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13c-metabolic-flux

Estimates intracellular metabolic fluxes from steady-state carbon-13 isotope-tracing measurements using validated atom maps, mfapy isotope simulation, constrained multistart fitting, and flux-profile diagnostics. Use for 13C-MFA, carbon tracing, mass isotopomer distributions (MDVs/MIDs), positional isotopomers, parallel tracer experiments, and determining whether labeling data constrain a pathway flux. Distinguishes measured-label inference from COBRA flux balance analysis and flags experiments requiring nonstationary MFA.

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# Carbon-13 metabolic flux inference

Turn reviewed carbon maps, explicit tracer mixtures, and corrected labeling measurements
into feasible flux estimates and evidence about which fluxes the experiment constrains.
Use the bundled solver rather than reconstructing isotope balances or fitting each
reaction independently. It runs mfapy's EMU forward simulator and fits fluxes in the
mass-balanced feasible space with SciPy. It does not use an FBA objective.

## Scope and required evidence

This implementation supports **metabolic and isotopic steady state**, a single shared
flux state across one or more tracer experiments, nonnegative one-way reaction fluxes,
and carbon-subset mass distributions. Reversible reactions are two separately mapped
directions. Measurement error is Gaussian with a supplied covariance or a disclosed