Magnetic Field Inversion — susceptibility imaging L1-280

Geophysics3D magnetic susceptibility inversionδ=5 · challengingL_DAG = 3📋 Stub — not mineable

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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.

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Forward model E

B (x_{o} b s) = in t c hi (x_{s} r c) \cdot H_{i} n d u ce d (x_{s} r c) \cdot d i p o l e_{k} er n e l (x_{o} b s - x_{s} r c) d V

Magnetic Field Inversion — susceptibility imaging forward model.

L-DAG

L.dipole_field -> L.linear_forward -> L.regularize -> int.spatial

L.dipole_fieldL.linear_forwardL.regularizeint.spatial

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: unstable
κ:: 500

Ill-posed similar to gravity; non-unique without priors.

Solvability C

Solver class:: MAG3D, VPMG, Mag-Net
Convergence rate q:: 1.5
Complexity:: O(N log N) per iteration

Specs (0)

No L2 specs registered yet for this principle.