We prove that the rescaled Weil generators Xq and Pq of the discrete Heisenberg group Heis₃ (Z) converge strongly to the position operator x and the momentum operator -iₓ as q, in the sense of Hypothesis H2 of the Cosmochrony Q5a programme. The proof rests on two structural lemmas. First, a discrete Sobolev estimate controls the error between the finite-difference operator and the continuous derivative at the ² level. Second, a quantitative Poisson aliasing lemma controls the transition from ² (Z) to L² (R) with an explicit rate O (q^-1) for data in S (R). As a consequence we obtain a quasi-isometry lemma for the sinc embedding q with the explicit rate\|\|q f\|₋ℂ² - \|f\|ℂ²| Cq\, N (), is a reusable for the identification of the effective metric constant A in terms of the Born-Infeld saturation constant c₁₈ (open problem Q5a-O5 and W1). The proof of H2 closes the last open hypothesis of the Q5a large-q limit theorem, completing the geometric emergence sub-programme of Q9, Q10, U1, W1.
Jérôme Beau (Sat,) studied this question.