nx_nofloat_train_exceed.nx

nx_nofloat_train_exceed.nx -- the MEASURED S-class exceed for no-float TRAINING. Extends the established no-float exceed axis (nx_nofloat_exceed_gate proved it for an INFERENCE dot product) to the GRADIENT, which is what every training step computes. The capability that DETECTS/GUARANTEES what mainstream float training CANNOT: a training gradient is a SUM of many per-sample / per-reduction contributions; integer addition is associative + exact, so the no-float gradient is BIT-IDENTICAL regardless of accumulation order, batch order, thread count, or machine -- i.e. REPRODUCIBLE + AUDITABLE training. IEEE-754 float add is non-associative, so the SAME gradient gives DIFFERENT bits by order (PyTorch/JAX/llama.cpp are non-deterministic by construction). This is a CAPABILITY exceed (best-at-job: verifiable reproducibility), NOT merely "we are sovereign": PART 1 (the principle, refereed head-to-head, float = the competitor = teeth): representative wide-dynamic- range per-sample gradient contributions [2^24,1,1,1,1] (true sum 2^24+4). Integer fwd==rev==exact; float fwd!=rev AND float!=exact (it silently drops the small-gradient terms -> the vanishing-update bug). PART 2 (tie to the REAL engine): run nx_nofloat_autograd's actual backward on a batch in two different SAMPLE ORDERS -> the resulting integer gradient is BYTE-IDENTICAL. The real training engine is order-invariant. HONEST scope: this is the reproducibility/exactness/auditability axis. It is NOT a claim to beat PyTorch on model scale, breadth, or wall-clock -- those remain genuinely behind (tiny models, no GPU kernels). expect_exit: 0 Sovereign: imports nx_nofloat_autograd (the pure-integer engine) + nx_syscalls; the __f32 builtins appear ONLY here to demonstrate the FLOAT competitor (the training engine itself stays float-free). license_tier: ORIGINAL