The Computational Architecture of Physical Reality
The Lattice Field Medium proposes a universe made from local lattice processing elements. Each cell stores a wave register and a chi response value, reads only its 19-point cubic neighbor fabric, evaluates GOV-01 and GOV-02, buffers the result, and commits on the next substrate tick.
Build a tiny LFM universe
Pick a starting pattern, press start, and watch a small cubic lattice evolve. The monitor looks for a bright, stable, spinning packet: the homepage-scale signature we label an electron candidate.
Canonical discrete core
The v37 documentation states the framework first as a discrete execution architecture. Continuum equations are long-wavelength readouts, not the primitive machine description.
GOV-01
Register updateD_t^2 Phi_i^n = c^2 (Delta_19 Phi^n)_i - (chi_i^n)^2 Phi_i^n
The wave register Phi is updated locally from its current value, previous tick, chi value, and 19-point neighbor stencil.
GOV-02
chi response updateD_t^2 chi_i^n = c^2 (Delta_19 chi^n)_i - (kappa/chi0) chi_i^n (N_k - E0^2) - 4 lambda_H chi_i^n ((chi_i^n)^2 - chi0^2)
The chi response field reacts to the register norm and returns toward the Mexican-hat vacuum.
L_bare = sum_i[1/2|dot Phi_i|^2 + B/2 dot chi_i^2 - 1/2 chi_i^2(N_k,i - E0^2) - B lambda_H(chi_i^2 - chi0^2)^2] - c^2/(2 Delta x^2) sum_<ij>_19 w_ij[|Phi_j - Phi_i|^2 + B(chi_j - chi_i)^2]
The homepage simulator uses this bare-core split: register dynamics, chi dynamics, private buffers, and simultaneous commit. Interaction extensions remain separate until they pass a full interacting-action audit.
From processor to physics
The research program now asks how much known physics can be compiled from repeated local execution of the substrate architecture.
Local execution
Each lattice cell reads only committed local and neighbor state.
Stable structures
Persistent field patterns are measured as candidate particles or effective sources.
Observer registers
R0, R1, and R2 are nested readout algebras of the same substrate run.
Continuum physics
Klein-Gordon, Dirac, gauge, and gravitational behavior are treated as effective readouts.
Research and tools
The site still includes the ML products and calculators, but the public front door now reflects the LFM computational-substrate program.
Universe Simulator
Run the existing complex-field universe simulator and compare chi, density, and phase views.
Equation Reference
Review the public formula catalog and discrete-governing-equation reference.
Papers
Read the derivation papers, red-team audits, and processor-specification release material.
LAdam Optimizers
Physics-inspired optimizers remain available as downstream engineering tools.
WaveTransformer
Wave-propagation architectures for efficient sequence modeling.
Contact
Licensing, research collaboration, and custom simulator work.
Research artifacts are published through OSF, Zenodo, and public experiment repositories.