Tootfinder

Chirality of a $Z_q$ Model as Directional Phase Shifts in Oscillator Networks
Yi Cheng, Zongli Lin
https://arxiv.org/abs/2607.16606 https://arxiv.org/pdf/2607.16606 https://arxiv.org/html/2607.16606
arXiv:2607.16606v1 Announce Type: new
Abstract: Chirality in a discrete $Z_q$ spin interaction distinguishes clockwise from counterclockwise phase differences, but its manifestation in continuous nonlinear dynamics is unclear. We show that any pairwise $Z_q$ Hamiltonian admits a unique equilibrium-preserving embedding into a continuous phase-energy landscape that matches the discrete energy on the $q$-state phase grid, where every grid point is stationary. This embedding reveals that a $Z_q$ kernel is nonchiral if and only if the sine components of the relaxation vanish. Chirality of the discrete $Z_q$ model is therefore exactly the odd part of the continuous phase interaction. In the induced nonlinear phase dynamics, this odd part becomes an orientation-dependent phase shift in the multi-harmonic coupling, and chiral reversal flips this shift while preserving the coupling magnitudes. In self-sustaining oscillator networks, the shift is further realized as a direction-dependent delay. Transistor-level ring-oscillator simulations validate the predicted phase locking and reversal of directed phase bias. These results show that algebraic handedness in a discrete spin Hamiltonian can be represented as tunable time-domain asymmetry in continuous nonlinear dynamics.
toXiv_bot_toot

Agnosiophobia in a virtual agent: behavioral and dynamical architecture in Lenia
Jesse Cool, Benedikt Hartl, Michael Levin, Samantha Petti
https://arxiv.org/abs/2605.30708 https…