Cramer's rule pins down the first unknown of a nonsingular 2x2 rational linear system

`build_rat_prelude` admits Rat.cramer_two_unique_x through the trusted `Kernel::add_declaration` gate, which re-checks the proof term against the stated type, so a line in this tool's output for the exact name is a machine-checked proof having been admitted. `theorem_dependency_inventory` exits non-zero for a named filter that matches nothing (a deleted theorem cannot read as a re-derived one), and `grep -c` (never `-q`) both avoids a SIGPIPE-under-pipefail false negative and independently asserts the exact tab-anchored line is present -- two ways the same absence would be caught. `--release` is MANDATORY: this tool now also builds `creal`/`complex`/`cpoint`, which recurse deep enough in a debug build to overflow the default thread stack (measured: release exits 0 with 1092 theorems, debug SIGABRTs at 134) -- the same resource-limit gotcha already documented for `prelude_theorem_inventory --include-constructed`.

`nat_axiom_inventory` builds the Rat environment as its own group and reports `rat: axiom=0 opaque=0 quotient=0 total_trusted=0` (re-measured on this tree). That bounds every individual Rat theorem's footprint by [], since a theorem cannot depend on a trusted declaration the environment does not contain -- and the enumeration covers Axiom, Opaque AND Quotient, not just Declaration::Axiom, because Opaque has no proof body and Quotient admits Quot.sound. `--require-axiom-free <name>` is an error (not a silent pass/zero) for a prelude this run never built, which is what makes `rat` here a claim rather than an absence.