FESADev/docs/linear-static-mitc4-shell/implementation-plan.md

Linear Static MITC4 Shell Implementation Plan

For agentic implementation workers: 이 문서는 사용자 승인 전 draft다. 승인 후 Implementation Planning Agent가 같은 내용으로 Harness phase planning files만 materialize한다. Implementation Agent는 승인된 phase의 pending Step을 docs/HARNESS.md와 docs/HARNESS_WORKFLOW.md에 따라 하나씩 실행해야 하며, Harness hook/runner lifecycle을 우회해서는 안 된다.

1. Metadata

• feature_id: linear-static-mitc4-shell
• document_type: implementation-plan
• status: ready-for-implementation
• approval_state: harness-step-draft-approved-2026-08-12
• owner_agent: implementation-planning-agent
• date: 2026-08-13
• source_requirement: docs/linear-static-mitc4-shell/requirements.md
• source_research: docs/linear-static-mitc4-shell/research.md
• source_formulation: docs/linear-static-mitc4-shell/formulation.md
• source_numerical_review: docs/linear-static-mitc4-shell/numerical-review.md
• source_io_definition: docs/linear-static-mitc4-shell/io.md
• source_reference_models: docs/linear-static-mitc4-shell/reference-model.md
• target_platform: Windows x64 / MSVC / C++17
• build_system: CMake + CTest
• execution_infrastructure: Python Harness
• current_numerical_verdict: pass-for-implementation-planning
• harness_task_name_candidate: linear-static-mitc4-shell
• implementation_authorized: true-user-requested-2026-08-12
• harness_execution_authorized: true-user-requested-2026-08-12
• phase_files_authorized: true-user-approved-2026-08-12

Goal

승인된 Abaqus .inp subset의 S4 및 S4R source element를 하나의 FESA FESA-MITC4 선형 정적 shell formulation으로 해석하고, 물리적으로 분리된 fixed drilling stabilization, deterministic sparse assembly, mandatory HDF5 shell results, sole declared S4 displacement reference case를 end-to-end로 연결한다.

Architecture

기존 B33 경로를 파괴하거나 speculative common element hierarchy를 만들지 않는다. Domain에 shell semantic records를 추가하고, 별도 concrete Mitc4Shell kernel과 shell-specific recovery를 만든다. 기존 Analysis lifecycle, six-DOF nodal load/constraint, sparse COO reduction, LinearSolver, generic ResultsWriter 경계, HDF5 temporary/self-check/atomic replacement는 재사용한다.

Tech Stack

• C++17, MSVC /W4 /WX
• CMake 3.25+, Visual Studio 18 2026 generator, x64 Debug
• GoogleTest/CTest
• Intel oneAPI MKL and TBB
• HDF5 schema version 0
• Python 3 Harness runner and repository hooks

Global Constraints

1. 모든 production behavior는 같은 Step 안에서 RED -> observed failure -> minimal GREEN -> focused VERIFY -> full VERIFY를 닫는다.
2. production C++ 파일 변경은 관련 C++ test와 함께 수행한다.
3. public solver headers에 MKL, TBB, HDF5, Win32/vendor type을 노출하지 않는다.
4. Node/Element에 equation ID를 저장하지 않고 DofManager만 numbering, scatter, constrained/free mapping 및 sparse pattern을 소유한다.
5. S4와 S4R은 같은 FESA numerical path를 사용하며 source metadata만 다르다.
6. physical 20-DOF kernel과 four numerical drilling coordinates를 recovery/output에서 분리한다.
7. reference files를 생성, 수정, rename, repair, normalize하지 않으며 Abaqus를 실행하지 않는다.
8. future geometrically nonlinear residual/tangent, distributed loads, mixed beam-shell models, reduced integration/hourglass, drilling calibration/energy output, NR-O03/NR-O04는 구현 범위 밖이다.
9. 이 draft의 승인은 phase planning files 작성만 허용한다. Harness 실행은 별도의 명시적 사용자 요청이 있어야 한다.

2. Readiness Check

gate	evidence	status	planning consequence
Requirements	docs/linear-static-mitc4-shell/requirements.md, 001-072 approved	pass	모든 must를 task/test에 추적
Research	docs/linear-static-mitc4-shell/research.md	pass	source-backed MITC4 tying/director/drilling 경계 유지
Formulation	docs/linear-static-mitc4-shell/formulation.md, approved-for-implementation-planning	pass	linear sections만 구현; Section 15 future nonlinear 제외
Numerical Review	docs/linear-static-mitc4-shell/numerical-review.md	pass	critical blocker 없음; planning authorized
I/O	docs/linear-static-mitc4-shell/io.md, approved-for-implementation-planning	pass	keyword, diagnostic, HDF5 schema를 그대로 구현
Reference Model	docs/linear-static-mitc4-shell/reference-model.md	pass	sole S4 input/CSV pair만 read-only acceptance input으로 사용
Repository seams	parser/model, element/analysis, result/reference 영역 read-only 조사	pass	candidate files와 current signatures 확인
Toolchain paths	GoogleTest/MKL/TBB/HDF5 config directories 존재	pass	Section 10의 exact configure command 사용 가능

Toolchain path evidence was resolved in this workspace on 2026-08-12with Test-Path -LiteralPathreturning Truefor all four literal directories used in Sections 10 and 12. They are environment-resolved paths, not placeholders. Each Step copies the fail-fast path precheck before CMake so a changed machine configuration stops before RED/GREEN evidence is recorded.

Declared read-only reference inventory:

case	source	displacement CSV	SHA-256
S4	reference/shell/shell.inp	reference/shell/shell displacements.csv	input 4005851E1AB22FD3A16AC17A8D5DA3E051233F69F37419079F3553AD134ECFCF; CSV C81D94E0B4A849F87AA0F79C83A79B94D5661AC79E44ED826919AB432C87746B

README, metadata.json, Abaqus provenance/version, canonical naming 및 추가 portfolio는 readiness gate가 아니다. 현재 열린 product/numerical 결정은 없다. 남은 승인 항목은 Section 12의 multi-Step Harness draft뿐이다.

3. Implementation Scope

Included behavior

• exactly one *STEP, *STATIC, small displacement/small rotation
• four-node S4/S4R parsing and one internal FESA-MITC4 identity
• stable source instance/label/type and four-node source ordering
• homogeneous isotropic E,nu and centered single-layer constant t
• deterministic positive-thickness nodal directors and right-handed frames
• six global nodal DOFs; 24-entry shell scatter
• physical membrane, bending, transverse shear with MITC edge-midpoint tying
• common 2x2x2 Gauss integration for S4 and S4R
• fixed k_d=10^-3 min(R+) drilling stabilization from the eight physical tangent-rotation diagonals only
• nodal BC and global CLOAD; aggregate director-parallel moment rejection
• deterministic global stiffness, constrained partition, factorize-before-load, effective RHS, solve, full residual/reaction
• physical-only shell recovery, energy/equilibrium/verification metrics
• exact mandatory HDF5 model/result schema and failure-atomic finalization
• direct HDF5-to-Abaqus-displacement comparison: U blocking, UR warning-only

Non-goals

• Abaqus S4/S4R algorithm equivalence
• B31 mapping, mixed B33/MITC4 model execution or common public element hierarchy
• *DLOAD, pressure, gravity, body/edge/follower load
• composite, offsets, variable thickness, explicit normal/orientation
• reduced integration, hourglass control, MITC4+
• nonlinear state, finite director update, nonlinear residual/tangent execution
• drilling physical strain/load/result/stress/energy, coefficient sweep or calibration
• NR-O03 smooth-angle and NR-O04 warp/distortion threshold sweeps
• extra shell benchmarks as a completion gate
• Abaqus execution or reference artifact mutation

4. Work Breakdown

Tasks are ordered by implementation dependency. Harness executes Steps 0-13 in strict order even when the minimal dependency set below is smaller.

task	depends on
TASK-00	none
TASK-01	TASK-00
TASK-02	TASK-01
TASK-03	TASK-02
TASK-04	TASK-03
TASK-05	TASK-04
TASK-06	TASK-00; executed after TASK-05
TASK-07	TASK-04, TASK-06
TASK-08	TASK-02, TASK-07
TASK-09	TASK-05, TASK-08
TASK-10	TASK-05, TASK-09
TASK-11	TASK-09, TASK-10
TASK-12	TASK-01, TASK-07, TASK-08, TASK-10, TASK-11
TASK-13	TASK-11, TASK-12
TASK-14	TASK-13
TASK-15	TASK-01, TASK-07, TASK-11
TASK-16	TASK-00 through TASK-15

TASK-00: shell-semantic-model

• Own only model semantic records and immutable Domain access.
• Candidate additions: Mitc4ShellDefinition, ShellSection, source type enum/value, internal formulation identity, four-node indices, material/section indices, node director/frame storage.
• Preserve current B33 records and stable source/internal identity; reject mixed models at mapping rather than designing a heterogeneous solver hierarchy.
• Tests: MITC4-MODEL-001, MITC4-MODEL-002.

TASK-01: shell-domain-mapping

• Extend AbaqusDomainMapper::map(const ParsedInput&); keep AbaqusInputReader syntax-only.
• Accept exact S4/S4R and single-layer SHELL SECTION grammar, resolve ELSET/material, identity wrappers and six-DOF BC/CLOAD.
• Fail closed with exact I/O diagnostic classes for connectivity, assignment, unsupported option/procedure/mixed model/distributed load.
• Tests: MITC4-MAP-001 through MITC4-MAP-004.

TASK-02: shell-director-geometry

• Add deterministic geometry preprocessing after instance expansion: element normal candidates, area-weighted nodal director, pairwise orientation validation and nodal frame tie-break.
• Validate center, eight stiffness points, four tying points and committed recovery points for finite bases, nonzero surface measure and positive finite Jacobian.
• Do not introduce calibrated angle, warp or distortion thresholds.
• Tests: MITC4-GEO-001 through MITC4-GEO-004.

TASK-03: mitc4-kinematics-constitutive

• Create concrete candidate Mitc4Shell without a public base hierarchy.
• Implement shape identities, local frames, T_p/T_d channel maps, direct membrane/bending terms, all four covariant MITC tying samples/interpolation, engineering-shear factors, C_ps/C_5/A/D/A_s and fixed point order.
• Keep all intermediate physical coordinates at 20 DOFs.
• Tests: MITC4-KIN-001 through MITC4-KIN-005.

TASK-04: mitc4-stiffness-drilling

• Form physical K20 with common 2x2x2 integration and embed by congruence.
• Build R+ only from the eight physical tangent-rotation diagonals, use exact k_d=10^-3 min(R+) and T_d^T(k_d I4)T_d; fail empty/nonfinite R+.
• Tests: MITC4-KERNEL-001 through MITC4-KERNEL-006.

TASK-05: mitc4-physical-recovery

• Add only the element-kernel physical recovery seam for generalized strain/resultant, bottom/middle/top stress and physical element energy.
• Prove pure numerical drill action contributes zero to every physical recovery value.
• Tests: MITC4-KERNEL-007, MITC4-PHYSREC-001.

TASK-06: shell-dof-scatter

• Retain six per-node full DOFs and add typed 24-entry shell scatter/pattern access; preserve existing 12-entry B33 behavior.
• Preserve stable full/free/constrained numbering and all-constrained 0x0 Kff.
• Tests: MITC4-DOF-001 through MITC4-DOF-003.

TASK-07: shell-sparse-assembly

• Dispatch shell topology to Mitc4Shell::globalStiffness().
• Emit 576 element-local COO entries with stable elementOrder/localOrder into worker-owned buffers; preserve canonical fixed reduction and diagonal slots.
• Tests: MITC4-ASM-001 through MITC4-ASM-003.

TASK-08: shell-load-validation

• Reuse global six-DOF LoadAssembler and existing constraint partition.
• Aggregate CLOAD deterministically before testing exact-zero or rho_M=abs(dot(d,M))/norm(M)<=1e-12; rejected moments never reach stabilization.
• Preserve force/moment units and factorization-before-load lifecycle.
• Tests: MITC4-LOAD-001 through MITC4-LOAD-004.

TASK-09: shell-analysis-state

• Add shell result rows to AnalysisState and result_records.hpp: four fixed midsurface locations, local frames, eight generalized strains/resultants, bottom/middle/top stress, physical energy, equilibrium and verification metrics.
• Preserve stable row order and expose candidate-owned containers only; perform no element calculation in this task.
• Tests: MITC4-STATE-001 through MITC4-STATE-003.

TASK-10: shell-result-recovery

• Recover full residual K*d-F for nodal reaction/equilibrium evidence but call the kernel physical-only recovery for shell quantities.
• Validate candidates fully before committing state; keep stable row order.
• Tests: MITC4-REC-001 through MITC4-REC-005.

TASK-11: shell-hdf5-output

• Extend Hdf5ResultsWriter behind the unchanged generic ResultsWriter::write boundary.
• Add exact schema paths/shapes/component attributes from the I/O contract without changing B33 dataset meaning.
• Reuse temporary write, finite/schema self-check, close/reopen and atomic replace.
• Tests: MITC4-H5-001 through MITC4-H5-004.

TASK-12: shell-linear-static-flow

• Route a shell Domain through the existing eight-hook Analysis::run() lifecycle.
• Preserve assemble/partition, factorize, load/effective RHS, substitute, reconstruct, full residual/recover, atomic write order and single factorization.
• Validate nonzero prescribed values, singular support and valid all-constrained solve.
• Tests: MITC4-FLOW-001 through MITC4-FLOW-004.

TASK-13: shell-reference-comparison

• Add a test-only MITC4 comparator rather than widening beam-specific assumptions.
• Consume exactly one declared input and displacement CSV per case; map instance, source node and six displacement components directly to HDF5.
• Precheck header/row set/duplicates/nonfinite/schema/identity before numeric work.
• Apply fixed absolute 1.0e-5 to every U/UR row without a scale-dependent decision term; U blocks, UR only emits deterministic warning; record all required metrics and worst row.
• Tests: MITC4-REF-001 through MITC4-REF-006.

TASK-14: shell-s4-end-to-end

• This is declared-case sub-work owned by TASK-13/Step 13's test-only reference module, not an independent production-module Step.
• Run the declared S4 deck through CLI, authoritative HDF5, schema checks and read-only comparator.
• Assert source type S4, internal FESA-MITC4 and U pass/UR report behavior.
• Tests: MITC4-E2E-S4-001, MITC4-E2E-S4-002.

TASK-15: shell-s4r-common-path-verification

• This is non-reference coverage distributed across the existing domain-mapping, sparse-assembly and HDF5 tests; Step 13 does not consume an S4R Abaqus artifact.
• Assert S4R selects the same FESA-MITC4 integration/kernel/assembly path as an otherwise identical S4 semantic fixture while preserving only source metadata.
• Tests: InpDomainMapping.MapsS4AndS4rThroughOneMitc4Identity, SparseAssembly.S4AndS4rSemanticFixturesAssembleIdenticalStiffness, and the existing shell HDF5 source-type metadata coverage.

TASK-16: mitc4-full-verification

• Run MSVC x64 Debug full build, CTest discovery, focused feature suites and full CTest.
• Audit warnings, deterministic repeat evidence, required HDF5 inventory, reference immutability and git diff scope.
• Produce only downstream implementation evidence; do not claim reference verification, physics sanity or release readiness.
• Tests/audits: MITC4-VERIFY-001 through MITC4-VERIFY-004.

5. TDD Test Plan

test id	initial RED assertion	minimal GREEN behavior	focused verification
MITC4-MODEL-001	four-node S4/S4R records/director/source identity do not exist	immutable shell records preserve source and internal identity	DomainModel.*
MITC4-MODEL-002	shell section/material/thickness ownership unavailable	one resolved centered homogeneous assignment per element	DomainModel.*
MITC4-MAP-001	valid S4/S4R and SHELL SECTION reject	both source types map to FESA-MITC4	InpDomainMapping.*
MITC4-MAP-002	duplicate/unresolved/conflicting section cases lack exact errors	exact assignment/material validation	InpDomainMapping.*
MITC4-MAP-003	excluded shell options/mixed models may be ignored	exact fail-closed diagnostics	InpDomainMapping.*
MITC4-MAP-004	second/nonstatic/NLGEOM/DLOAD cases lack shell boundary tests	exact procedure/load rejection; no-op output unchanged	InpDomainMapping.*
MITC4-GEO-001	planar/rotated/warped directors unavailable	deterministic unit director and right-handed frame	Mitc4Geometry.*
MITC4-GEO-002	incident orientation/tie-break is untested	stable area-weighted result across repeated order	Mitc4Geometry.*
MITC4-GEO-003	duplicate/bow-tie/zero/reversed/nonfinite geometry may pass	exact geometry failures	Mitc4Geometry.*
MITC4-GEO-004	required-point Jacobian inventory absent	every required point finite and positive	Mitc4Geometry.*
MITC4-KIN-001	shape/derivative identities unavailable	partition/unity/derivative identities	Mitc4ShellKinematics.*
MITC4-KIN-002	frame/T transforms unavailable	orthonormal/right-handed frames and channel selection	Mitc4ShellKinematics.*
MITC4-KIN-003	tying values/weights unavailable	four hand-computed covariant tying values	Mitc4ShellKinematics.*
MITC4-KIN-004	constitutive/section matrices unavailable	exact coefficients, symmetry, positivity, unit rescaling	Mitc4ShellConstitutive.*
MITC4-KIN-005	quadrature order not fixed	exact common 2x2x2 points/weights	Mitc4ShellKinematics.*
MITC4-KERNEL-001	no 24x24 shell stiffness	finite symmetric 24x24 stiffness	Mitc4ShellKernel.*
MITC4-KERNEL-002	energy congruence unavailable	20/24 virtual work and energy equal within 1e-12	Mitc4ShellKernel.*
MITC4-KERNEL-003	rigid/rank checks fail	six physical rigid modes, physical rank 14, stabilized rank 18	Mitc4ShellKernel.*
MITC4-KERNEL-004	deformation energy/patch fields unavailable	positive membrane/bending/shear/twist modes	Mitc4ShellPatch.*
MITC4-KERNEL-005	R+ membership/coefficient not implemented	exact rotational-only min and 1e-3 factor	Mitc4ShellDrilling.*
MITC4-KERNEL-006	empty R+ and pure drill behavior unspecified	deterministic failure; pure drill stabilized	Mitc4ShellDrilling.*
MITC4-KERNEL-007	drilling contaminates recovery/energy	physical recovery/energy exact zero for pure drill	Mitc4ShellDrilling.*
MITC4-PHYSREC-001	kernel recovery contract is not independently callable	exact physical strain/resultant/stress/energy for hand field	Mitc4ShellPhysicalRecovery.*
MITC4-DOF-001	shell scatter fixed at 12	stable 24-entry scatter in node/component order	DofManager.*
MITC4-DOF-002	shell pattern unavailable	sorted unique pattern with all diagonals	DofManager.*
MITC4-DOF-003	constraint roundtrip lacks shell-sized system	no/mixed/all constraints and nonzero values roundtrip	DofManager.*; EssentialConstraints.*
MITC4-ASM-001	assembler rejects four-node element	576 stable local contributions assemble	SparseAssembly.*
MITC4-ASM-002	thread/repetition may reorder	serial/TBB/repeated CSR bytes and values match	SparseAssembly.*
MITC4-ASM-003	S4/S4R could branch numerically	identical semantic fixtures produce identical K	SparseAssembly.*
MITC4-LOAD-001	shell force/moment fixture unavailable	six global components aggregate stably	LoadAssembly.*
MITC4-LOAD-002	director-parallel exact-zero branch untested	zero aggregate moment accepted	LoadAssembly.*
MITC4-LOAD-003	rho boundary/rejection untested	<=1e-12 accepted; >1e-12 exact diagnostic	LoadAssembly.*
MITC4-LOAD-004	rejected moment might enter drill channel	failure occurs before RHS/substitution	LoadAssembly.*
MITC4-STATE-001	AnalysisState has no shell row containers	exact shell row/component/location types are owned	AnalysisState.*
MITC4-STATE-002	physical energy/equilibrium/metrics are absent	finite candidate global evidence is stored	AnalysisState.*
MITC4-STATE-003	shell candidate rollback is unavailable	invalid candidate leaves prior state unchanged	AnalysisState.*
MITC4-REC-001	shell row types absent	four ordered location/frame/strain/resultant rows	ResultRecovery.*
MITC4-REC-002	bottom/middle/top stress absent	direct S11/S22/S12 recovery in fixed order	ResultRecovery.*
MITC4-REC-003	energy may include drilling	physical strain energy excludes stabilization	ResultRecovery.*
MITC4-REC-004	reaction/equilibrium semantics may diverge	full residual, force/moment balance, normalized metrics	ResultRecovery.*
MITC4-REC-005	invalid partial rows may commit	nonfinite/inventory failure preserves old state	ResultRecovery.*
MITC4-H5-001	shell metadata/model schema missing	exact metadata, elements, director/frame, material/section	Hdf5ResultsWriter.*
MITC4-H5-002	mandatory shell result paths missing	exact displacement/reaction/frame/strain/resultant/stress/global rows	Hdf5ResultsWriter.*
MITC4-H5-003	output request could filter or drilling paths appear	inventory unconditional; forbidden paths absent	Hdf5ResultsWriter.*
MITC4-H5-004	invalid shell candidate may replace final file	self-check failure preserves prior final	Hdf5ResultsWriter.*
MITC4-FLOW-001	shell cannot traverse Analysis lifecycle	exact hook order and one factorization	LinearStaticCli.*
MITC4-FLOW-002	prescribed shell RHS/reconstruction absent	Ff-Kfc*dc and full displacement correct	LinearStaticCli.*
MITC4-FLOW-003	singular/all-constrained behavior unproven	singular fails; 0x0 Kff succeeds	LinearStaticCli.*
MITC4-FLOW-004	failed output may commit state	candidate state/output commits only after validation	LinearStaticCli.*
MITC4-REF-001	six-column CSV header unsupported	exact MITC4 header maps instance/node/U/UR	Mitc4ReferenceComparison.*
MITC4-REF-002	invalid row inventory may be ignored	missing/extra/duplicate/nonfinite/schema mismatch fails first	Mitc4ReferenceComparison.*
MITC4-REF-003	tolerance could remain scale-dependent or clamp/row-normalize	exact fixed absolute 1.0e-5 for every U/UR row	Mitc4ReferenceComparison.*
MITC4-REF-004	UR may block verdict	U blocks; UR only warns	Mitc4ReferenceComparison.*
MITC4-REF-005	report metrics/order incomplete	row decisions, max, normalized, RMS, vector, worst row deterministic	Mitc4ReferenceComparison.*
MITC4-REF-006	comparator may require administrative files	only declared input/CSV/HDF5 required	Mitc4ReferenceComparison.*
MITC4-E2E-S4-001	S4 deck cannot produce valid shell HDF5	CLI succeeds with exact S4 metadata/schema	Mitc4S4Reference.*
MITC4-E2E-S4-002	S4 U comparison unavailable	all U rows pass; UR fully reported	Mitc4S4Reference.*
MITC4-VERIFY-001	feature tests not discoverable	all planned suites discovered/labeled	CTest JSON inventory
MITC4-VERIFY-002	warnings/regressions unknown	MSVC Debug full build passes /W4 /WX	full build
MITC4-VERIFY-003	nondeterminism unknown	repeated focused/full tests pass	full CTest
MITC4-VERIFY-004	artifact governance unknown	reference hashes/path and git diff unchanged	read-only audit

Numerical thresholds are fixed: frame/symmetry/transformation-energy <=1e-12; rigid action, linear residual and global equilibrium <=1e-10. Patch tests compare against independently hand-computed analytical fields and signs, not the production routine itself.

6. CMake/CTest Plan

Existing topology to preserve

• production library: fesa_solver
• CLI: fesa_cli
• unit: fesa_unit_tests
• integration: fesa_integration_tests
• reference: fesa_reference_tests
• aggregate: fesa_tests

No new executable target is required. New kernel/test/comparator source files are explicitly registered in existing source lists. Add linear-static-mitc4-shell as an additive CTest label without removing the B33 label. Because gtest_discover_tests() currently applies target-wide labels, focused Step verification uses exact suite regexes; label-based MITC4 filtering is enabled only if per-test labeling can be added without relabeling unrelated B33 tests.

Candidate registrations:

• src/fesa/CMakeLists.txt: candidate model/shell_geometry.cpp, elements/mitc4_shell.cpp and any separate shell recovery implementation.
• tests/CMakeLists.txt: candidate shell_geometry_test.cpp, mitc4_shell_test.cpp, optional focused shell recovery/HDF5 tests, and MITC4 reference comparator/test sources.
• Preserve existing runtime staging for MKL/TBB/HDF5 on all three test executables.

CTest discovery must show every suite named in Section 5 before implementation is considered verified.

7. Candidate Files and Ownership

All signatures in this section are candidates for the Implementation Agent to confirm against the approved contracts during the owning Step; they are not new approved APIs.

owner/module	candidate files	candidate interface/direction
model	include/fesa/model/model_types.hpp, include/fesa/model/domain.hpp, src/fesa/model/domain.cpp	separate shell records/accessors; no equation IDs
shell semantic geometry	candidate new include/fesa/model/shell_geometry.hpp, src/fesa/model/shell_geometry.cpp	director/frame and required-point geometry validation without parser/kernel dependency
Abaqus semantic map	include/fesa/io/abaqus/domain_mapper.hpp, src/fesa/io/abaqus/domain_mapper.cpp	keep map(const ParsedInput&) -> Result<Domain>
analysis view	include/fesa/analysis/analysis_model.hpp, src/fesa/analysis/analysis_model.cpp	non-owning active shell view only if record representation requires
shell kernel	new include/fesa/elements/mitc4_shell.hpp, src/fesa/elements/mitc4_shell.cpp	concrete create/stiffness/physical-recover API
DOF	include/fesa/fem/dof_manager.hpp, src/fesa/fem/dof_manager.cpp	typed array<size_t,24> shell scatter beside B33 scatter
sparse assembly	src/fesa/assembly/sparse_assembler.cpp	topology dispatch; unchanged public assemble signature
load	src/fesa/assembly/load_assembler.cpp only if aggregate director projection cannot live in semantic validation	reuse full six-DOF assembly
state/results	include/fesa/analysis/analysis_state.hpp, src/fesa/analysis/analysis_state.cpp, include/fesa/results/result_records.hpp	additive shell rows/global metrics
recovery	include/fesa/results/result_recovery.hpp, src/fesa/results/result_recovery.cpp or new shell-specific cpp	candidate-then-commit; physical/drill split
HDF5	src/fesa/io/hdf5/hdf5_results_writer.cpp	generic public writer unchanged
lifecycle	src/fesa/analysis/linear_static_analysis.cpp	preserve existing hook order
app	tests/integration/app/fesa_application_test.cpp; production app only if feature dispatch needs it	CLI syntax unchanged
reference tests	new tests/reference/mitc4_reference_comparison.hpp/.cpp and tests	test-only direct HDF5/CSV comparator
build graph	src/fesa/CMakeLists.txt, tests/CMakeLists.txt	explicit additive source/test registration

Candidate kernel seam:

class Mitc4Shell {
public:
    static Result<Mitc4Shell> create(
        std::array<const Node*, 4> nodes,
        std::array<Vector3, 4> initialDirectors,
        const ShellSection& section,
        const LinearElasticMaterial& material);

    [[nodiscard]] Matrix physicalLocalStiffness20() const;
    [[nodiscard]] Matrix globalStiffness24() const;
    [[nodiscard]] Result<ShellRecovery> recoverPhysical(
        const Vector& globalElementDisplacement24) const;
};

This candidate explicitly avoids returning drill energy/results and avoids a common public Element hierarchy. Exact value/reference ownership and math types are decided inside TASK-03 after compiling the first RED test.

8. Data Flow Contract

.inp bytes
  -> AbaqusInputReader (syntax/source locations only)
  -> AbaqusDomainMapper (approved semantics, S4/S4R provenance, section/material)
  -> geometry/director preprocessing
  -> immutable Domain
  -> non-owning AnalysisModel
  -> DofManager (6 DOF/node, 24-entry shell scatter, free/constrained maps)
  -> Mitc4Shell physical K20 + fixed drill embedding -> global K24
  -> worker-local COO -> stable SparseMatrix reduction
  -> Kff/Kfc/Kcf/Kcc partition -> Kff factorize
  -> aggregate CLOAD/director check -> Ff-Kfc*dc
  -> substitute -> full displacement
  -> full residual K*d-F
  -> physical-only shell recovery + global evidence
  -> validated candidate AnalysisState
  -> temporary results.h5 -> schema self-check -> atomic finalization

authoritative results.h5
  -> test-only MITC4 HDF5 projection
  -> exact source instance/node/component row-set precheck
  -> read-only declared Abaqus displacement CSV
  -> U blocking / UR warning-only deterministic report

Invariants:

• Domain outlives AnalysisModel; no Domain copying.
• Source labels/instances/types never become equation indices.
• S4/S4R source type is metadata; both call the same kernel/quadrature.
• full residual uses stabilized global K; shell strain/resultant/stress/physical energy use physical recovery only.
• HDF5 nodal/reaction is full residual; constraint mask decides reaction versus free residual evidence.
• result rows use fixed GP1..GP4 and BOTTOM/MIDDLE/TOP identity; no averaging or Abaqus integration-point relabeling.
• state/output mutation occurs only after complete validation.

9. Acceptance Traceability Matrix

The inclusive ranges below cover every must requirement 001 through 072 exactly once without gap or overlapping requirement range.

requirement range	owning tasks	test/evidence id	reference model id	acceptance
001	TASK-01, TASK-12	MAP-004, FLOW-001	N/A	one static step only; deterministic rejection otherwise
002-004	TASK-00, TASK-01, TASK-11, TASK-14, TASK-15	MODEL-001, MAP-001, H5-001, S4 E2E plus S4R common-path tests	shell-s4 for reference; S4R N/A	S4/S4R one kernel; distinct stable source identity
005	TASK-00, TASK-06, TASK-11	MODEL-001, DOF-001/003, H5-001/002	N/A	exact six-component order; no distributed equation ownership
006-010	TASK-00, TASK-01	MODEL-002, MAP-002/003	N/A	finite E,nu,t; one assignment; unsupported meanings fail
011-016	TASK-02, TASK-03	GEO-001..004, KIN-002	N/A	deterministic unit directors; exact geometry predicates
017-020	TASK-01, TASK-08	MAP-004, LOAD-001..004	N/A	six-DOF BC/CLOAD; drilling/distributed load fails
021-023	TASK-01	MAP-001..004 and existing no-op regression	N/A	approved parser subset/identity wrappers/no-op policy
024-030	TASK-00, TASK-06, TASK-07, TASK-09, TASK-10, TASK-12, TASK-16	MODEL, DOF, ASM, STATE, REC, FLOW, VERIFY suites	N/A	ownership, deterministic assembly, lifecycle, residual reaction
031-038	TASK-03, TASK-04, TASK-05, TASK-07, TASK-10	KIN, KERNEL, PHYSREC, ASM-003, REC-003	N/A	physical 5-DOF embedding, exact drilling, same quadrature, invariants
039-048	TASK-09, TASK-10, TASK-11, TASK-12	STATE-001..003, REC-001..005, H5-001..004, FLOW-004	N/A	mandatory finite schema/results and atomic commit
049	TASK-00 through TASK-16	every production Task records RED/failure/GREEN/focused/full VERIFY; VERIFY-001..003	shell-s4 where reference-dependent	TDD evidence, related C++ tests, MSVC Debug no-warning build and full CTest
050	TASK-02 through TASK-05, TASK-07	GEO-001/002, KIN-001/002, KERNEL-001..004, ASM-002	N/A	frames, Jacobian, symmetry, transformation, six modes, positivity and repeatability
051	TASK-02 through TASK-05, TASK-10, TASK-12	GEO-001, KERNEL-001..003, REC-004, FLOW-002	N/A	exact normalized 1e-12 and 1e-10 algebraic thresholds
052	TASK-03 through TASK-05, TASK-10	KIN-003/004, KERNEL-004, PHYSREC-001, REC-001/002	N/A	independent membrane, bending, shear, twist fields and recovery signs/order
053	TASK-04, TASK-05, TASK-14	KERNEL-001..007, PHYSREC-001, declared S4 E2E suite	shell-s4	formulation invariants/patches and the S4 reference case pass
054	TASK-02	GEO-001..004	N/A	exact valid/rejected geometry inventory; no NR-O03/O04
055	TASK-16	VERIFY scope audit	N/A	extra benchmark portfolio is explicitly nonblocking and absent from completion gate
056	TASK-04, TASK-05, TASK-07, TASK-10	KERNEL-005..007, PHYSREC-001, ASM-001/002, REC-003	N/A	exact fixed drilling, deterministic rank/action and physical-output exclusion
057	TASK-10, TASK-12, downstream Physics Evaluation	REC-002..004, FLOW-002, later physics report	shell-s4	implementation exposes equilibrium/sign/energy evidence; physical plausibility verdict is downstream
058-060	TASK-13, TASK-14	REF-003 and S4 E2E comparison	shell-s4	exact fixed absolute U tolerance 1.0e-5 without scale/clamp
061-062	TASK-13, TASK-14	REF-004/005 and S4 E2E test	shell-s4	UR fixed absolute 1.0e-5, deterministic warning only
063-064	TASK-13	REF-001/002/005	shell-s4	schema/row failure before numeric comparison; full metrics
065-068	TASK-13, TASK-14, TASK-15	REF-001/002/006, S4 case precheck and S4R non-consumption/common-path evidence	shell-s4	exact two S4 paths; unique finite mapped rows; no S4R artifact consumption
069-071	TASK-14, TASK-15	S4 E2E suite and S4R common-path tests	shell-s4	S4 U blocks/UR warns; S4R mapping has no Abaqus equality gate
072	TASK-13 through TASK-16	REF-006, VERIFY-004 and git/hash audit	shell-s4	no reference solver run or artifact mutation

10. Validation Commands

These commands are the environment-resolved Windows x64 Debug baseline. Planning does not execute build/tests. Each approved Harness Step first runs this literal path precheck and then repeats the relevant build/test subset after its RED and GREEN changes.

$requiredBuildPaths = @(
  "C:/git/googletest",
  "C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl",
  "C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb",
  "C:/Program Files/HDF_Group/HDF5/2.1.1/cmake"
)
foreach ($requiredBuildPath in $requiredBuildPaths) {
  if (-not (Test-Path -LiteralPath $requiredBuildPath)) {
    throw "Required configured build path is absent: $requiredBuildPath"
  }
}

cmake --fresh -S . -B .harness/build -G "Visual Studio 18 2026" -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"

cmake --build .harness/build --config Debug
ctest --test-dir .harness/build -C Debug --show-only=json-v1
ctest --test-dir .harness/build -C Debug --output-on-failure

Focused commands:

cmake --build .harness/build --config Debug --target fesa_unit_tests
ctest --test-dir .harness/build -C Debug -R "DomainModel|InpDomainMapping|Mitc4Geometry|Mitc4Shell|DofManager|EssentialConstraints|SparseAssembly|LoadAssembly|ResultRecovery|Hdf5ResultsWriter" --output-on-failure

cmake --build .harness/build --config Debug --target fesa_integration_tests
ctest --test-dir .harness/build -C Debug -R "LinearStaticCli|Mitc4ShellCli" --output-on-failure

cmake --build .harness/build --config Debug --target fesa_reference_tests
ctest --test-dir .harness/build -C Debug -R "Mitc4ReferenceComparison|Mitc4S4Reference" --output-on-failure

Planning-document verification:

git diff --check -- docs/linear-static-mitc4-shell/implementation-plan.md
git status --short
git diff --name-only

Reference immutability audit is read-only and fails on any mismatch:

$expectedReferenceHashes = [ordered]@{
  "reference/shell/shell.inp" = "4005851E1AB22FD3A16AC17A8D5DA3E051233F69F37419079F3553AD134ECFCF"
  "reference/shell/shell displacements.csv" = "C81D94E0B4A849F87AA0F79C83A79B94D5661AC79E44ED826919AB432C87746B"
}
foreach ($referencePath in $expectedReferenceHashes.Keys) {
  $actualHash = (Get-FileHash -Algorithm SHA256 -LiteralPath $referencePath).Hash
  if ($actualHash -ne $expectedReferenceHashes[$referencePath]) {
    throw "Reference artifact changed: $referencePath"
  }
}

Do not invoke scripts/hooks/*.py manually. Harness runner installs/uses the configured PreToolUse and Stop hooks automatically. Do not invoke scripts/execute.py until the user separately authorizes execution.

11. Risks and Downstream Handoff

risk	controlling plan decision	stop condition
beam-only ModelDefinition leaks through every layer	add shell semantic records first; preserve B33 access	stop if a Step requires unapproved mixed-model hierarchy
fixed 12-DOF scatter breaks B33	typed beam/shell scatter paths and B33 regressions	stop on any B33 focused/full regression
drilling contaminates physical output	separate physical recovery from stabilized full K	stop if pure-drill recovery/energy is nonzero
director/frame sign nondeterminism	source-order, area-weight and tie-break tests	stop on repeat/order/thread difference
S4R accidentally selects reduced integration	one internal formulation and ASM/E2E equality tests	stop if source type reaches quadrature dispatch
full residual confused with element resultants	keep reaction from Kd-F, physical recovery separately	stop if reaction is reconstructed from shell resultants
writer expansion changes B33 schema	additive shell branches plus full B33 CTest	stop on B33 schema regression
comparator inherits B33 four-file/Frame assumptions	dedicated test-only MITC4 comparator	stop if administrative files become required
reference artifacts staged by Harness	clean isolated worktree, hash/diff audit	stop immediately on any reference path change
future nonlinear equations enter production	scope and code review prohibition	stop if nonlinear state/tangent is allocated or called

Implementation Agent

• Read the approved implementation plan, docs/HARNESS.md and docs/HARNESS_WORKFLOW.md before every Step.
• Execute only the Harness-selected pending Step and use the repository hooks/scripts through the documented runner lifecycle.
• Never choose the next Step, edit executor-owned timestamps/statuses, batch multiple Steps, or implement outside the Step's file ownership.
• Record the RED command and observed failure before GREEN.

Build/Test Executor Agent

• Use Section 10 exact CMake/MSVC/CTest baseline after implementation Steps finish.
• Report new warnings, discovery gaps and exact failing test names without changing upstream contracts.

Correction Agent

• Apply only minimal failure-driven corrections inside approved file ownership.
• Do not reinterpret MITC4 mathematics, I/O schema or tolerance.

Reference Verification Agent

• Consume authoritative HDF5 and declared read-only CSV directly.
• Create the separate reference-verification report; only U affects pass/fail and every UR warning remains visible.

Physics Evaluation and Release Agents

• Physics evaluates equilibrium, directions, symmetry, energy and result signs after reference verification.
• Release readiness remains blocked until implementation, build/test, reference and physics gates all provide evidence.

12. Harness Step Draft

This approved draft is materialized under phases/linear-static-mitc4-shell/. Every Step is zero-based, kebab-case and closes RED/GREEN/VERIFY before the Executor advances it. TASK-14 is declared-case sub-work inside Step 13's single test-only reference module; TASK-15 is non-reference coverage already owned by Steps 1/7/11; TASK-16 is downstream Build/Test Executor evidence, not an Implementation Agent phase Step. During materialization, the exact required-reading paths, configure block, focused command and full VERIFY block shown here are copied verbatim into every stepN.md; a materialized Step never refers back to this draft or to an external conversation.

Every materialized Step copies this mandatory reading inventory before its Step-specific paths:

• AGENTS.md
• docs/PRD.md, docs/ARCHITECTURE.md, docs/ADR.md
• docs/HARNESS.md, docs/HARNESS_WORKFLOW.md
• this approved implementation plan and all source contracts listed in Metadata
• .codex/hooks.json
• phases/index.json, phases/linear-static-mitc4-shell/index.json and its own phases/linear-static-mitc4-shell/stepN.md
• every path created/modified by prerequisite Steps and their step output/status

If any mandatory or Step-specific path is missing or contradicts the approved plan, the Implementation Agent records blocked for the Executor-selected current Step and stops; it does not invent the missing contract.

Step-specific path ledger copied into the corresponding materialized Step:

Step	exact source/prerequisite paths
0	include/fesa/model/model_types.hpp; include/fesa/model/domain.hpp; src/fesa/model/domain.cpp; tests/unit/model/model_types_test.cpp; tests/unit/model/domain_test.cpp
1	Step 0 paths; include/fesa/io/abaqus/domain_mapper.hpp; src/fesa/io/abaqus/domain_mapper.cpp; tests/unit/io/abaqus/domain_mapper_test.cpp
2	Step 0-1 paths; candidate new include/fesa/model/shell_geometry.hpp; src/fesa/model/shell_geometry.cpp; tests/unit/model/shell_geometry_test.cpp; src/fesa/CMakeLists.txt; tests/CMakeLists.txt
3	Step 2 paths; candidate new include/fesa/elements/mitc4_shell.hpp; src/fesa/elements/mitc4_shell.cpp; tests/unit/elements/mitc4_shell_test.cpp; src/fesa/CMakeLists.txt; tests/CMakeLists.txt
4	Step 3 MITC4 kernel/header/test paths
5	Step 3-4 MITC4 kernel/header/test paths
6	Step 0 paths; include/fesa/fem/dof_manager.hpp; src/fesa/fem/dof_manager.cpp; tests/unit/fem/dof_manager_test.cpp; tests/unit/constraints/essential_constraints_test.cpp
7	Steps 4/6 paths; include/fesa/assembly/sparse_assembler.hpp; src/fesa/assembly/sparse_assembler.cpp; tests/unit/assembly/sparse_assembler_test.cpp
8	Steps 2/7 paths; include/fesa/assembly/load_assembler.hpp; src/fesa/assembly/load_assembler.cpp; tests/unit/assembly/load_assembler_test.cpp
9	Step 5 paths; include/fesa/results/result_records.hpp; include/fesa/analysis/analysis_state.hpp; src/fesa/analysis/analysis_state.cpp; tests/unit/results/result_records_test.cpp
10	Steps 5/9 paths; include/fesa/results/result_recovery.hpp; src/fesa/results/result_recovery.cpp; tests/unit/results/result_recovery_test.cpp
11	Steps 9/10 paths; include/fesa/io/hdf5/hdf5_results_writer.hpp; src/fesa/io/hdf5/hdf5_results_writer.cpp; tests/unit/io/hdf5/hdf5_results_writer_test.cpp
12	Steps 7-11 paths; include/fesa/analysis/linear_static_analysis.hpp; src/fesa/analysis/linear_static_analysis.cpp; tests/integration/analysis/linear_static_analysis_test.cpp; tests/integration/app/fesa_application_test.cpp
13	Steps 11/12 paths; candidate new tests/reference/mitc4_reference_comparison.hpp, tests/reference/mitc4_reference_comparison.cpp, tests/reference/mitc4_reference_comparison_test.cpp, tests/reference/mitc4_reference_cases_test.cpp; tests/CMakeLists.txt; the two exact read-only S4 reference paths in Section 2

The configure command copied before each Step's RED build is:

$requiredBuildPaths = @(
  "C:/git/googletest",
  "C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl",
  "C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb",
  "C:/Program Files/HDF_Group/HDF5/2.1.1/cmake"
)
foreach ($requiredBuildPath in $requiredBuildPaths) {
  if (-not (Test-Path -LiteralPath $requiredBuildPath)) {
    throw "Required configured build path is absent: $requiredBuildPath"
  }
}

cmake --fresh -S . -B .harness/build -G "Visual Studio 18 2026" -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"

The full VERIFY block copied at the end of every Step is:

cmake --build .harness/build --config Debug
ctest --test-dir .harness/build -C Debug --show-only=json-v1
ctest --test-dir .harness/build -C Debug --output-on-failure

Step 0 — shell-semantic-model

• Required reading: requirements 002-016/024, I/O Sections 3/5, architecture model ownership, current model_types.hpp/domain.* and their tests.
• Prerequisite: approved plan only; no production dependency on a prior Step.
• RED: add MODEL-001/002 tests and CMake registration if needed; run: cmake --build .harness/build --config Debug --target fesa_unit_tests then ctest --test-dir .harness/build -C Debug -R "DomainModel" --output-on-failure. Record the missing shell type/accessor failure. Unexpected pass is a stop.
• GREEN: minimally add shell semantic records/Domain const access; no parser/kernel.
• VERIFY: rerun the focused commands and common full VERIFY.
• Prohibitions: no equation IDs, element hierarchy, mixed-model execution, parser edits.

Step 1 — shell-domain-mapping

• Required reading: Step 0 outputs, requirements 001-010/017-023, I/O Sections 1-3/8-9, current domain_mapper.* and parser/model tests.
• Prerequisite: Step 0 completed.
• RED: add MAP-001..004; build fesa_unit_tests and run ctest --test-dir .harness/build -C Debug -R "InpDomainMapping" --output-on-failure. Record valid S4/S4R rejection and exact negative diagnostic failures.
• GREEN: minimally extend semantic mapping; keep input_reader syntax-only.
• VERIFY: focused parser/model tests, then common full VERIFY.
• Prohibitions: no element math, no silent unsupported keyword, no reference edits.

Step 2 — shell-director-geometry

• Required reading: requirements 011-016, formulation Sections 4/9/17, Numerical Review 5.2/5.5/6.1, I/O 3.3/9, completed semantic model/mapping.
• Prerequisite: Step 1 completed.
• RED: add GEO-001..004; build unit target and run ctest --test-dir .harness/build -C Debug -R "Mitc4Geometry" --output-on-failure.
• GREEN: implement deterministic director/frame and exact geometry inventory validation.
• VERIFY: focused geometry/mapping tests, then common full VERIFY.
• Prohibitions: no calibrated angle/warp/distortion threshold; no NR-O03/O04.

Step 3 — mitc4-kinematics-constitutive

• Required reading: formulation Sections 3-11/17, Numerical Review 5.1-5.6/6.1, current math adapters and Euler kernel style.
• Prerequisite: Step 2 completed.
• RED: add KIN-001..005 in new mitc4_shell_test.cpp, register it, build unit target, run ctest --test-dir .harness/build -C Debug -R "Mitc4ShellKinematics|Mitc4ShellConstitutive" --output-on-failure.
• GREEN: minimally add concrete shell kernel kinematics/constitutive seams; no global assembly or drilling.
• VERIFY: focused kernel tests, then common full VERIFY.
• Prohibitions: no public base hierarchy, no S4R branch, no nonlinear tangent code.

Step 4 — mitc4-stiffness-drilling

• Required reading: formulation Sections 10-14/17, requirements 031-038/050-056, Numerical Review 5.7/6.1-6.2, completed Step 3 kernel.
• Prerequisite: Step 3 completed.
• RED: add KERNEL-001..006; build unit target and run ctest --test-dir .harness/build -C Debug -R "Mitc4ShellKernel|Mitc4ShellPatch|Mitc4ShellDrilling" --output-on-failure.
• GREEN: implement K20, 20-to-24 congruence and exact fixed drilling only.
• VERIFY: focused kernel suite, then common full VERIFY.
• Prohibitions: translations in R+, coefficient sweep, recovery/result output, future nonlinear.

Step 5 — mitc4-physical-recovery

• Required reading: formulation Sections 14/16, requirements 035/042-046/052/056, I/O result component/location order, completed Step 4 kernel.
• Prerequisite: Step 4 completed.
• RED: add KERNEL-007 and PHYSREC-001; build unit target and run ctest --test-dir .harness/build -C Debug -R "Mitc4ShellDrilling|Mitc4ShellPhysicalRecovery" --output-on-failure.
• GREEN: minimally add kernel-local physical recovery and physical energy API only.
• VERIFY: focused physical recovery/drilling tests, then common full VERIFY.
• Prohibitions: no AnalysisState/global result rows, no drilling contribution or HDF5.

Step 6 — shell-dof-scatter

• Required reading: requirements 005/025, architecture DofManager ownership, current dof_manager.* and constraint tests, completed shell model.
• Prerequisite: Step 5 completed.
• RED: add DOF-001..003; build unit target and run ctest --test-dir .harness/build -C Debug -R "DofManager|EssentialConstraints" --output-on-failure.
• GREEN: minimally add typed 24-entry scatter/pattern while preserving 12-entry B33.
• VERIFY: focused DOF/constraint tests, then common full VERIFY.
• Prohibitions: no equation IDs in model, no constraint/load ownership move.

Step 7 — shell-sparse-assembly

• Required reading: requirements 027/030/037, architecture deterministic COO rule, current sparse_assembler.cpp/sparse_matrix.cpp tests, completed kernel/scatter.
• Prerequisite: Step 6 completed.
• RED: add ASM-001..003; build unit target and run ctest --test-dir .harness/build -C Debug -R "SparseAssembly" --output-on-failure.
• GREEN: minimally dispatch shell and emit stable 576-entry local buffers.
• VERIFY: focused assembly tests, then common full VERIFY.
• Prohibitions: no worker global CSR mutation, unordered reduction or S4R integration branch.

Step 8 — shell-load-validation

• Required reading: requirements 017-020/028, formulation 8/13, I/O 4.2-4.3, current load_assembler.* and constraint lifecycle.
• Prerequisite: Step 7 completed.
• RED: add LOAD-001..004; build unit target and run ctest --test-dir .harness/build -C Debug -R "LoadAssembly|EssentialConstraints" --output-on-failure.
• GREEN: minimally add aggregate nodal moment/director validation and reuse full DOF load.
• VERIFY: focused load/constraint tests, then common full VERIFY.
• Prohibitions: no distributed/equivalent/follower load; no drill load channel.

Step 9 — shell-analysis-state

• Required reading: requirements 026/041-046/048, I/O 6.3-6.5, current analysis_state.*/result_records.hpp and completed physical recovery types.
• Prerequisite: Step 8 completed.
• RED: add STATE-001..003; build unit target and run ctest --test-dir .harness/build -C Debug -R "AnalysisState" --output-on-failure.
• GREEN: minimally add candidate-owned shell row/global evidence containers and validation/commit mechanics.
• VERIFY: focused AnalysisState tests, then common full VERIFY.
• Prohibitions: no element calculation, ResultRecovery orchestration or HDF5 writing.

Step 10 — shell-result-recovery

• Required reading: requirements 029/035/041-046/048, formulation 14/16, I/O 6.3-6.5, current result_recovery.* and completed Steps 5/9.
• Prerequisite: Step 9 completed.
• RED: add REC-001..005; build unit target and run ctest --test-dir .harness/build -C Debug -R "ResultRecovery" --output-on-failure.
• GREEN: minimally orchestrate full-residual evidence and physical shell recovery into a fully validated candidate, then commit it.
• VERIFY: focused recovery tests, then common full VERIFY.
• Prohibitions: no new result record type, location averaging, drill recovery or writer edit.

Step 11 — shell-hdf5-output

• Required reading: requirements 039-048, I/O Section 6 exact schema, ADR atomic output, current HDF5 writer/self-check tests, completed recovery records.
• Prerequisite: Step 10 completed.
• RED: add H5-001..004; build unit target and run ctest --test-dir .harness/build -C Debug -R "Hdf5ResultsWriter" --output-on-failure.
• GREEN: add exact additive shell schema behind unchanged ResultsWriter boundary.
• VERIFY: focused HDF5 tests, then common full VERIFY.
• Prohibitions: no B33 schema reinterpretation, CSV solver output, partial final file.

Step 12 — shell-linear-static-flow

• Required reading: requirements 024-030, architecture eight-hook lifecycle, I/O CLI contract, current linear_static_analysis.*/application integration tests.
• Prerequisite: Step 11 completed.
• RED: add FLOW-001..004; build integration target and run ctest --test-dir .harness/build -C Debug -R "LinearStaticCli|Mitc4ShellCli" --output-on-failure.
• GREEN: minimally route shell through existing lifecycle; preserve one factorization.
• VERIFY: focused integration tests, then common full VERIFY.
• Prohibitions: no analysis lifecycle reorder, no 0x0 singular conversion, no early state commit.

Step 13 — shell-reference-comparison

• Required reading: requirements 058-072, I/O Section 7, Reference Model contract, the sole declared S4 paths and hashes, and current B33 comparator only as reusable identity/report precedent.
• Scope ownership: this one test-only reference module owns TASK-13 comparator behavior plus TASK-14 declared-case tests; it owns no solver production module.
• Prerequisite: Step 12 completed and valid MITC4 HDF5 fixture.
• RED: update REF-003 first so the existing scale-dependent comparator fails against literal fixed-boundary cases around 1.0e-5; build the reference target and run ctest --test-dir .harness/build -C Debug -R "Mitc4ReferenceComparison|Mitc4S4Reference" --output-on-failure. Record the expected old-tolerance assertion failure.
• GREEN: minimally replace only the MITC4 comparator decision value with fixed absolute 1.0e-5; keep reference scale as diagnostic report data only.
• If a declared case exposes a production defect outside this reference-test module, stop the Step and route a focused correction to the owning prior module; do not patch unrelated production layers inside this Step.
• VERIFY: focused comparator and the declared S4 tests, then common full VERIFY.
• Prohibitions: no reference artifact writes/Abaqus run, no metadata/README gate, no UR blocking, no B33 comparator change, and no scale/clamp substitution for fixed 1.0e-5.

After explicit approval, planning may create only:

• phases/index.json with task status pending and no creation timestamp;
• phases/linear-static-mitc4-shell/index.json with Steps 0-13 initially pending and no executor-owned timestamps;
• phases/linear-static-mitc4-shell/stepN.md containing the approved self-contained directions.

Approval does not authorize python scripts/execute.py linear-static-mitc4-shell or --push.

13. Open Issues

id	item	blocking now	resolution owner
OI-001	Section 12 multi-Step Harness draft was explicitly approved on 2026-08-12 and materialized.	resolved	user
OI-002	Candidate shell semantic representation and exact C++ value/reference types are not public API decisions.	no	owning RED test in Steps 0/3
OI-003	Per-test MITC4 CTest label can be added without relabeling B33 tests인지 확인한다. Exact suite regex remains sufficient.	no	Step 0 and downstream TASK-14 CMake verification

No mathematical, I/O, reference-inventory or tolerance decision remains open for implementation planning. The user separately authorized implementation and Harness execution on 2026-08-12; the Executor still owns branch, Step selection, timestamps, commits and advancement.