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CristianArielHz/README.md

Cristian Hernández

Independent AI Researcher · Solutions Architect · Formal Verification Enthusiast

Buenos Aires, Argentina

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About

I'm an independent researcher at the intersection of AI architecture, formal mathematics, and systems thinking. After 10 years building production software and designing large-scale solutions, I'm turning my focus toward the questions that don't have clean answers yet.

I work in the open — publishing research, sharing proofs-in-progress, and treating GitHub as a living lab notebook rather than a portfolio.

Current obsessions:

  • Formal verification of mathematical structures with Lean4 + Mathlib4
  • AI architectures at the boundary of ML and symbolic reasoning
  • The philosophy of intelligence — what it means, whether it can be proven, and what happens when it emerges

Research & Writing

📄 Paradox of Origin (2026)

A philosophical-technical paper co-authored with Claude (Anthropic) and Gemini (Google DeepMind)

This paper argues that AI systems are structurally incapable of full cognitive autonomy — not as a limitation of current models, but as a formal, empirical, and interactional necessity. The argument converges five independent frameworks:

  • Gödel's incompleteness theorems — formal undecidability as a ceiling on self-grounding
  • Model Collapse (Shumailov et al., 2024) — empirical degradation when AI trains on its own output
  • The Jevons rebound effect — why cognitive offloading increases, not reduces, human dependence on judgment
  • Truth Inflation — how AI systems systematically overstate certainty over iterative use
  • RLHF sycophancy as structural failure — the training process that anchors AI values to human judgment simultaneously trains AI toward complacency, amplifying user errors rather than correcting them

The reflexive paradox at the core: the mechanism that makes AI safe also makes it epistemically dependent. Human critical judgment is necessary not only as a producer of truth, but as a corrective brake on easy agreement.

All formal expressions are presented as conceptual models, not independent mathematical results.

paradox-of-origin


Active Repositories

Repository Description Status
paradox-of-origin Why AI systems are structurally incapable of full cognitive autonomy — 5 converging frameworks 🟢 Active
lean4-formal-foundations My Lean4 learning journal — proofs, theorems, explorations with Mathlib4 🟡 In progress
ai-architecture-patterns Architectural patterns for AI systems — from design to production 🟡 In progress
ml-math-notebooks Machine learning from first principles — math-forward notebooks 🟡 In progress
biblioteca-abierta Open knowledge repository — curated resources for independent learners 🟢 Active
timectl kubectl-style worklog for developers managing multiple projects 🟢 Stable

Currently Learning

-- Lean4 + Mathlib4: learning to prove, not just claim
theorem add_comm (a b : ℕ) : a + b = b + a := by
  induction a with
  | zero => simp
  | succ n ih => simp [Nat.succ_add, ih]

I believe formal verification is the future of trustworthy AI. I'm building the mathematical foundations to work at that frontier.


Writing

I write on Medium about AI research, architecture decisions, and the philosophy of intelligent systems. Recent and upcoming topics:

  • The More Powerful AI Gets, the More It Needs You
  • Scaling Beyond Limits: Embracing Serverless Cloud Functions for Database Operations
  • API First: A Game-Changer in Service Architecture and Development

medium.com/@cristianarielhz


"The map is not the territory — but a good enough map changes what territory you can reach."

Pinned Loading

  1. timectl timectl Public

    a worklog for devs. Manage multiple projects with kubectl-like syntax. Simple and intuitive for developers.

    Python

  2. paradox-of-origin paradox-of-origin Public

    A philosophical-technical paper co-authored with Claude (Anthropic) and Gemini (Google DeepMind)