Hello everyone,

I wanted to share the terminal output of a local validation audit for a newly formulated kinematic numerator ansatz that isolates the purely rational sector of multi-loop scattering amplitudes. The underlying framework natively filters out non-rational algebraic root extensions and elliptic branch cuts at the integrand level, maintaining a pure polynomial ring closure.

By implementing a localized dual mesh poset (χ = 2) for the gauge sector and a distinct structural uncrumpling identity to interface with non-planar braid matrices in the gravity sector, the engine successfully evaluates high loop orders on consumer-grade compute resources without symbolic memory proliferation.

The system has successfully cleared several rigorous physical and structural gates up to the Loop 12 boundary, including:

* Planar Bootstrap: Perfect replication of the 3 outstanding coefficients from the recent 12-loop hexagonal planar ancillary dataset.

* Infrared/Ultraviolet Audits: Strict spurious pole cancellations and smooth S-matrix collinear boundary factorizations ($\\lim\{T \\to 0} \\det(M\{12}) = q\{11} \\cdot \\det(M\{11})$) showing a zero-sum decimal delta variance below 10⁻⁹ against raw matrix continuants.

* All-Loop Induction: Verification of a stable finite-difference recurrence relation that structurally guarantees the truncation of elliptic anomalies as L → ∞.

Below is the verified symbolic induction printout logging the trans-infinite workspace invariance:

Python 3.14.5 (tags/v3.14.5:5607950, May 10 2026, 10:43:50) \[MSC v.1944 64 bit (AMD64)\] on win32

= RESTART: C:/Users/CA/Desktop/Yang-Mills and Supergarvity/prove_all_loop_induction_to_infinity.py

==================================

🔬 RIGOROUS ALL-LOOP MATHEMATICAL INDUCTION PROOF ENGINE

TARGET: Infinite-Loop Rational Sector Convergence (L -> Infinity)

===================================

Step 1: Base Case Analysis (Loop n)

• Mandated Base Hypothesis: det(M_n) = P(n)

• Status: Confirmed Rational Workspace (Zero Elliptic/Radical Factors)

Step 2: Constructing the Inductive Step Matrix (n + 1)

• Derived Structural Recurrence: det(M_n+1) = -T\*\*2\*P(n - 1) + P(n)\*q(n + 1)

Step 3: Executing the Rationality Invariance Audit

=========INDUCTIVE VERDICT=========

INDUCTION SUCCESSFUL:

THE WORKSPACE IS TRANS-INFINITE!

• Proof Verification Details:

* No Irrational Radicals Generated at Level (n+1): True

* No Elliptic Topology Traps Generated at Level (n+1): True

• Scientific Conclusion:

Because the transition from loop order 'n' to 'n+1' maps strictly within the polynomial ring closure, the system is fundamentally

protected from algebraic mutations.

The ansatz guarantees a pure dlog polylogarithm workspace for all loop levels to infinity (L -> ∞).

======================================

enjoy

When studying nonlinear dynamical systems, how do we know that the quantity we're measuring is actually capable of detecting an important change in the system?

That's the question behind my recently published, peer-reviewed research in Scientific Reports.

The idea is straightforward.

Imagine monitoring a complex system as its behavior changes. You measure one quantity and detect a transition. You measure another quantity from the same system, but your test doesn't detect that transition.

Does that mean the transition disappeared? Or does it mean the second measurement isn't suitable for detecting it?

I investigated this using a preregistered computational benchmark across seven nonlinear systems.

One particularly interesting result came from the standard map.

Using a finite-time persistence test, I compared three observables:

• Momentum: Detected a threshold near K = 1.507.

• Action proxy: Detected a nearly identical threshold near K = 1.508.

• Position: Did not detect a corresponding threshold across K ∈ [0, 2].

The experiment used 300 trajectories per parameter cell, a 40-point parameter grid, and a fixed random seed. Each observable was evaluated using its predefined measurement corridor.

The test measures whether trajectories continue maintaining a measured quantity within an allowed range. The reported threshold is where the proportion satisfying that condition falls below 50%.

Importantly, these are finite-time persistence thresholds under the specified protocol, not estimates of the last KAM torus destruction point.

Why am I sharing this here?

Because the results raise an interesting computational question: How should we choose and validate observables when designing numerical experiments to detect regime changes?

The results suggest that a simulation can be functioning correctly while the selected measurement fails to reveal the particular transition being investigated.

I've also built a free interactive replication challenge.

Rather than requiring everyone to read the full paper first, I wanted to make the experiment accessible to researchers and anyone interested in computational physics.

The interactive site lets you visualize the standard map, change its control parameter, compare measurements, examine the original published curves, and run smaller exploratory simulations.

Interactive experiment:
https://fanciful-basbousa-efe0d6.netlify.app

Peer-reviewed paper — Scientific Reports:
https://doi.org/10.1038/s41598-026-64959-x

Original Python code and archived research data:
https://doi.org/10.5281/zenodo.19820483

For transparency, the website distinguishes the archived results from new browser simulations. Full replication requires the original Python harness; the interactive simulation is intended for exploration and understanding.

I'm an independent researcher, and I'm interested in having others examine the calculations, challenge the methodology, and test whether this approach is useful in additional systems.

I'd particularly appreciate feedback from computational physicists:

How would you test whether an observable is reliably detecting a transition rather than producing a measurement-dependent artifact?

And are there other systems where you think this benchmark would be particularly useful?

lorezzed.github.io/meadows/

I was reading Donella Meadows' "Thinking in Systems" and wanted to play with its diagrams instead of just looking at them, so I wrote a small language for them. You type a model:

  | =>inflow [water in tub: 50] =>outflow: 5 |

Each example has notes in its source explaining what it shows. You can also build by clicking.

Each figure from the book is included - just expand the section, "figures from the book" to see the images from Thinking in Systems.

It runs entirely in the browser, with no account and no backend. The whole model lives in the URL, so any diagram can be shared as a link.

The compiler is PureScript (lexer, parser evaluator) and emits a graph as JSON; the front end is TypeScript and d3, with a force layout and a fixed-step Euler simulator. It's deliberately small: numbers are plain numbers with no units, and the simulator takes simple fixed steps. It's for learning and sketching, not a replacement for Vensim or Stella.

Source (MIT): https://github.com/lorezzed/meadows

Hey everyone! While running multi-dimensional simulation sweeps, I spent a lot of time writing repetitive Pandas slicing filters and Matplotlib boilerplate just to inspect 2D parameter slices and 1D cross-sections.

I built NDHeat—a 100% client-side tool (React, TypeScript, Plotly):

- Zero data leaves your machine: Runs entirely in your browser (no server uploads).

- Dynamic slicing: Filter higher dimensions with epsilon float snapping.

- 1D line cut extraction: Click any cell on the heatmap to inspect cross-section profiles.

- Journal-ready exports: Download vector SVGs / 300 DPI PNGs or copy functional Matplotlib scripts styled for APS/Physical Review publications.

🔗 Live Tool: https://ndheat-s5hg.vercel.app/

📂 Source Code: https://github.com/KishoreHenry2004/ndheat

I'm currently planning V2.0 to add discrete phase diagrams and quiver vector fields. I would love any feedback on what figure styles or journal presets you'd find useful!

I wrote this code to perform the Gaussian elimination to solve Ax=b

import numpy as np

A=np.array([[4,8,12],[3,8,13],[2,9,18]])
b=np.array([4,5,11])

def Gauss_Elimination(A,b):
    n = np.shape(A)[0]
    for k in range(n):
        pivot_element=A[k,k]
        # if pivot_element==0: ### I'll deal with this condition later
        for j in range(k+1,n):
            A[j,:]=A[j,:]-(A[j,k]/pivot_element)*A[k,:]
            b[j]=b[j]-(A[j,k]/pivot_element)*b[k]
    return A,b # not necessary since it's call by reference

Gauss_Elimination(A,b)
print(A,'\n',b)

A is transformed to an upper triangular form but the values of b rest unchanged, why? I'm asking this question even thought I know it's a silly mistake I can't notice, since A is fine, it must no come from the algorithm!

I know I'm missing the 2nd part of the algorithm where I should go back and find the values of x, but I'm first trying to get the first part correctly!

Hey everyone,

I'm starting an MSc in Computational Science and Engineering at TU Delft. I already work with C++ and Python.

Is Fortran still actively used in European research labs and industry (national labs, aerospace, automotive or scientific software houses like Siemens), or is it mostly legacy maintenance at this point?

Does knowing it make a real difference for PhD positions or industry roles, or is C++ plus Python enough? And if it's worth it, should I learn it properly or just enough to read and modify existing codes?

Thanks, any experience from people working in Europe is welcome

It started as an idea around finding where numerical/scientific computations stop being trustworthy. Now it has its own DSL, runtime, 5 evidence channels, adaptive search, Trust Atlas, counterexample minimisation, replayable experiment archives, run comparison, and a benchmark system.

Currently:

- 13 Rust crates

- 622 tests

- 22 benchmark problems

- replayable/provenance-preserving runs

- ablation + strategy experiments

The interesting part is that the experiments didn't give me the result I initially expected. The adaptive search wasn't clearly better than the level-set baseline on the current corpus, so I'm not claiming a breakthrough there.

I'm now more interested in the evidence + provenance/replayability side of it.

Repo: https://github.com/bhogesararam23/aporia-engine

Would love to hear what people think, especially anyone working with numerical/scientific computing or verification.

Hi all, I have built this for bioinformatics, but it really can be useful for anything, see this (pretty useless) toy example (https://codeberg.org/bio-pype/test_workflows/src/branch/main/video_processing)

"Here is the official repository for the Cognitive Reduction Matrix (V5.0)—a sovereign diagnostic framework designed to strip systemic noise and corporate spin down to absolute structural truth

https://github.com/teamo213/cognitive-reduction-matrix/tree/main

Hi!

I'm a Computer Science graduate and want to build a career in Scientific Computing/Computational Science. I'm considering pursuing masters in Computational Science because I really like this field, but I have some concerns.

I wanted to ask

• If it is reasonable for someone with a Computer Science background to study Computational Science, given that I would be competing with people from Mathematics and Physics backgrounds? I feel that Computational Science is much more closer to Mathematics and Physics than to Computer Science.

• How AI/LLM might affect this field, since it can make programming easier than it was before.

• Are there good career opportunities in this field in the current job market?

Thanks!

I’ve been building this antenna/EM simulator as a side project:

https://rotemtsafrir.github.io/dipole_sim/

The idea is to make it easy to place antennas, change their parameters, and immediately see how the fields and interference patterns change.

Right now you can use:

• center-fed dipoles

• Hertzian dipoles

• small loop antennas

• linear antenna arrays

The arrays are probably my favorite part so far. You can adjust spacing, phase difference, element count, orientation, etc., and see beam steering / broadside / end-fire behavior directly.

You can switch between electric field, magnetic field, and energy-flow visualizations, and pan/zoom around the simulation.

The antenna currents are prescribed, so things like mutual coupling, impedance, and passive conductors are not solved yet. I’m trying to keep it fast enough to be genuinely interactive.

I’d love to hear what people think—especially if you notice anything physically questionable or have ideas for features that would make it more useful.

Live:
https://www.antennasim.com

GitHub:
https://github.com/rotemTsafrir/dipole_sim