Add Satterthwaite and Kenward-Roger fixed-effect tests

README.md

@@ -25,6 +25,8 @@ The engine diagonalizes the GRM once, rotates the common design and every unique
 - Signed standard-deviation parameterization with a separate one-sided KKT check for the \(\sigma_g^2=0\) boundary.
 - No explicit dense \(P\) matrix.
 - Variable numbers of extra fixed-effect covariates per task through a CSR index.
+- Satterthwaite t/F fixed-effect inference by default, with optional
+  Kenward-Roger F tests and a joint test of task-specific covariates.
 - Atomic block output and safe resume/force semantics.
 - Generic Python CLI for manifest creation, validation, execution, provenance signatures, status, and result export.
 
@@ -139,6 +141,12 @@ python python/spectra_reml.py finalize \
 
 `results.tsv.gz` retains the complete per-task summary and stores the fixed-effect vector and row-wise packed lower covariance as JSON arrays.
 
+Fixed-effect inference defaults to Satterthwaite. Select Kenward-Roger or turn
+inference off with `--fixed-effect-test kenward-roger` or
+`--fixed-effect-test none`. Coefficient-wise standard errors, statistics,
+denominator degrees of freedom, and p-values are exported as JSON arrays; tasks
+with extra covariates also report their joint F test in the summary columns.
+
 ## Recovery and provenance
 
 Each block is written as four files, with `.complete` renamed last. The Python layer adds `run.signature.json`, which binds the canonical manifest, engine SHA-256, numerical options, thread settings, and block size.