The Reading Corner

Fujita Freeness for Toric Projective Bundles: Sharp Bounds

Introduction: Fujita freeness meets toric geometry, with a clean new proof If you’ve ever tried to answer “when do global...

Aug 31, 2026 0

Permanent Approximation Without Hitting the Bethe Wall

Introduction: Beating the Bethe barrier (deterministically) If you’ve ever run into a problem where the “best known method” is either...

Aug 31, 2026 0

Free Heyting Algebra Can’t Be a Topos Truth Lattice

If you’ve ever wondered whether “all intuitionistic truth” can be captured by a single kind of algebraic structure—namely a Heyting...

Aug 30, 2026 0

Rigidity on the 2-Torus: Sarnak’s Conjecture for a Big Class of Maps

Introduction: when a “two-dimensional rotation” acts almost like the identity If you’ve ever played with a system that “looks like...

Aug 30, 2026 0

Sequential futile-cycle networks and Hopf bifurcations: kinetic details decide everything

Cells love turning signals on and off with phosphorylation chains. But the math behind when these chains can start oscillating—specifically...

Aug 29, 2026 0

ChatGPT-Styled Dynamic Malfatti Circles Construction Solver

Introduction: When geometry proofs become a “converging algorithm” If you’ve ever played with circle tangencies—kissing circles, incircles, Apollonius problems—you know...

Aug 29, 2026 1

Polynomial-time Stable Matching for Coalition Markets

(Stable Matching on Network Hypergraphs) Introduction If you’ve ever tried to get a “fair and stable” allocation—think matching people to...

Aug 28, 2026 0

Geothermal Well Array AI Decision Support with LLMs

Geothermal energy is having a moment—but the hard part isn’t just finding heat underground. It’s planning what to build :...

Aug 28, 2026 0

Computational Semantics for AI: How Meaning Actually Gets Built

Introduction: “What does this word mean?”—and why AI needs the answer If you’ve ever tried explaining a word like “red,”...

Aug 27, 2026 0

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