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Constructing Self-Regulating Field Theoriesfrom Primal Wave Fields without Background Manifolds:The Emergence of the Coordinate Continuum

This paper introduces a rigorous mathematical framework in which the continuous space-time coordinate continuum and self-regulating field dynamics are derived from non-local, periodic primitives termed primal wave fields. Traditional continuum mechanics models physical phenomena over a pre-existing background of real numbers ($R$), an approach that inherently introduces unphysical, localized mathematical divergences (singularities) when computing point-like field interactions. We resolve these foundational vulnerabilities by constructing a three-tiered algebraic architecture - the base set $W_0$, the commutative ring $W_A$, and the field of fractions $W_I$ - independent of any background coordinate container. Utilizing a minimal set of primitive tracking operators over a universal synchronous clock lattice, we demonstrate that the smooth space-time coordinate continuum emerges naturally as the topological completion of a dense, intersecting rational resonance network $Q$. Finally, we show that formulating physical field operations directly within this wave-number fraction space natively regularizes interaction integrals, eliminating point-wise geometric infinities and rendering field propagation intrinsically bounded without relying on external mathematical cutoffs. An application of this approach demonstrates that the ultraviolet catastrophe is not an intrinsic property of the thermal diffusion process run backwards in time, but rather of the point-based representation of the classical diffusion equation.

arxiv.org

Original post on mathstodon.xyz

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Original post on mathstodon.xyz

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Original post on mathstodon.xyz

mathstodon.xyz

Original post on mathstodon.xyz

mathstodon.xyz

Original post on mathstodon.xyz

mathstodon.xyz

Original post on mathstodon.xyz

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Original post on mathstodon.xyz

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Yang-Mills theory for multiplicative Ehresmann connections

We develop a twofold generalization of classical Yang-Mills theory, extending it from principal bundles to the setting of possibly non-transitive and non-integrable Lie algebroids. The classical theory is recovered when one considers the Atiyah algebroid of a principal bundle. In our framework, principal bundle connections are replaced by the more general notion of (infinitesimal) multiplicative Ehresmann connections. An action functional for such connections is constructed, now including a curvature 3-form contribution, alongside the usual curvature 2-form term, and the resulting variational problem is naturally constrained by a cohomological condition. We derive the associated Euler-Lagrange equations, and define a class of self-dual solutions (instantons) in both 4 and 5 dimensions. We also show that the solution space is invariant under gauge transformations, and compute its tangent space at a solution. As an important example, we show that our framework produces a Yang-Mills theory for connections on bundle gerbes.

arxiv.org

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mastoxiv.page

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LARES-2 satellite measures frame-dragging effect around the Earth - Nature

Using LARES-2, LAGEOS and GRACE satellites, researchers measured Earth’s frame-dragging with unprecedented precision, strongly confirming general relativity, constraining alternative gravity theories, and improving measurements of Earth’s tides.

nature.com

Jordan Pair Quantum Theory and the Standard Model

Jordan pairs and hermitian Jordan triples were discovered by mathematicians studying Jordan algebras, which describe the possible algebras of observables in quantum mechanics. We point out a striking correspondence between the doubly exceptional hermitian Jordan triple (the so-called ``bi-Cayley'' triple) and the structure of the Standard Model of particle physics. We also point out how ordinary quantum mechanics may be reformulated, and generalized, using hermitian Jordan triples.

arxiv.org

Resigning from the editorial board of Statistics and Computing

Along with 17 other Associate Editors, I have just resigned from the editorial board of _Statistics and Computing_. This was a difficult decision, since it is a great journal, which has published many tremendous articles under the leadership of editor-in-chief Ajay Jasra, and before him David Hand, Gilles Celeux, and Mark Girolami. Springer Nature recently announced that for all future articles, authors would have to pay Article Processing Charges of $2990. This will impose massive financial barriers for colleagues who do not have access to funding, will create a further gap between institutions, and the journal will eventually lose its appeal as authors publish elsewhere. We do not wish to be part of this system. The full letter sent to the editor-in-chief is below, with the current list of signatories. Other members of the board who wish to sign it can get it touch. > Dear Ajay, > > We are writing to resign as Associate Editors of Statistics and Computing effective 31 December 2026, due to Springer Nature’s recent decision to impose Article Processing Charges (APCs) upon all authors. > > We have the greatest admiration for your hard work for this journal and for the scientific community: under your stewardship, and that of previous Editors, the journal has published many articles of extremely high quality and it is a leading journal in our field. It has been an honour to play a small part in this during our time as Associate Editors, and we resign with great regret. > > We understand that the decision to introduce APCs was not your own but was imposed by corporate management, and we are sorry that our resignation will put you in a difficult position. Nonetheless, the APCs that Springer Nature will introduce on 1st January 2027 are irreconcilable with our vision of science. They are not compatible with the goal of publishing the best science, whoever the authors; they exclude vast swathes of the scientific community; they are not a responsible use of the taxpayers’ money that funds our research; they are also at odds with the standards in Statistics. > > Our decision to resign due to this change should not be taken as support for the existing system. The current academic publishing system is built upon vast quantities of unpaid labour and establishes a financial paywall to view the final research articles. Funding bodies are quite rightly pushing back against this, requiring that publicly funded research be freely accessible. From this perspective the move to “open-access” at Statistics and Computing might seem to have some merit on the surface. However, achieving this through APCs simply moves the financial barrier to a different part of the system. The exploitation still remains, and now Statistics and Computing will no longer publish the best science, both due to financial exclusion of those researchers who cannot afford to pay, and those community-minded researchers who refuse to pay on principle. > > We would be very supportive of creating a new, genuinely open journal instead, possibly under the auspices of a learned society. We would welcome the opportunity to work with other members of the editorial board to create such a journal, and would be glad to submit future work there. We hope to have conversations with the editorial board and the community about such a move. > > We hope to remain in contact with you. Thank you for your confidence, Signatories so far: Pierre Alquier (ESSEC) Julyan Arbel (Inria Grenoble) Louis Aslett (Durham University) Joshua Bon (Adelaide University) Alice Cleynen (CNRS) Adrien Corenflos (University of Warwick) Francesca Romana Crucinio (University of Turin) Kamélia Daudel (ESSEC) Ritabrata Dutta (University of Warwick) Mathieu Gerber (University of Bristol) Sahani Pathiraja (University of New South Wales) François Portier (CREST-ENSAI) Sam Power (University of Bristol) Robin Ryder (Imperial College London) Leah South (Queensland University of Technology) Scott Sisson (University of New South Wales, Sydney) David Warne (Queensland University of Technology) Olivier Zahm (Inria Grenoble) ### Share this: * Email a link to a friend (Opens in new window) Email * Share on Facebook (Opens in new window) Facebook * Share on X (Opens in new window) X * Like Loading... ### _Related_

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