See also Noncommutative geometry and the spectral model of space-time by Alain Connes where he says (p. 183)

The traditional notions of geometry all have natural analogues in the spectral framework. We refer to [9] for more details. The dimension of a noncommutative geometry is not a number but a spectrum, the dimension spectrum (cf. [14]) which is the subset ? of the complex plane C at which the spectral functions have singularities.

and also The Spectral Model (A. Connes & A. Chamseddine), as you see do the mathematicians refer correctly to it as a model.

i know about Feynman's statement. of course. as for LQL theory, i think its a dead end because it makes no testable predictions. - see (https://www.youtube.com/watch?v=jEr038WOKFI) . i like Sorkin's causal set approach much better (i have no idea what, if anything it predicts but i like its aesthetics) but Stephen's trivalent network model seems best (i.e. appeals most) to me so far. even so, it hasn't as far as i know, produced any results that we didn't already have - e.g. Einstein's equations which we've had for exactly 100 years. personally, i don't have a preference for either continuum or discontinuum approaches or even combinations of the two. i think there is no way to know what reality IS. all we do is build models and we can chose between models using a variety of criteria such as the ability to agree with experimental results, conceptual intuitiveness and mathematical simplicity. i worked in soft matter physics where i and others had competing models describing the phenomena of the rubber elastic behavior of polymer networks, all of which give equally good in matching a wide variety of data. the models aren't right or wrong - they're simply diffeent representations of the effect of polymer chain entanglement. actually, caricatures of the effect, not even caricatures of the cause of the effects themselves - that would require representing the various entanglements which is impossible becuase there is no way to either control or characterize them (i'll note that my model would give the same result regardless of the nature of the entanglements because mathematically, it uses a universal scaling form. I basically agree with the statistician, George Box, who said "All models are wrong but some are useful". i just wanted to post Einstein's comments becuase they are prescient and they demonstrate what a profoundly deep thinker Einstein was - developing a continuous field model of GR while simultaneously considering the possibility of a discrete alternative (which he never developed).