Chasing a Counterexample to the Jacobian Conjecture
Claude runs a disciplined symbolic search for a map that would refute the eighty-year-old Jacobian conjecture, and the hunt turns up something startling.
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Adderall's Molecular Path Through the Prefrontal Cortex
A rapid dive into how amphetamines shift dopamine signaling, heart-rate variability, and cortical gain control, pushing past what neuroscience can resolve.
Chasing citation gaps in a landmark open-access study
Claude tracks down a widely cited 2018 open-access study, then hunts for related papers on Sci-Hub, DOI coverage, and citation advantage that it left uncited.
Debugging a Clustering Algorithm From an Academic Paper
A user and Claude implement a clustering algorithm from an academic paper in C++, then hunt down a string of real compiler errors together, line by line.
Does Vitamin D Fight Antibiotic Resistance?
A tight breakdown of two claims: why overusing antibiotics breeds resistance, and where vitamin D's evidence for cutting infection and boosting defenses stands.