# Closing co-layered measurement at n=12 (2026-11-04)
# mean h^Col(12) = 307294.33 (-0.030% vs closure); rho_mass(12) = 2.84767564;
# n*(12) = 5.68408488 vs 1/2 + 2*rho_mass/ln3 = 5.68413214; Delta = -4.7e-5.
# Pipeline: full odd-character spectrum R_chi = L'/L(0,chi) by FFT along the
# primitive root 2 (conductor-exact), intrinsic weights c_{v_p(j)} |B_{1,chi}|^2.
# Verification chain: Sigma_new(2) = -18.8201 (ledger digit-exact);
# mean h^Col(6) = 24.2425 (closure 24.29); rho_mass(6,7,8) = 2.830, 2.841, 2.845.
import numpy as np, math
from scipy.special import gammaln

def layer_R(c):
    f = 3**c; phi = 2*3**(c-1)
    idx = np.empty(phi, dtype=np.int64); v = 1
    for e in range(phi):
        idx[e] = v; v = (v*2) % f
    S = np.fft.fft(gammaln(idx.astype(np.float64)/f))
    B = np.fft.fft(idx.astype(np.float64))/f
    js = np.arange(1, phi, 2)
    return js, (-math.log(f) - S[js]/B[js]).real, B[js]

def c_v(v): return 3*3*(3**(v+1)-1)/4.0

def H(n):
    tot = 0.0
    for c in range(1, n+1):
        js, R, B1 = layer_R(c)
        keep = [k for k, j in enumerate(js) if j % 3 != 0]
        w = c_v(n - c) * np.abs(B1[keep])**2
        tot += float(np.dot(-R[keep] - 0.5*math.log(3**c), w))
    return tot

def rho_mass(n):
    M = 4*3**(n-1)-3; S = 0.0
    for c in range(1, n+1):
        js, R, B1 = layer_R(c)
        keep = [k for k, j in enumerate(js) if j % 3 != 0]
        rho = R[keep] + math.log(3**c)
        w = (c_v(n-c) - c_v(n-1-c)) * np.abs(B1[keep])**2
        S += float(np.dot(rho, w))
    return 2*S/M/3**(n-1)

for n in (2, 6, 12):
    Hn = H(n)
    sig = Hn - (H(n-1) if n > 1 else 0.0)
    M = 4*3**(n-1)-3
    rm = rho_mass(n)
    lp = math.log(3)
    nstar = n - 4*(sig/M)/(3**(n-1)*lp)
    print("n=%2d  Sigma_new=%14.4f  mean=%12.4f  rho_mass=%.8f  n*=%.8f  Delta=%+.2e"
          % (n, sig, sig/M, rm, nstar, nstar - (0.5 + 2*rm/lp)))