The BRUT Framework
Deriving cardiovascular dynamics, neural coherence, and metabolic coupling from a single partition capacity axiom: C(n) = 2n²
Core Equations
From one axiom, a complete mathematical physiology emerges.
Partition Capacity
The foundational axiom. The number of distinguishable categorical states at partition depth n follows a quadratic scaling law derived from spherical symmetry constraints.
S-Entropy
Entropy over the partition hierarchy. Connects information-theoretic capacity to thermodynamic entropy via the three coordinates (S_k, S_t, S_e).
Kuramoto Coherence
Cardiac coherence estimated from heart rate variability. CV = RMSSD·HR/60000 maps beat-to-beat variation to the Kuramoto order parameter.
Frank-Starling Law
Stroke volume as a function of preload, derived from partition boundary conditions on the pressure-volume loop.
Cardiac-Neural Coupling
The ratio of neural to cardiac coherence follows a universal scaling law, valid during coupled states. Breaks down during REM sleep.
Consciousness Window
The temporal integration window for conscious experience, derived from the geometric mean of cardiac and neural coherence.
Derivation Hierarchy
Each physiological system is derived from the same partition axiom, forming a unified hierarchy from cardiac mechanics to conscious experience.
Cardiovascular Mechanics
- ◆Pressure-volume loops from partition boundary conditions
- ◆Frank-Starling, Windkessel, and baroreflex as emergent properties
- ◆Cardiac equations of state: PdV + VdP = C(n)kT formalism
- ◆Disease classification via Kuramoto regime boundaries
Neural Coherence
- ◆EEG band structure from partition depth selection
- ◆Consciousness as temporal integration over coherence window
- ◆Sleep architecture as regime traversal sequence
- ◆REM active decoupling: cardiac-neural gap = 0.375
Metabolic Coupling
- ◆Oxygen transport as partition-level coupling constant
- ◆Temperature-dependent coherence via Arrhenius formalism
- ◆Metabolic cost of cognitive geometries (thought metabolism)
- ◆Altitude degradation curves from O2-partition coupling
Sensor Disambiguation
- ◆Partition-Coupled Heart Rate (PCHR) decomposition
- ◆S-entropy health coordinates from wearable sensors
- ◆Cross-Scale Coherence Index for inter-system coupling
- ◆Temperature-corrected coherence removing metabolic bias
Join the Research
We are seeking collaborators with expertise in clinical cardiology, computational neuroscience, and wearable sensor engineering. Investment opportunities available for sensor disambiguation IP.