A falsifiable emergence · lab notebook
Hearing from First Principles
A falsifiable emergence of the ear — wave → place → R19 switch → congenital deafness
This volume emerges hearing from one inherited cubic and one inherited place map. The R19 switch ṡ = g·s − s³ + h supplies detection, cube-root amplification, and the deafness failure modes; the √-law place map CF(x) supplies pitch-by-place across 19.848 Hz–20677.07 Hz. Every magnitude that is not forced is named as an open obstacle [O].
Contents
- §1The place map and the tip-link MET switch[F]
The hair-cell MET switch (TMC1/PCDH15/CDH23) emerges on the inherited √-law place map by R19 spinodal order; the traveling-wave peak place is parameter-free, the full envelope the named open obstacle.
- §2The cochlear amplifier: cube-root compression[F]
The outer-hair-cell amplifier (prestin/SLC26A5) emerges as the inherited R19 cubic at criticality: response compresses as the parameter-free cube root r∝F^(1/3); detection and amplification are one cubic in two regimes.
- §3Congenital deafness: the failure modes[F]
Congenital deafness emerges as the inherited R19 cubic’s failure modes — three loci plus the critical regime — each gene mapped by cited function to a direction-only, proposal-only lever. Two classes are honest negatives. Nothing is diagnosed or dosed.
- §4The readout synapse (otoferlin)[F]
The readout layer §3 left open is modelled: release is non-negative, monotone, saturating and NON-bistable, so it cannot be the R19 cubic — the minimal form is a rectified saturating Ca²⁺ sensor (otoferlin), reproducing auditory neuropathy and the OAE⁺/ABR⁻ fingerprint.
- §5The traveling-wave envelope[F]
The dispersive traveling-wave envelope — the seed’s deepest open obstacle — is characterised without tuning as a one-parameter family in the sharpness Q: every location is forced and Q-invariant, every magnitude scales with Q, so a number for Q would be tuning.
- §6The audible band: a geometry-carved bandpass[F]
Why we hear ~20 Hz–20 kHz is derived as a geometry-carved bandpass on the inherited √-law: the keystone N_oct = ½·log₂(S_base/S_apex) is exact; shape and every edge sign are forced; the absolute edges are the irreducible measured-geometry obstacle.
- §7Band-specific hearing loss (class × place)[F]
Characteristic audiogram shapes emerge by composing §3’s failure-class axis with §6’s place axis: because the place map is monotone, where a failure sits IS which band is lost (an order-isomorphism). Every direction is forced; every dB and notch-Hz is the irreducible measured obstacle.
Locked concepts
Open-obstacle ledger — every named [O]
Honesty is the method: each chapter forces a direction and an exponent, then names the magnitude it cannot supply without tuning. These are the live obstacles, not omissions.
| § | Open obstacle | Why it stays open |
|---|---|---|
| §1 | The full dispersive traveling-wave ENVELOPE | characterised in §5 down to a single scalar Q |
| §2 | Absolute amplifier gain / dB / sharpness Q | a number would require tuning a constant |
| §3 | Every physical magnitude of the deafness loci | only directions and exponents are forced |
| §4 | Sensor Kd/Rmax, releasable-pool size, nerve rate (Hz) | cooperativity m is cited biology, not derived |
| §5 | The sharpness Q (and the full 2-D/3-D hydrodynamics) | a closed numeric envelope = a choice of Q = tuning |
| §6 | Absolute band edges CF_min / CF_max and the three corners | measured geometry; a number = tuning |
| §7 | Every dB, slope, notch-Hz, and age of onset | a closed numeric audiogram = tuning |