A Human-AI Theorem Connecting Spontaneous and Field-Induced Mechanisms of Collective Behavior in One Dimension

arXiv:2609.00322 · cond-mat.stat-mech, cs.AI, cs.HC, math-ph, math.MP · Submitted 2026-08-31 · Read on arXiv

cond-mat.stat-mech, cs.AI, cs.HC, math-ph, math.MP

Submitted: 2026-08-31

Updated: 2026-09-23

Terminology

• Generalization — 6× in this paper · explained in 13 episodes
• Anisotropy — 4× in this paper · explained in 3 episodes
• Provenance — 3× in this paper · explained in 4 episodes
• Archetype — 1× in this paper · explained in 1 episode
• Artificial Intelligence (AI) — 1× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Department of Energy — 1× in this paper
• Frustration — 1× in this paper · explained in 2 episodes
• Hallucination — 1× in this paper · explained in 3 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Symmetry Breaking — 1× in this paper · explained in 3 episodes

Sources

• An explicit lower bound for the unit distance problem
• Remarks on the disproof of the unit distance conjecture
• Metamagnetic Transition in Low-Dimensional Site-Decorated Quantum Heisenberg Ferrimagnets
• Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips

Related papers

• Extreme First-Passage Time of Many Interacting Particles
• Decoherence-controlled collective criticality in a two-dimensional quantum Stag Hunt
• Measurement-induced phase transitions in disordered fermions
• Hierarchical Reduction of Invariant Subspaces: From Fragmentation to Many-Body Scars
• Quantum Thermalization beyond Non-Integrability and Quantum Scars in a Multispecies Bose-Josephson Junction
• Markov length can diverge in systems whose universal physics is spatially Markovian