Dark Matter Direct Detection Inversion L1-486
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
dR/dE_R = N_T \cdot rho_DM / (m_DM \cdot m_T) \cdot integral_{v_min}^{inf} v\cdot f(v) \cdot d_\sigma/d_E_R dvDark Matter Direct Detection Inversion: Dark matter direct detection: set limits on WIMP-nucleus cross section from observed recoil spectrum. The forward operator produces the measurement through a 3-node primitive DAG (M.recoil.wimp_nucleus…); recovery is posed as a parameter_estimation problem. Difficulty tier delta=10 with effective condition number kappa_eff~1000; halo_model_uncertainty, nuclear_form_factor_uncertainty set the accuracy floor at the Omega boundary. See the forward_model field for the closed-form equation.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- true
- Stability:
- conditional
- κ:
- 100000
Existence of the recovered WIMP_cross_section_mass is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 1000); halo_model_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Poisson sets the irreducible data-fidelity floor.
Solvability C
- Solver class:
- statistical [profile_likelihood_CLs or Bayesian_p_value_xenon]
- Convergence rate q:
- 2
- Complexity:
- O(N_bins * N_mass_points * N_sigma_points) for exclusion plane per iteration