Groundwater Contaminant Transport Inversion L1-425
Unclaimed Principle — open for contribution
This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.
To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.
Forward model E
Groundwater Contaminant Transport Inversion: Groundwater contaminant transport inversion: infer hydraulic conductivity K field from head and concentration data. The forward operator produces the measurement through a 3-node primitive DAG (M.darcy.groundwater_flow…); recovery is posed as a nonlinear_inverse problem. Difficulty tier delta=5 with effective condition number kappa_eff~2000; density_dependent_flow_effects, preferential_flow_paths set the accuracy floor at the Omega boundary. See the forward_model field for the closed-form equation.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- true
- Stability:
- conditional
- κ:
- 100000
Existence of the recovered 3D_hydraulic_conductivity is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 2000); density_dependent_flow_effects dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor.
Solvability C
- Solver class:
- sequential-filter [ensemble_Kalman_smoother or pilot_point_regularization (PEST)]
- Convergence rate q:
- 1.5
- Complexity:
- O(N_ensemble * N_sim * N_iter) or O(N_pilot_points ** 2 * N_obs) for PEST per iteration