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Proof theory and subsystems of second-order arithmetic: in particular the reverse mathematics of Godel's system $T$

While doing some research on reverse mathematics, I came across the following document under the address, www.andrew.cmu.edu>user>avigad>Talks>survey1: Proof theory and Subsystems of Second-Order ...
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The graph and sign of $p_n-\operatorname{ali}(n)$, where $p_n$ is the $n$-th prime and $\operatorname{ali}(n)$ the inverse of the logarithmic integral

I'm inspired in  to ask the following question. My problem is that I have not an implementation of the inverse of the logarithmic integral $\operatorname{Li}(x)=\int_2^x\frac{dt}{\log t}$, that ...
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On the existence of a globally generated vector bundle on a $K3$ surface

This is on some confusion on the proof of lemma $1.6$ of the paper titled Special divisors on curves on a $K3$ surface(For convenience I am attaching the link here: https://link.springer.com/article/...
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Collapsing an independet set in the icosahedral graph

Let $G$ be the icosahedron graph. If $I \subseteq V(G)$ is an independent set with $|I|>1$, does contracting $I$ necessarily increase the Hadwiger number?
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Show that the lub of a set of negative numbers cannot be positive [on hold]

How is this conclusion? If a set $S$ contains only negative numbers then $0$ by definition is an upper bound. Any positive number would be greater than $0$ therefore, the lub of set $S$ can never be ...
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Searching for an example of semicontinous function $\dots$

QUESTION. Can you construct a bounded, semi-continuous function that is nowhere continuous? Any reference is appreciated.
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history background forThe Cauchy–Schlömilch transformation

Do you know a history background of The Cauchy–Schlömilch transformation that I use for my thesis? contect me:hossein264.1375@email.kntu.ac.ir
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What is the value of the partition function of CFT on a compact conformal manifold?

Is the value of the partition function of a 2d CFT on a compact conformal manifold well defined? Or is there some kind of "anomaly" that makes it dependent on a bulk or some other kind of further ...
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Embeddability of all graphs of cardinality $\kappa$ into one graph of cardinality $\kappa$

Does every infinite cardinal $\kappa$ have the following property? There is a simple, undirected graph $G_0=(\kappa, E_0)$ such that every simple, undirected graph $G=(\kappa, E)$ is isomorphic to ...
Which properties, a warped product manifold $M$, can benefit from in having a complex subspace in its tangent space?
I have a Riemannian warped product manifold $M=B \times_f F$ where $M$ is not compatible with an almost-complex structure $J$, but (for example) $B$ is compatible with an almost-complex structure $J$. ...