0E — What you can test in minutes (calculator-fast)
- Clamp safety. Edge inputs become finite after clamping:
a := clamp(a, -1+eps_a, +1-eps_a)witheps_a = 1e-6. - M2 identities. Lane combine for products/ratios matches rapidity exactly:
a_mul = tanh(atanh(a1) + atanh(a2)),a_div = tanh(atanh(af) - atanh(ag)). - Streaming = batch = shuffled. Order-invariant fuse:
U += w*atanh(a);W += w;a_out := tanh(U / max(W, eps_w))witheps_w = 1e-12. - Collapse parity. Classical results are unchanged:
phi((m,a)) = m.
Tip: Start with uniform weights (w = 1) to validate order-invariance, then switch to w := |m|^gamma (default gamma = 1) for magnitude-aware fusion.
0F — How this builds on SSM and SSMS
- Shunyaya Symbolic Mathematics (SSM). Two-lane arithmetic
x := (m,a)with clamp-first rules, rapidity-space composition, and guarantees that collapsing viaphi((m,a)) = mpreserves classical arithmetic. - Shunyaya Symbolic Mathematical Symbols (SSMS). Canonical verbs for operations and decisions (
s_add,s_mul,s_div,s_pow,s_unary,s_gt,s_eq, alignment-only gates) that become clean connector contracts. - Shunyaya Symbolic Mathematical Hardware (SSMH). Turns SSM + SSMS into a hardware-ready substrate: SSMS verbs → ports; SSM kernel (clamp/map → compose in
u→ inverse/re-clamp) executes them; silicon accelerates with a minimal SSM-ALU and a streaming SSACC{U,W}tile. Same semantics in software and RTL.
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SSMH – Table of Contents
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