feat: unit extremal vector of the path observables on ℂ^d - #1666
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Add `PathObservables.sineMode` and `PathObservables.extremalState`, with the sum of squared sines `∑ sin² ((j + 1) π / (d + 1)) = (d + 1) / 2` and the normalisation of the state. Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com> Signed-off-by: Eduardo Nava Hernandez <naype888@gmail.com>
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…nor used Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com> Signed-off-by: Eduardo Nava Hernandez <naype888@gmail.com>
this PR what's on this Extremal State,
first one C^d vector with coordenates on (-i)^j*sin((j+1)pi/(d+1)) normalizated to 1 this mean extremal state.
what this confirm, Sumatory of sin² = (d+1/2) then extremal state itś equal = to 1, this mean normalized extremal state.
this tinny comits are only pices from a biggest theorem suporting the calculus infrestructure to isntance the big one theorem.