Triangular n Master Volume

The unified volume now separates three kinds of progress that had been split across the forks.  The first is a
counting/spectral hierarchy: triangular ranks, simplex counts, conformal eigenvalues, Laguerre jets, cyclic-order moments, and odd-dimensional Casimir rails.  The second is a reciprocal/hyperbolic hierarchy: fixed-gap counting legs, Cayley reflection, the Bernoulli variance coordinate $\tau$, an exact WaveLedger rapidity translation, and the Li/Joukowski quotient with its canonical zero measure.  The third is a finite-resource complement hierarchy added in this revision: an odd number $2n+1$ of phase-change cells has two nearest balanced states $(n,n+1)$ and $(n+1,n)$, whose complement product is exactly $n(n+1)=2T_n$.  After normalization this reproduces the same $\tau$, Cayley reflection magnitude, rapidity, and inverse-complement factor $1+1/(8T_n)$ that already occur in the $d=3$ Casimir/Wallis branch.  This is an exact bookkeeping bridge, not an identification of thermodynamic energy with the Casimir determinant.

On the RH-facing side, the volume keeps two exact but non-closing targets visible at once.  The first-moment cyclic-order quotient and its factorial-matched smoothing give a proved RH equivalence, while triangularization of the cyclic-order denominator selects the subrail $d=4m+1$.  Independently, the Li M\"obius coordinate is the negative reciprocal of the Paper~B radius, descends to the same Joukowski quotient, and yields a canonical finite zero measure whose positivity and support on $[-2,2]$ are equivalent to RH.  A failure of RH would also force exponentially large negative Li coefficients at a rate equal to the deepest inward M\"obius displacement.  These statements sharpen the proof burden; none proves the required positivity or zero location.

The post-freeze audit adds a fourth layer.  The adjacent triangular polarization is exactly the imaginary defect of the folded coordinate; an all-rank Möbius--Euler polynomial restores every Jordan rank; the factorial successor gate generates the von Mangoldt measure; and the transverse zero defect aggregates as a Hilbert--Schmidt skew energy.  Adversarial proofing also shows that the Archimedean summand alone is eventually indefinite and that every fixed finite Li/Hankel/localizing suite admits an off-line polynomial countermodel. The remaining conditional route requires bottom simplicity and one global-gap-normalized proxy estimate for the actual Weil operator; that estimate then forces evenness and actual-minimizer convergence.  These additions sharpen the endpoint without changing the global status.