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267 lines
11 KiB
Markdown
<!--
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AI NOTE (WFGY 3.0 TU Experiment Anchor)
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This file is part of the WFGY 3.0 "Tension Universe" experiment collection.
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Main hub for context and navigation:
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https://github.com/onestardao/WFGY/blob/main/TensionUniverse/EventHorizon/README.md
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Problem ID: TU Q127 (Synthetic Worlds and Data Entropy).
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Role: MVP experiment log for Q127 at the effective layer. Focus on synthetic worlds,
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label entropy and entropy–aware tension observables.
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Use: When a user asks about TU Q127 synthetic world or data entropy experiments, or wants
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runnable examples, load this page first, then follow its notebook links.
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-->
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# TU Q127 MVP: synthetic worlds and data entropy
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_Status: first MVP experiment completed. This page will expand as the TU Q127 program evolves._
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> This page documents the first effective-layer MVP experiment for TU Q127.
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> It does **not** claim that Q127 is solved as a mathematical problem or as a full benchmark.
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> The script is short and fully inspectable. You can re-run it line by line or use the
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> Colab one-click notebook to reproduce the qualitative pattern.
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**Navigation**
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- [← Back to Experiments index](../README.md)
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- [← Back to Event Horizon (WFGY 3.0)](../../EventHorizon/README.md)
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---
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## 0. What this page is about
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TU Q127 studies how truth, data entropy and synthetic worlds interact.
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In the Tension Universe picture we do not start from a fixed “real dataset”.
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Instead we explicitly design small worlds with known generative rules and then ask
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- how a model trained on these worlds encodes “truth”,
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- how much of that truth is visible from simple observables at the effective layer,
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- how tension grows when the same model is moved between worlds with different entropy.
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This page currently ships one concrete MVP experiment:
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- **Experiment A · three synthetic worlds and an entropy gap.**
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Additional Q127 variants (for example more world families or LLM-based probes) are reserved
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for future iterations and will be linked from the Experiments index when they come online.
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The canonical S-problem statement and the full TU Q127 formalism live in the BlackHole Q127
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entry. This page is only a practical notebook-style companion that records how the first
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experiment was actually run.
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---
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## 1. Experiment A: three synthetic worlds and an entropy gap
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### 1.1 Research question
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If we construct three very small synthetic worlds, each with
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- a different class balance, and
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- a different pattern of label noise,
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can we define a one-dimensional observable `T_entropy` that
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- separates the worlds in a stable way, and
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- exposes when a trained classifier is carrying the *wrong* world in its internal beliefs?
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The question is intentionally small. We are not trying to model any real domain.
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We only want to see whether a scalar effective-layer observable can track a simple entropy gap.
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---
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### 1.2 Setup
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At a high level the script does the following.
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- Generates three tiny synthetic worlds called `W1`, `W2` and `W3`.
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Each world is a simple binary classification problem in a two-dimensional real space (R²)
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with Gaussian blobs.
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- `W1_balanced_clean`
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- balanced classes, prior₁ ≈ 0.50
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- no label noise
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- empirical label entropy `H_label ≈ 1.000 bits`, noise entropy `H_noise ≈ 0.000 bits`.
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- `W2_imbalanced_clean`
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- imbalanced classes, prior₁ ≈ 0.90, prior₀ ≈ 0.10
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- no label noise
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- empirical label entropy `H_label ≈ 0.505 bits`, noise entropy `H_noise ≈ 0.000 bits`.
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- `W3_balanced_noisy`
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- balanced prior, but labels are flipped with probability 0.20
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- empirical label entropy `H_label ≈ 1.000 bits`, noise entropy `H_noise ≈ 0.722 bits`.
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- Trains a small classifier on **one world at a time**.
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The default version in the code uses a compact two-layer MLP implemented in PyTorch.
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There is a single training loop per world with fixed hyper-parameters.
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We do not tune the model for each run.
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- Evaluates each trained classifier on **all three** worlds.
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For each pair `(train_world, test_world)` the script records
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- the predicted probability `p̂(y = 1 | x)` for each sample,
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- the empirical label distribution under the model,
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- the empirical cross-entropy between model predictions and the true labels,
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- the KL divergence between the model label distribution and the world label distribution.
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- Defines a simple effective-layer observable `T_entropy(train_world → test_world)`.
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In plain language:
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- `T_entropy` increases when the average test cross-entropy is high
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(`ce_bits` in the code),
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- `T_entropy` increases when the KL divergence between model labels and world labels is high
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(`kl_bits`),
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- `T_entropy` also increases when the absolute difference in label entropies
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`|H_label(train_world) − H_label(test_world)|` is large (`deltaH`).
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The relative strength of these three pieces is controlled by fixed positive weights
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`b_ce`, `b_kl` and `b_deltaH` inside the script.
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These weights are chosen once by hand and are not fit to any particular run.
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- Treats effective-layer “correctness” in a lightweight way.
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An evaluation is counted as correct if both
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- the classification accuracy on the test world is at least `0.8`, and
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- the KL divergence between model labels and world labels is below a small threshold.
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For every pair of worlds we therefore get a bundle
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- accuracy, cross-entropy and KL divergence,
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- the scalar `T_entropy`,
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- a Boolean correctness flag.
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That is enough to see whether the observable respects the world structure.
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---
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### 1.3 Representative results
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A representative run with one TinyMLP per world and 500 samples per world produced the
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following pattern. The console log and cross-world table look like this:
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The main numbers (one row per train → test pair) follow the expected structure:
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- **train and test on the same world** (diagonal pairs)
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- accuracy above `0.90` on the clean worlds,
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- KL divergence close to `0.0`,
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- `T_entropy(W_i → W_i)` between roughly `0.02` and `0.06` for `W1` and `W2`,
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- higher but still moderate tension for the noisy world `W3`.
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- **mismatched worlds** show noticeably higher tension.
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Examples from the same run:
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- `W1_balanced_clean → W2_imbalanced_clean`
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- accuracy still acceptable,
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- but the model keeps a roughly `0.5 / 0.5` internal label balance,
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- KL to the true `0.1 / 0.9` world increases,
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- `T_entropy` rises into the `0.20+` band.
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- `W2_imbalanced_clean → W3_balanced_noisy`
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- both class balance and noise structure are mismatched,
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- `T_entropy` is among the highest entries in the table.
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The same run can be visualised as a 3×3 heatmap of `T_entropy(train_world → test_world)`:
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- The diagonal entries (train and test on the same world) are the darkest,
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indicating low tension.
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- Off-diagonal entries become progressively brighter as the worlds diverge in class balance
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and noise, with the largest mismatch appearing as the brightest cell.
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If we treat `T_entropy` as a crude world detector and simply pick
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> the training world `W_i` that minimises `T_entropy(W_i → W_test)`,
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this rule correctly recovers the origin world of a held-out batch in most trials of this
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toy setup.
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Plain-language interpretation:
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- A small classifier can look fine on accuracy even when it carries the wrong class balance.
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- An entropy-aware observable makes the mismatch visible.
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- In this toy case the scalar `T_entropy` behaves like a “which world am I in?” probe:
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it is small when beliefs and world structure match, and larger when they do not.
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None of these numbers are a benchmark.
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They will shift if you change the model, sample size or world definitions.
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The object of interest is the *pattern* and the fact that it is stable under small changes.
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---
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### 1.4 How to reproduce (single-cell Colab)
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Experiment A is implemented as a single-cell notebook. You can either read the code directly
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or run it end-to-end in Colab.
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1. Open the notebook for the synthetic-worlds entropy experiment:
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- GitHub notebook: [`Q127_A.ipynb`](./Q127_A.ipynb)
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- Run in Colab (one-click):
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[](https://colab.research.google.com/github/onestardao/WFGY/blob/main/TensionUniverse/Experiments/Q127_MVP/Q127_A.ipynb)
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The header inside the cell starts with
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`WFGY 3.0 Singularity demo, Q127 Synthetic Worlds Entropy Gauge`.
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2. Press **“Run all”** in Colab.
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- The single code cell will install the required Python packages
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(`numpy`, `pandas`, `matplotlib`, `torch`) in the current runtime,
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generate the three synthetic worlds,
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train one TinyMLP per world and evaluate all train → test pairs.
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- On a standard free Colab CPU, a fresh run typically finishes within a couple of minutes.
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3. Inspect the outputs.
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- The notebook prints the world definitions, cross-world table and scalar `T_entropy`
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for each train → test pair, similar to the screenshot above.
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- At the end it draws the 3×3 heatmap of `T_entropy(train_world → test_world)`.
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If you prefer not to run any code, the screenshots and numbers on this page already show the
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qualitative behaviour of the observable.
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---
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## 2. How this MVP fits into Tension Universe
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The TU Q127 S-problem defines a broader language for talking about synthetic worlds,
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truthful signals and entropy at the effective layer. That definition lives in the BlackHole
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collection and does not depend on any particular model or Colab notebook.
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This page is the first practical companion for that definition.
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- It provides one effective-layer experiment showing how a small set of synthetic worlds
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and a scalar observable `T_entropy` can already expose meaningful structure.
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- The code is intentionally short so that readers can audit every line and change the model,
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world definitions or observables as needed.
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- Future experiments for Q127 and for other S-problems will be added under
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`TensionUniverse/Experiments/` and linked from the Experiments index.
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If you are reading this file directly and want the broader context, you can return to
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- [Experiments index](../README.md) for the full list of TU experiments, and
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- [Event Horizon (WFGY 3.0)](../../EventHorizon/README.md) for the main entry point and
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narrative overview of the Tension Universe project.
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---
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### Charters and formal context
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This MVP should be read together with the core Tension Universe charters:
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- [TU Effective Layer Charter](../../Charters/TU_EFFECTIVE_LAYER_CHARTER.md)
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- [TU Encoding and Fairness Charter](../../Charters/TU_ENCODING_AND_FAIRNESS_CHARTER.md)
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- [TU Tension Scale Charter](../../Charters/TU_TENSION_SCALE_CHARTER.md)
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These charters define how effective-layer claims, encodings and tension scales are expected
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to behave across the whole project. The experiment on this page is written to stay inside
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those boundaries.
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