Nuclear Magnetic Resonance (NMR) Spectroscopy L1-146
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
Atomic nuclei with spin I>0 in a static magnetic field B0 precess at the Larmor frequency omega_0 = gamma * B0. Radio-frequency pulses tip the magnetization; free-induction decay (FID) is Fourier-transformed to yield a chemical-shift spectrum; chemical shift delta = (omega_0 - omega_ref)/omega_ref encodes molecular environment.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- peak assignment unique when delta-lines resolved (sufficient B0 and low B0-inhomogeneity)
- Stability:
- conditional
- κ:
- 200
Linear inverse via FFT; peak overlap in crowded spectra is dominant ill-posedness source. Mismatch: B0 shim drift, B1 miscalibration, phase drift.
Solvability C
- Solver class:
- FFT, peak picking + Voigt fitting, DOSY processing, 2D COSY/HSQC/HMBC deconvolution, non-uniform sampling reconstruction (CS-NMR), learned (DeepNMR)
- Convergence rate q:
- 2
- Complexity:
- FFT O(N log N); peak fit O(K*N*iter); 2D NMR O(N1*N2*log)