Does the Alternative Human Racial Trait "Heart of the Wilderness" and the Alchemist Discovery "Lingering Spirit" stack for the purpose of determining the negative HP necessary to kill the PC?
•Heart of the Wilderness: Humans raised in the wild learn the hard way that only the strong survive. They gain a bonus equal to half their character level on Survival checks. They also gain a +5 bonus on Constitution checks to stabilize when dying and add half their character level to their Constitution score when determining the negative hit point total necessary to kill them. This racial trait replaces the skilled racial trait.
Lingering Spirit (Ex)
Prerequisite: Alchemist 4
Benefit: The alchemist is familiar enough with the ties between his body and spirit that he lingers at death’s door far longer than a normal person. He treats his Constitution as 10 points higher than normal for the purpose of determining when hit point damage kills him (so an alchemist with a Constitution of 10 and this discovery dies at –20 hit points instead of –10). Reducing him to 0 Constitution or its equivalent (from ability damage, ability drain, Constitution penalties, and so on) makes him unconscious and comatose, but he is only killed after taking an additional 5 points of Constitution damage, drain, or penalty (in effect, the alchemist must be brought to –5 Constitution in order to be killed by these attacks).
I would say yes, they stack, according to RAW.