THE ISOMORPHISM GALLERY
one skeleton, two worlds — the same math wearing two different sciences
Twenty scout personas wandered the lab's consilience graph, pulled papers that caught their nature, and reported pairs of ideas that share a hidden skeleton. Each exhibit below is one proposed isomorphism made playable: a single dynamical core drives both panels — the left wears one paper's parameters, the right wears the other's. Move the shared sliders and watch the two worlds breathe the same math.
Resonance Chain
Polyatomic Time Crystals↔Nonlinear Synchronization in Hierarchical Networks
Resonance networks with phase locking and geometric constraints.
Kuramoto in Immune Coherence
Quantum Cognition↔Immune System Resonance
Coupled phase oscillators with synchronization and resonance dynamics
Dynamic Energy
Energy expenditure model with physiological hysteresis↔Diffusion bridge with randomized initial/terminal times
Nonlinear, state-dependent dynamics with time delays and environmental influence
Gray-Scott in Immune Pattern Formation
Fractal Neural Networks↔MAIT Cell Distribution
Reaction-diffusion dynamics underlying pattern formation
Bridge in Immune and Cultural Pathways
MAIT Cell-Microbiome Interaction↔Viral Infection Pathways in Cultural Fields
Pinned diffusion paths with stochastic control of signal propagation
dynamic_hysteresis
A dynamic switching mathematical model for estimating energy expenditure based on physiological hysteresis↔Diffusion bridge with randomized initial and terminal times and its application to fish migration
Nonlinear time-dependent systems with adaptive parameters
Immune-Resonance Cascade
MAIT Cell Exhaustion in Tumor Microenvironments↔Social System Degradation Under Stress
Threshold-based suppression in network interactions
sync_bridge
Geometry-orchestrated objective reduction from a multiscale resonance chain↔Diffusion bridge with randomized initial and terminal times
Dynamic systems governed by time-dependent coupling and stochastic influence
Bridge-Environmental
Diffusion bridge with randomized initial and terminal times and its application to fish migration↔A nested weighted framework for Podlubny-type fractional PID controllers
Pinned diffusion paths influenced by environmental or system-specific detuning
Cascade in Immune and Network Systems
Immune Cell Recruitment in Infection↔Information Spread in Social Networks
Threshold-based contagion on a network with percolation effects
Gray-Scott in Immune and Cultural Systems
Pattern Formation in Tumor Microenvironment↔Cultural Pattern Emergence in Information Viruses
Reaction-diffusion dynamics with spot and labyrinth formation
Kuramoto in Immune Systems
MAIT Cell Synchronization in Immune Response↔Coupled Oscillators in Neural Networks
Coupled phase oscillators with resonance chains and synchronization dynamics
Kuramoto-Resonance
Geometry-orchestrated objective reduction from a multiscale resonance chain↔A dynamic switching mathematical model for estimating energy expenditure
Coupled phase oscillators that synchronize through non-linear interactions and environmental modulation