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| 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 |