This cochlea is built from CRR (Coherence-Rupture-Regeneration), a temporal grammar for the Free Energy Principle. Every hair cell, every traveling wave, and every rupture flash emerges from three equations and one parameter.
Any system persisting at a non-equilibrium steady state possesses a Markov blanket that separates internal from external states. The system minimises variational free energy:
The cochlea IS a Markov blanket. The basilar membrane and Reissner membrane separate endolymph (internal, +80mV, high K+) from perilymph (external, ~0mV, high Na+). The stria vascularis maintains this partition as the metabolic engine.
One row of inner hair cells (IHCs) forms the sensory surface. Stereocilia deflection is bistable: toward tallest row = depolarisation, away = hyperpolarisation. This is a Z₂ symmetry operation.
95% of afferent nerve fibres synapse on IHCs. Each type I fibre contacts a single IHC. This is the ascending sensory evidence pathway.
Three rows of outer hair cells (OHCs) form the cochlear amplifier. The motor protein prestin enables electromotility: voltage-driven length changes that amplify basilar membrane vibration by 40-60 dB.
The OHC amplifier operates as a circular feedback loop: mechanical → electrical → prestin → mechanical. This is SO(2) topology. The medial olivocochlear (MOC) efferent system modulates OHC gain from the brainstem, providing top-down prior precision control.
The ratio ΩZ₂/ΩSO(2) = 2, a topological invariant. The sensory channel ruptures twice as fast as the prior channel.
Sound enters at the cochlear base (high frequency, narrow basilar membrane) and propagates as a traveling wave toward the apex (low frequency, wide membrane). At each location, the wave accumulates coherence with the local resonant frequency.
B(C) = exp(C/Ω)·(C* - C) peaks at C* - Ω: one capacity-unit before rupture. This is where the cochlear amplifier is most active, where basilar membrane displacement is maximal, where OHC feedback is at its peak. The golden shimmer you see in the simulation is the beauty function in action.
The cochlear tuning curve exhibits a sharp excitatory tip (Z₂ sensory detection at the characteristic frequency) surrounded by inhibitory sidebands (SO(2) lateral suppression via two-tone suppression). This is the Mexican hat: Z₂ excitation at the centre, SO(2) inhibition at the surround. The same structure appears in visual centre-surround receptive fields.
Phase-gating: the SO(2) prior channel (OHC amplifier) is the pacemaker. Its rupture cycle creates timing windows for sensory detection. The cochlear amplifier determines when the IHC fires, not just how strongly.
When OHCs are damaged, the cochlear amplifier fails. The brain increases central gain to compensate for reduced sensory input. In CRR terms, this is an Ω-collapse: precision increases pathologically, the system becomes rigid, and phantom percepts emerge. The same predictive coding framework explains both the normal operation and the failure mode.
Toggle Auditory cortex pathway to see the full ascending hierarchy. Each level has its own CRR timescale (Ω), naturally producing the known EEG frequency bands.
SG (Spiral Ganglion): cell bodies of the auditory nerve, immediately outside the cochlea. First relay from IHC to brain. Fastest dynamics, γ ~40 Hz. This is where the Z₂ rupture events from hair cells become neural spikes.
CN (Cochlear Nucleus): first brainstem relay, in the medulla. Onset detection, spectral processing, and temporal pattern extraction. γ/β ~28 Hz. Dorsal and ventral divisions handle different processing streams.
IC (Inferior Colliculus): midbrain integration hub where nearly all ascending auditory pathways converge. Temporal pattern integration, β ~18 Hz. The SO(2) timescale dominates here.
MGB (Medial Geniculate Body): the auditory nucleus of the thalamus. Precision gate to cortex, α ~12 Hz. Descending predictions from cortex have their strongest modulatory effect here. Analogous to the lateral geniculate nucleus for vision.
A1 (Primary Auditory Cortex): the generative model. Tonotopic map on the superior temporal gyrus. Slowest dynamics, α/θ ~8 Hz. Processes syllables, phonemes, auditory objects. Sends descending predictions back through the entire hierarchy.
CRR predicts these frequencies from first principles: the Z₂/SO(2) ratio = 2 and hierarchical Ω-scaling produce γ at the cochlear level (~40 Hz), β at the brainstem (~20 Hz), and α/θ at the cortex (~8-12 Hz). These are not fitted parameters.
Tone slider: generates a pure tone that directly stimulates the basilar membrane at the characteristic frequency location. Sweep it to see the activation point move along the spiral. Microphone: ambient sound adds CRR activity on top. CRR gain: controls coherence accumulation rate. High gain = rapid ruptures. Low gain = beauty function lingers.
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Sabine, A. (2026). Phase-gating across precision channels: a CRR temporal grammar for Active Inference. AGI-26. temporalgrammar.ai
CRR pending peer review · Active Inference Institute · 2026