{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AJSB2AC6ZLMTGEFVLMFIYKHP6Q","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":"58e0037b8b55b8daf58a56bf15f4ee3ccb6f06346e03c117557a0495a930a7f9","cross_cats_sorted":["cs.CC","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-31T17:54:11Z","title_canon_sha256":"d1a26f4f53861702b5188b3fe716de75b703fd997e8acfb29f301c5f1c111904"},"schema_version":"1.0","source":{"id":"2607.29672","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.29672","created_at":"2026-08-03T01:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"2607.29672v1","created_at":"2026-08-03T01:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29672","created_at":"2026-08-03T01:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"AJSB2AC6ZLMT","created_at":"2026-08-03T01:41:43Z"},{"alias_kind":"pith_short_16","alias_value":"AJSB2AC6ZLMTGEFV","created_at":"2026-08-03T01:41:43Z"},{"alias_kind":"pith_short_8","alias_value":"AJSB2AC6","created_at":"2026-08-03T01:41:43Z"}],"graph_snapshots":[{"event_id":"sha256:f586a76e4bbfdac1d92887d110ecbf8423c3ebb7b72003f55e8afae093ee4986","target":"graph","created_at":"2026-08-03T01:41:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.29672/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Planted noisy $k$XOR and the strong refutation of random $k$XOR are governed by a conjectured trade-off between signal strength and time: Level $\\ell$ of the Kikuchi hierarchy should achieve the smooth curve \\begin{equation*}\n  m\\ \\gtrsim\\ \\rho^{-2}n^{k/2}/\\ell^{k/2-1}\\ \\text{clauses}\n  \\quad\\Longleftrightarrow\\quad\n  \\text{solvable in time }n^{O(\\ell)}, \\end{equation*} where $\\rho$ is the bias of the planted signal or, for refutation, the target advantage. However, every spectral analysis of sparse $k$XOR to date loses polylogarithmic factors against this curve, a loss that enters the exponen","authors_text":"Alexander Schmidhuber, Matthew B. Hastings","cross_cats":["cs.CC","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-31T17:54:11Z","title":"The Kikuchi Hierarchy is Sharp for $k$XOR"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29672","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":"sha256:49468d89d0cace9fa2ec344519a2e4d780650561a7415cd6f5db6bd1496b0286","target":"record","created_at":"2026-08-03T01:41:43Z","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":"58e0037b8b55b8daf58a56bf15f4ee3ccb6f06346e03c117557a0495a930a7f9","cross_cats_sorted":["cs.CC","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-31T17:54:11Z","title_canon_sha256":"d1a26f4f53861702b5188b3fe716de75b703fd997e8acfb29f301c5f1c111904"},"schema_version":"1.0","source":{"id":"2607.29672","kind":"arxiv","version":1}},"canonical_sha256":"02641d005ecad93310b55b0a8c28eff438874e4d93ddcd841a3f758d1ba29d88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02641d005ecad93310b55b0a8c28eff438874e4d93ddcd841a3f758d1ba29d88","first_computed_at":"2026-08-03T01:41:43.079273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T01:41:43.079273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pfmGSf1IZDQQuae6YFFYjEVqEb+ZaVegj1QMFivwuS4b1+xRjroCxJKWjIYohFvZ2GoHu2oomdevErHTM0CzCw==","signature_status":"signed_v1","signed_at":"2026-08-03T01:41:43.080964Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.29672","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49468d89d0cace9fa2ec344519a2e4d780650561a7415cd6f5db6bd1496b0286","sha256:f586a76e4bbfdac1d92887d110ecbf8423c3ebb7b72003f55e8afae093ee4986"],"state_sha256":"1885587e8bb974883a7c9da00010ac0c7787870e62984cdbf76e37724bc15429"}