https://community.wolfram.com RSS Feed for Wolfram Community showing any discussions tagged with Physics sorted by new. https://community.wolfram.com/groups/-/m/t/3776785 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/ca70255a-dfd7-416b-8da4-ed33c0f3ed50 Sergi Sirera 2026-08-10T11:45:32Z https://community.wolfram.com/groups/-/m/t/3774755 ![Continuous quantum measurement, from Bayes' rule to the quantum Kalman filter][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=hero.png&userId=1539902 [2]: https://www.wolframcloud.com/obj/fd0dcb54-89a7-4d81-b176-b01eba9e2388 Mohammad Bahrami 2026-08-05T23:40:24Z https://community.wolfram.com/groups/-/m/t/3774166 ![Trailer sway and the tongue-weight bifurcation][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Trailerswayandthetongue-weightbifurcation.gif&userId=20103 [2]: https://www.wolframcloud.com/obj/b1ea26e5-d14d-4bf7-a449-f6f01c80ff90 Marco Thiel 2026-08-05T15:03:48Z https://community.wolfram.com/groups/-/m/t/3773775 The Ruliad—the entangled limit of all computation—can be constructed with universal computation using nothing but **pure, unlabelled 2D graphs** and a single primitive: the **NAND gate**. ### 1. Empty Vertices as Pure Relations Instead of labeled NAND input and output variables, the vertices are empty identifiers. Values are encoded purely as topological degree (leaf counts): * **Bit 0:** 1 attached leaf * **Bit 1:** 2 attached leaves For example, $1 \text{ NAND } 1 = 0$ is mapped directly to a simple directed graph: ```text Graph[{1->3, 2->3, 3->4, 1->5, 1->6, 2->7, 2->8, 4->9}] ``` * **Inputs (1 & 2):** Each has 2 leaves attached $\to$ **Bit 1** * **Hub (3):** Processes incoming edges to output node (4) * **Output (4):** Has 1 leaf attached $\to$ **Bit 0** ### 2. Timeless Computation & Infinite Unrolling In this framework, execution doesn't happen "over time." Iterative programs and infinite loops are **unrolled spatially** into infinite acyclic subgraphs: * Time becomes graph depth. * A loop isn't a state repeating in time—it is an endless forward path through the net. * The entire execution history exists simultaneously as a static, geometric feature (a Block Universe). ### 3. The Whole Ruliad Because NAND is functionally complete, a network of unlabelled NAND graphs can express any Turing machine or computational state. Unrolling all possible NAND configurations yields the complete Ruliad—achieving full computational universality on the simplest possible topological substrate. Anders Lindman 2026-08-05T12:53:04Z https://community.wolfram.com/groups/-/m/t/3771904 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/bb8613de-624f-41c1-b168-4eb187711926 Athanasios Paraskevopoulos 2026-08-01T21:41:34Z https://community.wolfram.com/groups/-/m/t/3771885 I conducted a study on the energy efficiency of a heating system with bypasses in a row house community with the aim of convincing the co-owners that the bypasses between the supply and return lines need to be removed. However, since most of them aren’t familiar with math and physics—and therefore can’t really evaluate the study—I thought there might be some engineers here who could share their opinion on it, as a sort of endorsement. I would then send the co-owners the link to this forum. Maybe that could help convince them. So, what do you think of this study? Ulrich Utiger 2026-08-01T20:17:53Z https://community.wolfram.com/groups/-/m/t/3768775 This July, the 87-year-old Jacobian conjecture fell: there is an explicit polynomial map C^3 -> C^3 whose differential is invertible at *every point*, yet which globally maps three distinct points to one. Local invertibility everywhere; global information loss. I wanted to know: **does the same phenomenon exist for hypergraph rewriting?** It does -- and the minimal example is small enough to run in two lines. ## The splice rule {{a, a}, {b, c}} -> {{a, b}, {c, a}} "Splice the loop at `a` into the edge `b -> c`." Note what this rule does *not* do: it creates no vertices, deletes no vertices, and preserves the edge count. Every application is undoable: given the result and the two edges the application produced, the predecessor is uniquely determined. In that per-application sense the rule is locally invertible. ## The collision Take these two states -- non-isomorphic (check the out-degrees), and neither reachable from the other: S1 = {{0,0}, {1,2}, {1,3}} (* loop + out-star *) S2 = {{0,0}, {1,2}, {3,2}} (* loop + in-star *) Try it: r = {{a, a}, {b, c}} -> {{a, b}, {c, a}}; s1 = ResourceFunction["WolframModel"][r, {{0,0},{1,2},{1,3}}, 1, "FinalState"] s2 = ResourceFunction["WolframModel"][r, {{0,0},{1,2},{3,2}}, 1, "FinalState"] IsomorphicGraphQ[Graph[DirectedEdge @@@ s1], Graph[DirectedEdge @@@ s2]] (-> True, verified in Wolfram Cloud. The default updating order picks one of the two possible events per state; the collision doesn't care, since all successors are isomorphic -- that is part of what's proven.) Each state has two possible updates -- and all four results are the same hypergraph up to renaming: the directed path on four vertices. So the one-step evolution on isomorphism classes is well-defined at S1 and S2 (unique successor, no updating-order choice involved), and it is **not injective**: two genuinely different states evolve to one. Where did the information go? The path does not remember *which interior vertex used to carry the loop*. Locally, every application knows its own undo; globally, the state forgets which application happened. The forgotten match is the discrete analogue of the forgotten branch of the covering map in the C^3 counterexample -- a discrete monodromy. ## What's proven, what's swept, what's conjectured - **Machine-checked:** the collision above -- non-isomorphism, successor uniqueness up to isomorphism, and terminality (successors admit no further application, so the two states are unconditionally mutually unreachable) -- is formalized in Lean 4 and compiles against Mathlib with zero sorrys. - **Swept:** all 489 rules in three small signature classes; 238 pass a semantic local-invertibility gate; 52 of them collide at states with <= 4 vertices and <= 3 edges, 182 at <= 4 edges. Every certificate is checked by an independently implemented verifier. Multiway (branchial) merges with distinct ancestry also occur, including certified merges that need two steps on each branch -- merging is not just one-step collision in disguise. - **Conjectured:** collision seems to be governed by *history ambiguity* -- whether some image can be "read backwards" at a different location than the one that produced it, yielding a different predecessor. Across every rule and tier tested, ambiguity was necessary for collision with zero exceptions. The rigidity conjecture (unambiguous implies injective) and a sharper dichotomy question are open. ## Why I think this matters for multiway systems Branch merging is usually discussed here as a *feature* (confluence, causal invariance, quantum interpretations). This example isolates a different mechanism: merging of branches with **disjoint ancestries**, forced by rules that are individually information-preserving. In Garden-of-Eden terms: for cellular automata on fixed geometry there is a century of theory linking local injectivity properties to global ones (Moore-Myhill, Gottschalk, Gromov); for rewriting that changes its own geometry, that theory appears not to exist yet. The nearest work (Arrighi et al. on reversible causal graph dynamics and space-time reversible rewriting) *designs* reversibility in via context-preservation conditions -- the splice rule shows those conditions are exactly the load-bearing ones: drop them and reversibility must fail, even census-preservingly. Everything -- code, 14 machine-verified certificates, sweep logs, the Lean proof, and a working-draft note -- is public: - Repository: https://github.com/walkthroughwonder/discrete-jacobian - Archived + citable: https://doi.org/10.5281/zenodo.21630926 I'd love help with: (1) the rigidity conjecture -- a proof should show unambiguity forces collisions to factor through isomorphisms of sources; (2) richer-tier searches (the pipeline is a few hundred lines of Python); (3) visualizations of the branchial picture of the splice -- the merge is begging for a good multiway graph rendering. *Disclosure: this project was carried out in close collaboration with an AI assistant (Claude, Anthropic), including the searches, the Lean proof, and this post. All certificates are independently machine-verified, and the flagship is fully formalized -- trust the proofs, not the process.* Edwin Rosero 2026-07-27T19:50:33Z https://community.wolfram.com/groups/-/m/t/3763652 ![Structure-Adaptive Evolutionary Framework for Navigating the Rule-space of Hypergraphs][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=poster_picture.png&userId=3760479 [2]: https://www.wolframcloud.com/obj/1804b84e-d758-47ed-ac93-51c89d7f4b4a Samuel Frerichs 2026-07-17T15:15:04Z https://community.wolfram.com/groups/-/m/t/3763898 ![Searching for d-3 Quantum Error Correcting Codes on a 27-qubit Superconducting Processor][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=heroimage.png&userId=3716623 [2]: https://www.wolframcloud.com/obj/5c30137b-03b9-437f-847a-b6f2ffa3fa7e Luis Cervantes 2026-07-17T14:17:23Z https://community.wolfram.com/groups/-/m/t/3763738 ![Evaluating Black-Box Physics Through Optical Emulation][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=bracelet.png&userId=3760415 [2]: https://www.wolframcloud.com/obj/a69cbbc1-44d8-4d3b-a1e1-2029814fd159 Hubert Kołcz 2026-07-17T12:40:37Z https://community.wolfram.com/groups/-/m/t/3763708 ![Casimir Energy and Geometry][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=stevie.png&userId=3760987 [2]: https://www.wolframcloud.com/obj/65d5c9b0-3112-4225-bafd-a3d479fb1b58 Pablo Gutierrez 2026-07-17T08:01:28Z https://community.wolfram.com/groups/-/m/t/3763367 ![HyperVacuum: A Dimension-Agnostic Hypergraph Lattice Model of the Quantum Vacuum][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=post.png&userId=3759777 [2]: https://www.wolframcloud.com/obj/8d235032-1a33-4170-b616-70cbad15f0aa Federico Selleri 2026-07-17T07:17:01Z https://community.wolfram.com/groups/-/m/t/3763419 ![The Shape of a Wrong Answer: Directions in Neural Robustness][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=heroo.png&userId=3761307 [2]: https://www.wolframcloud.com/obj/37f7a34c-f3b5-4e6c-93f2-09895c350030 Mohamed H Gouda 2026-07-17T05:55:30Z https://community.wolfram.com/groups/-/m/t/3763243 ![Estimating Satellite Collision Risk: An Ergodic Approach][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=heroanimation2.gif&userId=3763205 [2]: https://www.wolframcloud.com/obj/5839ddae-5025-40f1-8e8f-449e8a5f4ae7 Leyla Sozen-Kohl 2026-07-17T03:00:54Z https://community.wolfram.com/groups/-/m/t/3763192 ![Quantum Thickening of Reversible Block Cellular Automata: Analyzing Paths from S4 to U(4)][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=qca_evo.gif&userId=3760870 [2]: https://www.wolframcloud.com/obj/de1358df-9549-400e-9027-d2d41947c8c2 Deniz Yoldas 2026-07-17T02:22:33Z https://community.wolfram.com/groups/-/m/t/3762762 ![Inverting the Sitnikov Problem][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=InvertingtheSitnikovProblem.gif&userId=20103 [2]: https://www.wolframcloud.com/obj/17e33836-3400-41c4-9653-b7799ad426eb Suryansh Aryan 2026-07-17T01:09:31Z https://community.wolfram.com/groups/-/m/t/3762735 ![Running Computational Clinical Trials on Cellular Automata][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=7303hero_image.png&userId=20103 [2]: https://www.wolframcloud.com/obj/7dd5142f-2b05-4ff7-9869-11988dd0cbcf Iqra Sajid 2026-07-17T00:41:03Z https://community.wolfram.com/groups/-/m/t/3763003 ![Adaptive Evolution of Solid Structures under Simulated Incompressible Fluid Flows][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=image-2026-07-16T22-48-38Z.png&userId=3760122 [2]: https://www.wolframcloud.com/obj/358437eb-4168-4bc9-90fb-f756f4a92a7d Olgar Ozturk 2026-07-16T22:57:49Z https://community.wolfram.com/groups/-/m/t/3762924 ![Sandpile Model Dynamics on Radial Density Gradients][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=WSRI2026_ComputationalEssay_KeyImage.png&userId=20103 [2]: https://www.wolframcloud.com/obj/9d3127f0-3c54-4b5d-92f8-1256a7c92b44 Maria Luiza Cordeiro 2026-07-16T21:42:40Z https://community.wolfram.com/groups/-/m/t/3762346 ![Learning Mechanics of Neural Network: Chaotic Pendulum Metaphor][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Picture_poster1.png&userId=3760386 [2]: https://www.wolframcloud.com/obj/e95023e2-1371-48e9-a2a6-bef42df107eb Jinming Zhang 2026-07-16T19:50:36Z