Research proof index

The converse direction: DifferentiableAt on ℂ implies MDifferentiableAt on ℍ.

Concrete form of the hardness implication CDH ⇒ DLog: if a DLog adversary succeeds with probability p, the induced CDH adversary succeeds with probability at least p^2.

In the random DDH game, the CDH-to-DDH reduction only matches the target with the uniform baseline probability. The bijectivity assumption identifies scalar samples with uniformly sampled group elements in the subgroup generated by g.

toISQHom is injective: PhysLib dimensions include faithfully into ISQ.

Dirichlet's theorem on primes in arithmetic progressions. If $q\ge 1$, $a<q$, and $\gcd(a,q)=1$, then infinitely many primes satisfy $p\equiv a\pmod q$.

At every real $x$ for which $e^{ix}\ne1$, the finite-sum definition of the $N$th Dirichlet kernel agrees with the project’s closed-form expression:

$D_N(x)=D'_N(x).$