fix(random): correct six distribution bugs found in audit

[chaoming0625]

Summary

Audited brainstate.random for errors, bugs, and edge cases. Found six reachable correctness bugs, each contradicting the function's own NumPy-style docstring. All are fixed and covered by test-first regression tests (TestAuditRegressions in _fun_test.py), with statistical checks gated behind --run-slow.

#	Function	Bug	Fix
A	standard_t	Array df + size=None raised ValueError (dead u.math.shape(size) branch always yielded ())	Infer shape from df (matches sibling t + docstring)
B	weibull_min	Divided by scale instead of multiplying	r * scale (matches scipy.stats.weibull_min + weibull docstring)
C	triangular	Was 2*bernoulli-1 (Rademacher ±1) with a size-only signature; the documented triangular(-3, 0, 8, N) raised TypeError	Real triangular(left, mode, right, size) via inverse-CDF, with shared-unit support like uniform
D	geometric	Off-by-one (support {0,1,…} not {1,2,…}) and returned float	floor(…) + 1, cast to integer dtype, so P(k==1)==p
E	randint_like	Default high = max(input) (Python builtin) raised on >1-D templates	Use u.math.max
F	chisquare	Summed df squared normals — rejected non-integer scalar df (TypeError) and array df with size=None (NotImplementedError)	2 * Gamma(df/2), valid for any positive real / array df (mirrors t, noncentral_chisquare)

Tests that encoded the old buggy behavior (triangular ±1; chisquare NotImplementedError) are updated to assert the corrected contracts.

Out of scope (documented in audit, not changed here)

• ir_compilation=True breaks every named_scope-decorated method (even normal) because static_argnums indices reference size/dtype/key positions passed as kwargs. This is a transform-layer concern (brainstate/transform/_named_scope.py + jit), off by default, with no random test coverage — a fix belongs there with its own tests.
• Minor docstring inaccuracies (seed_context claims it touches NumPy state; __init__.py shuffle example implies in-place mutation).

Testing

• pytest brainstate/random/ --run-slow → 539 passed.
• No code outside brainstate/random/ references the changed functions.

🤖 Generated with Claude Code

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[codecov]

Codecov Report

❌ Patch coverage is 90.90909% with 3 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
brainstate/random/_state.py	90.62%	2 Missing and 1 partial ⚠️

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