Research question. Can a finite power-law implementation preserve both forward probability contracts and exponent sensitivity through a removable singularity?
Predict¶
At , predict a logarithmic CDF, finite normalization, exact support boundaries, monotone inversion, and one common parameter derivative approached from both sides.
Compute¶
uv run --no-sync python -m examples.investigations.powerlaw_removable_limitThe public log-density, CDF, and PPF use smooth removable-singularity kernels. The example returns normalization, round-trip, support, AD, finite-difference, and independently derived limiting-derivative metrics.
Audit¶
Use logarithmic-grid quadrature as an independent normalization check. Compare AD with a central finite difference and the series-derived coefficient. Verify both support endpoints and the CDF/PPF round trip.
Misconception check¶
An exact equality branch can produce the correct value at the limit while exposing the wrong derivative with respect to the exponent.
State the warranted claim¶
The tested kernel preserves its finite-support numerical and local derivative contracts. This does not establish that a power law is the correct physical stellar-mass distribution for a particular population.