Born's Rule from Record-Formation Constraints: A Thermodynamic-Information Axiomatics

Given the standard Hilbert space structure of quantum mechanics (including L^2 normalization from unitary dynamics), we show that the Born rule P = |psi|^2 is the unique probability rule compatible with phase-independent record formation. The derivation uses one thermodynamic axiom (classical records cannot retain quantum phase, an irreversible operation with Landauer cost k_B T ln 2 per bit) together with three structural axioms (normalization, tensor product factorization, continuity) and an operational interference consistency condition. The squared modulus is the unique function satisfying all five constraints; alternative powers |alpha|^n with n != 2 fail because the L^2 unit sphere is not an L^n unit sphere. This result complements Gleason's theorem: where Gleason proves the Born rule is mathematically necessary given non-contextuality, we identify the physical mechanism (phase information loss during record formation at finite temperature) that makes it realizable. The L^2 structure itself is not derived here; it is inherited from the requirement that unitary evolution preserve the inner product. The contribution is to show that, conditional on that structure, thermodynamics selects the squared modulus as the unique admissible probability map.