https://community.wolfram.com RSS Feed for Wolfram Community showing ideas tagged with Wolfram Fundamental Physics Project sorted by active. https://community.wolfram.com/groups/-/m/t/2965206 ![Multiway graph][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Untitled.png&userId=2964459 [2]: https://www.wolframcloud.com/obj/b6ad5a15-e8d2-4359-ae89-b72d3e3d06d4 Eric Archerman 2023-07-13T23:11:59Z https://community.wolfram.com/groups/-/m/t/3691199 Hi everyone in the Wolfram Physics / Fundamental Physics Project community, I’ve just finished a 29-page cumulative working document that takes a strictly graph-first approach to electromagnetism, charge, chirality, and family replication. The core is built on a finite oriented graph with compact U(1) links — very much in the spirit of causal graphs and hypergraph models. Quick summary of what’s in the paper: Charge is literally an integer-valued flux-divergence defect on the graph. Exact regional Gauss law, topological quantization from link compactness, exact lattice continuity, Coulomb law from graph-Laplacian minimization, and full Maxwell dynamics emerging in the aligned deconfined phase — all proved cleanly. A common topological language (cellular gauge data + relative current classes + twisted Spinc index theory) unifies charge, chirality, and three-family replication. Explicit finite toy model: product graph $ G = \Lambda_4 \times I_s \times T^2_F $ with domain-wall/overlap fermions and internal flux index 3 gives minimal charge + chirality + three replicated families from one parent generation. Preferred strong ontology (the part I’m most excited about): charged particles are reinterpreted as self-bound local causal shells. A charged lepton is a trapped spinor core coupled to a bosonic shell-deformation sector on a closed 2D simplicial surface. The minimal regular shell is naturally tetrahedral; the leading deformation multiplet is a geometric triplet whose microscopic anisotropy + holonomy collapse to a single-vector operator that automatically produces the exact cosine spectrum used in Koide-type charged-lepton relations. Strong coefficient locking and a codimension-one dynamical balance surface emerge from identical-link tetrahedral geometry and radial-wall tension. The paper is deliberately layered: theorems vs. constructions vs. strong-but-incomplete branches vs. ruled-out ideas. It overlaps structurally with tetrahedral A₄ flavor models but supplies a concrete geometric engine inside the shell rather than abstract flavons. Full PDF (master_working_document_v8.pdf) is attached. Transparency note: I used Grok (xAI) heavily to help me refine the writing, tighten the LaTeX, organize the sections, and make the ideas as clear as possible. The core physics ideas, and ontology are my own — but the AI was instrumental for making this possible. I’d love honest feedback from this community, especially on: how the compact-graph U(1) core and causal-shell picture might connect to hypergraph / causal-graph dynamics, any overlaps or tensions with the Wolfram Physics framework, suggestions for next steps or things I should stress/test. Happy to discuss any part of it. Thanks in advance! Aiden Smith 2026-04-17T01:09:09Z https://community.wolfram.com/groups/-/m/t/3682254 ![enter image description here][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=8239hero.png&userId=20103 [2]: https://www.wolframcloud.com/obj/27b9cbf2-47f5-4888-81b8-aa014c78b0c6 Myrto Terpsiadou 2026-04-11T13:27:03Z https://community.wolfram.com/groups/-/m/t/3663446 ![The Ruliad concept: some ideas and observations][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=TheRuliadconceptsomeideasandexamples.png&userId=20103 [2]: https://www.wolframcloud.com/obj/db1cd65f-d494-49cb-8414-bcaed8b4ffef Denis Ivanov 2026-03-17T04:57:25Z https://community.wolfram.com/groups/-/m/t/3636637 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/181086a3-2534-41da-92a6-762c33e102c4 Donald Airey 2026-02-08T20:17:36Z https://community.wolfram.com/groups/-/m/t/3642808 **Title: Exploring a Finite Multiway System: Exact Computability in the "S21" Discrete Quantum Gravity Model** Hello everyone, I’ve been reviewing a recent theoretical framework called "S21 Theory," and it shares significant conceptual DNA with the Wolfram Physics Project—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. Here is a breakdown of how the S21 model aligns with (and diverges from) the Wolfram approach: **1. The Foundation: A 6-Bit Postulate Instead of Arbitrary Rules** 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]. * This 6-bit postulate creates a finite 64-state configuration space (the $Q_6$ hypercube) [5]. * Applying topological consistency and action minimization filters this down to exactly 21 stable configurations [6]. * 20 of these states form a connected visible-sector vacuum manifold ($M_{20}$), while 1 isolated state becomes a Dark Matter candidate ($\sigma$) [6]. **2. Multiway Evolution and Exact Solvability** 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]. * **The "Wolfram Difference":** 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]. * The discrete Feynman path integral (summing over all paths in the multiway graph) is evaluated exactly, matching matrix-inverted Green'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]. **3. Emergent Curvature (Ollivier-Ricci)** 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]. **4. Topological Origin of the Standard Model** Instead of treating particle physics as an add-on, S21 claims the Standard Model is structurally inevitable from the graph topology: * **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]. * **Particle Spectrum:** The 43 "forbidden" 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]. * **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]. **Discussion Prompt for the Forum:** 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]. Has anyone here experimented with similarly constrained, finite multiway systems? I’d be very interested in hearing the community's thoughts on using a strictly finite 6-bit partition to solve the path integral convergence problem in discrete quantum gravity. Suhail Bachani 2026-02-21T00:32:44Z https://community.wolfram.com/groups/-/m/t/3589391 The Rule：{{x, y}, {y, z}} -> {{x, z}, {x, w}, {w, z}} This model investigates the emergence of causal geometry from a minimal graph-rewriting rule. Unlike standard branching trees, this rule facilitates state merging (interference), mimicking a Dynamic Programming optimization process within the causal graph. The evolution demonstrates Markovian properties where the spatial structure ('ripple') expands purely based on local connectivity, creating a discrete spacetime fabric that exhibits Causal Invariance. This serves as a computational candidate for interpreting the 'Many-Worlds' path integral as a deterministic graph optimization problem. Proposed Model Description (Short Explanation) Nodes represent discrete universe slices (microstates of spacetime). Each node encodes a complete instantaneous configuration of the universe. Directed edges represent causal relations between slices. An edge from node A to node B indicates that B is a possible successor state generated from A. The network is constructed through a recursive update process combining (1) a Markov-style probabilistic transition rule, and (2) a deterministic local causal rule. Together, these govern how new spacetime slices branch and evolve. A path from the root to any node corresponds to a possible history of the universe. Compressing such a path yields the emergent notions of time and macroscopic causality. The diagrams shown depict the evolving causal structure and the resulting spatial slice (wavefront) produced by these rules.![Causal Graph showing state merging and loop structures][1]![Final Spatial Slice exhibiting wavefront expansion][2]![20-times recursive version][3] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=yuz1.png&userId=3589356 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=yuz2.png&userId=3589356 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=222222.png&userId=3589356 Xin Wang 2025-12-11T13:21:31Z https://community.wolfram.com/groups/-/m/t/3608412 ![Holographic duality between causal and branchial graphs][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=adsss.png&userId=20103 [2]: https://www.wolframcloud.com/obj/5caba86f-013f-4f65-8d61-2d8d78f91365 Narmin Nasibova 2026-01-16T11:46:00Z https://community.wolfram.com/groups/-/m/t/3607969 ![Wolfram Physics Project Noncommutative Geometry Bridge][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=WPP-NCG-Bridge.png&userId=3607945 [2]: https://www.wolframcloud.com/obj/57ceecb3-2977-4fe1-9bc5-6e40e46dfd99 Jorge Plazas 2026-01-15T23:41:53Z https://community.wolfram.com/groups/-/m/t/3607514 ![Branchial graph stability][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2026-01-16004426.png&userId=3599863 [2]: https://www.wolframcloud.com/obj/9ee1946e-a652-4de6-a636-6efda46efac4 Rehab Almakrami 2026-01-15T21:49:27Z https://community.wolfram.com/groups/-/m/t/3599773 **This is a collaborative work by** [**Furkan Semih Dündar**][at0], [**Xerxes D. Arsiwalla**][at1], and [**Hatem Elshatlawy**][at2]. ![Figure adapted from (Dündar, Arsiwalla, Elshatlawy, 2025)][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2712hero.png&userId=20103 [2]: https://www.wolframcloud.com/obj/6954e3c7-a10d-460a-9a9a-ade61ae80043 [at0]: https://community.wolfram.com/web/fsemihdundar [at1]: https://community.wolfram.com/web/xdarsiwalla [at2]: https://community.wolfram.com/web/hatemelshatlawy Furkan Semih Dündar 2026-01-01T12:58:27Z https://community.wolfram.com/groups/-/m/t/3593059 **The Core Idea: Physics as Discretization Error** In continuous calculus, Green's Theorem ($\int_R dA = \oint_{\partial R} ds$) is exact. However, when applied to a discrete lattice with resolution limits, this equality fails. There is a "residue" or "defect" left over because the discrete boundary cannot perfectly capture the bulk interactions. I have been working on a model suggesting **Physical Law is this residue**. Specifically, I observe the discrete Green's Theorem on a recursive lattice (a Pentatope characteristic network). When this lattice attempts to fold from Dimension 4 (Bulk) to Dimension 3, the "counting error" forces specific constants to emerge. ![The "Golden Stencil" generated by the attached notebook. Visualizing the recursive $D=4$ fold scaling by $1/\phi$. The color gradient (Blue $\to$ Cyan $\to$ White) represents the descent through topological strata, and the central density represents the geometric residue (Mass).][1] **The Results (Zero Import)** Remarkably, this geometric residue yields values that match fundamental constants to high precision, without manual tuning: - **Fine Structure Constant** ($\alpha$): Matches to within **$0.00002\%$** **(0.014$\sigma$)** (derived from the impedance mismatch of the fold). - **Nuclear Stability**: The geometric residues scale to predict the Binding Energies of the Periodic Table (e.g., He-4, O-16, U-235) purely from the entropy of the lattice edges. - **Cosmic Structure**: The ratio of Dark Matter to Baryonic Matter matches Planck 2018 data with **0.01%** precision. - **Dark Energy**: Matches the vacuum tension of the bulk with **0.002% deviation**. **Why I am posting here** I come from a CFD/Aerospace background (Ph.D.), where we constantly deal with discretization errors. This "rabbit hole" is the direct result of chasing the residual while developing a CFD method free of approximations for many years. I have been trying to "break" this model, but the geometric coherence holds up across scales (from Quantum to Cosmic). And, I believe this community and Wolfram's theory is remarkably closely aligned. Reproducibility I have attached the full Wolfram Notebook below. It performs the exact calculations from first principles (zero imports, self-contained derivation). The full theory is available on Zenodo https://doi.org/10.5281/zenodo.17957211. I would appreciate your thoughts: Does this specific "Green's Theorem Residue" map to any topological defects you see in hypergraph rewriting? Charles Cook, Ph.D. &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=lattice.png&userId=3593023 [2]: https://www.wolframcloud.com/obj/ec7f9154-bd59-463f-a07b-791912d006c4 Charles Cook 2025-12-17T16:25:42Z https://community.wolfram.com/groups/-/m/t/3593931 Previous work has proposed mapping external theoretical frameworks onto WPP hypergraph dynamics (e.g., Malicse 2025), but to my knowledge none have operationalized such mappings as measurable causal graph observables and run validation experiments. This paper reports the first such attempt: testing whether Energetic First Principles (E1P), a structural framework for process dynamics, appears in WPP hypergraph evolution. Method: E1P's four-phase cycle was operationalized as causal graph observables—branching events (CC), merging events (AC), cumulative open branches (CA), inverse activity (AA)—and tested across 15 hypergraph rewriting rules. Results: Phase ordering (CC → CA → AC): 9/9 CI rules ✓ CA accumulation → drainage: 9/9 CI rules ✓ Merge rate consistency across evaluation orders: 9/9 CI rules ✓ Discrete τ threshold at ~87%: No rules in 1-85% range Four-class taxonomy emerges: Generative CI, Conservative CI, FixedPoint, CV Implication: E1P phase structure appears to be discovered structure within CI dynamics, not imposed interpretation. This suggests external frameworks can be empirically validated in WPP—not just proposed. Full paper with methodology, data tables, and reproducibility details: https://doi.org/10.5281/zenodo.17979892 Interested in whether others have attempted similar operationalizations, or observed comparable phase patterns in CI rule evolution. Note: This is empirical validation, not derivation of physical constants. The claims are limited to observable phase patterns in causal graphs—not cosmological correspondence. All results reproducible in Mathematica 14.0+ with SetReplace.&[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/a93df282-9b3d-4893-b13c-71b80c7ee82d Catalin Leescu 2025-12-18T17:41:53Z https://community.wolfram.com/groups/-/m/t/3497586 ![A Graph Theoretic Approach to Feynman Checkers][1] &[Wolfram Notebook][3] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=HeroImage.bmp&userId=3492774 [2]: https://www.wolframcloud.com/obj/f41c98b6-bfc7-4029-a616-666c2a8d4915 [3]: https://www.wolframcloud.com/obj/2bd729ea-edb4-4a60-aadd-512bdbbe2417 Gary Louw 2025-07-10T01:49:21Z https://community.wolfram.com/groups/-/m/t/3358036 ![Exploring ruliological engineering of well-defined geometries from hypergraph rewriting][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=projectImg.png&userId=2958656 [2]: https://www.wolframcloud.com/obj/df43d3c2-655c-44ae-91e6-c04c5ac15b89 Jacopo Uggeri 2025-01-16T18:01:51Z https://community.wolfram.com/groups/-/m/t/2959221 ![enter image description here][1]&[Wolfram Notebook][3] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=image.png&userId=2958976 [3]: https://www.wolframcloud.com/obj/0c130964-8090-46be-ab7d-83b7c6b4ccd8 Joel Choi 2023-07-12T20:33:45Z https://community.wolfram.com/groups/-/m/t/3534450 ![A Project to Find the Fundamental Theory of Physics by Stephen Wolfram][1] It's been five years since the original publication of *A Project to Find the Fundamental Theory of Physics* and the launch of the Wolfram Physics Project. Now the book is available in paperback for the first time! > **Order Now:** https://a.co/d/0uyBmEj The Wolfram Physics Project is a bold effort to find the fundamental theory of physics. It combines new ideas with the latest research in physics, mathematics and computation in the push to achieve this ultimate goal of science. Written with Stephen Wolfram's characteristic expository flair, this book provides a unique opportunity to learn about a historic initiative in science right as it is happening. *A Project to Find the Fundamental Theory of Physics* includes an accessible introduction to the project as well as core technical exposition and rich, never-before-seen visualizations. The paperback edition will be published on August 26, 2025. Preorders are available until that time. [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4950Book-3-edited.jpg&userId=20103 Paige Vigliarolo 2025-08-22T17:35:59Z https://community.wolfram.com/groups/-/m/t/3357787 ![Entanglement on quantum optics kit towards creating physical correlates of multiway diagrams][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=WWS25Mark.png&userId=20103 [2]: https://www.wolframcloud.com/obj/345e80e4-210b-4724-b510-4f4060c1d312 Mark Merner 2025-01-16T15:50:43Z https://community.wolfram.com/groups/-/m/t/3515353 Hi all, My book introducing lay readers to the Physics Project is at [Amazon][1]. But community members who want a copy need only reach out to me. I'm in it for the dissemination of ideas, not the money. --- *Developing ideas first introduced in A New Kind of Science two decades ago, Stephen Wolfram and his collaborators in the Wolfram Physics Project have created a completely new paradigm of fundamental physics. Delving deeper than the Standard Model and Einsteinian relativity, Wolfram's new model not only accommodates the traditional models but actually incorporates and, finally, reconciles them.* *The deep conundrums of space, time, and energy turn out to be consequences of a much deeper, more profound reality many orders of magnitude smaller and less tangible. The Universe Within explores this inconceivably small realm, where space itself is infinitesimally tiny pieces of all-but nothingness which, continually transforming and evolving through time and on a vast scale, comprise our reality -- and many others.* *The Universe Within gives the ordinary non-scientist reader a window into what may well be the most radical, most profound, most fundamental model of physics ever proposed.* --- Patrick Sutton ![enter image description here][2] [1]: https://www.amazon.com/dp/B0FHFJLP3F [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=81ZweIPOqL._SL1500_.jpg&userId=20103 Patrick Sutton 2025-07-19T05:14:09Z https://community.wolfram.com/groups/-/m/t/3497454 ![Searching for holes in the proof space][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=poster2.png&userId=3493769 [2]: https://www.wolframcloud.com/obj/17b93de6-1072-4700-a8e7-d3d400886a77 Saúl Bernal González 2025-07-10T00:30:27Z