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Transhuman Physiology makes unmodified wound rolls of 1-3 fail.

Armored Resilience inflicts a -1 to wound rolls against the targeted unit.

Now, it seems pretty clear to me that the two rules don't stack, but there's an argument in the Necron Tactics thread where someone insists they do.

Can we get a general consensus on this?

From 'Transhuman Physiology' (emphasis added):

Until the end of the phase, when resolving an attack made against that unit, an unmodified wound roll of 1-3 always fails, irrespective of any abilities that the weapon or the model making that attack may have.

From 'Armoured Resilience' (emphasis added):

Until the start of your next Psychic phase, when resolving an attack that targets that unit, subtract 1 from the wound roll.

No. They don't stack. The first says 'unmodified' and the second is a modifier.

That's correct, they don't stack. If both are in play, you remove the dice with 1s, 2s and 3s and then you apply the -1 (and any other modifiers) and resolve as usual.

If the targeted unit would be wounded on 2+, 3+ would be needed, when there is -1 to wound. When you roll 1,2,3,4,5,6 the dice with 1-3 would fail because of transhuman, and 4-6 would wound, because the result is 3-5, when you apply -1 from armoured resilience.

Agreed. If you need a 3 to wound due to SvT and have Transhuman Physiology and Armored Resilience in effect, a roll of 1-3 will fail as per Transhuman Physiology, and a roll of 4-6 (modified down to 3-5) will pass.

The only situation in which you can really argue that they "stack" is, for instance, being shot by a Hammerhead's Solid Shot Railgun profile.

S10 means it would be wounding on 2+, which is reduced to unmodified 4s, 5s, or 6s from Transhuman Physiology. And then Armoured Resilence would mean that it cannot roll a 6+ to wound, and can thus never inflict additional Mortal Wounds.

Edit.