Mathematician | Systems Engineer | Polyglot Enthusiast | Theoretical Innovator | Rustacean

Welcome to my corner of GitHub, where advanced mathematics meets operating‑system ingenuity, and where a passion for languages fuels creative problem‑solving.

I fuse deep theoretical insight with hands‑on engineering to shape the future of computation and knowledge. From pioneering custom OS kernels in Rust to exploring symbolic compression and SKI combinators, my work bridges abstract mathematics and scalable software systems. As a lifelong polyglot and voracious reader, I build tools that learn and evolve alongside human understanding.

I firmly believe that mastering languages sharpens analytical thinking and cultural empathy.

• Duolingo Achievements: its_me_sguzman — currently learning Japanese, Indonesian, ASL, and more.
• Fluent & Advanced: English, Spanish (native)
• Readable: French, German, Dutch, Italian, Portuguese
• Learning: Japanese, ASL, Indonesian, Egyptian Arabic, Russian, Chinese, Hebrew
• Linguistic Projects:
  • Phonological mnemonics and kinesthetic maps (ASL for Greek letters)
  • Automated subtitle parsing → Anki flashcard pipelines
  • Ontology‑driven multilingual glossaries (RDF, Wikidata)

My research spans pure theory to speculative frameworks:

• Symbolic Compression & Combinatory Logic: Minimal expression of computation via SKI calculus and Church numerals.
• Operator Theory & Curvature: Treating curvature as a computational primitive, linking geometry with information theory.
• Runtime Algebra & Process Semantics: Defining algebraic operations for OS process mobility, reproducibility, and morphism.
• Topology & Homotopy Dynamics: Homotopical function iteration, ambient space analysis of connectivity and turbulence.
• Mathematical UI Metaphors: Interactive scrollable coordinate systems, algebraic explorer interfaces.

• Convolution & Integral Transforms: Convolution with Gaussian kernels (e^{-x^2}) as mathematical cursors, nested Riemann sums, and novel integral transforms for orbit analysis.
• Curvature-Based Computation: Treating curvature as an information metric and computational primitive, linking geometric bending with semantic complexity.
• Operator Theory & Collatz Analysis: Leveraging operator-theoretic frameworks and fractional iterators to study Collatz orbits and fixed-point dynamics.
• Fractional & Holomorphic Function Application: Generalized function iteration as semigroup operators; decomposing real functions into holomorphic scaling and rotation components.
• Alternative Geometric Representations: Dot-product-based coordinate systems, boolean matrix curves, and algebraic operator sequences as spatial encodings.
• Topological Dynamics & Homotopy: Linear homotopy framed as fractional application, ambient space connectivity, homology preservation under turbulent flows.

1. Rust OS Kernel Modules
   Customized HID drivers and proof‑of‑concept microkernels in Rust, exploring reproducible runtime states.

2. Combinatory Logic Library (Haskell)
   SKI combinator calculus implementation with numeric encodings, fixed‑point types, and macro‑driven parsers.

3. Semantic Knowledge Graph Pipeline
   Automated RDF ingestion from RSS, arXiv, and books, enriched with Basic Formal Ontology and Wikidata links.

4. Interactive Math UI Prototypes
   React + D3 tools for scrolling R² function viewers, holographic equation maps, and curvature visualizers.

I devour books to fuel ideas and cross‑disciplinary breakthroughs, with a particular passion for economic and political history, alongside mathematics and philosophy.

• Goodreads: Salvador Guzman — Typically 50+ books/year spanning multiple fields.

• Focus Areas:

  • Economic & Political History: Deep dives into socioeconomic transformations and power dynamics.
  • Mathematics & Theory: From operator theory to topology and combinatory logic.
  • Philosophy & Ethics: Exploring the foundations of knowledge and epistemic frameworks.

• Influential Reads:

  1. Capital in the Twenty-First Century by Thomas Piketty — Analyzing wealth concentration and distribution.
  2. The Wealth of Nations by Adam Smith — Cornerstone of modern economic thought.
  3. The Rise and Fall of the Third Reich by William L. Shirer — Comprehensive political history.
  4. Why Nations Fail by Daron Acemoglu & James A. Robinson — Institutions and prosperity.
  5. Sapiens: A Brief History of Humankind by Yuval Noah Harari — Big‑picture cultural evolution.
  6. Guns, Germs, and Steel by Jared Diamond — Environmental determinism and societal development.

• Reading Projects:

  • Simplified classics in Basic English and RDF‑encoded ontologies of key works.
  • Audio‑synchronized EPUB readers and subtitle‑to‑Anki pipelines for language immersion.

• Open Source: Contributor to Rust ecosystem (Newsboat rewrite, Bevy engine plugins), Linux kernel modules, and combinatory‑logic libraries.
• Speaking & Workshops: Invited talks on OS design in Rust, symbolic computation, and language acquisition strategies.
• Publications & Blogs: Articles on operator theory in software, topology‑driven UIs, and the role of curvature in computation.

I’m always eager to explore new ideas, collaborations, or open discussions:

• 📧 Email: ...
• 🌐 Website/Portfolio: ...
• 🔬 Blog: [Prose and Con men)(https://sguzman.github.io/)
• 🔗 LinkedIn: ...

Thank you for stopping by—let’s push the frontiers of knowledge together! 🌐✨

I'm a big fan of brainstorming out short isolated thought. I have made repositories of my work.

• Math
• Computer Science
• To Research
• Ideas to develop