Carbon Cycle Biogeochemical Inversion L1-424
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
Carbon Cycle Biogeochemical Inversion: Carbon cycle inversion: estimate surface CO2 fluxes (NEE, ocean uptake) from atmospheric CO2 observations. The forward operator produces the measurement through a 3-node primitive DAG (M.agcm.tracer_transport…); recovery is posed as a linear_inverse problem. Difficulty tier delta=5 with effective condition number kappa_eff~2000; transport_model_error, prior_uncertainty_specification 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 NEE_flux_map 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); transport_model_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Observation gaussian sets the irreducible data-fidelity floor.
Solvability C
- Solver class:
- statistical [Bayesian_inversion_CarbonTracker or 4DVar_GEOS-Chem]
- Convergence rate q:
- 2
- Complexity:
- O(N_regions ** 2 * N_obs) for Hessian-based inversion per iteration