Jérôme Beau

Weight Stabilisation of the Admissible Dirichlet Form: Proof of Hypothesis [H-w] from Spectral Universality

We close open problem Q5a-O3 of the Cosmochrony spectral admissibility programme by proving Hypothesis [H-w]: the admissibility weights $a_q(s)$, which enter the filtered Dirichlet form ${\mathcal{E}_q}$, converge to a positive constant $A > 0$ uniformly in the generator $s \in S...

Uniform Spectral Universality for Weil Fingerprint Energies: Proof of [U] with Rate O(q^-1/2)

The Q10 paper of the Cosmochrony programme reduces the proof of isotropy $A_H = 2$ to the O-series spectral universality hypothesis [U]: $\max_c |\sigma_c(n) - \sigma_*(n)| \leq \varepsilon(q)\sigma_*(n) \to 0$ uniformly over the fitting window $n \leq n_*(q)$. The present paper...

Proof of the Lifting Hypothesis [H-lift]: Kinetic-Sector Identification via Generator Suppression

The companion paper Q5b introduces Hypothesis [H-lift]: the operator ${L_\Pi} = -A\partial_k^2$ produced by Q5a as the Mosco limit of the admissibility forms ${\mathcal{E}_q}$ is the image, under the Schr\"odinger representation $\pi_1$ at unit central character, of the kinetic s...

Sub-Principal Symbol of the Effective Operator and Casimir Rigidity of the Central Direction

Paper Q7 reduced the open problem Q5b-O2 of to a single computable criterion: whether the sub-principal symbol of the effective operator ${L_{\mathrm{eff}}}$ in the central direction ${\widetilde{Z}} = [{\widetilde{X}}, {\widetilde{Y}}]$ of ${\mathrm{Heis}_{3}(\mathbb{R})}$ carri...

Asymptotic su(2)-Isotropy of the Effective Quadratic Form and the Identification AH = 2

Papers Q7 Q9 of the Cosmochrony spectral geometry programme establish that the effective operator $L_{\mathrm{eff}}$ on $\mathbb{R}_\tau \times {\operatorname{Heis}}_3(\mathbb{R})$ has a principal symbol $\sigma_2(L_{\mathrm{eff}})|_{H_{\mathrm{eff}}} = A_H(k_X^2+k_Y^2) + A_Z k_Z...