totalPowerSet
plain-language theorem explainer
The sum from k=0 to 8 of binomial(8,k) equals 256, confirming the power set cardinality for any 8-element recognition state space. Cross-domain regulatory models cite this result to anchor the total configuration count under the Q3 ceiling. The proof is a direct evaluation by the decide tactic on the finite sum.
Claim. $\sum_{k=0}^{8} \binom{8}{k} = 256$
background
The Regulatory Ceiling module examines 8-element recognition states on Q3. It states that the maximum binomial coefficient is C(8,4)=70 and lies below twice the gap-45 value, yielding a prediction that regulatory modules maintain at most 70 mutually consistent half-activated configurations. The supplied theorem supplies the complementary total power set size of 256.
proof idea
One-line wrapper that applies the decide tactic to evaluate the finite binomial sum directly.
why it matters
This theorem supplies the total_256 field inside the regulatoryCeilingCert definition. It completes the bundle that records the peak value, its maximality, the double-gap fit, and the full power set. The result aligns with the eight-tick octave (period 2^3) from the unified forcing chain.
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