Closes #87.

Problem

An integer dimension with an active transform was int-cast in transformed space: (10, 5000, "log10") became internal bounds (1, 3), so internal rounding collapsed the dimension to decade exponents in natural scale — and proposals drawn from the un-cast lower/upper float arrays (1.0, 3.699) could round to exponent 4, i.e. 10000, silently exceeding the declared cap of 5000 (observed in a live spotforecast2 tuning run on 2026-06-05). The sqrt analogue restricted int dims to perfect squares.

Fix

The integer constraint belongs to the natural scale, not the transformed scale:

• transform_bounds keeps float internal bounds for int dims with an active transform (untransformed int and factor dims unchanged — pinned by a new companion test).
• New SpotOptim.internal_var_type property; all internal-space repair sites (initial design, user X0, design top-up, acquisition candidates/fallbacks) use it, so transformed int dims are searched continuously.
• New SpotOptim.repair_natural_X (+ utils.variables.repair_natural_X): rounds int dims in natural space and clips transformed ones to the declared bounds; applied in evaluate_function (the objective only ever sees admissible integers) and in the X_/best_x_ storage paths (serial, restart, steady-state parallel), so recorded history matches what the objective saw. Handles full- and reduced-dimension layouts.
• SpotOptimProtocol extended; docs/spotoptim_class.qmd member list updated.

Tests

• tests/test_int_log10_dims.py — 13 regression tests: continuous internal bounds, integer admissible values within [10, 5000] (never 10000), no decade collapse, bound respect in X_/best_x_ across serial and n_jobs=2, float+log10 unchanged, plain int dims unchanged, repair_natural_X unit behaviour.
• test_transform_bounds_mixed_var_types updated — it asserted the buggy int-cast.

Verification

• Full suite: 1743 passed (including slow tests, 13:54)
• Fast suite (-m "not slow" -n auto): 1633 passed
• ruff check src/ tests/ clean; black/isort applied to changed files
• Both new docstring {python} examples execute

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