912895Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.07491","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca65e08b8097b894f0af837c5a07e8ab3aaafdf653003070939136a641ae6ddb","sha256:c1660c9d9b94d3da65033e0b7e90f812f4a6ab57e19d4ff90ba79685fd7addec"],"state_sha256":"e1bfca87706ed71f32d7c6b3b4621f7bd84c1155178fe518766217ae41f0797a"}