The Bridge Is the Postulate: An Event Rate Cannot Become an Entropy Density in a Frame Whose Defects Carry No Energy

Discharges debt D-001-040-40 (house paper #10, Static Defects Carry No Nieh–Yan Charge, §6.2) by proving the general statement that paper #11's three bridges instance: no statistical bridge from an event rate to an equilibrium entropy density can exist inside the frame, because the object every bridge must supply — an equilibrium occupation for the defect sector — is provably not a frame quantity. The root is paper #10's exact result μ_line = 0: every defect state sits at energy E = 0, so in Bose, Fermi, and classical statistics alike its occupation is a function of a chemical potential μ alone — taking every value in (0, ∞) (Bose, diverging at μ = 0), a continuum in (½, 1) and beyond (Fermi), or any positive number (classical) — and no frame quantity fixes μ: the frame contains no defect thermodynamics, no bath, and no equation of state to differentiate for a fluctuation route. Hence the space of in-frame bridges is in bijection with values of an unowned parameter; paper #11's Bridge A (C = 1) is the saturation postulate spent, Bridge B (C = ℓ_P/ℓ_T = 2.176685×10⁻¹⁹ at the Planck dwell, C = 1 at the twist dwell) is the postulate composed with a dial, and Bridge C (C = 0) is the unique postulate-free member. The bridge debt closes as an identity: the statistical bridge = the occupation postulate = the saturation gap. A successor must supply defect states with a derived nonzero energy spectrum, a bath, and an equilibrium. Quantum gravity and the vacuum catastrophe remain not solved.