nx_evo_pbe.nx

nx_evo_pbe.nx -- EVOLUTIONARY SYNTHESIS roadmap RUNG 3 (THE HEADLINE): PROGRAMMING-BY-EXAMPLE / INDUCTIVE PROGRAM SYNTHESIS (X-AUT-006N). 006L/006M evolved a constant (hit one numeric target). This evolves a FUNCTION f(x): the genome computes over an INPUT x, fitness = total error across MANY (x_i -> y_i) TRAINING examples, and the champion is VERIFIED on HELD-OUT examples (x the search never trained on). Matching held-out = the engine INDUCED the true function from data (generalization), not memorized points. This is the research- leading capability: discover x*x, 2x*x+3, 3x+5 from EXAMPLES ALONE. It uses the 006M crossover GA as the searcher and an op set rich enough for polynomials. nx_evo_pbe <champion_basename> <target_id> <seed> target_id selects a hidden function used ONLY to GENERATE the dataset + the held-out ground truth (the SEARCH only ever sees the (x,y) pairs, never the formula): 0=x*x 1=2*x*x+3 2=3*x+5 3=x*x+x. op set (genome): 0 add n | 1 mul n | 2 sub n | 3 mul-by-x (acc*x) | 4 add-x (acc+x) | 5 square (acc*acc). start acc = x. -> trains on x in 1..NTRAIN minimizing sum|f(x)-y|; verifies on x in NTRAIN+1..NTRAIN+NHELD; prints train_err + heldout M/NHELD + GENERALIZES/ OVERFIT/NEAR; MATERIALIZES the champion as a real organ computing f at one held-out x (compile+run must equal the held-out ground truth). no-false-green: train_err=0 with heldout=NHELD/NHELD = induced the TRUE function (a memoriser would fail held-out); DIFFERENT target_id -> DIFFERENT discovered function, each generalising + champion compiles+runs. Sovereign, no gcc/.sh. HONEST SCOPE: polynomial op set, distance fitness, single i64 input; the seed of inductive synthesis -- branches/loops genomes (for abs/gcd) are a later rung. license_tier: ORIGINAL