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The Negative Exponent
Build exp(−x) from the EML operator family. Try all five. Watch them all fail.
The dashed white line is exp(−x) — the universal decay function. Every operator below uses exp(a) as its first component. Since leaves are {x, constants}, the exponent argument can never be −x for all x.
Try each operator (0/5 attempted)
The negative-exponent barrier is a fundamental limitation of the EML operator family. All five operators (EML, EDL, EXL, EAL, EMN) use exp(a) with a built from positive-coefficient leaves, so the exponent can never be −x for all x. This blocks every exponential decay law in physics and finance. The DEML dual gate — deml(x,y) = exp(−x) − ln(y) — resolves the barrier in one node: deml(x, 1) = exp(−x). DEML + EML together cover both signs. Data from §16 (operator comparison) and §19 (DEML gate) of the research notes.