Membrane, aperture, steepness
Derived Derived in Legibility A.2.3. The corpus treats each node's type as a prediction to be measured.
Source: Style sheet v22 §1.4 (source of record: Legibility A.2.3)
Definition (canon)
The chain, stated once and in full:
membrane → aperture (a) → steepness (k/a, β, n) → failure geometry
Each link is owned by a different thing. The membrane is a boundary; the aperture is a property of that boundary; the steepness is a property of the node inside it; the geometry is what the node then does. The two middle terms run inverse to one another: coarse aperture, high steepness. Merging them inverts a sign in any derivation that uses both.
- Membrane. The system boundary. It tunes embedded nodes (via aperture), compartmentalises, and bounds. It is not a node and does not bifurcate. By setting aperture it decides whether bifurcation is available at the nodes it encloses.
- Aperture (a). How finely incoming load is resolved. Fine aperture preserves magnitude information; coarse aperture discards it. Formally, steepness = k/a.
- Steepness. The slope of a node's transfer function. Shallow fails by gain loss (fold → pivot → τ↑); steep fails by jump (hinge → fracture).
Corrected 2026-11-06. This entry used to add "τ↓ + cascade" to the hinge. Both are withdrawn. See the erratum.
The metabolic instance of steepness is the Hill coefficient of CPT1's inhibition by malonyl-CoA. That is a property of the enzyme, modulated by its lipid environment, and not a property of the membrane.
In plain words
The surroundings decide how coarsely a node can see what is coming. The coarser it sees, the more all-or-nothing it acts, and so the more likely it fails by jumping than by fading.
It is not
- "The geometry knob". That phrase names the whole chain and is retired as a definition (D8).
- Transduction fidelity, which tracks aperture and so runs inverse to steepness.
What would defeat it
- Follows from the definition. A node whose measured steepness does not fall as its aperture is made finer, with the rest held fixed.
- Canon. The calibration case needs an aperture knob that can be swept. Extracting the aperture constant from the same sweep that tests the 3/2 exponent is an identifiability failure; the fix is independent variation, not better measurement.