# Geometric Spacetime Residuals **Project site:** This repository contains small reproducible experiments and short papers for a geometric-residual framing of the missing-mass problem. The central object is the mismatch between the geometry implied by observations and the geometry predicted from observed baryons. ## Context and Contributions Galaxy rotation curves define an inverse problem: observed baryons predict one weak-field acceleration profile, while the measured dynamics imply another. Rather than treating the mismatch only as a parameter-fitting residual for a single named model, this repo studies the leftover field itself. The guiding question is whether geometric residuals are structured, compressible, and learnable across a population of galaxies. The work develops three connected ideas: - A **geometric residual** view of missing mass, where $\Delta g(R) = [V_{\rm obs}^2(R)-V_{\rm bar}^2(R)]/R$ is treated as an inferred field rather than just an error term. - A **residual-of-residual** diagnostic: fit a physical baseline such as NFW, subtract it, and analyze the coherent structure that remains. - A **statistical learning layer** for real SPARC galaxies, using masked smooth dictionary learning to find stable population modes in those leftover fields. The main current result is the SPARC residual dictionary-learning paper in `papers/sparc_residual_dictionary_learning/`. It shows that residual profiles from 131 primary-quality SPARC galaxies are strongly compressible, that the first signed residual-of-residual modes are bootstrap-stable, and that learned coordinates align with independent central-overshoot diagnostics. The claim is model criticism, not theory selection: fit the baseline, learn what remains, and test whether the leftover geometry is coherent. ## Repository Layout - `src/`: shared Python modules for toy profiles, weak-field inversion, fitting, plotting, warp search, and report generation. - `figures/`: generated figures for the synthetic/toy experiments. - `results/`: generated CSV outputs for the synthetic/toy experiments. - `reports/`: generated Markdown/HTML reports from the root runners. - `papers/`: standalone manuscripts and compiled PDFs. - `experiments/`: self-contained real-data or specialized experiments. ## Experiments ### Geometric Residual AI Experiment Fits named toy residual families as a scaffold for decomposing a geometric residual into candidate latent generators. ```bash python run_experiments.py ``` Primary outputs: - `reports/geometric_residual_ai_experiment.md` - `reports/geometric_residual_ai_experiment.html` - `results/synthetic_experiment_summary.csv` - `results/model_comparison_metrics.csv` - `results/sparse_basis_weights.csv` ### Geometry-First Warp Grid Search Searches directly over weak-field metric perturbations, $g_{\mu\nu}^{\rm trial}=g_{\mu\nu}^{\rm bar}+h_{\mu\nu}(\theta)$, using radial perturbations of $\delta\Phi(r)$ and $\delta\Psi(r)$, rather than starting from named physical theories. ```bash python run_warp_grid_search.py ``` Primary outputs: - `reports/geometric_warp_grid_search.md` - `reports/geometric_warp_grid_search.html` - `results/warp_grid_search_all.csv` - `results/warp_top_candidates.csv` - `results/warp_family_summary.csv` - `results/warp_basis_weights.csv` - `figures/warp_rotation_fit.png` - `figures/warp_potentials.png` - `figures/warp_residual_acceleration.png` - `figures/warp_effective_profiles.png` - `figures/warp_lensing_proxy.png` - `figures/warp_log_parameter_heatmap.png` - `figures/warp_parameter_scatter.png` - `figures/warp_family_scores.png` - `figures/warp_basis_components.png` ### Synthetic NFW Residual-of-Residual Test Tests pure NFW against the synthetic flat-curve target and computes the leftover residual field. ```bash python run_nfw_residual_experiment.py ``` Primary outputs: - `figures/nfw_residual_of_residual.png` - `results/nfw_residual_experiment_summary.csv` - `results/nfw_residual_of_residual_profiles.csv` - `papers/nfw_residual_of_residual/nfw_residual_of_residual_JRLanders.tex` - `papers/nfw_residual_of_residual/nfw_residual_of_residual_JRLanders.pdf` ### SPARC NFW Residual-of-Residual Experiment Applies the residual-of-residual diagnostic to public SPARC rotation curves. This experiment is self-contained under: - `experiments/sparc_nfw_residuals/` Run it with: ```bash python experiments/sparc_nfw_residuals/run_sparc_nfw_residuals.py ``` It downloads missing SPARC source tables, fits NFW and cored/isothermal residual families, and writes its own results, figures, and paper in the experiment folder. ### SPARC Residual Dictionary Learning Learns population-level residual dictionaries from the SPARC residual profiles produced by the NFW residual-of-residual experiment. ```bash python experiments/sparc_residual_dictionary/run_sparc_residual_dictionary.py ``` This experiment is self-contained under: - `experiments/sparc_residual_dictionary/` It interpolates primary-quality SPARC residual profiles onto a common normalized radius grid, learns nonnegative and signed residual dictionaries, evaluates held-out radial-point reconstruction, bootstraps mode stability, and writes a Markdown report in the experiment folder. ## Papers - `papers/geometric_residual_missing_mass/`: original geometric-residual and weak-field warp-search manuscript. - `papers/nfw_residual_of_residual/`: synthetic NFW residual-of-residual note. - `papers/sparc_nfw_residuals/`: real-data SPARC residual-of-residual note. - `papers/sparc_residual_dictionary_learning/`: conference paper on masked dictionary learning for SPARC residual-of-residual fields. ## Scope The synthetic experiments use toy units, synthetic data, simplified radial/spherical proxies, and conceptual lensing/slip observables. The SPARC experiment uses real rotation-curve data but fixed mass-to-light ratios and a simplified residual-space fitting pipeline. These are diagnostic prototypes, not full GR metric reconstructions, particle-discovery pipelines, or final evidence for a new physical theory.