Shunyaya Symbolic Mathematical Hardware – Symmetries, Streaming & Parity (3.6–3.9)

3.6 — Test E4: Reciprocal symmetry (alignment-only)

3.7 — Test E5: Streaming sum is order-invariant (U/W)

Inputs. a1 = 0.2, a2 = 0.5, a3 = -0.3, all w = 1
Batch. atanh(0.2)=0.2027325540540822, atanh(0.5)=0.5493061443340548, atanh(-0.3)=-0.30951960420311175,
U = 0.4425190941850252, W = 3, U/W = 0.14750636472834175, a_out = tanh(U/W) = 0.14644577359353203
Stream (1,2,3). a_out_stream = 0.14644577359353203
Shuffle (3,1,2). a_out_shuffle = 0.14644577359353203
Verdict. PASS (batch == stream == shuffled within tol)

3.8 — Test E6: Collapse parity (classical results untouched)

Inputs. (m1,a1) = (2.0, +0.5), (m2,a2) = (3.0, -0.4)
Multiply. m_star = 6.0, a_star = tanh(atanh(0.5) + atanh(-0.4)) = 0.12500000000000006
Collapse. phi((m_star,a_star)) = 6.0
Verdict. PASS

3.9 — Test E7: Stable ratio visibility (practical division)

Inputs. (m_f,a_f) = (5.0, +0.8), (m_g,a_g) = (2.0, +0.2)
Magnitude. v = m_f / m_g = 2.5 (policy-dependent only for zero-handling; here non-zero)
Alignment. a_div = (a_f - a_g) / (1 - a_f*a_g) = 0.7142857142857144
Verdict. PASS (finite, bounded, informative)

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