X-ray Crystallography (single-crystal diffraction) L1-125
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
Monochromatic X-rays (typically 1.0-1.8 Å, from synchrotron or rotating anode) diffract off a single crystal; Bragg peaks at angles satisfying n*lambda = 2*d*sin(theta); intensities I(h,k,l) = |F(h,k,l)|^2 where F is Fourier transform of electron density. Phase problem requires SAD/MAD/MIR/MR methods; solvent flattening + refinement.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- up to enantiomorph + phase choice (resolved by experimental phasing or MR)
- Stability:
- conditional
- κ:
- 1000
Phase problem fundamentally ill-posed from intensities alone; experimental phasing (MAD/SAD) adds constraints. Well-posed at atomic resolution (<1.2 Å) via direct methods.
Solvability C
- Solver class:
- Direct methods (SHELX), MIR/MAD phasing, molecular replacement (Phaser), density modification (DM), learned (AlphaFold-priors)
- Convergence rate q:
- 2
- Complexity:
- Direct methods O(N_atoms^1.5); SAD phasing O(N_atoms * N_refl); DM iteration O(N_refl * log)