报告摘要：
| By examining asymptotic behavior of certain infinite basic ($q$-) hypergeometric sums at roots of unity (that is, at a `$q$-microscopic' level) we prove polynomial congruences for their truncations. The latter reduce to non-trivial (super)congruences for truncated ordinary hypergeometric sums, which have been observed numerically and proven rarely. A typical example includes derivation, from a $q$-analogue of Ramanujan's formula $$sum_{n=0}^inftyfrac{binom{4n}{2n}{binom{2n}{n}}^2}{2^{8n}3^{2n}},(8n+1)=frac{2sqrt{3}}{pi},$$ of the two supercongruences $$S(p-1)equiv pbiggl(frac{-3}pbiggr)pmod{p^3} quadtext{and}quad SBigl(frac{p-1}2Bigr) equiv pbiggl(frac{-3}pbiggr)pmod{p^3},$$ valid for all primes $p>3$, where $S(N)$ denotes the truncation of the infinite sum at the $N$-th place and $bigl(frac{-3}{cdot}bigr)$ stands for the quadratic character modulo~$3$.
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