king ؘ✮ TVL & HOTD SPOILERS
ALT We study the N=2, large–d sector of BFSS/BMN-type matrix quantum mechanics on the lattice in the Gaussian regime. We develop a radial endpoint formulation in which the bulk, gauge, and longitudinal degrees of freedom are integrated out, leaving transverse endpoint variables governed by an effective holonomy potential. We show that this planar endpoint formulation is equivalent to the angular Molien–Weyl description of the gauge-projected partition function, up to a universal spectator factor. This relation allows the low-temperature expansion of the endpoint partition function to be obtained from the Molien–Weyl result, whose quadratic coefficient d(d 1)/2 counts Gaussian singlet states above the vacuum. We then analyze the continuum limit of the quadratic coefficient and show that it separates into a Gaussian contribution, a D-channel, and a β-channel. The naive Gaussian term becomes trivial, while the exact holonomy kernel generates finite continuum contributions through singular dep
ALT We study the singlet-sector structure of mass-deformed BFSSd₊₁ matrix quantum mechanics by combining the large–d Gaussian reduction with the Molien–Weyl projection. The Gaussian reduction captures the bulk matrix dynamics through a gauged harmonic oscillator, while the Molien–Weyl integral imposes the Gauss law and reorganizes the physical Hilbert space into holonomy-projected singlet excitations. We show that the very-low-temperature bosonic singlet spectrum is universally controlled by the quadratic Gram operators \Tr(XₐXb), whose number is d(d 1)/2. For N=2, this result is established by explicit residue computations and character methods; for N>2, it is supported by the character analysis. Thus the infrared spectrum begins as a collection of BFSS₂–like Gram towers, although higher invariant structures generally modify the full partition function. We also give a Hamiltonian derivation of the exceptional exact factorization at (d,N)=(2,2), where the BFSS₃ singlet partition function e
