Please Help!!!
what is the standard tolerance for gaps between the boards? We have a 3/4 in thick 4" wide Hickory and we have gaps that are small and some up to as much as 3/16 of inch. and the boards vary in height and width. When they installed the floor they also filled the gaps with putty. The entire floor about 800 sq feet of flooring. Now when I vacuum the floor the putty is coming out and the gaps are more noticeable. This is a new house that was built last fall.

Hickory is very volatile. Wider planks even more so as in most species
If it related to milling then the material itself is defective.
However manufacturers may not honor any warranty as it was installed andinstallation is deemed 'accepted'

The claim needed to be made at time of install and materials not installed.

Thank you ... How do I find a certified inspector?
If the flooring was milled wrong or the flooring was improperly installed
should a inspector find these problems?
What is a acceptable variance in widths of 4" wide solid Hickory?
and what is normal or abnormal gap widths?

Go to the NWFA site.... You can find an inspector there.
They will find all wrong with the floor and calculate the acceptable shrinkage rate... There is a formula used by width and if not mistaken... Species..

If the gaps are mailing related I refer you to previous post.

Width variations are a direct result of inconsistent kiln dry before milling.
Some wetter boards and some drier boards, get milled at 4". When the get acclimated either before.... or after the installation. The wetter boards could shrink and the drier boards could swell in dimensions across the width and in extreme cases, the thickness.

Gaps that are consistent, never closing, even during the spring/summer higher humidity rise, after the winters heating systems drying the wood out, are considered abnormal.

With woods shrink & swell from season to season, filler will always show signs of stress.

Gaps right after installation should never happen unless
a. Mfg nailing schedule not followed.
b. Moisture levels in wood at the time of installation were too high indicating improper acclimation. No, time in the house is not acclimating it. After a period of time moisture readings of the wood and subfloor should have been taken documented to prove it was correct at the time of install.
c. All mfg's state if there is a problem at the time of installation stop and find out why. We install on average 160,000 sq feet a year and I cannot recall the last time we ever had to use putty to cover gaps at the time of installation. Normal gaps in winter might be the thickness of a dime and should diminish in the summer or periods of high relative humidity. It is not normal to have gaps right after installation.