Concept guide
CLT qualification and a finite lattice audit
Separate finite-n moments from the named CLT application.
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Concept guide
Finite-valued IID strong-law qualification and fixed-n boundaries
Match the named SLLN hypotheses while separating prefix audits from a.s. proof.
Concept guide
Pointwise coverage, averaging and selection
Compute pointwise and worst-case coverage of a fixed interval procedure.
Concept guide
Complete inverse pairing and both Wilson directions
For n>1, (n-1)!=-1 mod n exactly when n is prime; the full modulo-7 inverse table checks 6!=6 mod 7.
Concept guide
Extracting 3-adic factors of signed integers
v3(-108)=3,v3(18)=2,v3(-1944)=5,v3(-90)=2; zero uses infinity.
Concept guide
Star closure with epsilon and a complete length slice
Give typed AST semantics, complete bounded enumeration and membership obligations.
Concept guide
DFA-loop quantifiers and the a^n b^n contradiction
Expose quantifier order, the all-pump-count loop argument and every legal split.
Concept guide
Qualified Newton updates and a finite trace
Take two exact Newton steps for x^2-2 from one, and audit root-first stopping and a cycle boundary.
Concept guide
Nonuniform trapezoids and signed error
For f(x)=x^2 and nodes (0,1/2,2), compute T, I-T and absolute error.
Concept guide
Safe descent steps for a positive diagonal quadratic
Take two steps with alpha=1/4 for a specified quadratic and prove the per-step descent condition.
Concept guide
Regular multipliers and a complete squared-distance solution
Minimize the squared distance to (1,2) subject to x_1+x_2=0; find the point and multiplier and independently prove the minimum.