FESADev/docs/nonlinear-static-newton-raphson/requirements.md

Nonlinear Static Newton–Raphson 요구조건

1. Metadata

• feature_id: nonlinear-static-newton-raphson
• title: Nonlinear Static Analysis Using Newton–Raphson
• status: approved
• owner_agent: requirement-agent
• date: 2026-08-22
• approved_by: user
• approval_date: 2026-08-23
• authoritative_scope: materially linear, geometrically nonlinear S4/S4R -> FESA-MITC4
• independence: FESA는 독립 solver이며 Abaqus 또는 Midas의 내부 알고리즘 동등성을 주장하지 않는다.
• unit_policy: .inp 단위계를 추론하거나 변환하지 않고 사용자가 일관되게 제공한 단위계를 보존한다.

Parent needs: NEED-NSNR-001 nonlinear procedure, NEED-NSNR-002 physics/numerical correctness, NEED-NSNR-003 state/output integrity, NEED-NSNR-004 independent verification.

2. Purpose and Expected Behavior

FESA는 하나의 지원 nonlinear static step을 scalar load factor로 증가시키며 Full Newton–Raphson으로 각 증분의 평형을 구한다. 수렴한 증분만 atomically commit하고 authoritative accepted result로 기록한다. 기존 linear-static physics와 결과 의미는 보존하되 repository-wide derived output naming은 이 기능과 함께 적용할 승인 방향이다.

3. In Scope

• Abaqus source S4, S4R의 FESA-MITC4 mapping과 homogeneous isotropic linear elasticity
• fixed-initial-reference Total Lagrangian geometric nonlinearity와 finite rotational state
• same-trial residual/algorithmically consistent tangent, fresh factorization/solve의 Full Newton
• fixed scalar load-factor increments, common proportional load/BC path, fixed-global dead *CLOAD
• factor-1 absolute prescribed *BOUNDARY targets와 four-value nonlinear *STATIC
• four-channel residual/correction convergence, maximum 100 iterations, no line search
• separate trial state, atomic commit/rollback, accepted-frame HDF5와 per-iteration text log
• deterministic assembly, iteration, frame, result, diagnostic order와 stored-reference verification

4. Out Of Scope

• material nonlinearity, nonlinear material history, combined material/geometric nonlinearity
• Updated Lagrangian, corotational procedure, multiple or mixed nonlinear steps, cross-step propagation
• follower load, non-proportional path, controlled-displacement, arc-length/path-following
• modified/adaptive Newton, tangent reuse, line search, damping, automatic growth/cutback/retry
• energy/work convergence, trial-state HDF5 history, direct reference-solver execution
• Abaqus/Midas formulation, stabilization, state update 또는 결과 절차의 내부 동등성

5. Analysis Definition

item	approved meaning
analysis	exactly one nonlinear static step from a no-prior-history baseline
elements	S4, S4R source types map to materially linear FESA-MITC4
DOFs	global [UX, UY, UZ, URX, URY, URZ]; rotational correction is dimensionless
kinematics	Total Lagrangian relative to one fixed initial configuration
rotation state	committed orthonormal right-handed triad Q; director is its third axis; separate trial triad/director; multiplicative finite-rotation update
material	homogeneous isotropic linear elasticity; no nonlinear material state
control	one dimensionless scalar load factor with fixed increments and final shortening to factor 1
Newton	same-trial residual and consistent tangent, fresh factorization and correction solve every iteration
convergence	translational-force residual, rotational-moment residual, translational correction, rotational correction; all four must pass with <=
loads/BCs	fixed-global dead *CLOAD; factor-1 absolute *BOUNDARY targets on one proportional path
state	candidate/trial remains separate; complete converged increment commits atomically
coordinates/units	nodal values are global unless an approved element-local quantity states otherwise; user-consistent units without inference/conversion

Exact Total Lagrangian shell equations, strain/stress measures, rotation map details, drilling treatment and consistent derivatives belong to Research/Formulation and Numerical Review without changing this approved scope.

6. Input Requirements

• Nonlinear execution requires exactly one supported nonlinear static source step and one semantic step.
• Supported first-release meanings are limited to the approved MITC4 material/section, nonlinear *STATIC, *CLOAD, and *BOUNDARY subset.
• Nonlinear *STATIC has four positive finite values: first is the fixed increment, second represents endpoint 1 exactly, and third/fourth are accepted for compatibility but unused by stepping.
• Nonzero prescribed *BOUNDARY values are factor-1 absolute global-DOF targets; approved *CLOAD components are fixed-global dead forces or moments.
• Unsupported, ambiguous, missing, nonfinite, or out-of-scope meanings fail closed rather than falling back to linear or alternate nonlinear behavior.

7. Output Requirements

• Successfully committed increments map one-to-one to authoritative accepted HDF5 frames in load-factor order and include the factor-1 frame; trial history is not authoritative output.
• <stem>_results.h5 is completed as a sibling candidate and replaces the final only after success; failure preserves a prior valid final.
• <stem>_log.txt is replaced/truncated at invocation start and remains the current-run live audit after controlled success or failure.
• Every entered Newton iteration has one deterministic diagnostic-only text summary; exact representation and low-level I/O mechanics belong to I/O Definition.
• Every analysis procedure uses input-directory <stem>_results.h5 and <stem>_log.txt; every invocation containing literal --output treats it as unrecognized and fails with exit code 2 before input parsing, Analysis, result-candidate, log, or output creation, with no compatibility alias or deprecation window. Result and log lifecycles are independent, not a cross-file all-or-nothing commit.
• Exact HDF5 paths/shapes, factor-0 projection, triad projection, compression/chunking and path/collision conventions belong to I/O Definition.

8. Requirement Records

- id: FESA-REQ-NSNR-001
  statement: "The FESA solver shall execute nonlinear static analysis through a separate procedure only when exactly one supported nonlinear source step maps to exactly one semantic step from a no-prior-history baseline."
  category: functional
  rationale: "Procedure cardinality and lifecycle must be unambiguous."
  source: user
  priority: must
  verification_method: test
  acceptance_criteria: "One valid step selects one nonlinear procedure; zero, multiple, mixed, or ambiguous nonlinear steps fail before an attempted nonlinear increment, while unselected approved linear analysis retains its established behavior."
  tolerance: "Exact source/semantic cardinality and procedure identity."
  trace_to: {parent_need: "NEED-NSNR-001", downstream_agents: ["I/O Definition Agent", "Implementation Planning Agent"]}
  status: approved
- id: FESA-REQ-NSNR-003
  statement: "The FESA solver shall support only materially linear, geometrically nonlinear FESA-MITC4 for source types S4 and S4R in the first release."
  category: physics
  rationale: "The approved release is geometric-only and must not create nonlinear material state."
  source: user
  priority: must
  verification_method: test
  acceptance_criteria: "Supported S4/S4R cases use homogeneous isotropic linear elasticity and MITC4; material-nonlinear or combined-nonlinearity input fails closed."
  tolerance: "Exact supported element/material inventory."
  trace_to: {parent_need: "NEED-NSNR-002", downstream_agents: ["Research Agent", "Formulation Agent", "Numerical Review Agent"]}
  status: approved
- id: FESA-REQ-NSNR-041
  statement: "The FESA solver shall use Total Lagrangian kinematics relative to one fixed initial reference configuration."
  category: physics
  rationale: "The formulation reference must not change across increments."
  source: user
  priority: must
  verification_method: analysis
  acceptance_criteria: "Every increment and accepted state retains the same initial-reference identity; current geometry is only a derived observable and never re-bases the formulation."
  tolerance: "Reference identity exact; numerical kinematic tolerances are owned by Numerical Review."
  trace_to: {parent_need: "NEED-NSNR-002", downstream_agents: ["Research Agent", "Formulation Agent", "Numerical Review Agent"]}
  status: approved
- id: FESA-REQ-NSNR-074
  statement: "The FESA solver shall retain global DOFs [UX, UY, UZ, URX, URY, URZ], use a dimensionless incremental rotation correction, and maintain separate trial and committed finite-rotation triad/director states."
  category: physics
  rationale: "Large rotations require an objective state distinct from failed candidates."
  source: user
  priority: must
  verification_method: analysis
  acceptance_criteria: "Committed Q is orthonormal and right-handed, its third axis is the director, candidate updates are multiplicative, successful commit transfers the complete state, and failure preserves the prior committed state."
  tolerance: "State identity exact; Q invariants use Numerical Review-approved tolerances."
  trace_to: {parent_need: "NEED-NSNR-002, NEED-NSNR-003", downstream_agents: ["Research Agent", "Formulation Agent", "Numerical Review Agent"]}
  status: approved
- id: FESA-REQ-NSNR-006
  statement: "The FESA solver shall perform Full Newton iterations using the same current-trial residual and algorithmically consistent tangent, followed by a fresh tangent factorization and correction solve."
  category: numerical
  rationale: "Residual, tangent, factorization, and correction must describe one trial state."
  source: user
  priority: must
  verification_method: test
  acceptance_criteria: "Each entered iteration records one trial identity shared by residual and tangent, factorizes that tangent after evaluation, and solves its correction with that fresh factorization before convergence or update."
  tolerance: "Trial/factorization identity and event order exact."
  trace_to: {parent_need: "NEED-NSNR-002", downstream_agents: ["Formulation Agent", "Numerical Review Agent", "Implementation Planning Agent"]}
  status: approved
- id: FESA-REQ-NSNR-007
  statement: "The FESA solver shall accept an increment only when its free-DOF equilibrium residual and same-iteration free-DOF Newton correction gates all pass."
  category: numerical
  rationale: "Equilibrium and update size are both required convergence evidence."
  source: user
  priority: must
  verification_method: test
  acceptance_criteria: "All four channel results are combined by logical AND; constrained DOFs are excluded from convergence and their full-equilibrium residual retains reaction meaning."
  tolerance: "The four channel policies in NSNR-069 and NSNR-070 apply with inclusive <= comparisons."
  trace_to: {parent_need: "NEED-NSNR-002", downstream_agents: ["Numerical Review Agent", "Implementation Planning Agent"]}
  status: approved
- id: FESA-REQ-NSNR-069
  statement: "The FESA solver shall evaluate translational-force and rotational-moment free-residual convergence with channel-separated infinity-norm gates."
  category: numerical
  rationale: "Force and moment dimensions require separate scales."
  source: user
  priority: must
  verification_method: test
  acceptance_criteria: "For a nonzero matching-channel denominator max(||internal||inf, ||external||inf), the same-trial residual ratio passes iff <=1e-2; an exact-zero denominator instead passes iff its numerator is <=1e-3 model-consistent force or <=1e-3 model-consistent force-length, respectively."
  tolerance: "Relative 1e-2 dimensionless; zero-scale absolute 1e-3 force and 1e-3 force-length."
  trace_to: {parent_need: "NEED-NSNR-002", downstream_agents: ["Numerical Review Agent", "Implementation Planning Agent"]}
  status: approved
- id: FESA-REQ-NSNR-070
  statement: "The FESA solver shall evaluate translational and rotational free-correction convergence with channel-separated infinity-norm gates."
  category: numerical
  rationale: "Translation and rotation corrections have different dimensions."
  source: user
  priority: must
  verification_method: test
  acceptance_criteria: "For a nonzero current-trial incremental-solution denominator relative to the step-start committed state, the fresh-correction ratio passes iff <=1e-2; an exact-zero denominator instead passes iff its numerator is <=1e-3 model-consistent length or <=1e-3 dimensionless rotation, respectively."
  tolerance: "Relative 1e-2 dimensionless; zero-scale absolute 1e-3 length and 1e-3 dimensionless rotation."
  trace_to: {parent_need: "NEED-NSNR-002", downstream_agents: ["Numerical Review Agent", "Implementation Planning Agent"]}
  status: approved
- id: FESA-REQ-NSNR-008
  statement: "The FESA solver shall permit entered Newton iteration identities 1 through 100 and shall reject nonfinite required iteration data."
  category: numerical
  rationale: "The iteration limit and finite-data boundary must be deterministic."
  source: user
  priority: must
  verification_method: test
  acceptance_criteria: "A pass at iteration 100 may commit; otherwise iteration 100 ends in nonconvergence without iteration 101, and any nonfinite required residual, tangent, correction, state, load, or recovery value fails before acceptance."
  tolerance: "Iteration identities and finite predicates exact."
  trace_to: {parent_need: "NEED-NSNR-002, NEED-NSNR-003", downstream_agents: ["Numerical Review Agent", "Implementation Planning Agent"]}
  status: approved
- id: FESA-REQ-NSNR-014
  statement: "The FESA solver shall apply each successful fresh Newton correction unchanged when another iteration is required and shall use no line search, damping, solver fallback, or energy/work convergence gate."
  category: constraint
  rationale: "The approved first release uses direct Full Newton updates only."
  source: user
  priority: must
  verification_method: test
  acceptance_criteria: "The next candidate uses the fresh solve output without scalar or component modification; convergence depends only on NSNR-069 and NSNR-070."
  tolerance: "Correction/update identity exact."
  trace_to: {parent_need: "NEED-NSNR-002", downstream_agents: ["Numerical Review Agent", "Implementation Planning Agent"]}
  status: approved
- id: FESA-REQ-NSNR-046
  statement: "The FESA solver shall advance one scalar load factor by a fixed positive increment, shortening only the final increment to reach factor one without growth, cutback, or retry."
  category: numerical
  rationale: "Fixed stepping provides the approved deterministic load path."
  source: user
  priority: must
  verification_method: test
  acceptance_criteria: "The intended and accepted factor sequence starts at zero, never overshoots one, ends at the discrete factor-one identity on success, and analysis failure creates no replacement attempt."
  tolerance: "Factor/order identity exact; endpoint arithmetic is fixed by Numerical Review before implementation."
  trace_to: {parent_need: "NEED-NSNR-002", downstream_agents: ["Numerical Review Agent", "Implementation Planning Agent"]}
  status: approved
- id: FESA-REQ-NSNR-048
  statement: "The FESA solver shall advance every approved CLOAD and nonzero prescribed BOUNDARY target on one common proportional scalar load-factor path."
  category: physics
  rationale: "Loads and prescribed values must share one path identity."
  source: user
  priority: must
  verification_method: test
  acceptance_criteria: "Factor zero reproduces step-start values, intermediate states use the same factor for all approved targets, and factor one reproduces every target."
  tolerance: "Load-factor and target identity exact."
  trace_to: {parent_need: "NEED-NSNR-002", downstream_agents: ["Formulation Agent", "Numerical Review Agent"]}
  status: approved
- id: FESA-REQ-NSNR-018
  statement: "The FESA solver shall interpret approved CLOAD force and moment components as dead loads fixed in global directions while the common factor scales magnitude only."
  category: physics
  rationale: "Follower-load behavior would change equilibrium and tangent meaning."
  source: user
  priority: must
  verification_method: test
  acceptance_criteria: "Force and moment source DOF directions remain unchanged with deformation, moments retain force-length dimensions, and no follower external-load tangent is used."
  tolerance: "Global component identity exact; values use the model-consistent unit system."
  trace_to: {parent_need: "NEED-NSNR-002", downstream_agents: ["Formulation Agent", "Numerical Review Agent"]}
  status: approved
- id: FESA-REQ-NSNR-063
  statement: "The FESA solver shall interpret each approved nonzero BOUNDARY value as a factor-one absolute global-DOF target interpolated from its step-start committed value."
  category: physics
  rationale: "Absolute prescribed values must not be confused with correction increments."
  source: user
  priority: must
  verification_method: test
  acceptance_criteria: "The prescribed current value follows the common factor, zero start/target remains zero, the constrained correction is distinct from that value, and failed candidates do not change the step-start value."
  tolerance: "Prescribed path/source identity exact; values use model-consistent displacement or rotation units."
  trace_to: {parent_need: "NEED-NSNR-002, NEED-NSNR-003", downstream_agents: ["Formulation Agent", "Numerical Review Agent"]}
  status: approved
- id: FESA-REQ-NSNR-016
  statement: "The FESA solver shall map nonlinear STATIC four-value data with the first positive finite value as fixed increment, the second as endpoint one, and positive finite third and fourth values accepted but unused by stepping."
  category: input
  rationale: "The approved compatibility fields must not alter fixed stepping."
  source: user
  priority: must
  verification_method: test
  acceptance_criteria: "Valid four-value data records the first value for runtime use and identifies the third/fourth as unused; invalid arity, nonfinite/nonpositive required values, or period not representing one fails closed."
  tolerance: "Parsed endpoint-one identity exact; warning representation is owned by I/O Definition."
  trace_to: {parent_need: "NEED-NSNR-001", downstream_agents: ["I/O Definition Agent", "Implementation Planning Agent"]}
  status: approved
- id: FESA-REQ-NSNR-011
  statement: "The FESA solver shall keep trial state separate and atomically commit a complete converged displacement, rotation/director, load-factor, frame, force, and recovery state while preserving the prior committed state on failure."
  category: functional
  rationale: "Partial nonlinear state commits would corrupt continuation and results."
  source: user
  priority: must
  verification_method: test
  acceptance_criteria: "Successful validation commits one coherent state identity; iteration, increment, recovery, or output failure leaves the prior committed state and authoritative final result unchanged."
  tolerance: "State and commit identity exact."
  trace_to: {parent_need: "NEED-NSNR-003", downstream_agents: ["Formulation Agent", "Numerical Review Agent", "Implementation Planning Agent"]}
  status: approved
- id: FESA-REQ-NSNR-019
  statement: "The FESA solver shall preserve stable source identity and stable assembly order and shall derive free residual and constrained reaction from the complete assembled equilibrium at the same state."
  category: physics
  rationale: "Equilibrium evidence must remain traceable to source entities and DOFs."
  source: docs
  priority: must
  verification_method: test
  acceptance_criteria: "Input instance/label/component maps deterministically through assembly, state, diagnostic, result, and comparison; full residual at a trial or accepted state yields free-equilibrium evidence and constrained reactions."
  tolerance: "Source/component identity and discrete order exact; equilibrium uses approved numerical tolerances."
  trace_to: {parent_need: "NEED-NSNR-002, NEED-NSNR-004", downstream_agents: ["Formulation Agent", "Numerical Review Agent", "I/O Definition Agent"]}
  status: approved
- id: FESA-REQ-NSNR-020
  statement: "The FESA solver shall fail closed on every input or model meaning outside the approved element, material, load, boundary, step, and solver scope."
  category: input
  rationale: "Unsupported nonlinear behavior must not become a warning-only or linear fallback."
  source: docs
  priority: must
  verification_method: test
  acceptance_criteria: "A negative inventory for each unsupported class rejects the model before nonlinear state or authoritative output is committed."
  tolerance: "Exact supported/unsupported inventory."
  trace_to: {parent_need: "NEED-NSNR-001", downstream_agents: ["I/O Definition Agent", "Implementation Planning Agent"]}
  status: approved
- id: FESA-REQ-NSNR-021
  statement: "The FESA solver shall create authoritative accepted HDF5 frames one-to-one with committed increments, including factor one, using a sibling candidate that replaces the final only on success and preserves a prior valid final on failure."
  category: output
  rationale: "Authoritative results must contain accepted states only and remain failure-safe."
  source: user
  priority: must
  verification_method: test
  acceptance_criteria: "Committed increment and accepted-frame identities match in factor order, the successful result includes factor one, trial Newton history is absent, and controlled failure does not expose the candidate as final or damage a prior valid final."
  tolerance: "Commit/frame identity exact; numerical quantities use their approved verification tolerances."
  trace_to: {parent_need: "NEED-NSNR-003", downstream_agents: ["Numerical Review Agent", "I/O Definition Agent", "Implementation Planning Agent"]}
  status: approved
- id: FESA-REQ-NSNR-024
  statement: "The FESA solver shall replace or truncate the single derived text log at invocation start, retain it as the current-run live audit on controlled success or failure, and produce one deterministic diagnostic-only summary for every entered Newton iteration."
  category: output
  rationale: "Iteration evidence is required without making trial states authoritative results."
  source: user
  priority: must
  verification_method: test
  acceptance_criteria: "Completed and early-failure iterations preserve their stable iteration/stage and convergence meaning in entered order; the log remains current-run diagnostic evidence and is not HDF5 trial history or reference data."
  tolerance: "Summary cardinality and semantic identity exact; representation and low-level failure presentation are owned by I/O Definition."
  trace_to: {parent_need: "NEED-NSNR-003", downstream_agents: ["I/O Definition Agent", "Implementation Planning Agent"]}
  status: approved
- id: FESA-REQ-NSNR-083
  statement: "The FESA solver shall apply repository-wide input-directory names <stem>_results.h5 and <stem>_log.txt, treat every invocation containing literal --output as unrecognized and fail it with exit code 2 before input parsing, Analysis, result-candidate, log, or output creation without a compatibility alias or deprecation window, and use independent asymmetric result/log lifecycles without cross-file all-or-nothing commit."
  category: output
  rationale: "Public output identity and authority must be consistent across procedures."
  source: user
  priority: must
  verification_method: test
  acceptance_criteria: "Every existing and future procedure derives the two approved names beside its input and preserves linear-static numerical/HDF5 meaning under the migration; every argument form containing literal --output fails as unrecognized with exit code 2 before input parsing, Analysis, result-candidate, log, or output creation and has no accepted alias or deprecation form; log initialization does not commit HDF5 and HDF5 failure does not roll back the live log."
  tolerance: "Names, exit code, lifecycle independence, and regression identity exact; path and ownership mechanics are downstream decisions."
  trace_to: {parent_need: "NEED-NSNR-003", downstream_agents: ["I/O Definition Agent", "Implementation Planning Agent", "Numerical Review Agent"]}
  status: approved
- id: FESA-REQ-NSNR-026
  statement: "The FESA solver shall produce deterministic increment, iteration, assembly/reduction, accepted-frame, result-row, and diagnostic ordering for the same input and approved runtime configuration."
  category: constraint
  rationale: "Reproducible numerical and reference evidence requires stable discrete ordering."
  source: docs
  priority: must
  verification_method: test
  acceptance_criteria: "Repeated runs and approved thread configurations preserve the same intended/attempted/accepted factor identities, Newton event sequence, sparse/reduction structure, frame order, result identities, and log order."
  tolerance: "Discrete structure/order exact; floating equality policy is set by Numerical Review from repository conventions."
  trace_to: {parent_need: "NEED-NSNR-003, NEED-NSNR-004", downstream_agents: ["Numerical Review Agent", "Implementation Planning Agent"]}
  status: approved
- id: FESA-REQ-NSNR-030
  statement: "The FESA solver shall pass an approved verification portfolio covering the materially linear small-displacement limit, tangent consistency, equilibrium/reaction, symmetry or objectivity, and commit/rollback behavior."
  category: verification
  rationale: "Convergence alone does not establish nonlinear solver correctness."
  source: docs
  priority: must
  verification_method: analysis
  acceptance_criteria: "Numerical Review defines blocking cases and quantities for every listed category, and implementation passes each approved analytical, invariant, physics, or comparison gate."
  tolerance: "Case-specific tolerances are owned by Numerical Review; existing linear-limit tolerance remains unchanged."
  trace_to: {parent_need: "NEED-NSNR-004", downstream_agents: ["Research Agent", "Formulation Agent", "Numerical Review Agent"]}
  status: approved
- id: FESA-REQ-NSNR-034
  statement: "The FESA solver shall compare only approved accepted-state quantities against stored reference artifacts using stable source/component matching and the common docs/TOLERANCE.md policy."
  category: verification
  rationale: "Reference acceptance must be deterministic and independent of solver execution."
  source: docs
  priority: must
  verification_method: reference-comparison
  acceptance_criteria: "Numerical Review selects the exact existing input and required CSV quantities; precheck rejects missing, extra, duplicate, or nonfinite required rows before blocking/warning family comparison, without averaging or row-order matching."
  tolerance: "docs/TOLERANCE.md family-scale policy; exact artifacts and families are a Numerical Review-owned readiness gap."
  trace_to: {parent_need: "NEED-NSNR-004", downstream_agents: ["Numerical Review Agent", "I/O Definition Agent"]}
  status: approved

9. Verification Quantities

quantity	dimension / coordinates	role
nodal displacement and committed rotation/director state	length and dimensionless rotation; global	accepted-state kinematics and rollback
full residual and constrained reaction	force or force-length; global DOF	equilibrium and reaction evidence
MITC4 internal force, stress and strain	model-consistent dimensions; approved element frame/configuration	formulation, physics and reference verification
scalar load factor and accepted frame identity	dimensionless	path, commit and output ordering
four convergence channels	typed as NSNR-069/070	internal iteration acceptance only
iteration summary	diagnostic identity, not a physical reference quantity	convergence/failure audit

10. Tolerance Policy

• .inp values remain in the user's consistent unit system; FESA performs no unit inference or conversion.
• Only nonzero-scale convergence ratios are dimensionless and pass with <=1e-2.
• Exact-zero residual thresholds are 1e-3 force and 1e-3 force-length; correction thresholds are 1e-3 length and 1e-3 dimensionless rotation. Equal literals do not merge their dimensions.
• External comparisons use docs/TOLERANCE.md; internal invariant, tangent, endpoint-arithmetic and physics tolerances are fixed by Numerical Review before implementation.

11. Reference Case Requirements

• The current Stage-1 gap is selection of exact stored nonlinear input and only the CSV quantities required for acceptance.
• Numerical Review owns artifact readiness, blocking/warning families, source/component identity and HDF5 projection; this gap does not require another Stage-1 user question.
• Agents do not run Abaqus, Nastran or another reference solver and do not create, rename, repair or normalize stored reference artifacts.

12. Requirement Verification Matrix

id	category	source	priority	method	compact acceptance	tolerance	downstream	status
NSNR-001	functional	user	must	test	exactly one supported source/semantic nonlinear step	exact cardinality	I/O; Planning	approved
NSNR-003	physics	user	must	test	MITC4 geometric-only, linear isotropic material	exact inventory	Research; Formulation; Numerical Review	approved
NSNR-041	physics	user	must	analysis	fixed initial reference, no re-basing	identity exact	Research; Formulation; Numerical Review	approved
NSNR-074	physics	user	must	analysis	finite committed/trial triad/director state and rollback	invariant tolerance downstream	Formulation; Numerical Review	approved
NSNR-006	numerical	user	must	test	same-trial residual/tangent and fresh factorization/solve	identity/order exact	Formulation; Numerical Review; Planning	approved
NSNR-007	numerical	user	must	test	all four free-DOF gates pass; constrained residual is reaction	NSNR-069/070	Numerical Review; Planning	approved
NSNR-069	numerical	user	must	test	force/moment residual relative or typed zero-scale gates	1e-2; typed 1e-3	Numerical Review; Planning	approved
NSNR-070	numerical	user	must	test	translation/rotation correction relative or typed zero-scale gates	1e-2; typed 1e-3	Numerical Review; Planning	approved
NSNR-008	numerical	user	must	test	finite data, iterations 1..100, pass at 100 allowed	predicates/count exact	Numerical Review; Planning	approved
NSNR-014	constraint	user	must	test	unchanged full correction; no line search/fallback/energy gate	identity exact	Numerical Review; Planning	approved
NSNR-046	numerical	user	must	test	fixed increment, final shortening, no retry	factor/order exact	Numerical Review; Planning	approved
NSNR-048	physics	user	must	test	one proportional factor for all load/BC targets	identity exact	Formulation; Numerical Review	approved
NSNR-018	physics	user	must	test	fixed-global dead force/moment and no follower tangent	component exact	Formulation; Numerical Review	approved
NSNR-063	physics	user	must	test	absolute factor-one BC target and separate correction	path/source exact	Formulation; Numerical Review	approved
NSNR-016	input	user	must	test	four-value STATIC mapping and validation	endpoint exact	I/O; Planning	approved
NSNR-011	functional	user	must	test	separate trial, atomic commit, prior-state preservation	state exact	Formulation; Numerical Review; Planning	approved
NSNR-019	physics	docs	must	test	stable source/assembly and full-equilibrium residual/reaction	identity/order exact	Formulation; Numerical Review; I/O	approved
NSNR-020	input	docs	must	test	unsupported meaning fails closed	inventory exact	I/O; Planning	approved
NSNR-021	output	user	must	test	accepted commit/frame bijection and failure-safe HDF5 final	identity exact	Numerical Review; I/O; Planning	approved
NSNR-024	output	user	must	test	one ordered diagnostic summary per entered iteration and persistent live log	semantic identity exact	I/O; Planning	approved
NSNR-083	output	user	must	test	repository names; every literal --output form unrecognized with pre-input/pre-Analysis/pre-output exit 2 and no alias/deprecation; asymmetric lifecycle; linear regression	public identity/precedence exact	I/O; Planning; Numerical Review	approved
NSNR-026	constraint	docs	must	test	deterministic factor/iteration/assembly/frame/result/log order	discrete order exact	Numerical Review; Planning	approved
NSNR-030	verification	docs	must	analysis	blocking small-limit/tangent/physics/rollback portfolio	case-specific downstream	Research; Formulation; Numerical Review	approved
NSNR-034	verification	docs	must	reference-comparison	stored artifacts, deterministic matching and precheck	docs/TOLERANCE.md	Numerical Review; I/O	approved

13. Open Questions

없음. Specialist gaps are owned by downstream stages and are escalated only if they would change approved scope, physics, tolerance, authoritative output or public compatibility.

14. Downstream Handoff

• Research/Formulation: exact Total Lagrangian MITC4 equations, strain/stress measures, rotation map/side/frame, drilling and consistent derivatives.
• Numerical Review: endpoint arithmetic, tangent/objectivity/state-invariant checks, benchmark portfolio, performance adequacy and exact reference artifacts/quantities.
• I/O Definition: HDF5 schema/projection/chunking/factor-0 handling, log representation/failure presentation and path/collision conventions.
• Implementation Planning: backend adapters, output ownership primitive, candidate filename, performance targets and requirement-traced TDD plan.
• Coordinator: escalate only a downstream proposal that changes the approved scope, physics, convergence tolerance, authoritative-result meaning or public output contract; do not advance the workflow on this document alone.