goldenwrite

null resultcertificatePython · NumPyModel behavior & reasoningJuly 24, 2026

the question

Is the delta-rule write Jacobian I - a k^T non-expansive with spectral norm 1 for every write direction?

what came out

The delta-rule write Jacobian I - a k^T is the projector with norm 1 only when write direction a equals key k. In closed form ||I - a k^T||_2 = sqrt(((3-2c)+sqrt(5-4c))/2), reaching the golden ratio 1.618 at orthogonality. This refutes a per-step norm-1 stability claim; matches SVD to 1.3e-15 over 20000 pairs.

method & receipts

Result: null result — an honest negative, reported as it came out.
Reproducible — one script re-runs the whole thing from scratch.
Tested — a correctness/benchmark suite ships alongside the code.

→ read the code and re-run it

github.com/v-code01/goldenwrite