Proton Radiography & CT (pRad, pCT) L1-131
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
High-energy protons (50-250 MeV) traverse a sample; multiple Coulomb scattering (MCS) blurs the trajectory while energy loss dE/dx (Bethe-Bloch) depends on relative-stopping-power (RSP). Modern pRad records proton position/angle before and after sample via silicon trackers, plus residual energy via calorimeter; RSP map recovered by inverting most-likely-path (MLP) trajectories.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- RSP unique from full-angle pCT; 2D pRad provides integrated RSP along MLP
- Stability:
- conditional
- κ:
- 300
CT reconstruction via FBP with MLP curvilinear path (not straight-line like X-ray). Spatial resolution ~0.5-1 mm limited by MCS.
Solvability C
- Solver class:
- FBP with MLP weighting, iterative SART along MLP, TV-regularized ADMM, learned (pCT-Net)
- Convergence rate q:
- 2
- Complexity:
- FBP-MLP O(N_proton * N_voxel + N^2 log N); SART O(iter * N_proton * L_MLP)