Arithmetic-Kakeya forcing certificate at S = 7/4.
An explicit, machine-verified 2×2-minimal forcing certificate reaches the FrontierMath warm-up threshold S = 7/4. The note also isolates evidence that the present certificate framework floors at γ ≈ 1.6751308705666 unless a new inequality and a new certificate format enter.
What is new here?
The contribution is the explicit minimal artifact: a written-out certificate and linear-algebra witness chain showing how the forbidden direction (1,-1) is synthesized at the corner and then cascades through the remaining vertices.
The companion finding is negative-space evidence: exhaustive 2×2 search plus bounded-slope theory indicate that the certificate format itself may asymptote at γ. That makes the small win useful as a basin map: it clarifies where the current framework stops.
Disclosure membrane
- 7/4 is the Katz–Tao slope-set bound, not a new mathematical bound.
- The arithmetic-Kakeya record at 1.67513… is untouched.
- All pass/fail statements are against a reconstructed verifier, with no official public submission channel for this track.
- The framework-floor claim is evidence and characterization work, not a theorem.
Wonder with receipts: the public artifacts above contain the full witness arithmetic and caveats.