CMS collaboration 2026 dijet angulat distributions

 CMS collaboration:

Measurement of dijet angular distributions and search for

beyond the standard model physics in proton-proton

collisions at √s = 13TeV

https://arxiv.org/abs/2603.25458

13, 17, and 37. Very interesting, and these numbers are combinatoric between homologies of geometric sphere packing. Moving averages of 13 bands at minimum above nyquist limit flattens peak clusters of Fourier bands in icosahedral sections. 37 is the number of polarization states yet identified for photons. So, ordinal and cardinal duality is a feature of the limiting cases of the physical world, which is evidence that the Universe engages in a kind of topological dynamical system equivalent to semiosis, a higher-order degeneracy with modular implications in quotidian structural invariance across all stable scales. These structures typify the stability of oscillator lattice couplings. The permutations between the collision energy and test energies are perhaps meaningful, as 17 is a synthetic value between 13 and 37, and expected value for the 37 TeV result was 2*17 TeV (34). 

Magnetospheric sawtooth events average 10.5 and 11.1/year. This is an ~35,33-day duality of phases (365/10.5≈35, 365/11.1≈33), also related to the Islamic AH calendar system. The modulus of water at sea level, 1, relates to the mode of density of water in interstellar space, 0.945... . (10.5/11.1)=35/37=0.945... . 

A similar modulus is achieved for the Lorentz factors (gamma) of beta[1/phi] and beta[1/sqrt2]. Gamma[1/phi]=sqrt[phi], and gamma[1/sqrt2]=sqrt2. gamma[1/sqrt2]*beta[1/sqrt2]≡1; beta[1/sqrt2] is well known to be the matter limit, with vg[beta]*vp[gamma]; the coupling relation to gauge theoretic lattice root functions maintains ×^1/2 with beta[1/phi]*gamma[1/phi]^2≡1. 

This is yet another example, found to my knowledge only in my work, of the kind of modular function that maintains duality in M-theories, related to eigenvalues of modular groups, that suggests limit cycle combinatoric relations perpetuate a kind of cardinal|ordinal conservation of number theoretic minima self-referencing a specific numerical motif. 

Solar wind does this: escape velocity from the solar corona is 1000/phi=618 km/s=1/phi*1000, which when multiplied by 1.37=alpha/100, yields the max spreading rate of the magnetopause, and when this is divided by phi, yields the mean v of solar wind during magnetospheric sawtooth events, mentioned above. 

Max. spreading rate magnetopause≈847 km/s, 

847/[phi≡1.618...]=523.5 km/s, median magnetospheric sawtooth mode solar wind speed. 847/[(1/alpha=137.036)/100]=618 km/s, solar corona escape v. 618/[phi^(1/3)=1.174]=526.4.

618/[(1/alpha=137.036)/100]=450 km/s, the transition point from slow to fast solar wind, where Parker spiral gains coherence and structure, and He ions (A_He) transition to Alfven/cyclotronic resonance accelerated mode, exceeding proton v, around 1 AU.

523.5/[2^(1/2)≡1.414]=370.2, the heliospheric motion relative to the Cosmic Microwave Background.

Another is in a correspondence I found with free neutron lifetimes and the AU: the rate at which neutrons decay, ~888 seconds, relates directly to v*c=1/sqrt[pi]=v=1/(v*pi)=0.564, and various empirical orbital distances of Earth from Sun, given our slight elliptical orbit, yield (v^2)*pi values at ranges equivalent to 37/35=11.1/10.5, and the sum of 1/(1+sqrt2)^(1/2) to the difference between max and min Earth orbital values yields approx this number, etc. 

Also the bottle|beam lifetime discrepancy can be solved by relating alpha and 1/7*c to their empirical values, suggesting EM coupling and velocity are not accounted for from the process of the experimental ensemble. This is interesting when the ground state v of electrons in the hydrogen atom is alpha*c. Further, 7/37=(10.5/11.1)/5. And 0.189 is the primary invariant mode weight of droplet and carbon fulgurites, and all fulgurites scale by this constant value. This is 1/5 the mass of 1cc of water in interstellar space. 

So, a 5D metric is proposed, with relations to 10 and 11D higher order dimensional symmetries. Quasicrystals that can be spectrally flattened/discretized by averaging 13 spectral bins have a 5-fold axis, and Magnetospheric sawtooth events share their phase proportions, related by phi and the silver ratio=1+sqrt2. phi is the lattice constant of icosahedral quasicrystals, and 1+sqrt2 is for octagonal quasicrystals. Icosahedral quasicrystals show combinatoric/compactified 1D symmetries for equivalent compactification of 2,3,5 fold=10, and 2,3,6 fold=11 axes. 

So, the duality and automorphic principles of 10.5 and 11.1 are 10+(10/2/10) and 11+(1/10). A mirroring at lower magnitude of a folding value and continuity of coefficient at lower magnitude that is 1/10th plus 10. 

This is the M-theoretic vacuum speaking. This is sensibility of quantum gravity. This is the M-brane homology, with gravity a nonlinear and combinatoric modularity.