Cardiac Electrophysiology (Monodomain) L1-399
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
Cardiac Electrophysiology (Monodomain): Cardiac EP inversion: recover 3D transmembrane potential distribution from body surface ECG recordings. The forward operator produces the measurement through a 3-node primitive DAG (M.pde.monodomain_bidomain…); recovery is posed as a nonlinear_inverse problem. Difficulty tier delta=5 with effective condition number kappa_eff~2000; torso_conductivity_uncertainty, electrode_placement_error_mm 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_transmembrane_potential 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); torso_conductivity_uncertainty 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 [Tikhonov_regularization or Bayesian_electrocardiographic_imaging]
- Convergence rate q:
- 2
- Complexity:
- O(N_mesh_nodes ** 2) for transfer matrix computation per iteration