Research · Papers · The quadratic hull and its defects · ML-016
Wrong Fixed Points in Rank 5/5 Deterministic Quadratic-Atlas Charts
Two deterministic Quadratic-Atlas charts attain rank 5/5 with 14 and 21 wrong fixed points; all others terminate at rank ≤4 or qdim 6
Published 2026-08-29
For everyone
Plain summary
This entry tests whether a coordinate search using degree-two relations can synthesize an exact Boolean function. Two charts reached full rank (5/5 independent directions), but both failed the first test required to eliminate wrong fixed points, leaving 14 and 21 spurious matches. Every other chart stalled at rank ≤4 or stopped at qdim 6. The register points to foundational project dossiers and fleet artifacts, but records no per-entry receipt file or prior-art position.
Result
Two deterministic Quadratic-Atlas charts attain rank 5/5 but fail the exact row-0 cover, leaving 14 and 21 wrong fixed points. All remaining charts terminate at rank ≤4 or qdim 6. Status: EXHAUSTED.
Setting and definitions
Candidates are deterministic Quadratic-Atlas charts evaluated against target rank 5/5, with qdim 6 serving as an alternate stopping label. Row-0 cover provides the exact first-stage exclusion criterion.
Method
Route-level evidence and fleet artifacts keyed by route name are preserved in this paper's downloadable evidence pack. The founding note provides a certificate description without specifying an individual per-entry receipt file.
Discussion
Conclusions apply strictly to deterministic Quadratic-Atlas charts and leave open alternate chart families and synthesis formulations. Corrections: NONE. The register logs no prior-art position.
For everyone — the takeaway
What this means
The two best candidates cleared the strongest intermediate rank test, yet both failed the first exact filter. All other candidates fell short earlier. A strong search score does not mean a candidate works if it fails the exact cover condition. This result closes the deterministic Quadratic-Atlas family without ruling out exact synthesis under different representations.
Register references
- Entry: ML-016
- Receipts:
ZKGOLF-HANDOFF-REPORT.md;ZKGOLF-RESEARCH-BRIEF-2026-08-12.md; fleet artifacts inzkgolf_sha256_continuation/, with the route section identified by route name. - Per-entry receipt file: the register does not record this.
- Prior art: the register does not record this.
Every artifact named above is bundled in, or hashed by, this paper's evidence pack below.
Evidence pack
Everything needed to check this entry against its receipts: the register text, a manifest with a SHA-256 hash for every named receipt, and 0 of 0 receipt files bundled (1 KB). Anything not bundled is still hashed in the manifest and lives in the compute-box working trees.
Changelog
Last reviewed 2026-08-29
- 2026-08-29Published on this site.