id,slug,title,subtitle,preview,image,video,category,tags,date,status,confidence,importance,state
1,cauchy-riemann-equations,Understanding the Cauchy-Riemann Equations,A deep dive into the conditions for complex differentiability.,Explore how the Cauchy-Riemann equations govern holomorphic functions in the complex plane.,https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg,https://cdn.krisyotam.com/videos/cauchy-riemann.mp4,Complex Analysis,"[""holomorphic functions"", ""CR equations"", ""complex variables""]",2025-04-30,Finished,certain,7,active
2,galois-theory-fundamentals,Exploring Galois Theory Fundamentals,Foundations of the symmetry groups underlying polynomial solvability.,An introduction to Galois groups and their role in solving polynomial equations.,https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg,https://cdn.krisyotam.com/videos/galois-theory.mp4,Algebra,"[""field theory"", ""group theory"", ""symmetry""]",2025-04-30,Finished,highly likely,6,active
3,riemann-hypothesis-explained,The Riemann Hypothesis Explained,Unpacking the famous unsolved conjecture in analytic number theory.,A survey of the Riemann zeta function and its implications for primes.,https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg,https://cdn.krisyotam.com/videos/riemann-hypothesis.mp4,Number Theory,"[""zeta function"", ""prime distribution"", ""unsolved problems""]",2025-04-30,In Progress,possible,9,active
4,intro-topological-manifolds,An Intro to Topological Manifolds,Exploring the local Euclidean nature of abstract spaces.,Learn what it means for a space to be a manifold and why it matters.,https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg,https://cdn.krisyotam.com/videos/topological-manifolds.mp4,Topology,"[""manifolds"", ""topological spaces"", ""geometric structures""]",2025-04-30,Finished,likely,5,active
5,measure-theory-lebesgue-integral,Measure Theory and the Lebesgue Integral,The rigorous framework for modern integration.,An introduction to sigma-algebras and Lebesgue integrals.,https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg,https://cdn.krisyotam.com/videos/measure-theory.mp4,Measure Theory,"[""integration"", ""sigma algebra"", ""real analysis""]",2025-04-30,Finished,certain,6,active
6,spectral-theorem-basics,Spectral Theorem Basics,Diagonalizing operators on inner-product spaces.,A walkthrough of self-adjoint operators and their spectra.,https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg,https://cdn.krisyotam.com/videos/spectral-theorem.mp4,Linear Algebra,"[""eigenvalues"", ""operators"", ""inner product spaces""]",2025-04-30,Finished,likely,5,active
7,intro-sheaves-schemes,Introduction to Sheaves and Schemes,Bridging algebra and geometry with local data.,"Overview of sheaves, schemes, and their geometric significance.",https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg,https://cdn.krisyotam.com/videos/sheaves-schemes.mp4,Algebraic Geometry,"[""sheaves"", ""schemes"", ""varieties""]",2025-04-30,Notes,possible,7,hidden
8,sobolev-spaces-simplified,Sobolev Spaces Simplified,Function spaces for PDEs and beyond.,Understanding Sobolev embeddings and applications.,https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg,https://cdn.krisyotam.com/videos/sobolev-spaces.mp4,Functional Analysis,"[""Sobolev spaces"", ""partial differential equations"", ""normed spaces""]",2025-04-30,Finished,likely,5,active
9,godels-theorems-depth,Gödel's Theorems in Depth,Limits of formal axiomatic systems.,Exploring Gödel's first and second incompleteness theorems.,https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg,https://cdn.krisyotam.com/videos/godel-theorems.mp4,Logic,"[""incompleteness"", ""formal systems"", ""proof theory""]",2025-04-30,Finished,certain,8,active
10,overview-lie-algebra-theory,An Overview of Lie Algebra Theory,Structures that underlie continuous symmetries.,A survey of Lie algebras and their representations.,https://i.ytimg.com/vi/DxREm3s1scA/maxresdefault.jpg,https://cdn.krisyotam.com/videos/lie-algebra.mp4,Lie Theory,"[""Lie groups"", ""algebras"", ""representation theory""]",2025-04-30,Finished,likely,6,active