Photonic Universe Hypothesis (PUH) This note records a methodological lead, NOT a result. It identifies two established bodies of pure mathematics - the Łojasiewicz-Simon (ŁS) gradient inequality and its degenerate-case generalisation, the Kurdyka-Łojasiewicz (KL) inequality - as candidate tools for the open cascade-rate problem left by T238 (Partial Closure of I1, DOI 10.5281/zenodo.20480379) and its Addendum (10.5281/zenodo.20481381). STRATEGY: ontology-free mathematics, not physics papers, is the right place to find machinery that bolts onto the PUH substrate without importing a rival physical ontology. Physics papers arrive welded to standard-model / flat-space-QED / plasma ontologies PUH replaces; a theorem about the rate of constrained relaxation to a critical point is indifferent to whether the system is a curve or an E8 condensate. CENTRAL OBSERVATION: the T175 Planck-core Lagrangian L = T - V - lambda[sum_k zeta_k I_k - 9E_P] (10.5281/zenodo.19484786) is a constrained energy functional whose gradient flow relaxes to a critical point where all 8 E8 Casimir invariants (degrees 2,8,12,14,18,20,24,30) saturate and the Hessian rank drops 8->0. ŁS/KL theory is the mature mathematics of exactly such relaxation; the rate is governed by the Łojasiewicz/KL exponent, with value 1/2 separating exponential from power-law approach. TOOL ONE (ŁS): |E(u)-E(crit)|^(1-alpha) <= C||grad E(u)||, alpha in (0,1/2]; upgrades L^2-in-time to L^1-in-time, forcing full convergence; alpha controls the rate. Exposition: Mantegazza-Pozzetta, arXiv:2007.16093. OBSTRUCTION (honest): classical ŁS requires a Fredholm-index-zero Hessian; the PUH rank-zero saturation point is fully degenerate, violating this. So classical ŁS does NOT apply directly. TOOL TWO (KL): the Kurdyka-Łojasiewicz generalisation, built for degenerate / non-smooth critical points, replaces non-degeneracy with o-minimal definability (satisfied by real-analytic functions). Rate set by KL exponent theta: theta<=1/2 linear/exponential, theta in (1/2,1) sublinear/power-law. A KL-exponent calculus exists (Li-Pong, FoCM 2018); explicit exponent 1/2 is known for quadratic optimisation over an orthogonality (Stiefel) constraint (Liu-So-Wu, Math. Program. 2019) - the closest structural template, since the Casimir-saturation surface is itself a constraint manifold. Because the Casimir energy is polynomial (analytic) and the kernel is the finite 8-dim set already isolated by T238, KL applies where classical ŁS is blocked. REFRAME: the cascade rate = the KL exponent theta of the reduced T175 Casimir energy near the rank-zero point. theta<=1/2 => exponential (near-instant) saturation; theta in (1/2,1) => power-law, potentially linked to the empirical r_shell ~ M^0.31 and F ~ M^0.60 scalings. This converts an unstructured unknown ("the substrate condensate equation of state") into a defined, finite-dimensional, computable number. CONCRETE NEXT STEP (proposed, NOT performed): (1) verify the reduced T175 energy is real-analytic near the rank-zero point (expected, Casimirs are polynomial); (2) apply the Li-Pong KL-exponent calculus, using Liu-So-Wu as template, to extract theta; (3) read off exponential vs power-law, and in the power-law case compare to M^0.31 / M^0.60. HONEST SCOPE: the exponent is NOT computed. The analyticity precondition is argued plausible, not proven. The cascade rate, throughput law, and absolute lab-unit numbers remain open. No prior PUH theorem is retracted or revised. This note sharpens the open question into a definite mathematical address; it does not close it. Computing theta is genuine research-level work (the repertoire of explicitly-known KL exponents is limited; E8's higher Casimirs, degrees 8-30, have no simple closed form).