r/u_ceosingularitycode

For context, my background and long-term focus have been in physics research. I’ve previously worked with professional tools such as Wolfram Mathematica and MATLAB to explore and render physics-based models, simulations, and empirical data. Some of the material I shared was derived from that work, including conceptual research and early-stage data exploration. At the time, I was not fully aware that this account or community had specific posting rules beyond general conduct, and any missteps were unintentional. Recently, my account experienced a rapid drop in karma (down to –17 within a short period). I’m not sure how common that is, but those points have since begun recovering. Notably, the

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I've developed a PDE solver in Mathematica using hierarchical subdivision and want to ensure it's actually working correctly before applying to harder problems. Current benchmarks: Hydrogen atom ground state: E = -13.5989 eV (exact: -13.6000 eV, error 0.008%) 2D harmonic oscillator: energies match within 0.01% Wave packet dispersion: agrees with analytical Gaussian spreading Convergence study: Three grid resolutions show consistent error reduction. RMSE ratio (coarse/fine) ≈ 0.98-0.99, suggesting near-asymptotic regime. Max residual: |iℏ∂ψ/∂t - Ĥψ| ~ 3.08-3.09 across all resolutions (should decrease with refinement - why isn't it?) Question: What additional validation tests should I run? I w

I'm trying to understand why different temporal discretization schemes perform so differently when spanning many orders of magnitude. Problem: Simulate system from τ_min = 10⁻³⁵ s (Planck time) to τ_max = 1 s. Direct uniform grid needs 10⁴⁴ points. Logarithmic spacing needs ~100 points but loses resolution at intermediate scales. Method I'm testing: Adaptive anchoring where each subdivision creates new reference point: t_{n+1} = t_n × (1 + δt/t_anchor)^(-1) Anchor updates when |t_{n+1} - t_anchor| > threshold. Result: Requires only ~140 effective points (log(10⁶¹) digits precision) and maintains second-order accuracy at all scales. Question: This seems similar to adaptive timestepping (RK45,

I've spent 2 years developing a computational framework for multi-scale physics simulations. Before submitting to arXiv, I need expert eyes on the mathematics to catch errors I might have missed. What I have: 30,000-word dissertation with full derivations Wolfram Mathematica implementation (~1000 lines) Convergence validation across 3 grid resolutions Benchmark comparisons to analytical solutions Stable solutions over 200+ iterations maintaining quantum coherence What I need: Review of differential geometry formalism (extending Einstein equations to 5D) Validation of numerical stability analysis (second-order convergence proof) Feedback on whether algorithm has prior art (seems related to wa

I've implemented a hierarchical subdivision method for solving PDEs across extreme scale ranges (10⁶¹ orders of magnitude) that achieves logarithmic complexity instead of the typical O(N³). Core idea: Instead of storing absolute values at every scale, compute only deltas (differences) between hierarchical levels using adaptive anchor points. Combined with memoization, this reduces a 10¹⁸³-node problem to ~10⁵ effective nodes. Validation: Tested on 2D Schrödinger equation with harmonic potential. Three grid resolutions (80×48, 120×72, 200×120) show RMSE ratios of 0.984 and 0.988, indicating second-order convergence. External fit to analytical solution gives χ² = 0.004925. Performance: Runs on

I'm running split-operator Fourier method (SOFM) simulations and getting unexpectedly stable results. Power spectrum analysis shows flat baseline (~20-25 across all frequencies) with single resonant peak, sustained over 200+ temporal iterations without decoherence. Setup: 2D wavefunction evolution with spatial domain x,z ∈ [-10,10], time steps Δt=0.01. Using hierarchical grid refinement with adaptive precision management. Observation: Standard implementations I've tested show coherence decay (τ_decoh ~ 10-50 iterations) from accumulated roundoff error. This method maintains coherence indefinitely (limited only by total sim time). Hypothesis: Storing delta values instead of absolute amplitude

What this is: Computational validation of a 5-dimensional mathematical framework Hierarchical temporal fractalization algorithm achieving O(log N) complexity Wolfram Mathematica implementation with convergence testing (RMSE ratios 0.984-0.988) What this is NOT: A claim to have "solved quantum gravity" A demand you accept the physical interpretation Requesting funding or attention Reproducibility: Full Mathematica notebooks available on request Convergence data: 3 grid resolutions tested (80×48, 120×72, 200×120) External validation: χ² = 0.004925 against analytical solutions Context: I have sudden savant syndrome (acquired after neurological event 2 years ago). I independently developed thes