The Planck Units as a Token System: A Mechanism for the Reasonable Effectiveness of Mathematics in Physics

We give a formal treatment of a structural step, common to several apparentlyindependent foundational problems in physics, that existing accounts presupposewithout specifying: the conversion by which dimensionless mathematical contentbecomes the dimensional quantities physics measures. Dimensional physics, onthis account, is dimensionless structure registered in a determinate system ofdiscrete denominations, in the technical sense the word token carries ininformation theory; we call the conversion tokenization and formalize itas a map T:M(M). The token system is not afree choice: the natural units Planck constructed in 1899 from , c, andG are the unique such system for fundamental physics. The intended contribution is a method and the connections it makes visibleacross branches usually treated separately. The measurement problem'stransition to a definite outcome is identified with the registration step thestandard interpretations presuppose; the Standard Model's free parameters arerecharacterized as tokenizations of dimensionless ratios awaiting derivation.The conversion relations form a graph whose closure is a checkable condition,and the one loop that does not close automatically fixes the Planck scale,generated rather than assumed. We propose no new dynamics; we specify the bridgeon which any such derivation must operate. The account honors Einstein'sintuition of a deeper completion while respecting Bell's theorem in full: nothidden variables but hidden mechanism.