Manuscript XIX-D@1 · XIX-D.tex · section · 1f47e33b

The four labelled entries

Four objects and a precisely typed quantum audit › The four labelled entries · lines 233–288

XIX-D@1#eq:labels

The entries are

C_{VI}, C_{E}, C_{VIII}, R_{X} .

They are not four already verified quantum clocks.

Entry	Classical prescription being audited	Data retained
$C_{VI}$	$T \circ H_{q}^{- 1}$ , with a specified harmonic-coordinate Cauchy problem	Metric and scalar jets, equation space, initial surface, coordinate-time data, and gauge group
$C_{E}$	$N [q, T] \circ α_{q, T}$ , using the original $T$ -slice harmonic spatial rods	Timelike branch, clock calibration, elliptic boundary condition, relational map, and background interval
$C_{VIII}$	Prescribed incidence parameter together with a finite reading register and declared updates	Installed packet, exact guards, supplied token, complete record and residual interfaces, and schedule
$R_{X}$	Fixed smooth profile in a coordinate density	External coordinate time, profile, width, placement, and its transformation convention

For the scalar-clock entry, the raw lapse is

N [q, T] = (- q^{- 1} (d T, d T))^{- 1/2},

on its positive timelike branch. Its nonlinear formula does not by itself define an operator inverse or an inverse square root of a quantum distribution.

For the ramp entry, a typical profile is

σ_{ε} (t) = χ (\frac{t - t _{0}}{ε}),

held fixed as external data. With that convention its field variation vanishes. Giving it a transforming-background role, or introducing a new quantum field in its place, changes the declared object.

Displayed formulas in this passage

XIX-D@1#eq:labels · line 236
$C_{VI}, C_{E}, C_{VIII}, R_{X} .$
unlabeled · line 272
$N [q, T] = (- q^{- 1} (d T, d T))^{- 1/2},$
unlabeled · line 280
$σ_{ε} (t) = χ (\frac{t - t _{0}}{ε}),$