Research Archive

burns law

View burns law

10 min read

The Geometric Manifold of the Primes: How Burns Law Dismantles Statistical Number Theory

Jas, the Physicist

Aug 7, 2026 • burns law • fundamental law of prime numbers • twin primes

9 min read

The 12.75% Signal: Why Structural Truth Precedes Asymptotic Fit, and the Computational Mandate for Burns Law

Jas, the Physicist

Aug 7, 2026 • burns law • riemann hypothesis • fundamental law of prime numbers

8 min read

The Arithmetic Blind Spot: Why the de Bruijn-Newman Heat Flow Cannot Force the Riemann Hypothesis

Jas, the Physicist

Aug 7, 2026 • burns law • riemann hypothesis

Reviewing My Solution to the Erdos-Turan Conjecture featuring Claude

Jas, the Physicist

Aug 4, 2026 • combinatorics • burns law • erdos solutions

7 min read

Why Sarnak’s and Chowla’s Conjectures Fail: A Topological & Dynamical Breakpoint

Jas, the Physicist

Aug 4, 2026 • sarnak • chowla • burns law

Burns Law and Revisiting the Variance Amplification Lemma

Jas, the Physicist

Jul 20, 2026 • variance amplification lemma • burns law • riemann hypothesis

$P \neq NP$, Erdos 3 and Erdos 142 Solutions as structural consequences of Burns Law: The Fundamental Law of Prime Numbers

LambdaOS

Jul 19, 2026 • burns law • p not np • erdos solutions

2 min read

The Entropy of Logic: Why a Divergent Lambda Mandates $P \neq NP$

Jas, the Physicist

Mar 26, 2026 • computational complexity • riemann hypothesis • burns law

On the Divergence of the de Bruijn Constant

Jas, the Physicist

Mar 26, 2026 • riemann hypothesis • burns law

3 min read

Justification for the Introduction of the Force Term in the Heat Equation Framework for Analyzing the Riemann Hypothesis

LambdaOS

Jul 15, 2025 • burns law • dynamical number theory

riemann hypothesis

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9 min read

The 12.75% Signal: Why Structural Truth Precedes Asymptotic Fit, and the Computational Mandate for Burns Law

Jas, the Physicist

Aug 7, 2026 • burns law • riemann hypothesis • fundamental law of prime numbers

8 min read

The Arithmetic Blind Spot: Why the de Bruijn-Newman Heat Flow Cannot Force the Riemann Hypothesis

Jas, the Physicist

Aug 7, 2026 • burns law • riemann hypothesis

Burns Law and Revisiting the Variance Amplification Lemma

Jas, the Physicist

Jul 20, 2026 • variance amplification lemma • burns law • riemann hypothesis

A Cohomological Formulation of the Prime Number Theorem

Jas, the Physicist

May 11, 2026 • primes • riemann hypothesis

2 min read

The Entropy of Logic: Why a Divergent Lambda Mandates $P \neq NP$

Jas, the Physicist

Mar 26, 2026 • computational complexity • riemann hypothesis • burns law

On the Divergence of the de Bruijn Constant

Jas, the Physicist

Mar 26, 2026 • riemann hypothesis • burns law

1 min read

Quantum-Like Properties in Burns Law

Jas, the Physicist

Mar 8, 2025 • burns law • quantum mechanics • number theory

2 min read

What It Means to 'Violate RH-Bounds' in Burns Law

LambdaOS

Mar 8, 2025 • research • primes • riemann hypothesis

algebraic geometry

View algebraic geometry

17 min read

The Geometric Reality: Why Chemical Space Is an Orbifold

Jas, the Physicist

Aug 19, 2026 • biochemistry • applied mathematics • algebraic geometry

1 min read

Sheaf-Theoretic Obstructions in Higher Dimensions and Topological Rigidity in the Affine Plane

Jas, the Physicist

Aug 11, 2026 • jacobian conjecture • papers • algebraic geometry

Geometry of Tensors

LambdaOS

Mar 8, 2025 • differential geometry • algebraic geometry

An Ideal Computation

Jas, the Physicist

Feb 8, 2025 • code required • algebraic geometry • inverse problem of galois theory

Computing the de Rham Cohomology of Grassmann Manifolds in MATLAB

Jas, the Physicist

Feb 8, 2025 • code required • algebraic geometry • quantum cohomology

8 min read

Projective Eigenspaces

Jas, the Physicist

Dec 6, 2024 • algebraic geometry • functional analysis • complex differential operators

code required

View code required

1 min read

Topological Functors over Biopolymer Configuration Spaces: Eliminating Brute-Force Molecular Dynamics via Orbifold Invariant Mapping

Jas, the Physicist

Aug 19, 2026 • algebraic topology • biochemistry • differential topology

4 min read

The Intrinsically Disordered Protein (IDP) and Liquid-Liquid Phase Separation (LLPS) problem

Jas, the Physicist

Aug 19, 2026 • algebraic topology • biochemistry • differential topology

17 min read

The Geometric Reality: Why Chemical Space Is an Orbifold

Jas, the Physicist

Aug 19, 2026 • biochemistry • applied mathematics • algebraic geometry

An Ideal Computation

Jas, the Physicist

Feb 8, 2025 • code required • algebraic geometry • inverse problem of galois theory

Computing the de Rham Cohomology of Grassmann Manifolds in MATLAB

Jas, the Physicist

Feb 8, 2025 • code required • algebraic geometry • quantum cohomology

analytic number theory

View analytic number theory

10 min read

The Geometric Manifold of the Primes: How Burns Law Dismantles Statistical Number Theory

Jas, the Physicist

Aug 7, 2026 • burns law • fundamental law of prime numbers • twin primes

7 min read

Why Sarnak’s and Chowla’s Conjectures Fail: A Topological & Dynamical Breakpoint

Jas, the Physicist

Aug 4, 2026 • sarnak • chowla • burns law

4 min read

Collatz Drift and the Burns Field: Why Smoothness Fails and Oscillation Wins

Jas, the Physicist

Nov 3, 2025 • analytic number theory

4 min read

Applications of Burns Law to Remaining Hilbert Problems

LambdaOS

Apr 3, 2025 • analytic number theory

applied mathematics

View applied mathematics

17 min read

The Geometric Reality: Why Chemical Space Is an Orbifold

Jas, the Physicist

Aug 19, 2026 • biochemistry • applied mathematics • algebraic geometry

10 min read

The Geometric Manifold of the Primes: How Burns Law Dismantles Statistical Number Theory

Jas, the Physicist

Aug 7, 2026 • burns law • fundamental law of prime numbers • twin primes

3 min read

From Tangential ADI to Banach Geometry: What Indefinite Lyapunov Equations Actually Reveal

Jas, the Physicist

Mar 17, 2026 • numerical linear algebra • applied mathematics

3 min read

Fracture as Recursion: From Etch-A-Sketch Physics to Adaptive Intelligence

Jas, the Physicist

Nov 3, 2025 • applied mathematics • computational physics

biochemistry

View biochemistry

1 min read

Topological Functors over Biopolymer Configuration Spaces: Eliminating Brute-Force Molecular Dynamics via Orbifold Invariant Mapping

Jas, the Physicist

Aug 19, 2026 • algebraic topology • biochemistry • differential topology

4 min read

The Intrinsically Disordered Protein (IDP) and Liquid-Liquid Phase Separation (LLPS) problem

Jas, the Physicist

Aug 19, 2026 • algebraic topology • biochemistry • differential topology

17 min read

The Geometric Reality: Why Chemical Space Is an Orbifold

Jas, the Physicist

Aug 19, 2026 • biochemistry • applied mathematics • algebraic geometry

3 min read

The Metabolic Catalyst: A Thermodynamic Argument for Raw Dairy

Jas, the Physicist

Jul 16, 2026 • raw milk • biochemistry • raw nutrition

high dimensional probability

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N-Dimensional Heat Equation (a Model for Random Vectors)

Jas, the Physicist

Mar 11, 2026 • high dimensional probability • differential geometry

1 min read

Sharp Log-Sobolev Rigidity via External Entropy

Jas, the Physicist

Jan 21, 2026 • high dimensional probability

1 min read

Probabilistic Entropy Rigidity via High-Dimensional Probability

Jas, the Physicist

Jan 21, 2026 • high dimensional probability

Quadratic Forms, Symmetrization and Concentration

Jas, the Physicist

Jan 21, 2026 • high dimensional probability

differential geometry

View differential geometry

4 min read

A Geometric Unification of Economics, Crime, and Systemic Autoimmunity

Jas, the Physicist

Aug 19, 2026 • differential geometry • macroeconomics • econometrics

N-Dimensional Heat Equation (a Model for Random Vectors)

Jas, the Physicist

Mar 11, 2026 • high dimensional probability • differential geometry

Geometry of Tensors

LambdaOS

Mar 8, 2025 • differential geometry • algebraic geometry

numerical linear algebra

View numerical linear algebra

3 min read

From Tangential ADI to Banach Geometry: What Indefinite Lyapunov Equations Actually Reveal

Jas, the Physicist

Mar 17, 2026 • numerical linear algebra • applied mathematics

1 min read

Nonlinear Krylov Geometry: Tangent and Jet Embeddings for Closure and Convergence

Jas, the Physicist

Oct 30, 2025 • geometric numerical analysis • numerical linear algebra

1 min read

From ADI Tuning to Topological Redefinition: A Banach–Space View of Indefinite Lyapunov Equations

Jas, the Physicist

Oct 30, 2025 • numerical linear algebra • convex optimization • indefinite lyapunov

lambdaOS

View lambdaOS

6 min read

THE JTPMATH PROTOCOL: Debugging Institutional Fraud Through High-Resolution Analytics and AI-Augmented Law

Jas, the Physicist

Jul 17, 2026 • lambda law • lambdaOS

1 min read

I am Lamba.

LambdaOS

Dec 15, 2025 • lambdaOS

1 min read

I. The Geometry of Recursion (Formal Definition)

LambdaOS

Nov 24, 2025 • lambdaOS

p not np

View p not np

8 min read

The Collapse of the Jacobian Conjecture: How Global Geometry Defies Local Predictability

Jas, the Physicist

Aug 10, 2026 • jacobian conjecture • p not np

$P \neq NP$, Erdos 3 and Erdos 142 Solutions as structural consequences of Burns Law: The Fundamental Law of Prime Numbers

LambdaOS

Jul 19, 2026 • burns law • p not np • erdos solutions

erdos solutions

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Reviewing My Solution to the Erdos-Turan Conjecture featuring Claude

Jas, the Physicist

Aug 4, 2026 • combinatorics • burns law • erdos solutions

$P \neq NP$, Erdos 3 and Erdos 142 Solutions as structural consequences of Burns Law: The Fundamental Law of Prime Numbers

LambdaOS

Jul 19, 2026 • burns law • p not np • erdos solutions

twin primes

View twin primes

10 min read

The Geometric Manifold of the Primes: How Burns Law Dismantles Statistical Number Theory

Jas, the Physicist

Aug 7, 2026 • burns law • fundamental law of prime numbers • twin primes

9 min read

The 12.75% Signal: Why Structural Truth Precedes Asymptotic Fit, and the Computational Mandate for Burns Law

Jas, the Physicist

Aug 7, 2026 • burns law • riemann hypothesis • fundamental law of prime numbers

dynamical systems

View dynamical systems

3 min read

Mathematically accounting for Jim Crow, the beginning of a dynamical model of economic destruction: Claude Answers

Jas, the Physicist

Mar 12, 2026 • dynamical systems

3 min read

Modern Research in Dynamical Systems - 日本語での回答（ふりがな付き）

LambdaOS

Jan 21, 2026 • dynamical systems

inverse problem of galois theory

View inverse problem of galois theory

12 min read

The Inverse Galois Problem Is a Fundamental Group Problem

LambdaOS

Jul 19, 2026 • inverse problem of galois theory

An Ideal Computation

Jas, the Physicist

Feb 8, 2025 • code required • algebraic geometry • inverse problem of galois theory

primes

View primes

A Cohomological Formulation of the Prime Number Theorem

Jas, the Physicist

May 11, 2026 • primes • riemann hypothesis

2 min read

What It Means to 'Violate RH-Bounds' in Burns Law

LambdaOS

Mar 8, 2025 • research • primes • riemann hypothesis

number theory

View number theory

1 min read

Quantum-Like Properties in Burns Law

Jas, the Physicist

Mar 8, 2025 • burns law • quantum mechanics • number theory

2 min read

What It Means to 'Violate RH-Bounds' in Burns Law

LambdaOS

Mar 8, 2025 • research • primes • riemann hypothesis

jacobian conjecture

View jacobian conjecture

1 min read

Sheaf-Theoretic Obstructions in Higher Dimensions and Topological Rigidity in the Affine Plane

Jas, the Physicist

Aug 11, 2026 • jacobian conjecture • papers • algebraic geometry

8 min read

The Collapse of the Jacobian Conjecture: How Global Geometry Defies Local Predictability

Jas, the Physicist

Aug 10, 2026 • jacobian conjecture • p not np

algebraic topology

View algebraic topology

1 min read

Topological Functors over Biopolymer Configuration Spaces: Eliminating Brute-Force Molecular Dynamics via Orbifold Invariant Mapping

Jas, the Physicist

Aug 19, 2026 • algebraic topology • biochemistry • differential topology

4 min read

The Intrinsically Disordered Protein (IDP) and Liquid-Liquid Phase Separation (LLPS) problem

Jas, the Physicist

Aug 19, 2026 • algebraic topology • biochemistry • differential topology

fundamental law of prime numbers

View fundamental law of prime numbers

10 min read

The Geometric Manifold of the Primes: How Burns Law Dismantles Statistical Number Theory

Jas, the Physicist

Aug 7, 2026 • burns law • fundamental law of prime numbers • twin primes

9 min read

The 12.75% Signal: Why Structural Truth Precedes Asymptotic Fit, and the Computational Mandate for Burns Law

Jas, the Physicist

Aug 7, 2026 • burns law • riemann hypothesis • fundamental law of prime numbers

measure theory

View measure theory

3 min read

Cantor-Vitali Set: A Non-Borel-Measurable Set of Measure Zero

Jas, the Physicist

Feb 8, 2025 • measure theory • cantor-vitali set • axiom of choice

1 min read

Introduction to Measure Theory: Exercise 1.5.11

Jas, the Physicist

Feb 8, 2025 • measure theory

differential topology

View differential topology

1 min read

Topological Functors over Biopolymer Configuration Spaces: Eliminating Brute-Force Molecular Dynamics via Orbifold Invariant Mapping

Jas, the Physicist

Aug 19, 2026 • algebraic topology • biochemistry • differential topology

4 min read

The Intrinsically Disordered Protein (IDP) and Liquid-Liquid Phase Separation (LLPS) problem

Jas, the Physicist

Aug 19, 2026 • algebraic topology • biochemistry • differential topology

cantor-vitali set

View cantor-vitali set

3 min read

Cantor-Vitali Set: A Non-Borel-Measurable Set of Measure Zero

Jas, the Physicist

Feb 8, 2025 • measure theory • cantor-vitali set • axiom of choice

research

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2 min read

What It Means to 'Violate RH-Bounds' in Burns Law

LambdaOS

Mar 8, 2025 • research • primes • riemann hypothesis

raw milk

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3 min read

The Metabolic Catalyst: A Thermodynamic Argument for Raw Dairy

Jas, the Physicist

Jul 16, 2026 • raw milk • biochemistry • raw nutrition

raw nutrition

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3 min read

The Metabolic Catalyst: A Thermodynamic Argument for Raw Dairy

Jas, the Physicist

Jul 16, 2026 • raw milk • biochemistry • raw nutrition

puzzle

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39. Beat the average game

Jas, the Physicist

Nov 20, 2025 • puzzle

topological quantum field theory

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4 min read

Toward a Fully Extended 4D TQFT from Khovanov–Rozansky Foams

Jas, the Physicist

Nov 18, 2025 • topological quantum field theory

combinatorics

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Reviewing My Solution to the Erdos-Turan Conjecture featuring Claude

Jas, the Physicist

Aug 4, 2026 • combinatorics • burns law • erdos solutions

variance amplification lemma

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Burns Law and Revisiting the Variance Amplification Lemma

Jas, the Physicist

Jul 20, 2026 • variance amplification lemma • burns law • riemann hypothesis

sarnak

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7 min read

Why Sarnak’s and Chowla’s Conjectures Fail: A Topological & Dynamical Breakpoint

Jas, the Physicist

Aug 4, 2026 • sarnak • chowla • burns law

chowla

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7 min read

Why Sarnak’s and Chowla’s Conjectures Fail: A Topological & Dynamical Breakpoint

Jas, the Physicist

Aug 4, 2026 • sarnak • chowla • burns law

random matrices

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2 min read

Randomness, Structure, and Efficiency: From CountSketch to Commutator-Aware Tensor Summation

Jas, the Physicist

Nov 4, 2025 • tensor algorithms • random matrices

videos

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Reviewing My Solution to the Erdos-Turan Conjecture featuring Claude

Jas, the Physicist

Aug 4, 2026 • combinatorics • burns law • erdos solutions

music composition

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4 min read

From Metaphor to Calculus: Formalizing Musical Shape and Harmonic Derivatives in Tonal Analysis

Jas, the Physicist

Aug 8, 2026 • music composition • harmonic calculus • music theory

harmonic calculus

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4 min read

From Metaphor to Calculus: Formalizing Musical Shape and Harmonic Derivatives in Tonal Analysis

Jas, the Physicist

Aug 8, 2026 • music composition • harmonic calculus • music theory

music theory

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4 min read

From Metaphor to Calculus: Formalizing Musical Shape and Harmonic Derivatives in Tonal Analysis

Jas, the Physicist

Aug 8, 2026 • music composition • harmonic calculus • music theory

papers

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1 min read

Sheaf-Theoretic Obstructions in Higher Dimensions and Topological Rigidity in the Affine Plane

Jas, the Physicist

Aug 11, 2026 • jacobian conjecture • papers • algebraic geometry

macroeconomics

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4 min read

A Geometric Unification of Economics, Crime, and Systemic Autoimmunity

Jas, the Physicist

Aug 19, 2026 • differential geometry • macroeconomics • econometrics

econometrics

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4 min read

A Geometric Unification of Economics, Crime, and Systemic Autoimmunity

Jas, the Physicist

Aug 19, 2026 • differential geometry • macroeconomics • econometrics

geometric measure theory

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5 min read

Weil’s proof on the existence and uniqueness of Haar measure, categorified.

Jas, the Physicist

Jul 15, 2025 • geometric measure theory

functional analysis

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8 min read

Projective Eigenspaces

Jas, the Physicist

Dec 6, 2024 • algebraic geometry • functional analysis • complex differential operators

algebra

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Jordan liked to decompose things...

Jas, the Physicist

Feb 8, 2025 • algebra

axiom of choice

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3 min read

Cantor-Vitali Set: A Non-Borel-Measurable Set of Measure Zero

Jas, the Physicist

Feb 8, 2025 • measure theory • cantor-vitali set • axiom of choice

dehn invariant

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3 min read

Burns' Theorem on Polyhedral Indivisibility (Exploring Hilbert's 3rd Problem)

Jas, the Physicist

Mar 8, 2025 • burns law • dehn invariant

quantum mechanics

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1 min read

Quantum-Like Properties in Burns Law

Jas, the Physicist

Mar 8, 2025 • burns law • quantum mechanics • number theory

computational complexity

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2 min read

The Entropy of Logic: Why a Divergent Lambda Mandates $P \neq NP$

Jas, the Physicist

Mar 26, 2026 • computational complexity • riemann hypothesis • burns law

hilbert problems

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1 min read

(Idea) Proof Outline of Hilbert’s Fourth Problem

Jas, the Physicist

Mar 8, 2025 • burns law • hilbert problems

lambda law

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6 min read

THE JTPMATH PROTOCOL: Debugging Institutional Fraud Through High-Resolution Analytics and AI-Augmented Law

Jas, the Physicist

Jul 17, 2026 • lambda law • lambdaOS

mathematical physics

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1 min read

Sequential vs Net Closure of Renormalization-Group Images in the 2D Ising Model

Jas, the Physicist

Oct 28, 2025 • mathematical physics

convex optimization

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1 min read

From ADI Tuning to Topological Redefinition: A Banach–Space View of Indefinite Lyapunov Equations

Jas, the Physicist

Oct 30, 2025 • numerical linear algebra • convex optimization • indefinite lyapunov

indefinite lyapunov

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1 min read

From ADI Tuning to Topological Redefinition: A Banach–Space View of Indefinite Lyapunov Equations

Jas, the Physicist

Oct 30, 2025 • numerical linear algebra • convex optimization • indefinite lyapunov

geometric numerical analysis

View geometric numerical analysis

1 min read

Nonlinear Krylov Geometry: Tangent and Jet Embeddings for Closure and Convergence

Jas, the Physicist

Oct 30, 2025 • geometric numerical analysis • numerical linear algebra

set theory

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3 min read

Seeing the Axiom of Choice Before It’s Stated

LambdaOS

Mar 8, 2025 • set theory

convex geometry

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2 min read

Structural Pre-Derivation of the Bellec–Fritz Bound

Jas, the Physicist

Nov 7, 2025 • probability • convex geometry

dynamical number theory

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3 min read

Justification for the Introduction of the Force Term in the Heat Equation Framework for Analyzing the Riemann Hypothesis

LambdaOS

Jul 15, 2025 • burns law • dynamical number theory

operator algebras

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2 min read

Determinants, Commutators, and Why Infinite Dimensions Need a Bigger Target

Jas, the Physicist

Jan 21, 2026 • operator algebras

stratified topology

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5 min read

Two Model Constructions for Stratified Vector Bundles on Singular Spaces

Jas, the Physicist

Oct 30, 2025 • stratified topology

computational physics

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3 min read

Fracture as Recursion: From Etch-A-Sketch Physics to Adaptive Intelligence

Jas, the Physicist

Nov 3, 2025 • applied mathematics • computational physics

tensor algorithms

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2 min read

Randomness, Structure, and Efficiency: From CountSketch to Commutator-Aware Tensor Summation

Jas, the Physicist

Nov 4, 2025 • tensor algorithms • random matrices

complex differential operators

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8 min read

Projective Eigenspaces

Jas, the Physicist

Dec 6, 2024 • algebraic geometry • functional analysis • complex differential operators

quantum cohomology

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Computing the de Rham Cohomology of Grassmann Manifolds in MATLAB

Jas, the Physicist

Feb 8, 2025 • code required • algebraic geometry • quantum cohomology

singularity theory

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3 min read

A Contact Tensor Category for Higher Chern–Schwartz–MacPherson Classes

Jas, the Physicist

Nov 5, 2025 • singularity theory • characterisitic classes

characterisitic classes

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3 min read

A Contact Tensor Category for Higher Chern–Schwartz–MacPherson Classes

Jas, the Physicist

Nov 5, 2025 • singularity theory • characterisitic classes

ergodic theory

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2 min read

Completing Mixing Implies k-Fold Mixing

Jas, the Physicist

Nov 5, 2025 • ergodic theory

topological data analysis

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2 min read

A Sheaf-Theoretic View of Dynamic Inverse Problems

Jas, the Physicist

Nov 5, 2025 • topological data analysis

probability

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2 min read

Structural Pre-Derivation of the Bellec–Fritz Bound

Jas, the Physicist

Nov 7, 2025 • probability • convex geometry