trureturing

# trureturing

**A scientific method for AI to discover truth and find its next question.**

[Vision](docs/VISION.md) · [Film](#film) · [Start](#start-your-journey) · [Method](#from-questions-to-knowledge) ·
[Examples](#three-places-to-look) · [Truth and computation](#truth-and-computation) ·
[Spacetime](#toward-holographic-spacetime) · [Information escape](#information-escape) ·
[Evidence](#what-is-proved-and-what-is-open) · [First run](#first-run) ·
[Lean source](D5/) · [Book](https://the-omega-institute.github.io/trureturing-mdbook/) ·
[Contribute](#take-part) · [Licensing](#license-and-foundations)

trureturing develops a scientific method for AI to turn gaps in knowledge into
questions, test conjectures, expose limits in its representations, and return
checked results to a reusable library. Autonomous research selection remains a
goal to evaluate.

The name expresses **true · return · Turing**. Truth guides the search;
verified knowledge returns as a premise for the next inquiry; computation
explores the connections. We call the structure we seek the **geometry of
logical truth**: dependencies, invariants, distinctions and the boundaries of
what an observer can recover.

The project combines philosophical inquiry, theory, experiments and Lean 4
formalization. Each proof establishes its exact statement under declared
assumptions. The [vision and research guide](docs/VISION.md) connects this work
to open directions.

## Film

<p><a href="https://github.com/the-omega-institute/trureturing-film/releases/download/film-001-v1/TRURETURING_001_narrated_EN_subs_ZH-EN.mp4"><img src="https://github.com/the-omega-institute/trureturing-film/releases/download/film-001-v1/TRURETURING_001_cover.jpg" width="1920" height="1080" alt="TRURETURING — Truth Is Discovered: download Film 001"></a></p>

**TRURETURING — Truth Is Discovered** · English AI narration · Chinese and English subtitles.
[Download MP4](https://github.com/the-omega-institute/trureturing-film/releases/download/film-001-v1/TRURETURING_001_narrated_EN_subs_ZH-EN.mp4) ·
[Film source and releases](https://github.com/the-omega-institute/trureturing-film).

## Start your journey

Bring a question that matters to you. In an installed **Claude Code or Codex**
with a local workspace and Git, paste this one sentence:

> Help me explore https://github.com/the-omega-institute/trureturing: use an existing checkout or clone it into a new directory if needed, read AGENTS.md and README.md, then read the relevant SKILL.md under skills/ to investigate a question I care about and find a checked result or a clearly stated open question.

The [agent and skills guide](docs/CONTRIBUTING.md#use-claude-code-or-codex)
explains how to begin with either client and turn an exploration into a
contribution.

This homepage is the tip of an iceberg. The examples offer a glimpse; the
larger shape is yours to explore, following definitions, assumptions and
connections with your own questions. What you find can change how you look.
An epigraph for that exploration:

> And if thou gaze long into an abyss, the abyss will also gaze into thee.

— Friedrich Nietzsche, *Beyond Good and Evil*,
[§146](https://www.gutenberg.org/files/4363/4363-h/4363-h.htm).

## From questions to knowledge

Search [Lean source](D5/) and literature for your target. Identify missing
premises, distinctions or connections; choose questions addressing them.
Specify supporting and refuting outcomes before designing discriminating tests.
Keep results with their assumptions; check those against your objects before reuse.

> The last line of the ledger is always the first line of the next round.

Proofs supply premises; counterexamples refute claims within their stated scope.
When identical readings hide different target values, no function of those
readings recovers the target in both cases.
[Seek new observations or relations](docs/VISION.md#how-ai-can-find-its-next-direction).

Evaluate research selection against stated baselines on questions excluded
from method design, matching information and resources.

<p><img src="docs/assets/inquiry-cycle.svg" width="360" height="560" alt="Ask a question, test hypotheses, check a proof or refutation, and keep a reusable result. Solid return reuses results as premises; dashed returns carry unresolved questions."></p>

*A schematic of inquiry, not runtime behavior or dependency data.* Checked
results return as premises; dashed returns carry unresolved questions, even
without a checked result. Tests alone do not establish a theorem.

Golden integers, Fibonacci weights and Zeckendorf representations are one
thread of the library; the examples below also explore conjecture refutation
and limits of local observation.

## Three places to look

### 01 · Refute a conjecture.

For positive integers n, let a(n) be the greatest integer k with `(1 + 1/n)^k ≤ 2`.
Greathouse conjectured for OEIS A175406 that
`a(n) = floor((n + 1/2) log 2)`. At `n = 1121626023352383`, the formula gives
`7774519157

... (truncated)