Cosmological N-body (Large-Scale Structure) L1-365
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
Cosmological N-body (Large-Scale Structure): Cosmological N-body: evolve dark matter particles in expanding universe under gravity to form large-scale structure. The forward operator produces the measurement through a 3-node primitive DAG (F.fourier.pm_gravity…); recovery is posed as a parameter_estimation problem. Difficulty tier delta=5 with effective condition number kappa_eff~10000.0; cosmological_parameter_uncertainty, baryonic_feedback_neglect 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:
- 100000000
Existence of the recovered 3D_dark_matter_density 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 ~= 10000.0); cosmological_parameter_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Cosmic variance sets the irreducible data-fidelity floor.
Solvability C
- Solver class:
- classical [TreePM (Gadget) or PM (PMFAST) or AMR (RAMSES)]
- Convergence rate q:
- 2
- Complexity:
- O(N_particles * log N_particles) per timestep (TreePM) per iteration