[WIP] Implicit derivatives for CTMRG

[leburgel]

Adds implicit gradients for CTMRG contractions.

Reference: https://arxiv.org/abs/2607.15030

[codecov]

Codecov Report

❌ Patch coverage is 0.46620% with 427 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
...hms/contractions/ctmrg/characteristic_equations.jl	0.63%	313 Missing ⚠️
...lgorithms/optimization/implicit_differentiation.jl	0.00%	114 Missing ⚠️

Files with missing lines	Coverage Δ
src/Defaults.jl	85.71% <ø> (ø)
...lgorithms/optimization/implicit_differentiation.jl	27.43% <0.00%> (ø)
...hms/contractions/ctmrg/characteristic_equations.jl	0.63% <0.63%> (ø)

... and 10 files with indirect coverage changes

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[github-actions]

After the build completes, the updated documentation will be available here