SAXS — Small-Angle X-ray Scattering L1-126
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 small momentum transfer q = 4*pi*sin(theta)/lambda < 0.5 Å^-1 from inhomogeneities ~ 2*pi/q nm. Radially integrated intensity I(q) encodes pair-distance distribution function P(r) via Fourier transform (Fourier-Bessel). For biomolecules, provides radius of gyration Rg and maximum dimension Dmax.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- Rg, Dmax unique up to buffer matching; 3D shape ambiguous (envelope only)
- Stability:
- conditional
- κ:
- 500
Inverse Fourier transform from I(q) to P(r) is ill-posed (ATSAS-GNOM uses regularization); shape reconstruction requires ab-initio bead models. Mismatch: aggregation, polydispersity, buffer mismatch.
Solvability C
- Solver class:
- Guinier fit (Rg), GNOM (indirect FT), DAMMIN/DAMMIF (bead ab-initio), EOM (ensemble models), learned (BIFT, SAX-ML)
- Convergence rate q:
- 2
- Complexity:
- Guinier O(N_q); GNOM O(N_r * N_q); DAMMIF O(iter * N_beads * N_q)