README.md

---
title: Cosmology Gravity Lab
emoji: 👀
colorFrom: indigo
colorTo: purple
sdk: gradio
sdk_version: 6.1.0
app_file: app.py
pinned: false
license: other
short_description: 'Welcome to RFTs cosmology and gravity model '
thumbnail: >-
  https://cdn-uploads.huggingface.co/production/uploads/685edcb04796127b024b4805/TOp7INVJ6aRZAKMDObeGn.png
---


# Rendered Frame Theory — Cosmology & Gravity Lab

This space is the primary interactive lab for **Rendered Frame Theory (RFT)** in cosmology and gravity.  
Every module is driven by the same global coherence operator

\[
U_{\rm RFT} = \Phi\,\Gamma\,\mathcal{R}\,(1 - \Xi)\,\Psi
\]

and by the pair

\[
\Phi\Gamma = \Phi \cdot \Gamma
\]

which controls redshift mappings, lensing amplification and analytic rotation-curve scaling.

The point is simple: you see exactly how changing the **same five sliders** reshapes rotation curves, κ maps, BAO/CMB structure, black hole radii, and observer-driven collapse — in one coherent framework, not a zoo of unrelated “free parameters.”

---

## 🔧 Global controls — what the sliders actually do

These are the sliders at the top of the app. They feed every tab.

- **Φ (phase / amplification)**  
  Overall strength of coherence amplification. Higher Φ makes RFT effects stronger across all modules (rotation curves, lensing, redshift, BH radius, collapse).

- **Γ (recursion scale)**  
  Sets the microscopic recursion strength that builds BAO/CMB-like structure. Through  
  \(\Gamma_{\rm eff} = \Gamma (1 + \Phi (1 - e^{-\Gamma}))\)  
  it controls the effective BAO scale \(r_{\rm BAO}\) and the ℓ-peaks.

- **ℛ (curvature gain)**  
  Large-scale curvature gain. Multiplies the entire coherence operator \(U_{\rm RFT}\). Increasing ℛ globally boosts cosmological deformations (expansion, BH radius, coherence crest strength).

- **Ξ (susceptibility)**  
  How close the system is to collapse. As Ξ → 1, \(U_{\rm RFT}\) is suppressed and the system is driven towards measurement / collapse. In the observer tab we explicitly track when Ξ_total crosses 1.

- **Ψ (observer phase weight)**  
  Strength of the observer’s coupling into the field. Higher Ψ tightens the link between coherence and what is actually rendered. It appears directly in \(U_{\rm RFT}\) and in the collapse drive \(\lambda_{\rm RFT}\).

Everything you see in the plots is just these five numbers being pushed through the same mathematics in different physical contexts.

---

## 🧩 Modules in this lab

Each module is a tab in the UI.

### 1. Coherence dashboard

- Shows the derived quantities from your current global sliders:
  - \(U_{\rm RFT}\), \(\Phi\Gamma\), \(\Gamma_{\rm eff}\)
  - \(r_{\rm BAO}\) (coherence BAO scale)
  - Approximate CMB-like peaks \(\ell_1, \ell_2, \ell_3\)
  - Two redshift mappings: exponential and compression
- Includes a BAO-scale vs \(\Gamma_{\rm eff}\) plot with your current point highlighted.

**What to look for:**  
Dial Φ and Γ and watch how \(\Gamma_{\rm eff}\) and \(r_{\rm BAO}\) move together. This is the “engine room” of the whole lab.

---

### 2. Rotation curves (analytic)

- Standard baryonic rotation curve \(v_{\rm bar}(r) = \sqrt{GM(r)/r}\) for a disk + bulge.
- RFT curve:
  \[
  v_{\rm RFT}(r) = v_{\rm bar}(r)\,\sqrt{\max(\Phi\Gamma, 0)}.
  \]
- You choose:
  - Disk mass, bulge mass, disk scale length.
- The plot shows:
  - “Baryons only” vs “RFT amplified”.
  - A 220–240 km/s band for Milky Way-like flatness.

**What to look for:**  
How much of the “dark matter” effect can be mimicked purely by \(\Phi\Gamma\) without touching the baryonic profile.

---

### 3. RFT gravity disk sim (N-body toy)

- N-body toy galaxy disk with:
  - Central mass + particle disk.
  - Same initial conditions evolved with:
    - Newtonian gravity.
    - RFT-deformed gravity,
      \[
      g_{\rm RFT} = \tfrac{1}{2}\left(g_N + \sqrt{g_N^2 + 4 g_N a_0}\right),
      \]
      where \(a_0\) is tied to \(\Gamma_{\rm eff}\).
- Outputs:
  - Rotation curves for Newton vs RFT.
  - Final spatial distribution plots for both runs.

**What to look for:**  
Whether the RFT run can sustain a flat, high-velocity outer disk without inserting a “dark halo,” purely by changing the gravitational law via \(\Gamma_{\rm eff}\).

---

### 4. Lensing κ maps

- Computes a κ map for a Gaussian or Plummer lens using:
  - Standard critical density:
    \[
    \Sigma_{\rm crit} = \frac{c^2}{4\pi G} \frac{D_s}{D_l D_{ls}}.
    \]
  - RFT convergence:
    \[
    \kappa_{\rm RFT} = \frac{\Sigma}{\Sigma_{\rm crit}} (\Phi\Gamma).
    \]
- Uses `astropy` distances if available; falls back to a simple mapping otherwise.

**What to look for:**  
How κ_RFT scales with \(\Phi\Gamma\) at fixed baryonic mass profile. This is the transparent alternative to “dark lens” explanations.

---

### 5. BAO + CMB (toy recursion spectrum)

- Builds a toy recursion spectrum:
  \[
  P_{\rm RFT}(k) \propto k^{-1} \left[1 + \Phi\Gamma \cos\!\left(\frac{kD_A}{\sqrt{\Gamma_{\rm eff}}}\right)\right].
  \]
- Reports:
  - \(\Gamma_{\rm eff}\)
  - \(r_{\rm BAO}\)
  - Approximate harmonic peaks \((\ell_1, \ell_2, \ell_3)\).

**What to look for:**  
How a single recursion parameter set (Φ, Γ, ℛ, Ξ, Ψ) maps to both the BAO scale and CMB-like peak spacing.

---

### 6. Redshift mapping

- Compares three curves:
  - FRW baseline: \(z_{\rm metric} = z_{\rm obs}\)
  - Exponential mapping:
    \[
    1 + z_{\rm eff} = e^{\Phi\Gamma}
    \]
  - Compression mapping:
    \[
    1 + z_{\rm RFT} = (1 + z_{\rm obs}) \frac{1}{1 + \Phi\Gamma}.
    \]
- Plots \(z_{\rm rendered}\) vs \(z_{\rm obs}\) for your current ΦΓ.

**What to look for:**  
How much “redshift stretch” can be reinterpreted as coherence/observer effect instead of a hard-wired expansion history.

---

### 7. Black holes & LISA coherence crest (toy)

- Classical Schwarzschild radius:
  \[
  R_S = \frac{2GM}{c^2}.
  \]
- RFT radius:
  \[
  R_{\rm RFT} = U_{\rm RFT} R_S.
  \]
- Adds a **coherence crest** on top of a toy LISA-band chirp by making \(\Phi\Gamma(t)\) peak around merger and perturb the frequency.

**What to look for:**  
How a temporary spike in coherence would show up as a small, structured deviation from a GR chirp in the LISA band.

---

### 8. Observer field & collapse

- Effective susceptibility:
  \[
  \Xi_{\rm total} = \Xi_{\rm baseline} + \lambda_{\rm obs}\,\kappa_{\rm obs} + \Xi_{\rm slider}.
  \]
- Collapse drive:
  \[
  \lambda_{\rm RFT} = \Phi\,\Gamma\,\Xi_{\rm total}\,\Psi.
  \]
- The module:
  - Plots Ξ(t) and λ_RFT(t).
  - Flags whether Ξ_total ≥ 1 (“collapse triggered”) or not.

**What to look for:**  
How much observer coherence κ_obs you need, at your chosen Φ, Γ, Ψ, to push the system over the collapse threshold.

---

### 9. Math & case notes

Static summary of:

- The defining equations used in the lab.
- How each module ties back to \(\Phi\Gamma\), \(U_{\rm RFT}\), and \(\Gamma_{\rm eff}\).
- Enough detail for anyone to trace what the app is doing without guessing.

---

### 10. Provenance

- Every run of a module logs:
  - Module name
  - Timestamp (UTC)
  - Inputs (slider values, physical parameters)
  - Outputs (key scalars)
  - A **SHA-512 hash** over those fields
- Records are stored in memory and (when allowed) appended to a `*.jsonl` file.

You can inspect the table in the **Provenance** tab.

---

## ⚙️ Running the lab

Locally:

```bash
pip install -r requirements.txt
python app.py
On Hugging Face Spaces, the app runs automatically with gradio as defined in app_file: app.py.

Basic usage pattern:
	1.	Set your global coherence field (Φ, Γ, ℛ, Ξ, Ψ) at the top.
	2.	Pick a tab (rotation curves, lensing, disk sim, etc.).
	3.	Adjust the physical parameters (masses, distances, timesteps).
	4.	Click the button in that tab to compute.
	5.	Interpret the plot using the descriptions above. All dependencies on Φ, Γ, ℛ, Ξ, Ψ are explicit.

⸻

🔒 Legal position & allowed use
	•	Authorship
Rendered Frame Theory (RFT), its coherence operators, field equations and applied models are authored by Liam Grinstead.
	•	Protection
This work is protected under UK copyright law and the Berne Convention. All rights are reserved unless explicitly granted in writing.
	•	You are allowed to
	•	Use this lab to explore and understand RFT.
	•	Make plots, screenshots, and share results for education, open research, and discussion, with proper attribution.
	•	Cite RFT in scientific work, referencing the relevant Zenodo DOIs.
	•	You are not allowed to
	•	Use RFT, its equations, or this lab to design or optimise weapons or harmful systems.
	•	Repackage the RFT framework, operators, or code, rebrand them, and claim ownership.
	•	Commercially exploit RFT (products, services, proprietary models, or derivative frameworks) without explicit written permission from the author.
	•	Intent
RFT was built to crack open the gatekeeping around cosmology and consciousness, not to hoard knowledge.
This lab is intentionally public and mathematically transparent.
The line is clear: no weaponisation, no quiet commercial theft, no erasing authorship.

⸻

📚 Citation

If you use this lab or RFT concepts in your work, cite at least:

Grinstead, L. (2025). Rendered Frame Theory’s Mathematical model. Zenodo.
https://doi.org/10.5281/zenodo.17644885

(Include any additional RFT DOIs that match the specific equations or predictions you use.)
---
Check out the configuration reference at https://huggingface.co/docs/hub/spaces-config-reference