Malus' Law from Pre-Record Admissibility: A Minimal Photon Model of Interface-Mediated Admission

This note reconstructs Malus’ law as the minimal optical expression of interface-mediated admission. A prepared photon polarization is treated not as a fully pre-existing physical record, but as a pre-record admissibility structure QBγ(φ). A polarizer at angle θ acts as a finite admissibility interface Iθ. The detector outcome is an irreversible binary distinction IBD, recovered as a physical detector record PD. The standard projection calculation is retained: a prepared linear polarization is represented by u(φ) = (cos φ, sin φ), the polarizer admits the component along e(θ) = (cos θ, sin θ), and the admitted amplitude is a(φ,θ) = e(θ) · u(φ) = cos(φ − θ). Squaring the admitted amplitude gives Malus’ law: P(D = 1 | φ, θ) = cos²(φ − θ). The note then treats the three-polarizer experiment as a direct consequence: while direct 0° → 90° transmission is zero in the ideal case, insertion of an intermediate 45° interface gives total transmission 1/4 relative to light already prepared at 0°. The intermediate polarizer is therefore interpreted as establishing a new admissible polarization condition rather than merely acting as a passive obstruction. The result is not presented as a new optical law. It is a primitive reconstruction of a known law: Malus’ law appears as the simplest quantitative signature of finite interface-mediated admission, linking the foundational chain τ0 → QB → IB to a laboratory optical law.