Cryo-Electron Tomography (cryoET) — in-situ 3D biology at nm scale L1-092
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
Cryo-Electron Tomography (cryoET) — in-situ 3D biology at nm scale: cryo electron transmission produces the measurement through a 5-node primitive DAG L.transmit_sample -> S.scan.angular -> L.backproject -> L.subtomogram_average -> int.angular, with multi-angle tomographic integration and photon-shot-noise-limited (Poisson counting). Recovery is posed as a linear inverse problem that inverts the forward operator to estimate the scene-side 3D density. Difficulty tier delta=10 with effective condition number kappa_eff~35; calibration-level mismatch (tilt_angle_error, CTF_per_tilt, beam_damage) 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:
- 700
Existence of the recovered 3D density is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is moderately conditioned (kappa_eff ~= 35); tilt_angle_error dominates the stability cliff; CTF_per_tilt 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 [WBP] | iterative projection (ADMM / GAP) + optimisation [SIRT] | linear-operator + deep neural prior [IsoNet-cryoET, CryoCARE]
- Convergence rate q:
- 2
- Complexity:
- O(H * W * Z * log(...)) per iteration; learned variants: O(H W Z * F_theta_cost) per forward pass