…ging current behavior: added constraint count/name setters and used them to size Jacobian/state vectors and extend variable names, while carrying the count into StateParameters (include/micm/solver/solver_builder.hpp, include/micm/solver/solver_builder.inl). State now honors the provided constraint count when building identity masks and Jacobian dimensions (include/micm/solver/state.inl). AlphaMinusJacobian applies αI using a row-aware identity mask, preparing for masked constraint rows (include/micm/solver/rosenbrock.inl). Tests: cmake --build build and ctest --output-on-failure (all 48 tests passed).

Modified AlphaMinusJacobian() to add alpha to ALL diagonal elements,
not just ODE rows. This treats algebraic constraints as stiff ODEs
(ε*z' = g(y,z) with ε=hγ), ensuring K values scale with step size H
and preventing numerical instability from c/H terms in Rosenbrock
stage computation.

Changes:
- rosenbrock.inl: Add alpha to all diagonals in both vectorized and
  non-vectorized AlphaMinusJacobian() implementations
- test_equilibrium.cpp: Add DAESolveWithConstraint integration test
  demonstrating working DAE solve with projection step
- Update ARCHITECTURE.md and TODO.md with fix documentation

Co-Authored-By: Claude Opus 4.5 <[email protected]>

Custom skills for building, testing, and debugging MICM:
- /micm-test: Build and run tests (all, filtered, or build-only)
- /debug-test: Debug failing tests with tracing support
- /solver-debug: Investigate numerical solver issues

These skills codify the debugging strategies used during DAE
constraint development, including matrix conditioning checks,
K value tracing, and sign convention verification.

Co-Authored-By: Claude Opus 4.5 <[email protected]>

Documents DAE constraint system architecture, debugging strategies,
and available skills for AI-assisted development sessions.

Co-Authored-By: Claude Opus 4.5 <[email protected]>

Created comprehensive test case library for DAE constraint validation:
- Atmospheric equilibria (carbonate, ammonia, SO2)
- Multi-constraint systems (iron-oxalate, O3-NOx PSS)
- Stiff/numerical challenges (extreme K, temperature-dependent)
- Practical applications (ISORROPIA-style, Chapman mechanism)
- Edge cases (constraint switching, near-singular)

Updated TODO.md: Chapman mechanism with QSSA constraint is next.
This will require QSSAConstraint or CustomConstraint implementation.

Co-Authored-By: Claude Opus 4.5 <[email protected]>

Tests should write CSV to stdout for plotting:
- Header line with column names
- One line per timestep with all state variables
- Include analytical values where available
- Redirect to file: ./test_chapman > results.csv

Enables visual validation with Python/gnuplot.

Co-Authored-By: Claude Opus 4.5 <[email protected]>

Provides a copy-paste prompt to continue DAE work:
- Points to TODO.md and TESTS.md
- Identifies Chapman mechanism as next task
- Suggests build/test verification first

Co-Authored-By: Claude Opus 4.5 <[email protected]>

Documents the approach for merging the DAE constraint system
into main via three incremental, reviewable PRs.

Co-Authored-By: Claude Opus 4.5 <[email protected]>