P
Physics World Model
← All principles

Magnetic Flux Leakage (MFL) — pipeline & rail inspection L1-121

Industrial InspectionFerromagnetic defect detection via DC fluxδ=3 · standardL_DAG = 3📋 Stub — not mineable
📋

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

Magnetic Flux Leakage (MFL) — pipeline & rail inspection: magnetic flux leakage produces the measurement through a 4-node primitive DAG L.dc_magnetize -> L.flux_leakage -> D.hall_sensor -> int.spatial, with spatially-projected accumulation and additive Gaussian thermal/electronic noise. Recovery is posed as a non-convex inverse problem that inverts the forward operator to estimate the scene-side 2D defect geometry. Difficulty tier delta=3 with effective condition number kappa_eff~10; calibration-level mismatch (liftoff_variation, magnetization_non_uniformity, external_interference) sets the accuracy floor at the Omega boundary. See the forward_model field for the closed-form imaging equation.

L-DAG

L.dc_magnetize -> L.flux_leakage -> D.hall_sensor -> int.spatial
L.dc_magnetizeL.flux_leakageD.hall_sensorint.spatial

Well-posedness W

Existence:
true
Uniqueness:
true
Stability:
conditional
κ:
200

Existence of the recovered 2D defect geometry is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 10); liftoff_variation dominates the stability cliff; magnetization_non_uniformity and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.

Solvability C

Solver class:
linear-operator + convex optimisation [Dipole-Model] | linear-operator + deep neural prior [NN-MFL, Deep-MFL]
Convergence rate q:
2
Complexity:
O(H * W * log(...)) per iteration; learned variants: O(H W Z * F_theta_cost) per forward pass

Specs (0)

No L2 specs registered yet for this principle.