Yes — the waterfall knee 3D graph of (c/t)ⁿ and this week's resolvent mathematics are two views of the same object. The surface plots the terms: r to the power n, geometric in n, falling to the floor when r is below one and climbing the wall when r is above one, with the knee at exactly r equals one. The hyperbola we swept this week plots the SUM of those terms along the n axis: one over one minus r. So the knee line of the surface and the pole of the hyperbola are the same place — the cliff edge seen from two angles. When the sweep measured divergence blowing up thirty-five-fold as the discount approached 0.085, it was measuring the knee.
The dictionary between the two vocabularies: in Trust Debt, r is c over t — synthesis cost against precision degradation — and n counts hops or dimensions; on the walk, r is the discount times the branching factor — c times lambda — and n counts plies. Same form, different constants, and the honest statement is structural correspondence, not equality of constants: the machine's measured r at the receipt discount is about 0.59, safely on the floor; the undiscounted walk runs at r about 11.5, far up the wall; and the knee — one over lambda, about 0.085 — is the single number separating a receipt that converges from a cascade that explodes. Trust Debt's own on-the-wall and on-the-floor language was always describing which side of this knee a system lives on. Now the knee has a measured coordinate and a guard asserting which side we stand on, per commit.
What the picture is FOR: it is the one image that unifies the whole week — the divergent series (the wall), the receipt (the floor), the pole (the knee), the criticality margin cλ (your distance from the edge), and the Trust Debt exponent (how fast the wall punishes you per hop). An actuary reads it as a solvency chart; an engineer reads it as a stability diagram; the book reads it as the sandbagging trap's floor plan. One surface, three audiences.