# Argument selection for T573

This build follows the coordinated local and live skill archived in
`agents/runs/20261028T054431Z-build-skills/manifest.json`. Both versions have
SHA-256 `e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c`.
The current source snapshot has the same bytes. The family conventions are
numberdb-data issue 227, read before screening and building.

## Quantity and conventions

One quantity is tabulated: the expected von Neumann entropy of the smaller
reduced state of a complex Haar-uniform bipartite pure state. The parameters
are `N`, `K`, `unit`, in that order. Entropy in nats and bits is one number in
two invertible conventions, with `bits = nats/log(2)`. The ensemble is not
real, Bures, energy constrained, or an average of a density matrix followed by
its entropy. Page (1993), equations (1)-(5) and (11), and Sen (1996), equation
(9), specify the object and finite formula. Życzkowski–Sommers (2001), equations
(3.5)-(3.8), identify the equivalent normalized complex Gaussian ensemble.

## Every free parameter

- **N, subsystem dimension (discrete_index).** N is the integer complex
  dimension of the retained Hilbert space, with domain N >= 2. It selects a
  documented family of quantum subsystems, not a sampling of a continuous
  input. The dimension-one case has identically zero entropy and is omitted
  from the table's defined domain. All dimensions N = 2 through 11 allowed by
  the joint budget are included, rather than only qubits or famous examples.
- **K, environment dimension (discrete_index).** K is the integer complex
  dimension of the factor traced out, with domain K >= N. The nonzero spectra
  of the two reduced density matrices agree, so interchanging N and K does
  not supply a second object. All K allowed by NK <= 128 are retained. The
  two parameters are coupled by the actual total dimension, not independently
  sampled on an arbitrary rectangular grid.
- **unit, logarithmic unit (documented_application).** `nats` and `bits` are
  the natural-logarithm and base-two units of entropy. Every dimension pair
  receives both. This is the one-number-in-two-conventions exception: the
  known factor log(2) converts either value into the other. There is no
  selector for a different observable, ensemble, or spectrum. Page uses
  natural logarithms; the base-change law is an exact identity. The existing
  NumberDB table of Shannon entropies uses the same unit names.

## Extent and breadth

The selection is exactly all integer pairs 2 <= N <= K and NK <= 128, in
both units: 200 pairs and 400 entries. The cutoff 128 is a noncanonical
practical size budget. It measures total Hilbert-space dimension and is
independent of how integers are written; powers of two are not privileged
inside the selection. A reader computing bipartite average entanglement for
small or moderate systems can encounter any such dimension pair.

This choice covers balanced states N = K for N = 2,...,11, nearly balanced
splits, and small systems with larger environments (up to N = 2, K = 64).
It covers these qualitatively different parts of the discrete family before
extending only qubit environments or a diagonal slice. The finite bound is
not claimed to be a theorem, an application cutoff, or a claim that every
pair has a separate famous use. There are no exploratory continuous inputs,
quantiles, or probability meshes.

The generator orders N increasingly, then K increasingly, then nats followed
by bits, so the two conventions are adjacent. The completeness note and
checks use the same product bound; an independently written exhaustive
predicate verifies every selected identity and its order.

## Measured cost and independent review boundary

The dry run has 400 entries. The longest serialized value is 113 characters;
the full flat-record JSON is 57,194 bytes, comfortably under the target.
Nats are exact rationals, and all 200 bit values have finite narrow Arb
balls at 397 working bits. See numerical-evidence.json for controls,
independent integrals, error bounds and software versions.

The builder has justified this selection but has not accepted it on behalf
of an independent critic. The separate critique must evaluate all three
parameters, fingerprint the actual draft and generator dependencies, and
write its own sidecar. This build creates no argument-review acceptance.