Muon Tomography (cosmic-ray scattering imaging) L1-132
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
Atmospheric cosmic-ray muons (GeV energies, flux ~1/cm^2/min at sea level) traverse samples; multiple-Coulomb-scattering angle sigma_theta = (13.6/p) * sqrt(L/X_0) encodes radiation length X_0, which varies as ~1/Z^2. Tracker detectors above/below the sample record incoming/outgoing trajectories; voxelized reconstruction of X_0 via PoCA or EM.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- Z_eff map approx unique given uniform cosmic-ray angular distribution
- Stability:
- conditional
- κ:
- 500
Reconstruction is Poisson-limited at low flux; angular resolution O(10 mrad) at GeV. Hybrid stopping-power techniques (muon decay counting) add info.
Solvability C
- Solver class:
- PoCA (Point of Closest Approach), EM / MLEM over voxels, MART, learned (muon-CNN)
- Convergence rate q:
- 2
- Complexity:
- PoCA O(N_muon); MLEM O(iter * N_muon * N_voxel)