A predicate satisfying the HBL conditions provably mirrors all provability facts, so the distinction between 'really meaning' consistency and merely expressing it collapses under reflection.

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Collapsing a distinction(logical analysis): Failing to keep apart two different ideas or categories that should remain separate; treating different things as if they're the same.
HBL conditions(as used in mathematical logic): A specific set of technical requirements or criteria in formal logic (the abbreviation stands for particular logical conditions); without them, a logical statement may not work as intended.
Provability(as the standard by which large cardinal hypotheses are being compared): The ability to prove something is true using logical rules and established facts—whether a statement can be demonstrated with certainty.
Provably mirrors(as used in mathematical logic): Accurately reflects or exactly matches something in a way that can be mathematically proven. If A 'provably mirrors' B, you can logically demonstrate they correspond perfectly.

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