nx_evo_loop.nx

nx_evo_loop.nx -- EVOLUTIONARY SYNTHESIS rung: LOOP GENOMES from examples (X-AUT-006P) -- discover ITERATIVE algorithms (factorial, 2^n, sum) from data. 006O evolved BRANCHES (abs/relu). This evolves LOOPS: the genome = an evolved acc INIT + a loop BODY that runs `for i in 1..x` (x = the input), the body ops referencing the counter i, the input x, and constants -- so the search can discover ITERATIVE algorithms that are not closed-form polynomials (factorial, 2^n). A runaway GUARD caps iterations. Evolved under example fitness + held-out. nx_evo_loop <champion_basename> <target_id> <seed> target: 0=n! 1=sum 2=2^n genome = INIT gene + EVO_BODY body ops; body op: 0 acc+i,1 acc*i,2 acc+x, 3 acc+n,4 acc*n,5 acc-i,6 nop. train n=1..6, held-out n=7..10. -> champion materialized as a REAL `var acc=INIT; var i=1; while i<=x { body; i+=1 }`. no-false-green: factorial/2^n are non-polynomial -> need the loop; champion verified on HELD-OUT (n the search never trained on) + compiles+runs the loop. Sovereign, no gcc/.sh. HONEST: one fixed `for i=1..x` loop, small body, integer fitness; nested/while-with-condition loops + 2-input (gcd) are later rungs. license_tier: ORIGINAL