feat(PhyslibAlpha): saturation of the uncertainty relation in the maximal current state

[naype888-cloud]

hello guys joseph, timeroot, i'm here with the next one. what this PR does?
it adds "TightBindingChain/Saturation.lean" (216 lines). it's stacked on #1716 (maxCurrentState), so until #1716 merges the diff shows that commit too, i will rebase it right after.
the energy-position uncertainty relation it's an equality exactly when the centered Gram defect vanishes, when the energy and position fluctuations are parallel. on the maximal current state with N ≥ 2 sites and t ≠ 0, the first two sites force 4 cos²(pi/(N+1)) = N - 1, and that only happens for N = 2 and N = 3.

1.- "inner_energyFluctuation_maxCurrentState", "inner_positionFluctuation_maxCurrentState": both fluctuations, site by site.
2.- "centeredGramDefect_maxCurrentState_eq_zero_iff": the defect vanishes iff N = 2 or N = 3.
3.- "robertson_schrodinger_maxCurrentState_eq_iff": the relation is an equality iff N = 2, 3.
4.- "robertson_schrodinger_maxCurrentState_lt": from four sites on, the relation is strict.

tks again guys, im here ready to make any changes after review¡

[github-actions]

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[naype888-cloud]

the chain isn't finished yet, this one #1718 just need the #1716 wich remains open, when te PR goes merge, this one it's ready to marge, tks Joseph, Timeroot

[naype888-cloud]

#1716 is merged and this PR is rebased on master: one commit, all checks pass, no open dependencies. Could the blocked-by-PR label be removed? Thanks for every thing, and have a nice day¡

[jstoobysmith]

@naype888-cloud I think you might be able to remove the blocked-by-pr label by commenting "-blocked-by-PR". Would you mind trying?

[naype888-cloud]

-blocked-by-PR

[jstoobysmith]

Approved will merge now