PALM / STORM (single-molecule localization microscopy) L1-011
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
PALM / STORM (single-molecule localization microscopy): single molecule localization produces the measurement through a 4-node primitive DAG K.psf.airy -> D.threshold.isolated -> L.gaussian_fit -> int.temporal, with time-integrated exposure and photon-shot-noise-limited (Poisson counting). Recovery is posed as a non-convex inverse problem that inverts the forward operator to estimate the scene-side point list. Difficulty tier delta=10 with effective condition number kappa_eff~30; calibration-level mismatch (drift_nm_per_frame, multi_emitter_overlap, background_bias) sets the accuracy floor at the Omega boundary. See the forward_model field for the closed-form imaging equation.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- true
- Stability:
- conditional
- κ:
- 600
Existence of the recovered point list is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 30); drift_nm_per_frame dominates the stability cliff; multi_emitter_overlap and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega.
Solvability C
- Solver class:
- linear-operator + convex optimisation [ThunderSTORM] | linear-operator + deep neural prior [DECODE, DeepSTORM]
- Convergence rate q:
- 2
- Complexity:
- O(H * W * log(...)) per iteration; learned variants: O(H W Z * F_theta_cost) per forward pass