mathematical-physics

On the maximal compact subalgebras of E9 and E10, respectively, and their finite-dimensional linear representations: Relating the E10 U-duality covariant sigma-model description of, hypothetically, M-theory to D=3 gauged supergravity: On tensor hierarchies in gauged supergravity: On relation of Borcherds algebras to tensor hierarchies in gauged supergravity: Jakob Palmkvist, Tensor hierarchies, B…

A connective spectrum is a connective object in the stable -category of spectra, hence a spectrum whose homotopy groups in all negative degrees are trivial: . These are equivalently: Connective spectra form a sub-(∞,1)-category of spectra There are objects in Spectra, though, that do not come from “naively” delooping a topological space infinitely many times. These are the non-connective spectra.…

This work presents a philosophical and mathematical research highlight on the ontological structure of space understood as a compact, simply connected, boundaryless three-dimensional manifold: M ≃ S³. Instead of treating space as a local product of physical emergence, the treatise argues that the manifold should be regarded as a persistent global structure, while cosmological evolution describes …

Hello everyone, I'm Dickinson. Glad to join the PF community. I am an amateur of mathematics and physics, and I spend much spare time studying classic textbooks intensively. ## My Persistent Learning Style I have long been accustomed to deriving formulas independently without referring to... Read more

vector bundle, 2-vector bundle, (∞,1)-vector bundle real, complex/holomorphic, quaternionic The basic line bundle on the 2-sphere is the complex line bundle on the 2-sphere whose first Chern class is a generator , equivalently the tautological line bundle on the Riemann sphere regarded as complex projective 1-space. This is the pullback bundle of the map to the classifying space/Eilenberg-MacLane…

Despite Timothy Gowers's relief that this recent AI solution of the Erdos Unit Distance Problem only involves a counterexample and not a proof in the positive (see the companion document in the link ...

This paper studies the selection of a terminal effective algebra in a finite spectral algebraic-dynamical framework. Given the three finite algebraic in puts C −→ H −→ M3(C), and requiring the terminal algebra to satisfy finite-dimensional semisimplicity, factor preservation, center preservation, absence of redundant factors, and compatibility with the noncommutative-geometric finite spectral rep…

Nature, Published online: 22 May 2026; doi:10.1038/d41586-026-01651-0 The late Hungarian mathematician Paul Erdős thought he had the last word on a geometry problem. Now an OpenAI chatbot has proved him wrong.

physics, mathematical physics, philosophy of physics theory (physics), model (physics) experiment, measurement, computable physics Axiomatizations Tools Structural phenomena Types of quantum field thories examples The term soliton originates as an abbreviation of “solitary wave”, in the tradition of naming fields and particles ending on “-on”. A soliton solution of a nonlinear wave equation is a …

Let G be a transitive permutation group on a finite set X. How many essentially different G-equivariant category structures exist on X with finite group endomorphism monoid M_0? We identify a combinatorial invariant — the thin radical D of the Schurian coherent configuration CC(G,X) — and conjecture that the isomorphism classes biject with H^2(D, Z(M_0)). We prove this classification at two struc…

Mathematical structuralism holds that mathematical objects are determined by their structural roles — the pattern of relations they bear to other objects — rather than by intrinsic properties (Benacerraf, 1965; Shapiro, 1997). We prove the converse side of this thesis in the categorical setting: bare objects do not canonically determine structure. Our central result is the Symmetry Rigidity Theor…

physics, mathematical physics, philosophy of physics theory (physics), model (physics) experiment, measurement, computable physics Axiomatizations Tools Structural phenomena Types of quantum field thories examples When the theory of gravity in the form of general relativity was developed at the beginning of the 20th century, the abstract notion of a smooth manifold independently of its coordinate…

physics, mathematical physics, philosophy of physics theory (physics), model (physics) experiment, measurement, computable physics Axiomatizations Tools Structural phenomena Types of quantum field thories examples algebraic quantum field theory (perturbative, on curved spacetimes, homotopical) quantum mechanical system, quantum probability interacting field quantization The description of quantum…

Scientific Reports, Published online: 21 May 2026; doi:10.1038/s41598-026-41761-3 Modeling of complex physical and biological problems using bi-univalent function calculus

Artificial intelligence built by OpenAI has cracked a decades-old conjecture by Paul Erdős, which mathematicians have hailed as a monumental moment for AI in mathematics

Water, at exactly zero degrees, doesn’t know what it wants to be. Add the tiniest nudge of energy and it stays liquid; subtract the same and it snaps into ice, New! Sign up for our email newsletter on Substack. New! Sign up for our email newsletter on Substack. Water, at exactly zero degrees, doesn’t know what it wants to be. Add the tiniest nudge of energy and it stays liquid; subtract the same …

A chatbot’s result for the 80-year-old “unit distance” conjecture is the first AI proof that would likely be published in math’s top journal if humans had done it alone

Some time ago I asked this question about planning a pure math career today (without being a genius). I just saw that the Unit Distance Problem has been solved by a machine, and generally that a lot ...

Prior art formally verified compound discoveries and verifications. all formally verified 0 sorry compounds are prior art and timestamped. Any use without citation will be detected by SNSFL-PRIME · Prior-art Reduction and Integrity Method for Evaluation Engine V1 Substrate-Neutral Structural Foundation Laws-SNSFL PNBA Identity Physics Substrate-Neutral Structural Foundation Laws (SNSFL) PNBA Iden…