Why we could be very happy that a Higgs boson has been discovered

Possible insights from the 125 GeV Higgs boson in a spectral hypothesis perspective
After reading a recent post by Peter Woit on his blog Not Even Wrong, I left there an accepted comment that retrospectively appears to me as a bold attempt to put across the exact opposite of the following views:

The only place left to look for a way out of this swamp [the variety of electroweak symmetry breaking theories], it seems to me, is in strongly interacting chiral gauge theories. Many talented theorists have thought about this.... There are surely wonders hidden in the subject of strongly interacting chiral gauge theories. If we are forced to deal with them to deal by physics at the SU(2)×U(1) breaking scale, we may find them. If instead a Higgs is discovered and the physics at the SU(2)×U(1) breaking scale can be described by perturbation theory, we probably never will. This would be the real source of my sadness if a Higgs were discovered. It would mean that nature had missed a chance to teach us some new and interesting field theory. Personally, I don’t think that she would be so malicious.
Howard Georgi 
Perspective on Higgs Physics II, ed. G.L. Kane. World Scientific, 1997.

I do not think either that nature is malicious but subtle, just like the Lord ... or quantum field theory. 

Indeed as regular posts in this blog try to argue, nature or more specifically the 125 GeV Higgs boson has already not missed the opportunity to teach us - but in a barely audible voice - some new and interesting quanta of geometry that might provide insight about the ultra-high scale of seesaw mechanism and leptogenesis and hints to enlighten the adelic sectors* of astrophysics and cosmology namely black holes, dark matter and dark energy (*this neologism, beyond a wink to the suffix used to create adjectives imparting a specific form of verve, is inspired by the greek adjective ἄδηλος which means literally "not self-evident" and figuratively "obscure").

I talk about "a barely audible voice" for two reasons. The first one is anecdotal and has to do with the fact that contemporary high energy physics papers reporting about noncommutative spectral developments derived from the 125 GeV Higgs boson are relevant but rare while it appears to me that the spectral noncommutative geometrization of the Higgs could find a place in the theoretical physics ecosystem behind the discovery of the Higgs boson as it is nicely reviewed by James D. Wells (in an article from which I borrowed the above Georgi's quote). The second one is more substantial and refers to the fact that the insight physicists could gain from taking at face value the spectral noncommutative post-diction of the Higgs boson 125 GeV mass relies on the effectively very weak mixing (10-9) between the electroweak higgs doublet and a computed ultra heavy higgs standard model singlet responsible for the seesaw mechanism and the spontaneous breaking of a Pati-Salam gauge group.

One can criticize my argument about a "spectral higgs brother hypothesis" (not to mention the quanta of geometry) as immoderate speculation(s) of course. But with the hindsight from history J.D Wells writes : 
... the Higgs boson hypothesis was an immoderate speculation, and therefore faith in theory argumentation and speculation was mandatory for the discovery program to proceed and reach its fulfillment. The Higgs boson could not have been discovered experimentally by accident.  

Then I ask my reader : why do we not try to take advantage of a mathematically coherent formalism that provides effective computational tools to follow the breadcrumb trail from the standard model higgs at the TeV scale to his big brother at the  ZeV one or even YeV, investigate the possibility that electroweak symmetry breaking is related to gravity through an almost commutative extension of spacetime and is triggered somehow by noncommutative fluctuations that impart a proper dynamics to geometry with consequences as mimetic dark matter, dark energy and a limiting spacetime curvature? 

Nature is not malicious but the human Hi(gg)story of the understanding of the electroweak symmetry breaking definitely proves to be devilish.

At least it was for spectral noncommutative geometers of whom it is worth reminding here the basic paradigm:

We thus view a given geometry as an irreducible representation of the algebraic relations between the coordinates and the line element, while the choice of such representations breaks the natural invariance group of the theory. The simplest instance of this view of geometry as a symmetry breaking phenomenon is what happens in the Higgs sector of the standard model.
Alain Connes 

These new geometers of physics have failed first to predict the correct mass of the standard model Higgs boson. But they learned from its very value and works it triggered among physicists worried about the stability of the Higgs potential at ultra heavy scales how to remove an incorrect assumption they made. To improve then the coherence of their framework they have subsequently understood how to give up an axiom of noncommutative geometry and uncovered new inner fluctuations of geometry that impact the structure of the Higgs fields and make them composite somehow. As a consequence they could postdict - following a more constrained theory - the correct SM Higgs boson mass, predicting a mixing with another scalar field responsible for the spontaneous symmetry breaking of a Pati-Salam gauge symmetry as I have already reported above. Last but not least, this new impetus has lead them to write an elaborate Heisenberg-like equation and they have established the mathematical demonstration that the two very specific Clifford algebra required for a Pati-Salam gauge unification model in the spectral point of view are exactly the pair required in the Feynman slash of the proper coordinates to recover with a generalized Dirac operator any 4 dimensional Riemannian manifold with a quantized volume! (19/02/2017 update: A. Connes has made available yesterday a new paper in English that covers specifically this point that is the core of the first six hours of last lecture at the Collège to reach an audience as broad as possible).

So to conclude let me come back to Howard Georgi and be bold once again to write him the following message:
Dear Sir, 
I hope you have welcomed too the discovery of the 125 GeV Higgs boson in 2012 even if you had some doubts or prejudices against its existence. I cannot say if the wonders lying in strongly interacting chiral gauge theories are realy hidden by this scalar boson but I notice you have not lost the expectation to connect the Higgs phase and the confining phase.  
I wonder what would be your take on the possible spectral noncommutative world hidden behind the specific electroweak symmetry breaking nature has chosen for us. Insofar as this new geometric paradigm suggests an extension of space where the program of unification of the standard model gauge interactions that you initiated with a few others is the natural result of a subtle dynamic extending that of gravity, I do not doubt that you would be interested to learn how discrete extra dimensions or rather some fine structure of spacetime could be more than a metaphor thanks to the Higgs boson discovery.
Yours respectfully.

This post is dedicated to a spectral heroine researcher: Charlotte Dempière and a fantasized student of her dreaming of a subtle loose way to connect unparticle physicsscale invariance at low accelerations and mimetic matter in a new quantum world.

// Last edit 18 february 2017