# Volume 3 – Kernel Builder Specification
# ---------------------------------------
# This file defines the immutable pivot function g(D) and the
# tridiagonal construction rules for the reproduction‑kernel matrix M.
# Every script or notebook must read these lines directly (no edits).

# 1. Pivot function
g(D) = D / 3

# 2. Tridiagonal kernel construction
#    For each verified fractal dimension D_i (row i):
#
#      Diagonal entry       :  M_{i,i}   =  D_i  -  2 * g(D_i)
#      Upper off‑diagonal   :  M_{i,i+1} =  g(D_i)        (if i < N-1)
#      Lower off‑diagonal   :  M_{i,i-1} =  g(D_i)        (if i > 0)
#
#    All other entries are zero, making M strictly tridiagonal.

 # 3. Notes
 #    • g(D) is parameter‑free; do not substitute alternative forms.
 #    • The context index ordering in D_values.csv defines the row/column order.
+#    • Supports any real or fractional context indices (e.g. n = ±1.5) as long as they appear in D_values.csv.
 #    • Scripts may reconstruct one full M per row i (to evaluate ρ_i),
 #      or build a single global M if a collective spectral radius is desired.


# End of specification
