WAXS — Wide-Angle X-ray Scattering L1-133
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
X-rays scatter elastically at wide angle (q = 4*pi*sin(theta)/lambda, typically 5-30 Å^-1) from atomic-scale structure in polymers, glasses, liquids, nanocrystals. For crystalline samples, Bragg peaks; for amorphous, diffuse scattering encodes pair-distribution function g(r).
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- g(r) unique from I(q) via Fourier inversion (Zernike-Prins); crystalline fit unique under Rietveld constraints
- Stability:
- conditional
- κ:
- 200
Fourier inversion is ill-conditioned for truncated q-range; regularization (max-entropy, oversampling) stabilizes. Mismatch: background subtraction, termination ripples.
Solvability C
- Solver class:
- Fourier inversion, Warren-Bodenstein analysis, Rietveld crystalline fit, max-entropy g(r), learned (WAXS-Net)
- Convergence rate q:
- 2
- Complexity:
- FFT O(N_q log); Rietveld O(iter * N_peak * N_param)