Bounded complete-record certificates

A positive log-contrast margin does not automatically imply a positive single-copy linear-program gap. The logarithm is nonlinear; convexification can introduce intersections not present in the original law families. Route A remains a valid separate inferential construction under its assumptions. Route B is the preferred apparatus-facing certificate when its positive gap has actually been established.

For specified laws, the full-record likelihood ratio is

and their classical Chernoff information is

Endpoint terms use support conventions. This is an asymptotic simple-hypothesis exponent Chernoff1952, not a uniform composite-family certificate.

Local nuisance-rank diagnostics can guide settings. With all probability coordinates retained, define $v_G={\partial }_{\lambda }p$, $J_{\nu }={\partial }_{\nu }p$, and $W=\mathrm{diag}(1/p_z)$ for positive $p_z$. The nuisance-orthogonal information is

It vanishes precisely when $v_G\in \mathrm{range}{J}_{\nu }$. The normalization constraints are retained in the derivative columns; one must not drop a probability coordinate and then use an unmodified diagonal Fisher weight. This tangent-space condition is not a global exclusion theorem.