Equilibrium pH, and the number 4.6
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What equilibrium means in a thick sauce
Acid added to a pot does not distribute instantly, and in a thick sauce it distributes slowly. Solids hold their own interior pH for a while after the liquid around them has come down. The finished equilibrium pH is the figure after everything has settled, and it is the one the definition is written about.
This is why a thick sauce is a harder case than a thin one even for the measurement. A thin sauce equalizes quickly and reads true. A chunky sauce can read acid in the sauce and not in the middle of a piece of vegetable sitting in it, and the piece is part of the product.
Why 4.6
It is the threshold in the federal definition: a low-acid food to which acid is added to reach a finished equilibrium pH at or below that figure, with water activity above 0.85. Below the line the product sits in the acidified foods regime with a filed process behind it. The whole commercial shape of this business follows from being inside it.
Measuring it properly
On a settled jar, at room temperature, with a calibrated meter. Not warm, not on filling day, not by taste. A thick sauce also has to be prepared for the measurement rather than dipped: the published methods exist because a probe in a chunk reads the chunk.
Your figure comes from your process authority
The 4.6 threshold is the definition. The number your sauce is built to hit, with whatever margin your process specifies, comes from the authority who established that process for your formulation. Work to theirs.