feat(linear-static-3d-euler-beam): step 19 - essential-constraints

docs/implementation-plans/linear-static-3d-euler-beam-implementation-report.md

@@ -809,3 +809,54 @@
 | REVIEW1-targeted | `ctest --test-dir .harness/build -C Debug -R SparseAssembly --output-on-failure` | 0 | Exact SparseAssembly suite passed 5/5 |
 | REVIEW1-full | `ctest --test-dir .harness/build -C Debug --output-on-failure` | 0 | Full accumulated suite passed 47/47 |
 | REVIEW1-reference | `git diff --exit-code 59da6c6 -- reference/`; `git status --short -- reference/` | 0 | Approved reference artifacts remain unchanged and reference status is empty |
+
+## Step 19 — essential-constraints
+
+- task_id: `TASK-19`
+- status: `completed`
+- changed_files: `include/fesa/constraints/essential_constraints.hpp`,
+  `src/fesa/constraints/essential_constraints.cpp`,
+  `tests/unit/constraints/essential_constraints_test.cpp`,
+  `src/fesa/CMakeLists.txt`, `tests/CMakeLists.txt`,
+  `docs/implementation-plans/linear-static-3d-euler-beam-implementation-report.md`,
+  `phases/linear-static-3d-euler-beam/index.json`
+- requirement_ids: `FESA-REQ-LS3DEB-007`, `FESA-REQ-LS3DEB-022`,
+  `FESA-REQ-LS3DEB-027`, `FESA-REQ-LS3DEB-034`,
+  `FESA-REQ-LS3DEB-035`
+- test_ids: `T19-CONSTRAINT-001`, `T19-CONSTRAINT-002`,
+  `T19-CONSTRAINT-003`, `T19-CONSTRAINT-004`
+
+| stage | exact command | exit_code | expected_or_observed_result | evidence_tail |
+| --- | --- | ---: | --- | --- |
+| RED-build | `cmake --build .harness/build --config Debug --target fesa_tests` | 1 | Exactly four planned tests were registered before production and the public constraint API was absent | MSVC C1083 reported missing `fesa/constraints/essential_constraints.hpp` from `essential_constraints_test.cpp` |
+| GREEN-build | `cmake --build .harness/build --config Debug --target fesa_tests` | 0 | Minimum partition/mapping implementation and all four tests compiled and linked | `essential_constraints.cpp`, its test, `fesa_solver.lib`, and `fesa_unit_tests.exe` built without a FESA warning under `/W4 /WX` |
+| GREEN-test | `ctest --test-dir .harness/build -C Debug -R EssentialConstraints --output-on-failure` | 0 | Hand-computed blocks, no/all/mixed constraints, nonzero reconstruction, and invalid dimensions passed | 4/4 exact `EssentialConstraints` tests passed |
+| VERIFY-configure | `cmake -S . -B .harness/build -A x64 -DFESA_GTEST_SOURCE_DIR=C:/git/googletest "-DMKL_DIR=C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl" "-DTBB_DIR=C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb" "-DHDF5_DIR=C:/Program Files/HDF_Group/HDF5/2.1.1/cmake"` | 0 | Approved explicit-dependency MSVC x64 build tree generates | Windows SDK, oneMKL 2026.1, oneTBB, and HDF5 resolved; configure/generate completed |
+| VERIFY-build | `cmake --build .harness/build --config Debug` | 0 | Full Debug build passes without a new FESA warning | `fesa_solver.lib` and `fesa_unit_tests.exe` built under `/W4 /WX` |
+| VERIFY-targeted | `ctest --test-dir .harness/build -C Debug -R EssentialConstraints --output-on-failure` | 0 | Focused Step 19 suite remains green | 4/4 exact `EssentialConstraints` tests passed |
+| VERIFY-discovery | `ctest --test-dir .harness/build -C Debug --show-only=json-v1` | 0 | CTest discovers the accumulated suite and all four exact names | 51 tests discovered, including 4 `EssentialConstraints` tests |
+| VERIFY-full | `ctest --test-dir .harness/build -C Debug --output-on-failure` | 0 | Full accumulated C++ suite has zero failures | 51/51 tests passed |
+| VERIFY-contract-scans | Public backend and forbidden load/RHS/penalty/MPC scans, exact-test-count scan, `git diff --check`, and reference status/diff checks | 0 | Essential partition remains isolated behind backend-free public types | backend leaks 0; forbidden scope 0; exact tests 4; whitespace clean; reference unchanged |
+
+- contract_checks: `partition` validates the input CSR, exact square/full-DOF
+  dimensions, stable increasing free/constrained order, disjoint complete
+  coverage, free-equation correspondence, and prescribed-vector size before
+  extracting any block.
+- contract_checks: each full CSR slot maps at most once into
+  `Kff/Kfc/Kcf/Kcc`. Filtering the stable full rows and sorted columns retains
+  numeric values, local row/column order, and exact structural zeros; every
+  returned block revalidates through the canonical 0-based CSR constructor.
+- contract_checks: no/all/mixed constraint cases include valid zero-sized
+  rectangular blocks. `gatherFree`, `gatherConstrained`, and
+  `reconstructFull` reject vector-size mismatch and preserve caller-supplied
+  constrained values exactly, including nonzero prescribed displacement.
+- contract_checks: the module does not assemble loads, form an effective RHS,
+  implement penalty/MPC behavior, or expose MKL/oneTBB/HDF5/PARDISO types.
+- generated_evidence: `.harness/build/src/fesa/Debug/fesa_solver.lib`,
+  `.harness/build/tests/Debug/fesa_unit_tests.exe`
+- reference_diff: unchanged; `git diff --exit-code -- reference/` exit 0
+- handoff: Step 20 may factorize the validated `kff`; Step 21 may use `kfc`
+  with `DofManager::prescribedValues()` to form the nonzero prescribed
+  effective RHS without changing this module's mapping responsibility.
+- concerns: none; no critical implementation or upstream contract conflict
+  was found.