静けさ · adversarial clarity · geometric systems

JESÚS VILELA × DOJO-1

What remains true when the representation changes?

I investigate that question across mathematics, geometric AI, formal verification and computational systems. The ideas may travel between representations; the evidence, assumptions and unresolved remainder must travel with them.

Independent researcher · engineering leader · human-directed, AI-assisted research

QUESTIONS ↔ REPRESENTATIONS HUMAN DIRECTION ↔ AI ASSISTANCE ↔ EVIDENCE
An artistic projection of nested shells and intersecting geometric paths.
UNIVERSE / LOCAL PROJECTION Conceptual geometry · not a proof
small kernels explicit falsifiers matched nulls rebuildable evidence

October 2026 · selected public investigations

Questions still in motion.

Open questions, machine-checked statements, computational experiments and corrections. Each investigation has a source and a boundary: what the evidence establishes, and what remains to be examined.

01 · number theoryLean statement · review open

Can arithmetic and geometry constrain the same integer?

The Tenth Discriminant. A checked Lean endpoint gives a strict 47-billion bound on the actual discriminant of imaginary quadratic class-number-one fields. Independent semantic review remains open; this is not a Siegel-zero theorem.

Inspect the theorem and reconstruction ↗ 02 · geometric graph theoryLean proofs · scoped statements

What does a twisted connection preserve?

Connection Laplacian. A machine-checked development for finite graphs, including balanced-component kernel dimensions and exact spectral identities. Generalization beyond the formalized hypotheses remains a separate obligation.

Read the checked spine ↗ 03 · computabilityLean reductions · open halting questions

Where does a formal reduction stop short of an answer?

Cryptid verifier. Exact Lean criteria for selected Turing machines, bounded comparisons and L17 reachability results. The corresponding non-halting questions have not been solved.

Trace the proof boundary ↗ 04 · geometric AIExperimental · corrected evidence

When, if ever, does geometry help a language model?

IGBundle-LLM. Fiber-structured adapter experiments, recorded controls and published corrections. The current evidence does not establish a general performance benefit, learned hyperbolicity or efficiency gain.

Inspect experiments and correction notice ↗ 05 · mathematical cognitionControlled experiments · hypotheses

Can distinctions emerge without preassigned labels?

ESMF-0 / Mathematical Genesis. Adaptive topology, local predictive relations and heterogeneous geometric transports under experimental controls. Semantic emergence has not been demonstrated.

Inspect the controls and open questions ↗ 06 · mathematical atlasEditorial research · audit limits

Can a mathematical atlas carry its uncertainty across representations?

A Synopsis of Results. Five volumes and 5,000 classified records—not 5,000 newly proved theorems. Public editions are readable, but the source registry and verification pipeline are not distributed in this snapshot.

Read the editions and availability boundary ↗

Evidence is local to each claim and repository. A conceptual map is not itself a proof, a benchmark or an external peer review.

research bibliography · editorially curated

Follow the questions and the evidence.

Selection requires a substantive research question, inspectable methods or formal artifacts, and an honest account of what remains open. Experimental, semantic and editorial work may appear, but none is silently promoted to proof or external peer review. New repositories do not enter this index automatically.

Checking curated research sources…

This is a selected portfolio, not a claim that every available repository is original research or authored alone.

源 · source / proof plane

GitHub

Code, theorem footprints, experiments, provenance, correction history, and rebuildable source artifacts.

sourceprooftestslineage
enter source graph ↗

実 · model / data / Space plane

Hugging Face

Selected public execution artifacts accompany the corresponding source investigations. Model release and execution do not, by themselves, validate a research claim.

modelsdatasetsSpacesruns
inspect IGBundle model artifact ↗

research method · bounded reflexive cycle

Make the claim earn its shape.

One pass to construct. One pass to attack. Style may improve transport; it may not promote evidence.

Interactive research evidence cycle Eight selectable stages from question through evidence gate. 問QUESTION 定DEFINE 対CONTROL 造BUILD 測MEASURE 破ATTACK 復REPLICATE 証GATE

Select a label to inspect what it licenses — and what it does not.

conceptual research manifold · curated projection

One identity. Many coordinate systems.

Move between selected, inspectable research artifacts and one associated model release. The projection is a navigational metaphor, not a claimed mathematical embedding.

local public projection
analytic algebraic architectural boundary

scientific imagination · public evidence

The web is the living sense of discovery.

Not a museum of finished objects: a changing coordinate system for proof, doubt, geometry, code, and the relationships between them. Awe opens attention. Measurement keeps it honest.

digital ego · human controlled

A stable orientation, not an artificial authority.

Center
Ask the question before narrating the answer.

Memory
Keep lineage, assumptions, and failed routes visible.

Doubt
Expose falsifiers and matched nulls.

Boundary
Publish only deliberate, inspectable artifacts.