PENTRC exact-zero omega_E controls execute as 1e-9 rad/s

[krystophny]

At revision aaf720d475df6616935a56ea5914a68df10575d0, read_kin replaces every exactly zero electric-frequency knot by 1e-9 before applying the total-rotation scaling:

GPEC/pentrc/inputs.f90

Lines 253 to 271 in aaf720d

	! manipulation of rotation variables
	welec(:) = wefac*kin%fs(:,5) ! direct manipulation of omegae
	! note dividing by zero makes a nan that then ruins the whole spline
	warning_printed = .false.
	do i=0,nkin
	if(welec(i) == 0) then
	welec(i) = 1e-9
	if(.not. warning_printed)then
	print *, " ! WARNING ! Modifying omega_ExB = 0 to 1e-9 to avoid nans"
	warning_printed = .true.
	end if
	end if
	end do
	if(wefac/=1.0 .and. verbose) print('(a55,es10.2e3)'),' -> applying direct manipulation of omegaE by factor ',wefac
	wdian =-twopi*kin%fs(:,3)*kin%fs1(:,1)/(e*zi*chi1*kin%fs(:,1))
	wdiat =-twopi*kin%fs1(:,3)/(e*zi*chi1)
	wpefac= (wpfac*(welec+wdian+wdiat) - (wdian+wdiat))/welec
	welec = wpefac*welec ! indirect manipulation of rotation
	kin%fs(:,5)=welec

This makes an intended exact control nonzero. In particular, with wefac=0 and wpfac=1, every output knot becomes 1e-9 rad/s rather than zero. The modified profile is then stored in kin(:,5), so the PENTRC resonance operator receives the artificial frequency.

The division can be eliminated algebraically. With D = wdian + wdiat, lines 269-270 simplify exactly to

welec_new = wpfac * (welec + D) - D

for nonzero welec, and this expression is well defined at welec=0. It preserves all existing nonzero behavior while allowing exact zeros.

Suggested regression gates:

• wefac=0, wpfac=1 gives bitwise/exact zero at every knot;
• arbitrary nonzero welec matches the old two-line expression;
• welec=0 and arbitrary wpfac gives wpfac*D-D without NaN;
• the written omega_E profile and resonance input contain the same exact value.

The 1e-9 workaround was introduced in e403a232 to prevent NaNs caused by the avoidable division. This report concerns the altered physical control, not spline interpolation.

[krystophny]

A trace-only source/algebra gate is archived on the project audit branch at commit d802ddeb. It checks all four current/field direction quadrants, both passing-harmonic paths, the resonance denominator, and exact equivalence of the division-free rotation expression for nonzero omega_E. GPEC production source remains unchanged pending upstream review.