SSM-AI – What You Can Test in Minutes (0E)

Calculator-fast validation of everything that matters

A tiny checklist that proves the whole system:

• Collapse parity
phi((m,a)) = m always. Numbers remain identical, byte-for-byte where declared.

• Order invariance
Batch, stream, or shuffled rows produce the same a_out and RSI within fixed epsilon using:

a_out := tanh( (SUM w*atanh(a)) / max(SUM w, eps_w) )

• Lens → align → RSI
A declared contrast produces a bounded chooser:

a_in  := tanh(-c*e_in)
a_out := tanh(+c*e_out)
RSI   := tanh( (V_out - U_in) / max(W_in, eps_w) )

• Calm gate purity
Scaling the chooser affects alignment only:

RSI_env := g_t * RSI      # g_t in [0,1]

• Bands at a glance
Global defaults:

A++: a >= +0.90
A+ : +0.60 <= a < +0.90
A0 : -0.60 <  a < +0.60
A- : -0.90 <  a <= -0.60
A--: a <= -0.90

• Distribution and division policy
M2 lane rules for mul/div; division only when manifest allows it:

a' := tanh(atanh(a1) +/- atanh(a2))
division_policy := "strict"

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Ready-to-copy test vectors

E1) Lens → align → RSI

c = 1.0, w = 1, eps_w = 1e-12
e_in  = 0.2
e_out = 0.5

a_in  = tanh(-0.2)
a_out = tanh(+0.5)
U_in  = -0.2
V_out = +0.5

RSI ≈ tanh(0.7) ≈ 0.6044   → Band A+

E2) Calm gate purity

g_t = 0.60
RSI_env ≈ 0.60 * 0.6044 ≈ 0.3626   (m unchanged)

E3) Streaming fuse (order invariant)

a1 = tanh(0.2), a2 = tanh(0.4)
w1 = w2 = 1
a_out = tanh(0.3) ≈ 0.2913   # shuffle order → identical

E4) Collapse parity

m = 0.73
any a
phi((m,a)) = m = 0.73

E5) Lane mul or div (M2 rule)

a1 = tanh(0.7)
a2 = tanh(0.1)

a_mul = tanh(0.8) ≈ 0.6640
a_div = tanh(0.6) ≈ 0.5371

E6) Banding defaults

0.2913  → A0
0.6044  → A+

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Pocket pseudocode

def clamp_align(a, eps_a=1e-6):
    return max(-1+eps_a, min(+1-eps_a, a))

def fuse_stream(a_list, w_list, eps_w=1e-12):
    U = sum(w*atanh(clamp_align(a)) for a, w in zip(a_list, w_list))
    W = sum(w_list)
    return tanh(U / max(W, eps_w))

def rsi(e_in, e_out, c=1.0, w=1.0, eps_w=1e-12):
    a_in  = tanh(-c*e_in)
    a_out = tanh(+c*e_out)
    U_in  = w*atanh(a_in)
    V_out = w*atanh(a_out)
    return tanh((V_out - U_in) / max(w, eps_w))

def apply_gate(RSI, g_t):
    return g_t * RSI

One-minute self-check
Collapse matches. Shuffle test passes. Bands right. RSI_env scales alignment only. Manifest fixed. Everything reproducible.

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