The thermodynamic cost of reading a bit: a corollary of the informational root (GIT)

Within the framework in which spacetime, the Standard Model and late-time cosmologydescend from a single object - the mutual information I of an entanglement feld, transposedfrom a two-dimensional structure to observable 3+1 physics by a fixed Born projection, weisolate one consequence and develop it on its own terms. We show that the Born projection,which sends an amplitude e −N to its shadow e −2N , generates a definite local entropy whileremaining globally unitary, and that the entropy generated per projected bit equals thevariance x(1−x) that already appears in the framework as quantum measurement uncertaintyand as the cosmological H0/S8 tension. Combined with the Jacobson-Landauer identity∆E = T ∆S, this yields a closed-form prediction: reading one bit costs more than erasing it,the excess being kBT x(1−x). The result distinguishes computation from measurement, is inprinciple falsifiable, and - because the excess is entropy redistributed rather than created carries no net energy that could be extracted. The reading entropy x(1 − x) is then deriveddirectly from the modular Hamiltonian of the basis of I, so that the result is closed fromboth sides: from the amplitude/shadow relation and from the modular structure.