# Literal reset-to-target diagnostic

The requested update was implemented on the saved 4,095-coefficient approximation:

    F_new = F + r,   where r=1-F.

Pointwise, F_new=1 and its squared error is exactly zero. This is an algebraic identity everywhere, not an inference from a finite numerical sample.

**The zero belongs to an enlarged model that explicitly adds the exact residual as a new feature. The original RH approximation problem is unchanged.**

An independent membership check rejects the update. Take the prime p=4127>4096 and the functional

    L(H)=H_1+H_(p-1)-H_p.

Every allowed original g_k, for 2<=k<=4096, satisfies L(g_k)=0, because k cannot divide p. Hence every allowed finite update has functional value zero. But

    L(1)=1,   L(F)=0,   L(r)=1.

Thus neither the reset target nor the proposed correction is representable in this fixed original basis. More generally, the constant target is not a finite combination at any basis size: for a proposed largest index N, repeat the same argument with a prime p>N.

For the original infinite closed span S, r belongs to S if and only if 1 belongs to S, since the existing F already belongs to S. Therefore assuming that the correction is admissible in the limit would assume the unresolved RH-equivalent statement. The reset does not establish it.

Run `python3 research/swc-rh/teleport_diagnostic.py` to reproduce the exact checks. `teleport-diagnostic-results.json` records zero error for the enlarged model alongside the rejected original-basis membership. The saved optimization candidates, original objective, and earlier paper are not modified. RH remains unproved.
