There are a few possible solutions of what foldspace technology might be, given our current standard model of particle theory. Since we expect a sci-fi author to at least vaguely draw from what we think we know, let's assume Frank was either taking from modern theory, or at least speculating based on modern theory. But before I list the few options, let's see what we know for sure about Holtzman engines:
1) The tech behind them is derived from Holtzman's equations.
2) There are a few other techs also derived from Holtzman's equations:
-Suspensors (secondary (low-drain) phase of a Holtzman field generator. It nullifies gravity within certain limits prescribed by relative mass and energy consumption.)
-Shields (the protective field produced by a Holtzman generator. This field derives from Phase One of the suspensor-nullification effect.)
-Glowglobes (suspensor-buoyed illuminating device, self-powered (usually by organic batteries).)
This tells us a lot. We know for certain, therefore, that Holtzman's equations relate to gravity-effects, as evidenced by all techs that derive from them. Given that anti-gravity is a prominent feature of these techs, we know, therefore, that the equations detail how to manipulate the effects of gravity; in current sci-fi terms this would mean that the equations lead to the ability to create focused graviton or anti-graviton fields.
We can conclude that foldspace tech is a form of gravity drive. I'll describe a few types of gravity drive that we can currently conceptualize, although not yet create:
1) Wormholes. This would, presumably, require a specific application of gravity fields at two different points in the universe, as well as some means of establishing both the stability of the wormhole as well as the ability to enlarge its capacity to permit large objects inside. Star Trek DS9 delves into some sci-fi aspects of this mode of transport. In the Duniverse, though, we appear to see none of the signs we'd expect if this was the method used to transport large ships. Also worth noting is that this mode of transport would also probably be disastrous to introduce anywhere near a star system.
2) Warp drive. This tech is as we see it in Star Trek, and is currently NASA's leading candidate for future propulsion technology.
Source: http://www.nasa.gov/centers/glenn/techn ... paper.html
This drive entails contracting spacetime in front of a vessel and subsequently re-expanding it behind the vessel. This allows for FTL travel because the space to traverse is shrunk and therefore can be crossed quickly, while in the current inertial frame the ship may not be moving quickly at all. Further, due to the effects of relative pressure, the ship would be propelled forward automatically by this process (due to being drawn towards the shrunk, more dense and therefore massive, spacetime), thus removing the need for a method of propulsion other than the warp drive itself while in FTL mode. This tech would be more or less effective depending on how powerful the gravity generator was on the ship; more powerful graviton fields would shrink space in front of the ship more effectively. If this is the tech in Dune it could very well explain how one Guild ship could be faster than another. It would also be safer to use than wormholes in proximity to star systems.
3) Space folding. This would involve applying gravity forces so powerful that space in a given region was bent tremendously. Think of the metaphor of folding a piece of paper in half to cross from one end to the other, to get the idea. This tech would be similar to wormhole tech insofar as roughly instantaneous travel would be the result, except that here the folding would be done through brute force, rather than by exploiting Nth dimensional physics. Unlike with wormholes, however, the jump here would only be across the folded portion of space, and couldn't effectively teleport a ship across the universe or very far away. This tech, if it is what is used in Dune, could also explain why some ships are 'faster'; if a strong space-folding resulted from a strong gravity drive, then a larger space-fold could be done and require fewer jumps to get to a far-off destination. Wormhole tech would never require more than one jump, in theory, but space folding would require multiple jumps depending on how powerfully space is folded. I don't really have a clue how safe it would be to jump near to a star system - I would guess not that safe.
Given these three options, I would immediately cross wormholes off the list. The other two are both tempting, but given what we know of Guild Navigators and their need to plot a safe course prior
to travelling, I would suggest that #3, space folding, is what we see in Dune. I would surmise, then, that faster Guild ships are ones with more powerful gravity generators that can do longer jumps and require fewer stops and recalculations. After every jump we imagine the Navigator would have to reassess things and calculate the next jump, which would take time, and also might take time to realign the jump engines (i.e. foldspace engines). That Lynch described folding space in the way he did, which must be this method, suggests that it might also be what Frank had in mind, or at least a concretization of what Frank alludes to. I also fully expect that Frank developed this idea further by the time of HoD, as the rest of sci-fi and science had advanced by then and produced a bit of clarity regarding what this type of tech might really entail.
Here is one piece of evidence that tangles things, though: The use of the term "the known universe." This term, as appearing in Dune, is telling. It means that space exploration (as opposed to stellar cartography, which we can even do now) detailed what part of the universe was known through first-hand experience. And from what we can see in terms of the important planets in the Imperium up until GEoD, the entire known universe comprises only a tiny bit of our corner of the Milky Way galaxy. When measuring the distance of colonized planets from Earth, the farthest distance we know of for any planet is Arrakis, which is 310 LY away. The others tend to be much closer (150 LY or less), with some being in the immediate vicinity, such as Caladan, Poritrin, and Giedi Prime. Given that our galaxy is ~70,000 LY across, and other galaxies are much further, we can conclude one of two things: 1) Dune's foldspace tech in the first four books is limited to jumps of only up to around 300 LY (or maybe even much less, if multiple jumps are done to reach a system). 2) Guild Navigators cannot foresee a safe route of travel beyond this distance or less (either due to their mental limitations, or because it's impossible). I guess a third possibility is that prior to the Hubble Space Telescope we didn't know jack about galactic distances and so Frank sort of just made do with what he knew at the time.
There does seem to be a bit of a shift by the time of HoD and CH:D, insofar as we are led to believe that foldspace tech would now be capable of transporting a ship to unlimited distance in one single jump. This would seem to suggest that either foldspace engine of type #3 got a lot stronger, or that the Ixian Navtech is a lot more effective than Guild Navigators. It's also possible this means it was wormholes all along (but this still doesn't jive with what we know would be required to open a stable wormhole and yet is never mentioned). I still favor option #3 as being the consistent tech throughout the Dune series, especially Since Duncan, in CH:D, essentially specifies that no one since Holtzman has determined new uses for his equations since no one but him understood them (except, perhaps, for M&D). This would eliminate the possibility that the Imperium shifted from one form of gravity drive to another after Leto II's reign. I think it's more likely that the ability to use space folding technology simply improved in effectiveness, and it's a good bet that the Ixian tech ended up exceeding what humans could do.
Since merely understanding gravity fields would not, of itself, lead to knowledge of how to construct wormholes, and since it is claimed that no one other than Holtzman understood his own equations, which relate to gravity fields, I maintain that the Imperium would not have the knowledge of wormhole construction and therefore that they had to have been using space folding technology, as Lynch suggests.