Deep in every particle's 28-component state vector sit two numbers that were never derived — a pressure-gradient threshold and an energy barrier. Are they physics, or scaffolding? An audit.
Every particle in the engine carries a 28-dimensional state vector. Two of its components are scaled by hardcoded numbers.
SDT keeps a whitelist: every constant is supposed to flow from {ℓP, c, ℏ, kB, TCMB, α, me, mp}. Two numbers in state28d.hpp don't — yet. They are the subject of this investigation.
Neither is a fitted observable, and neither is a first-principles result. FLM01 asks the direct question: are these physics to be derived, or scaffolding to keep the manifold numerically stable?
Occlusion screening runs through a tanh. Below the threshold the force passes; above it, the gate closes.
The curve above is the whole story of T₅. A torus with a gentle internal pressure gradient sits on the left — its occlusion passes through almost untouched. Push the gradient past 10¹⁰ Pa/m and the tanh saturates: the force is throttled to a bounded contribution, because a torus whose internal gradient runs that steep is already close to structural instability.
Convergence pressure (Law I) lands near 10³⁰ Pa — the electrostatic scale. But the gate is set at 10¹⁰, twenty orders below. That gap is the crux: the number sits well inside the physical range, yet no single derivation pins it exactly there.
The phase-space factor opens accessible configuration space when the topology is free to change.
Φ₅ = 10⁻²⁰ J is about one millionth of the electron's binding energy (~10⁻¹⁴ J). Read as an energy cost, that says something concrete: the price to flip topology is far below the price to hold structure together.
The interpretation writes itself: topology is roughly a thousand times more fluid than the binding scaffold it decorates. Flips happen continuously, not only at recombination — so their barrier is small.
Each first-principles path lands in the right neighbourhood. None pins the exact value.
| Route | Lands at | Gap |
|---|---|---|
| Convergence pressure (Law I) | 10³⁰ Pa ✓ electrostatic | T₅ uses 10¹⁰, not 10³⁰ |
| Coulomb binding energy | 10⁻¹⁴ J ✓ | Φ₅ is 10⁻²⁰ J (×10⁻⁶) |
| Internal pressure gradient | 10⁴⁴ Pa/m | off by 10³⁴ |
| Density of states | 10⁻¹⁶ J | off by 10⁻⁴ |
Every route brackets the constant; not one derives it. Bracketing is not predicting — so the label is not derived.
Not a magic number. Not a derivation. Named scaffolding, labelled.
T₅ and Φ₅ are physically sensible, documented with purpose, and necessary to keep the 28-D components in a stable range — but they are not uniquely fixed by Laws I–IV. So they carry the tag:
The fork is left open on purpose. If these are fundamental, the next move is Law VI: the winding numbers (W=1 and W=3 stable, W=2 unstable) may encode both scales directly. If they are regularisation, they belong in laws.hpp with a CALIBRATED label and this audit as their justification.