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        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3656731" />
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  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3656731">
    <title>SU(2) gauge theory in classical mechanics in UD</title>
    <link>https://community.wolfram.com/groups/-/m/t/3656731</link>
    <description>&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/545ac7e4-f815-43fb-9d0f-33d85e0f5e2d</description>
    <dc:creator>Brian Beckman</dc:creator>
    <dc:date>2026-03-10T23:44:24Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3601488">
    <title>[WSG26] Daily Study Group: Computational Food and Nutrition</title>
    <link>https://community.wolfram.com/groups/-/m/t/3601488</link>
    <description>A Wolfram U Daily Study Group on computational food and nutrition begins on February 23, 2026.&#xD;
&#xD;
Join me and fellow food and nutrition enthusiasts to learn how to compute, analyze and visualize data from Wolfram Language&amp;#039;s built-in knowledgebase of foods. Our topics for the study group include easy-to-use nutrition data retrieval and analysis tools, nutrient comparison plots and visualizations, statistical analysis of nutrition data, recipe management with LLMs, and food chemistry and physics with curated data and built-in formulas.&#xD;
&#xD;
No prior Wolfram Language experience is required.&#xD;
&#xD;
Please feel free to use this thread to collaborate and share ideas, materials and links to other resources with fellow learners.&#xD;
&#xD;
**Dates**&#xD;
&#xD;
February 23-27, 2026 (Monday through Friday), 11am-12pm CT (5-6pm GMT)&#xD;
&#xD;
&amp;gt; [**REGISTER HERE**][1]&#xD;
&#xD;
&#xD;
I hope to see you there!&#xD;
&#xD;
![enter image description here][2]&#xD;
&#xD;
&#xD;
  [1]: https://www.bigmarker.com/series/computational-food-and-nutrition-wsg75/series_details?utm_bmcr_source=community&#xD;
  [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4505hero.png&amp;amp;userId=20103</description>
    <dc:creator>Gay Wilson</dc:creator>
    <dc:date>2026-01-06T00:18:12Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3656544">
    <title>Black Hole Vision: an interactive iOS application for visualizing black holes</title>
    <link>https://community.wolfram.com/groups/-/m/t/3656544</link>
    <description>[![Black Hole Vision: an interactive iOS application for visualizing black holes][1]][2]&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][3]&#xD;
&#xD;
&#xD;
  [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=BlackHoleVision-aninteractiveiOSapplicationforvisualizingblackholes.jpg&amp;amp;userId=20103&#xD;
  [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=BlackHoleVision-aninteractiveiOSapplicationforvisualizingblackholes.jpg&amp;amp;userId=20103&#xD;
  [3]: https://www.wolframcloud.com/obj/c94b0ce3-acb0-4f23-adb6-e8aa2d4158f3</description>
    <dc:creator>Alex Lupsasca</dc:creator>
    <dc:date>2026-03-10T20:30:37Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3651250">
    <title>Computational dynamics of the classical and perturbed circular restricted three-body problem</title>
    <link>https://community.wolfram.com/groups/-/m/t/3651250</link>
    <description>![Computational dynamics of the classical and perturbed circular restricted three-body problem][1]&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][2]&#xD;
&#xD;
&#xD;
  [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=10346hero.png&amp;amp;userId=20103&#xD;
  [2]: https://www.wolframcloud.com/obj/f37e309d-f41e-45e5-a952-bb2953a400c4</description>
    <dc:creator>Akram Masoud</dc:creator>
    <dc:date>2026-03-06T16:49:26Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3636637">
    <title>Gravity and Cosmic Expansion from the Parabolic Metric Evolution of a Complex Manifold</title>
    <link>https://community.wolfram.com/groups/-/m/t/3636637</link>
    <description>&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/181086a3-2534-41da-92a6-762c33e102c4</description>
    <dc:creator>Donald Airey</dc:creator>
    <dc:date>2026-02-08T20:17:36Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3648128">
    <title>Bohmian trajectories and the role of nodal surface manifolds in hydrogen eigenstates: Part 2</title>
    <link>https://community.wolfram.com/groups/-/m/t/3648128</link>
    <description>![Bohmian trajectories and the role of nodal surface manifolds in hydrogen eigenstates: Part 2][1]&#xD;
&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][2]&#xD;
&#xD;
&#xD;
  [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Bohmiantrajectoriesandtheroleofnodalsurfacemanifoldsinhydrogeneigenstates-crop-video-.gif&amp;amp;userId=20103&#xD;
  [2]: https://www.wolframcloud.com/obj/57d77365-9bdd-4072-b8da-4686c29f6f82</description>
    <dc:creator>Klaus von Bloh</dc:creator>
    <dc:date>2026-03-03T10:25:54Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3647724">
    <title>SO(3) Gauge Theory for Classical Mechanics in UD</title>
    <link>https://community.wolfram.com/groups/-/m/t/3647724</link>
    <description>![SO(3) Gauge Theory for Classical Mechanics in UD][1]&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][2]&#xD;
&#xD;
&#xD;
  [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=5904SO%283%29gaugetheoryforclassicalmechanicsinUD.gif&amp;amp;userId=20103&#xD;
  [2]: https://www.wolframcloud.com/obj/d2ea36cc-f66d-4bd4-ac0d-f75831617d79</description>
    <dc:creator>Brian Beckman</dc:creator>
    <dc:date>2026-03-02T03:13:38Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3647422">
    <title>How few basis functions does one need to approximate any wavefunction?</title>
    <link>https://community.wolfram.com/groups/-/m/t/3647422</link>
    <description>&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/6e9d9326-7297-433f-8f78-fcc4c875f934</description>
    <dc:creator>Aisha Benzine</dc:creator>
    <dc:date>2026-03-01T04:17:27Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3631132">
    <title>A testable quantum graph theory of spacetime: seeking collaboration for simulation</title>
    <link>https://community.wolfram.com/groups/-/m/t/3631132</link>
    <description>Hello everyone,&#xD;
&#xD;
I am developing a model of spacetime that shares some fundamental concepts with the Wolfram Physics Project but introduces a specific focus on testability and quantum noise signatures.&#xD;
In my theory, spacetime is represented as a finite directed quantum graph. The core idea is that the connectivity of the graph isn&amp;#039;t just an abstract representation but directly dictates the physical observables we see in quantum systems.&#xD;
&#xD;
Key features of the model:&#xD;
&#xD;
Discrete Topology: Nodes represent Planck-scale events, and directed edges represent causal relationships.&#xD;
&#xD;
Emergent Physics: I have derived that the Einstein field equations and Maxwell&amp;#039;s equations emerge as a low-energy limit of these graph dynamics.&#xD;
Experimental Predictions: Most importantly, the model predicts specific spectral signatures in the decoherence noise of current NISQ-era quantum processors and anomalies in high-energy particle scattering.&#xD;
&#xD;
Iam looking for collaborators who are interested in:&#xD;
&#xD;
Visualizing the graph dynamics using the Wolfram Language.&#xD;
&#xD;
Simulating the noise patterns to compare them with existing data from IBM or Google quantum hardware.&#xD;
&#xD;
I believe that by identifying the right &amp;#034;rewrite rules&amp;#034; for this directed graph, we can bridge the gap between discrete spacetime models and experimental verification.&#xD;
&#xD;
Looking forward to your feedback and potential collaboration!</description>
    <dc:creator>Sergej Materov</dc:creator>
    <dc:date>2026-01-30T11:52:49Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3644908">
    <title>Looking for help cleaning up a Mathematica notebook into a reference implementation</title>
    <link>https://community.wolfram.com/groups/-/m/t/3644908</link>
    <description>**TL;DR** I&amp;#039;m looking for someone to refactor a Mathematica notebook I&amp;#039;ve got from a fellow researcher so I can use it as a reliable reference implementation. I expect it&amp;#039;s a few hours of work for the right person. I can offer financial compensation and/or my own technical expertise.&#xD;
&#xD;
Hello Wolfram community!&#xD;
&#xD;
I hope this is the right place for this kind of request. If not, my apologies!&#xD;
&#xD;
I&amp;#039;m a PhD student in the final stage of my project, an attempt at closed-loop control of water jets from firefighting robots using UAV imagery as feedback. The controller design is based on the Smith predictor architecture, which requires a predictive model to compensate for the long dead time of the system. Accurately predicting the trajectory of water jets is far from trivial. One of the most promising models I could find is described in https://link.springer.com/article/10.1007/s10694-021-01175-1. The model is formulated as a system of ordinary differential equations.   &#xD;
  &#xD;
I tried implementing it in Python so I can integrate it with my other components. It&amp;#039;s almost complete, but despite several months of debugging I haven&amp;#039;t been able to resolve the remaining issues. So I contacted the corresponding author. They confirmed some errors I found in the printed versions of the equations, and kindly provided their original Mathematica implementation. This helped, but my own implementation is still incomplete. The issues could stem from additional errors in the printed equations I/we haven&amp;#039;t found yet, mistakes in my implementation, or differences in solver behavior (Mathematica&amp;#039;s vs. SciPy&amp;#039;s solve_ivp() function). &#xD;
&#xD;
Unfortunately, the notebook is hard for me to follow and differs quite a bit from the published paper (structure, variable naming, angle conventions, etc.). I&amp;#039;ve never worked with Mathematica and don&amp;#039;t have the time nor patience to properly learn it before my deadline. &#xD;
&#xD;
The author is currently unable to provide further support, but since I&amp;#039;m getting more and more desperate to finish this subproject, I&amp;#039;m now seeking third-party help. I&amp;#039;m looking for someone to refactor the notebook into a clean, well-structured reference implementation. Specifically, I&amp;#039;d like them to&#xD;
&#xD;
 - remove unused and redundant code (many expressions are duplicated)&#xD;
 - improve structure&#xD;
 - improve documentation&#xD;
 - add small quality-of-life improvements if appropriate&#xD;
 - flag any noticeable discrepancies&#xD;
&#xD;
The refactored version must reproduce the original results, in particular the figures shown in the paper. Ideally, it should make it easy to experiment with the equations and parameters. One specific goal is to verify whether the rearranged equation forms I use in Python (to match SciPy&amp;#039;s solver interface) produce the same results as the original formulation.&#xD;
  &#xD;
If you&amp;#039;re interested, I&amp;#039;ll obtain the author&amp;#039;s permission and share the notebook privately so you can assess the scope before we discuss compensation. Bonus points if you have experience with physics-based simulations and are open to occasional follow-up questions :)&#xD;
&#xD;
Many thanks and regards!</description>
    <dc:creator>Merlin Stampa</dc:creator>
    <dc:date>2026-02-24T20:34:23Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3642590">
    <title>Investigating validity of AI-derived stripped gluon amplitudes with symbolic computation</title>
    <link>https://community.wolfram.com/groups/-/m/t/3642590</link>
    <description>![Investigating equality of stripped gluon amplitudes. How might we quickly verify the equality of key equations in using the Wolfram Language?][1]&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][2]&#xD;
&#xD;
&#xD;
  [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1772127905442.jpg&amp;amp;userId=20103&#xD;
  [2]: https://www.wolframcloud.com/obj/db42602f-f735-4297-97ff-e9a355634273</description>
    <dc:creator>Dennis Foren</dc:creator>
    <dc:date>2026-02-20T21:02:13Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3645941">
    <title>Bohmian trajectories and the role of nodal surface manifolds in hydrogen eigenstates: Part 1</title>
    <link>https://community.wolfram.com/groups/-/m/t/3645941</link>
    <description>![Bohmian trajectories and the role of nodal surface manifolds in hydrogen eigenstates: Part 1][1]&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][2]&#xD;
&#xD;
&#xD;
  [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=BohmiantrajectoriesandtheroleofnodalsurfacemanifoldsinhydrogeneigenstatesPart1.jpg&amp;amp;userId=20103&#xD;
  [2]: https://www.wolframcloud.com/obj/50b8fe54-bc05-4ab0-9989-60fc9612833f</description>
    <dc:creator>Klaus von Bloh</dc:creator>
    <dc:date>2026-02-26T13:51:25Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3645288">
    <title>The solvation entropy of different simulation models of the hydrated electron</title>
    <link>https://community.wolfram.com/groups/-/m/t/3645288</link>
    <description>![The solvation entropy of different simulation models of the hydrated electron][1]&#xD;
&#xD;
![enter image description here][2]&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][3]&#xD;
&#xD;
&#xD;
  [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=HydratedElectron3.gif&amp;amp;userId=20103&#xD;
  [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2493_1772117967979.jpg&amp;amp;userId=11733&#xD;
  [3]: https://www.wolframcloud.com/obj/e9c01359-55d2-4bcd-87f5-c12cd1c938ae</description>
    <dc:creator>Will Borrelli</dc:creator>
    <dc:date>2026-02-25T21:54:29Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3645153">
    <title>Currents in a closed dish</title>
    <link>https://community.wolfram.com/groups/-/m/t/3645153</link>
    <description>Hello all!&#xD;
&#xD;
I am trying to solve a problem of calculating induced electrical currents in a varying magnetic field. The field originates from current through a coil. I am only interested in the steady state solution, but also the time dependence might be interesting to solve.&#xD;
&#xD;
I already calculated the A field from the coils. There are two coils, each has 2 layers with 5 turns each, so a total of 2 turns (see code below). This is the field for a constant current of 1A, but my actual field would have a slope of e.g. 1 A/s.&#xD;
&#xD;
What I am interested now is:&#xD;
&#xD;
A circular dish is filled with conducting medium, and no current across the dish walls.The dish has a size of e.g. 35mm diameter and 5 mm height, and its bottom center is at the origin. How do the currents look that are induced by the changing field? Can we also determine the distribution of charges?&#xD;
&#xD;
    (*Magnetic Field Simulation for Two Coils*)&#xD;
    &#xD;
    (*Coil Parameters*)&#xD;
    x0 = 0.04;           (* Coil axis offset from origin = 40 mm *)&#xD;
    n0 = 5;                  (* Number of turns in each layer *)&#xD;
    d1 = 0.005;            (* distance of turns = 5 mm *)&#xD;
    r0 = x0 - (n0 - 1/2)*d1;         (* Inner coil radius *)&#xD;
    &#xD;
    m0 = 2;                  (* Number of layers *)&#xD;
    d0 = 0.014;         (* distance of layers = 14 mm *)&#xD;
    d2 = 0.006;        (* offset from origin = 6 mm *)&#xD;
    i0 = 1.0;              (* Current = 1A *)&#xD;
    &#xD;
    (* Permeability of free space[H/m] *)&#xD;
    mu0 = 4*Pi*10^-7; &#xD;
    &#xD;
    (*Each coil is defined by {xc, r, zc, I}*)&#xD;
    leftCoilTurns = &#xD;
      Flatten[Table[&#xD;
        Table[{-x0, r0 + n*d1, -l*d0 - d2, i0}, {n, 0, n0 - 1}], {l, 0, &#xD;
         m0 - 1}], 1];  &#xD;
    rightCoilTurns = &#xD;
      Flatten[Table[&#xD;
        Table[{x0, r0 + n*d1, -l*d0 - d2, -i0}, {n, 0, n0 - 1}], {l, 0, &#xD;
         m0 - 1}], 1];  &#xD;
    allTurns = Join[leftCoilTurns, rightCoilTurns];&#xD;
    &#xD;
    AFieldTurn[{x_, y_, z_}, {xc_, yc_, zc_}, r_, i_] := &#xD;
     Module[{dx, dy, dz, rho, k2, k, aphi},&#xD;
      dx = x - xc; dy = y - yc; dz = z - zc;&#xD;
      rho = Sqrt[dx^2 + dy^2];&#xD;
      If[rho != 0,&#xD;
       rho = Sqrt[dx^2 + dy^2];&#xD;
       k2 = 4 r*rho/((r + rho)^2 + dz^2);&#xD;
       k = Sqrt[k2];&#xD;
       aphi = mu0*i/(Pi*k)*Sqrt[r/rho] ((1 - k2/2) EllipticK[k2] - EllipticE[k2]);&#xD;
       {-aphi*dy/rho, aphi*dx/rho, 0},&#xD;
       {0, 0, 0}]&#xD;
      ]&#xD;
    &#xD;
    AFieldTotalXYZ[x_?NumericQ, y_?NumericQ, z_?NumericQ] := &#xD;
     Plus @@ (AFieldTurn[{x, y, z}, {#[[1]], 0, #[[3]]}, #[[2]], #[[&#xD;
           4]]] &amp;amp; /@ allTurns)&#xD;
    AMagnitude[x_, y_, z_] := Norm[AFieldTotalXYZ[x, y, z]]&#xD;
    ContourPlot[AMagnitude[x, 0, z], {x, -0.1, 0.1}, {z, 0, 0.05}, &#xD;
     Contours -&amp;gt; 20, ColorFunction -&amp;gt; &amp;#034;Rainbow&amp;#034;, AspectRatio -&amp;gt; Automatic,&#xD;
      PlotPoints -&amp;gt; 30]&#xD;
    ContourPlot[AMagnitude[x, y, 0], {x, -0.1, 0.1}, {y, -0.05, 0.05}, &#xD;
     Contours -&amp;gt; 20, ColorFunction -&amp;gt; &amp;#034;Rainbow&amp;#034;, AspectRatio -&amp;gt; Automatic,&#xD;
      PlotPoints -&amp;gt; 30]&#xD;
&#xD;
&#xD;
Thank you for your ideas and help!&#xD;
&#xD;
Max</description>
    <dc:creator>Maximilian Ulbrich</dc:creator>
    <dc:date>2026-02-25T15:24:32Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3644671">
    <title>Self-directed learning with notebooks: students&amp;#039; experiences in a chemical thermodynamics exercise</title>
    <link>https://community.wolfram.com/groups/-/m/t/3644671</link>
    <description>[![Self-directed learning with notebooks: students&amp;#039; experiences in a chemical thermodynamics exercise][1]][2]&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][3]&#xD;
&#xD;
&#xD;
  [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Self-directedlearningwithnotebooksstudents%E2%80%99experiencesinachemicalthermodynamicsexerc.jpg&amp;amp;userId=20103&#xD;
  [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Self-directedlearningwithnotebooksstudents%E2%80%99experiencesinachemicalthermodynamicsexerc.jpg&amp;amp;userId=20103&#xD;
  [3]: https://www.wolframcloud.com/obj/c863fe35-3afe-4103-b447-ca6e6feb3f4c</description>
    <dc:creator>Michael Haring</dc:creator>
    <dc:date>2026-02-24T19:19:08Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3643786">
    <title>Gauge theory in UD</title>
    <link>https://community.wolfram.com/groups/-/m/t/3643786</link>
    <description>&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/b8200a51-6f4e-4ebe-ae47-a8d223594c8f</description>
    <dc:creator>Brian Beckman</dc:creator>
    <dc:date>2026-02-23T19:58:27Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3644501">
    <title>3D printing and visualizing Fermi surfaces in Wolfram Language</title>
    <link>https://community.wolfram.com/groups/-/m/t/3644501</link>
    <description>&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/00f106b5-05e6-4f07-a413-7aa01bfda03c</description>
    <dc:creator>Furkan Semih Dündar</dc:creator>
    <dc:date>2026-02-24T10:38:11Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3643430">
    <title>Parallel-plate viscometer: symbolic computations of dynamic viscosity</title>
    <link>https://community.wolfram.com/groups/-/m/t/3643430</link>
    <description>&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/3a661d87-7c7f-4644-92f2-fed752a570f9</description>
    <dc:creator>Housam Binous</dc:creator>
    <dc:date>2026-02-22T17:22:34Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3643405">
    <title>Cone-and-Plate Viscometer: Dynamic Viscosity Calculation</title>
    <link>https://community.wolfram.com/groups/-/m/t/3643405</link>
    <description>&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/a96a4215-964f-42cb-81ec-bb4b06e2a64f</description>
    <dc:creator>Housam Binous</dc:creator>
    <dc:date>2026-02-22T08:42:43Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3642808">
    <title>Exploring a finite multiway system: exact computability in the &amp;#034;S21&amp;#034; discrete quantum gravity model</title>
    <link>https://community.wolfram.com/groups/-/m/t/3642808</link>
    <description>**Title: Exploring a Finite Multiway System: Exact Computability in the &amp;#034;S21&amp;#034; Discrete Quantum Gravity Model**&#xD;
&#xD;
Hello everyone, &#xD;
&#xD;
I’ve been reviewing a recent theoretical framework called &amp;#034;S21 Theory,&amp;#034; and it shares significant conceptual DNA with the Wolfram Physics Project&amp;#x2014;specifically regarding multiway systems and the emergence of continuous physics from discrete graphs [1, 2]. I thought it would be an interesting model to discuss here, particularly because of how it approaches the problem of infinite state spaces and exact computability.&#xD;
&#xD;
Here is a breakdown of how the S21 model aligns with (and diverges from) the Wolfram approach:&#xD;
&#xD;
**1. The Foundation: A 6-Bit Postulate Instead of Arbitrary Rules**  &#xD;
While the Wolfram approach often searches empirically for generative rewriting rules across an infinite space of possible strings [2, 3], S21 derives its structure from a single discrete postulate: spacetime at the Planck scale admits exactly six binary degrees of freedom (bits) per cell [4].   &#xD;
* This 6-bit postulate creates a finite 64-state configuration space (the $Q_6$ hypercube) [5].   &#xD;
* Applying topological consistency and action minimization filters this down to exactly 21 stable configurations [6].  &#xD;
* 20 of these states form a connected visible-sector vacuum manifold ($M_{20}$), while 1 isolated state becomes a Dark Matter candidate ($\sigma$) [6].  &#xD;
&#xD;
**2. Multiway Evolution and Exact Solvability**  &#xD;
S21 explicitly utilizes the multiway evolution paradigm [1]. Dynamics in the S21 vacuum occur as a multiway directed acyclic graph (DAG) where the system simultaneously explores all allowed paths on a 20-node physical transition graph ($G_E$) [7].  &#xD;
* **The &amp;#034;Wolfram Difference&amp;#034;:** The S21 author explicitly compares the two models, noting that because S21 is restricted to a finite 20-state manifold rather than an infinite state space, its multiway evolution is *exactly solvable* [2, 3].   &#xD;
* The discrete Feynman path integral (summing over all paths in the multiway graph) is evaluated exactly, matching matrix-inverted Green&amp;#039;s functions to machine precision ($10^{-14}$) [8]. This provides a convergent, explicit sum without the need for Monte Carlo approximations or dealing with divergent infinities [9].&#xD;
&#xD;
**3. Emergent Curvature (Ollivier-Ricci)**  &#xD;
Just as Wolfram models look for continuum limits of discrete hypergraphs, S21 proves that continuous relativistic geometry emerges from the discrete graph $G_E$. By computing the Ollivier-Ricci curvature using optimal transport (Wasserstein-1 distance) between the neighborhoods of adjacent vertices, the theory proves the graph has a uniform negative curvature ($\kappa = -1/3$) [10, 11]. This establishes the vacuum as a constant-curvature homogeneous space satisfying the discrete Einstein equations [12].&#xD;
&#xD;
**4. Topological Origin of the Standard Model**  &#xD;
Instead of treating particle physics as an add-on, S21 claims the Standard Model is structurally inevitable from the graph topology:  &#xD;
* **Fermion Generations:** The topological skeleton of the 20-state manifold has a first Betti number of $b_1 = 3$, which exactly matches the 3 generations of fermions [13].  &#xD;
* **Particle Spectrum:** The 43 &amp;#034;forbidden&amp;#034; states ($F_{43}$) outside the vacuum manifold act as an encoding space for the particle spectrum. The boundary membrane between the forbidden sector and the vacuum yields exactly 39 observable states (1 Higgs + 12 gauge bosons + 16 quarks + 10 leptons), which perfectly divides into 13 particles across 3 generations [14, 15].  &#xD;
* **Cosmology:** The framework tracks the minimal CP-odd closed walk on the graph, finding a length of $l_{min} = 7$ [16]. This single integer invariant is used to derive both the baryon asymmetry ($\sim 10^{-10}$) and the cosmological constant ($\sim 10^{-119}$) [17, 18].&#xD;
&#xD;
**Discussion Prompt for the Forum:**  &#xD;
The S21 framework suggests that by restricting a multiway system to a highly constrained, finite topological manifold ($M_{20}$), we can bypass the computational intractability of infinite state spaces and extract exact, quantitative cosmological parameters [2, 3]. &#xD;
&#xD;
Has anyone here experimented with similarly constrained, finite multiway systems? I’d be very interested in hearing the community&amp;#039;s thoughts on using a strictly finite 6-bit partition to solve the path integral convergence problem in discrete quantum gravity.</description>
    <dc:creator>Suhail Bachani</dc:creator>
    <dc:date>2026-02-21T00:32:44Z</dc:date>
  </item>
</rdf:RDF>

