4.22 — What “works everywhere” really means
- The number remains the same; the lane is bounded, composable, and stream-safe.
batch == stream == shuffledfor the lane viaU/W.- A tiny set of knobs makes tests deterministic and economics auditable.
- Software first, silicon later — unchanged semantics across the stack.
4.23 — Quick calculator checklist (replicate any example)
- Rapidities. For each input
a_i, computeu_i := atanh(a_i). - Multiply lane.
a_mul := tanh(u1 + u2)(closed forma_mul = (a1 + a2) / (1 + a1*a2)). - Divide lane.
a_div := tanh(u_f - u_g)(closed forma_div = (a_f - a_g) / (1 - a_f*a_g)). - Fuse (weighted).
U := sum(w_i*u_i),W := sum(w_i),a_out := tanh( U / max(W, eps_w) ). - Clamp everywhere.
a := clamp(a, -1+eps_a, +1-eps_a)before mapping tou. - Classical parity. Always report
phi((m,a)) = m.
4.24 — Tiny ready-reckoner (common values)atanh(0.1)=0.1003353477atanh(0.2)=0.2027325541atanh(0.3)=0.3095196042atanh(0.4)=0.4236489302atanh(0.5)=0.5493061443atanh(0.6)=0.6931471806atanh(0.7)=0.8673005277atanh(0.8)=1.0986122887
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Disclaimer
The contents in the Shunyaya Symbolic Mathematical Hardware (SSMH) materials are research/observation material. They are not engineering advice, not a safety standard or certification, and not operational guidance. Do not use for safety-critical, medical, legal, or financial decisions. Use at your own discretion; no warranties are provided; results depend on correct implementation and inputs.
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