Neutron Radiography and Tomography L1-130
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
A collimated thermal (2.5 meV) or cold (1 meV) neutron beam traverses the sample; attenuation is governed by mu_n(r, lambda) = Sigma_tot = n * sigma_tot (Sigma ~ 1/E for thermal). Neutrons excel at light elements (H, Li, B, Cd) hidden behind heavy metals (Pb, W) where X-rays fail. Scintillator (LiF/ZnS:Ag) + CCD or MCP+Timepix records transmitted beam.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- Radon inversion unique with full-angle coverage; limited angle ill-posed
- Stability:
- conditional
- κ:
- 200
Beer-Lambert linear; CT reconstruction via FBP/ASTRA. Mismatch: beam hardening (lambda-dependent), scatter, flux inhomogeneity, motion.
Solvability C
- Solver class:
- FBP, iterative SART, TV-regularized ASTRA, learned (DnCNN denoise, FBP-ConvNet)
- Convergence rate q:
- 2
- Complexity:
- FBP O(N^2 * log N); SART O(N_iter * N_ray * N_voxel)