nx_nofloat_lm_gate.nx

nx_nofloat_lm_gate.nx -- THE CAPSTONE: a tiny TRANSFORMER LANGUAGE MODEL trains END-TO-END on next-token prediction, in PURE INTEGER Q16 (CAP-NF-LM). Full LM forward: X = embed(E, ids) -> pre-norm transformer block (attn+RoPE+causal-softmax+SwiGLU-FFN+residuals) -> rmsnorm_rows -> logits = H_n . W_lm -> loss = softmax-cross-entropy(logits, next-token ids) Composed ENTIRELY from gradcheck-verified ops + the two new LM-head ops (embed gather/scatter, fused softce). A1 embed gradcheck : dE (gather backward = scatter-add) == finite difference. A2 softce gradcheck : dlogits (fused CE identity softmax-onehot) == finite difference. A3 full-LM gradcheck wrt W_lm : the LM-head gradient through CE == finite diff. A4 full-LM gradcheck wrt E : the LONGEST chain -- E's gradient flows back through head+norm+FFN+attention +RoPE+softmax+embed (the WHOLE model) == finite diff. This proves end-to-end backprop of the LM. D neg-control teeth ; C bit-exact. B THE LM FITS (memorizes a FIXED sequence) : train E + W_lm (through the full forward; gradient traverses the whole block) on a next-token task (ids 0,1,2,3 -> 1,2,3,0); assert CE loss drops substantially from ~ln(V). Evidence -> knowledge/status/nofloat_lm.log. Sovereign: nx_nofloat_autograd + nx_syscalls (pure integer). HONEST scope: single-head, single-block, tiny vocab; multi-head/GQA + deeper stack + scale remain. expect_exit: 0