concurrence

Track 2.B of the master plan links pure two-qubit entanglement to strict positivity of von Neumann entropy. A pure two-qubit state is written $|\psi\rangle=\sum_{ij}A_{ij}|ij\rangle$ with amplitude matrix $A:\mathrm{Fin},2\times\mathrm{Fin},2\to\mathbb{C}$. For normalized pure states the general Wootters formula collapses to twice the absolute value of $\det A$.

The module treats $C$ as the algebraic entanglement witness: $C>0$ iff $\det A\neq 0$. Downstream, the reduced density matrix $\rho_1=\mathrm{tr}2|\psi\rangle\langle\psi|$ has eigenvalues $(1\pm\sqrt{1-C^2})/2$, so the entanglement entropy equals the binary entropy of that argument. The same $C$ appears in the Gravity-side BMV positivity carry as the hypothesis that forces $E{\mathrm{VN}}(\rho_1)>0$.

Pure definitional abbreviation: expand to $2$ times the complex norm of $\mathrm{Matrix.det},A$. No lemmas are applied; non-negativity and the zero/positive characterizations are proved in the immediate sibling theorems by unfolding this definition and using $|z|\ge 0$ together with $|z|=0\Leftrightarrow z=0$.

This is the scalar that closes Track 2.B. Sibling lemmas (concurrence_nonneg, concurrence_eq_zero_iff_det_zero, concurrence_pos_iff_det_ne_zero, bounds under Frobenius normalization) all unfold it. The Gravity master theorem packages unconditional BMV entropy positivity as: normalized $A$ with $C(A)>0$ implies positive reduced von Neumann entropy, witnessed by the pure-two-qubit entropy theorem in this module. It also matches the algebraic entanglement witness already used in the det-factored branch-amplitude argument on the Gravity/QuantumChannel side. No new RS assumptions; the definition is the standard pure-state simplification of Wootters concurrence.