The Boundary Postulate, Priced: Nernst's Heat Theorem and the Integration Constant It Sets to Zero

Census pricing (row CC-106) of the heat theorem of Nernst (Gottingen Academy, Dec 1905; Nachr. Ges. Wiss. Gottingen, 1906), against a fixed bench (what is postulated, what is derived, what the postulates return numerically, what they cannot reach). The step -- the boundary postulate that the entropy change of a reaction between condensed phases approaches zero as T approaches 0, putting the Gibbs-Helmholtz integration constant equal to zero -- is postulated, not derived; the record states it could not be deduced from the first two laws, and Planck's stronger S(0) = 0 form is a further strengthening of the same postulate. Priced in the notebook (25 checks, exit 0) on DECLARED model inputs (a pricing instrument, not a real reaction: Delta H0 = -10000 J/mol, Delta Cp = gamma T, gamma = 0.050 J/mol/K^2): Delta H and the Gibbs-Helmholtz slope are identical for every value of the constant (Delta H = -7777.66 J/mol at 298.15 K for I = -20, 0, +20 alike -- calorimetry cannot see I), while K at 298.15 K is the exponential family K(I) = K(0) exp(I/R), running 12.49 (I = -20) through the postulate's 138.44 (I = 0) to 1534.38 (I = +20), a span of 122.84. Remainders at full size: the postulate silently requires Cp to vanish at 0 K (constant-Delta Cp countermodel: the entropy integral diverges logarithmically, +11.51 J/mol/K per decade of lower cut; Cp to 0 is Einstein 1907 / Debye 1912, later work), and its perfect-crystal domain was found by exception -- frozen disorder stands outside it (Pauling R ln(3/2) = 3.371 J/mol/K computed, against the named measured residual entropy of ice, 3.43 J/mol/K). Scout grade throughout: no verbatim primary reading claimed. EXTENSION. Vacuum catastrophe NOT SOLVED; quantum gravity NOT SOLVED.