SSM-AI – Appendix J — SDK Packaging & Golden Tests (J4–J6)

# V1 — clamp + round-trip
a_in = 0.9999999; eps_a = 1e-6
a_c  = 0.999999
# u := atanh(a_c) finite; tanh(u) ≈ 0.999999 within tolerance

# V2 — fuse invariance (order/shard)
a1 = tanh(0.2) = 0.197375
a2 = tanh(0.4) = 0.379949
U = 0.2 + 0.4 = 0.6; W = 2
a_out = tanh(U/W) = tanh(0.3) = 0.291313   # swap/shard -> identical

# V3 — lane mul/div (M2)
a1 = tanh(0.5) = 0.462117; a2 = tanh(0.2) = 0.197375
a_mul = tanh(0.5 + 0.2) = 0.604368
a_div = tanh(0.5 - 0.2) = 0.291313

# V4 — chooser (bounded index)
U_in = -0.2; V_out = +0.5; W_in = 1
RSI = tanh((0.5 - (-0.2))/1) = tanh(0.7) = 0.604368

# V5 — gate modes (alignment-only)
RSI = 0.700000; g = 0.81
mul     : RSI_env = 0.567000
u_scale : RSI_env = tanh(0.81 * atanh(0.70)) ≈ 0.605961

# V6 — path pooling
u_steps = [0.586900, 0.400000, 0.200000]; w = 1
U = 1.186900; W = 3
RSI_path = tanh(U/W) = tanh(0.395633) ≈ 0.375900

# Tolerances
float64: 1e-12 ; float32: 1e-5   # bands must match across dtypes

# Shuffle test
assert fuse(seq) == fuse(random_permutation(seq))

# Shard test
U1,W1 = fuse_to_UW(partA); U2,W2 = fuse_to_UW(partB)
assert tanh((U1+U2)/max(W1+W2, eps_w)) == fuse(full)

# Gate purity
RSI_env = apply_gate(RSI, g, mode)
assert collapse((m,a)) == m   # phi((m,a)) = m

from math import tanh, atanh
from collections import namedtuple

# 1) lens -> alignment (single contrast; Unit=1, c=1 for demo)
e = (+1.0*0.9 + 0.5*0.6 + 0.4*0.5 - 0.8*0.2 - 0.5*0.1) / 1.0
a = tanh(1.0 * e)                                  # a in (-1,+1)

# 2) fuse multiple cues (order-invariant)
U=W=0.0
for z in [a, tanh(0.3)]:
    x = max(-0.999999, min(0.999999, z))
    U += atanh(x); W += 1.0
a_pool = tanh(U / max(W, 1e-12))

# 3) chooser + gate (alignment-only)
RSI = tanh((atanh(a_pool) - 0.0) / max(1.0, 1e-12))  # no penalties
g   = 0.80
RSI_env = g * RSI                                    # or tanh(g*atanh(RSI))