Fiber-Optic Endoscopy L1-048
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
Fiber-Optic Endoscopy: fiber endoscopy produces the measurement through a 4-node primitive DAG L.fiber_illumination -> L.fiber_transmission -> K.psf.bundle -> int.spatial, with spatially-projected accumulation and additive Gaussian thermal/electronic noise. Recovery is posed as a linear inverse problem that inverts the forward operator to estimate the scene-side 2D intensity. Difficulty tier delta=3 with effective condition number kappa_eff~12; calibration-level mismatch (fiber_bending, pixelation_comb, dynamic_range_compression) 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:
- 240
Existence of the recovered 2D intensity 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 ~= 12); fiber_bending dominates the stability cliff; pixelation_comb and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.
Solvability C
- Solver class:
- linear-operator + convex optimisation [Comb-Interp] | linear-operator + analytic regularisation [Wiener-Bundle] | linear-operator + deep neural prior [FiberNet]
- Convergence rate q:
- 2
- Complexity:
- O(H * W * log(...)) per iteration; learned variants: O(H W Z * F_theta_cost) per forward pass