This is probably a stupid question, but I am puzzled as to why this has not been solved by brute force and appropriate computing power. By analogy, think of how the four-color (or should that be for-colour?) map conjecture was eventually proved by reducing the problem to a finite (relatively small) number of maps and then checking them all. Here, at the level of actual moves, there is only a finite (and relatively small) number of four move combinations.

I'm aware, of course, that this is a simplification, because more than the pure moves come into play: there is a large (though still finite) set of possible initial placements on the board; token loadings can take on a large (though still finite) number of values; n-furcations are possible; and there are several continuous variables to worry about, such as LV and token weightings. Still, if this four-move combination is not a measure-zero possibility, one would expect that even a crude algorithm could easily limit the search space and pin down permissible ranges for LV and token weightings.

I must be missing something, but I'm not sure what.

[CdM] Speaking only for myself; I'm too lazy to program it.

Anyway, did some more work on this today, and spotted an interesting complementary move to my Friday's suggestion.

Alperton->Kensal Green->St John's Wood->Mornington Cresent. This is just a straight horizontal. But curiously in the complex plane the sequence has five components

.. not four, because it cuts the Metropolitan line between Finchley Road and Baker Street.

Anyway, I'm still looking, though.

[CdM] Well, I've got 347 stations in my database including N.L.L. and ghosts - and that doesn't yet have the old Met line stations to Brill - nor the Southend branch, nor some of the old District line stations. Memo: Must update database ! : So say there are 380 stations all told - then as you say, as (M=0) = Alperton by definition, and (M=4) = M.Cresc, again by definition, then we only need to calculate M1,M2 and M3 i.e. 380 x 379 x 378, just 54,439,560 possible combinations. But of course that is without taking into account LV, token placings, Becks variance, Transient moduli etc. etc. It would be naïve in the extreme to think that the four-station solution would work under just any old set of initial conditions. So, let's hypothesise that about 0.1% of possible initial condition combinations will allow the required result then the figure of 54 million needs multiply be 1000 to 54 billion. This may take a bit of processing after all - as the initial conditions will have to be set up each time. I think we're back to skill, I'm afraid.

The more calculations are carried out I am sure it will end up staring us in the face. I have been struck by the elegant simpicity of a the General Theory of Relevance: where e=mc².( e being Euston)
I disagree with this in one aspect and the is the appropriatness of the mc² given the Euston conflagration. The more sensible move and theory is e²=mc, (e being Euston Square) thus avoiding inverse coefficient of the magnetic modulus of previous BR station.
This brings me neatly to what may to some be a moment of de jvu. I question at this stage about Alperton as a first move and propose the usage of

rabmc²

where
r=Ravenscourt Park: a=Alperton: b=Blackhorse Road : with the ²on the diagonal being Euston Square. Geometrically this three sided quadrilateral could work in parallell to a divergence of LV on the Jubilee Line.

I proved all this ages ago with a Fronsky diagram drawn on a napkin. It was far too trivial for me to bother reproducing it here.

Maybe I overlooked that napkin... I was wondering where I heard this could be done. I have a feeling Bank maybe involved somewhere...

Ahh! a most interesting poser

I suspect that Kilydd could be on the right track. The e=mc² seems to be the signal in this discussion. Change it to e=(mc)² and a whole new, previously unseen, network appears. Of course, the square root of (mc) is still unkown, the history of (mc) having been hidden in the depths of iniquity for time untold - plus - what "e" equates to is also a problem.

The referent "e" could be, as stated, a local station (or somewhere on the projected line) but it could also be the symbol for Euclid. This raises very deep and meaningful questions. Like other governmental organisations, the word "TIME" enters the equation - as indeed both Einstein and Euclid intended. Anyway, unlike rab with his Sinclair I am about to bring into the endeavour my whiz-bang VIC20 super computer; unlike rab's ancient device, this has at least twice the power... a bit like ticket inspectors really. Please check in occasionally as it should take no more than twenty years to bring this conundrum to its final conclusion.

Now, come on, it's quite simple. The establishment where time is of the most importance, indeed the one where it is called out by name, is the licensed purveyors of intoxicating liquor. TIME, gentlemen, please. Therefore, e is clearly Elephant and Castle. From here, it's obvious. So I'll let you fill in the gaps. *looks shifty, legs it from scene*

Now then, according to CAMREC, who seem collectively to have taken a leaf (or several leaves) from the EEC when it comes to drafting their more recent legislation :
"A strile that is non-composite (other than demi-semi-striles set out for that purpose) may only be considered a strile in relation to stations which are neither perpendicular nor oblique. Furthermore, non-adjacent stations may be striled freely provided their quadrant ratios are zero, or +/- 1 ond. Semi-striles shall be considered impertinent in these circumstances and are only allowed when (a) all bridges have been lowered, (b) the token weighting at Hammersmith does not exceed the combined Becks-equivalent at Kew, (c) The DLR is not in spoon, or if in spoon has an obviated L.V. above 4.5, (d) There are no emus. All part-striles smaller than semi striles, and notwithstanding the demi-semi-strile alluded to parenthetically above, shall in non-polar conditions be wavered automatically, or alternatively put in vanche for three (or in exceptional circumstances, two) moves. However if any of the striles are semi-cubical, proto-parabolic or Gaussian then all transient vectors about the turning point must be considered neuter - or at best quasi-masculine. Trimming may occur in these circumstances. All the forgoing is reversed and/or transcended in the case of counter-striles which inherit their characteristic from the originating strile or part-strile. Unified Strile Theory suggests that a counter-ellipsoid-demistrile may in this instance be considered frank."
From this it is pretty clear that at least one of the stations must be Royal Oak, surely to goodness ?

Well, since it's been six weeks in this position, I think we have to conclude it's just not possible to reach Mornington Crescent from here.