Hemodynamics (Navier-Stokes Cardiovascular) L1-400
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
Hemodynamics (Navier-Stokes Cardiovascular): Cardiovascular hemodynamics: infer blood flow, pressure, and wall shear stress from 4D flow MRI data. The forward operator produces the measurement through a 3-node primitive DAG (M.ns.incompressible…); recovery is posed as a parameter_estimation problem. Difficulty tier delta=5 with effective condition number kappa_eff~2000; MRI_velocity_noise, vessel_wall_motion 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_velocity_pressure_field 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); MRI_velocity_noise 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:
- classical [OpenFOAM_CFD or SimVascular or ANSYS_Fluent]
- Convergence rate q:
- 2
- Complexity:
- O(N_mesh * N_timesteps * N_Newton_iter) for CFD per iteration