Lattice QCD Path Integral L1-480
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
Lattice QCD Path Integral: Lattice QCD: compute hadron masses and matrix elements from first principles via Monte Carlo path integral on discrete spacetime lattice. The forward operator produces the measurement through a 3-node primitive DAG (S.hmc.hybrid_monte_carlo…); recovery is posed as a statistical_inverse problem. Difficulty tier delta=50 with effective condition number kappa_eff~1000000.0; discretization_error_O_a2, finite_volume_error 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:
- 10000000000
Existence of the recovered QCD_observable_spectrum 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 ~= 1000000.0); discretization_error_O_a2 dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Monte carlo statistical sets the irreducible data-fidelity floor.
Solvability C
- Solver class:
- statistical [HMC_gauge_generation + multi_mass_CG_inversion]
- Convergence rate q:
- 2
- Complexity:
- O(N_L ** 3 * N_T * V_gamma ** 4 * N_CG_iter) per config; dominated by fermion matrix inversion