docs: simplify MITC4 verification and drilling scope

2026-08-12 03:39:57 +09:00
parent 188bf31e44
commit 73df844979
3 changed files with 214 additions and 369 deletions
@@ -8,9 +8,9 @@
 - source_numerical_review: `docs/numerical-reviews/linear-static-mitc4-shell-review.md`
 - status: `ready-for-numerical-review`
 - owner_agent: `formulation-agent`
- date: `2026-08-11`
+- date: `2026-08-12`
- revision_basis: numerical review commit `0a5aad4`; findings `NR-C01` through
+- revision_basis: approved independent-reference policy, fixed drilling rule, and
-  `NR-C05` and decisions `NR-D01` through `NR-D02`
+  removal of calibration gates `NR-O01` through `NR-O04`
 - revision_state: `ready-for-numerical-rereview-not-implementation-planning`
 - product_execution_scope: `small-strain, small-rotation linear static only`
 - future_formulation_scope: `geometrically nonlinear Total Lagrangian residual/tangent; not executable`
@@ -41,11 +41,10 @@ Source labels `S4` and `S4R` both select this one FESA formulation by an approve
 semantic mapping. They do not select Abaqus integration or stabilization behavior,
 and this document makes no Abaqus formulation-equivalence claim.
-Exact drilling reference family/coefficient, drilling-energy warning ratio,
+The drilling rule is fixed below by the approved requirements. Coefficient sweeps,
-smooth-director angle, and geometry thresholds remain Numerical Review decisions.
+drilling-energy warnings and datasets, smooth-director calibration (`NR-O03`), and
-The common dimensionless drilling coordinate, geometry-measure inventory,
+distortion/warp threshold calibration (`NR-O04`) are outside the implementation gate.
-drilling-load projection tolerance, and normalized algebraic checks are fixed below
+The drilling-load projection and normalized algebraic checks remain fixed below.
 by the first Numerical Review. No remaining open symbol is an implementation default.
 ## 2. Scope and assumptions
@@ -218,18 +217,10 @@ $$
 \mathbf d_I=\frac{\mathbf s_I}{\|\mathbf s_I\|}.
 $$
-Incident elements are accumulated in the same stable order. After averaging, every
+Incident elements are accumulated in the same stable order. No additional
-incident deviation
+`theta_smooth` rejection is applied. Nonfinite or zero cross products and averaged
-
+vectors fail; they are never replaced with a global axis. The pairwise orientation
-$$
+rule above remains the exact supported-patch predicate.
 \theta_{eI}=\cos^{-1}\!\left(
 \operatorname{clamp}(\mathbf n_e\cdot\mathbf d_I,-1,1)\right)
 $$
 must satisfy an approved smooth-patch bound `theta_smooth`. The research value
 `20 degrees` is only the first Numerical Review candidate. It is not fixed here.
 Zero or near-zero cross products and averaged vectors fail using approved
 scale-aware tolerances. They are never replaced with a global axis.
 ### 4.3 Deterministic nodal tangent frame
@@ -575,7 +566,7 @@ Duplicate nodes, self-intersection, degenerate midsurface area, and reversed
 connectivity are separate fail-closed geometry errors. No failed location is
 discarded or replaced by a value from another point.
-### 9.3 Scale-aware measures
+### 9.3 Basic geometry predicates
 Let the consecutive midsurface edge inventory be
@@ -585,73 +576,21 @@ $$
 \boxed{L_e=\max_{(I,J)\in\mathcal E}\|\mathbf X_J-\mathbf X_I\|}.
 $$
-`L_e` must be finite and strictly positive. It is the common element length used by
+`L_e` must be finite and strictly positive. At every center, Gauss, tying, and
-geometry checks and the DOF scaling in Section 12.5. At every distinct in-plane
+committed recovery location required by Section 9.2, the following quantities must
-location in the center, Gauss, tying, and committed recovery inventory, define
+be finite and satisfy
 $$
 a(\xi,\eta)=\|\mathbf A_\xi\times\mathbf A_\eta\|,
 \qquad
 \boxed{a_g(\xi,\eta)=\frac{a(\xi,\eta)}{L_e^2}},
 $$
 $$
 \mathbf n_s(\xi,\eta)=
 \frac{\mathbf A_\xi\times\mathbf A_\eta}{a(\xi,\eta)},
 \qquad
 c_d(\xi,\eta)=\mathbf n_s\cdot\overline{\mathbf d}.
 $$
 `a_g` is the normalized surface-collapse/aspect measure. In particular, for
 `A_xi=(1,0,0)` and `A_eta=(0,epsilon,0)` with `L_e=O(1)`, `a_g -> 0` as
 `epsilon -> 0`; the angular measure below alone cannot detect that collapse.
 At every full three-dimensional validation point, define the dimensionless
 angular/director determinant measure
 $$
 j_s=\frac{J}
 {\|\mathbf G_\xi\|\,\|\mathbf G_\eta\|\,\|\mathbf G_\zeta\|}.
 $$
 For all positive finite point determinants, define the element-variation measure
 $$
 \boxed{r_J=\frac{J_{min}}{J_{max}}},
 \qquad
 J_{min}=\min_{p\in\mathcal P_V}J_p,
 \quad
 J_{max}=\max_{p\in\mathcal P_V}J_p,
 $$
 and the surface-normal warpage measure relative to the center normal
 $$
 \boxed{\theta_w=
 \max_{p\in\mathcal P_S}
 \cos^{-1}\!\left(\operatorname{clamp}
 (\mathbf n_s(0,0)\cdot\mathbf n_s(p),-1,1)\right)}.
 $$
 Here `P_V` contains every volume Gauss point, tying point at `zeta=0`, center, and
 every committed bottom/middle/top recovery point; `P_S` contains their distinct
 in-plane projections. A valid element must satisfy, without denominator clamping,
 $$
 \boxed{
-J_p>0,\quad
+\|\mathbf A_\xi\times\mathbf A_\eta\|>0,
-j_{s,p}>\tau_{ang},\quad
+\qquad J>0.}
 a_{g,p}>\tau_{area},\quad
 c_{d,p}>\tau_{dir},\quad
 r_J>\tau_{var},\quad
 \theta_w<\theta_{warp}.}
 $$
-The measures and their location inventory are fixed by this formulation revision.
+The covariant vectors and reciprocal bases must also be finite. Duplicate nodes,
-The positive dimensionless thresholds remain `needs-numerical-calibration`; they
+self-intersection, zero-area mappings, and nonpositive determinants fail before
-must separate valid distortion/warp sweeps from collapsed negative sequences before
+stiffness or recovery is committed. No failed location is omitted, averaged, clamped,
-Numerical Review may approve them. No `max(1, geometry_scale)`, zero denominator,
+or repaired. This feature defines no calibrated distortion, aspect, warpage, or
-failed-point omission, or pointwise orientation repair is permitted.
+director-angle threshold; `NR-O03` and `NR-O04` are not acceptance tests.
 ## 10. Linear kinematics and MITC4 shear projection
@@ -846,97 +785,40 @@ $$
 \mathbf f_{phys}^{24}=\mathbf K_{phys}^{24}\mathbf q_g.
 $$
-### 12.2 Drilling candidate contract
+### 12.2 Fixed drilling stabilization
-Let
+Let `R` be the index set of the eight director-tangent rotational coordinates in the
 physical local ordering `q_20`. Form the finite strictly positive diagonal inventory
 $$
-\mathbf K_d^l=\operatorname{diag}(k_{d,1},k_{d,2},k_{d,3},k_{d,4}),
+\mathcal R_+=\{(K_{20})_{ii}\mid i\in\mathcal R,
-\qquad k_{d,I}>0,
+(K_{20})_{ii}>0,\ (K_{20})_{ii}\text{ finite}\}.
 $$
-with rotational-stiffness units `force*length`. The common physical normalization is
+Every member has rotational-stiffness units `force*length`. For an otherwise valid
 element, an empty `R+` is a deterministic numerical-validation failure. Define
 $$
-D_{iso}=\frac{Et^3}{12(1-\nu^2)},
+\boxed{k_{ref}=\min\mathcal R_+,\qquad k_d=10^{-3}k_{ref}},
 \qquad
 \boxed{\rho_{d,I}=\frac{k_{d,I}}{D_{iso}}}.
 $$
-`rho_d,I` is dimensionless and is the only common coordinate for comparing drilling
+and use the same positive scalar at all four local drilling coordinates:
 families. For any candidate `c` written as
 $$
-k_{d,I}^{(c)}=\alpha_d^{(c)}k_{ref,I}^{(c)},
+\boxed{\mathbf K_d^l=k_d\mathbf I_4}.
 $$
-the candidate-specific conversion is
+Translational diagonals have units `force/length` and shall never enter `R+`.
 Off-diagonal entries, nonpositive entries, and nonfinite entries also do not enter
 the minimum. The fixed coefficient is a project numerical-stability choice informed
 by the thesis rule; it is not a physical constitutive parameter, an Abaqus algorithm,
 or a claim of coefficient optimality.
-$$
+There is no `rho_d`, coefficient sweep, stable-plateau selection, conditioning
-\boxed{
+calibration, artificial-energy ratio, or drilling-specific output contract in this
-\rho_{d,I}^{(c)}=\alpha_d^{(c)}
+feature. Verification checks only the exact selection rule, dimensions, symmetry,
-\frac{k_{ref,I}^{(c)}}{D_{iso}},
+positivity, four-mode regularization, deterministic repeatability, and separation
-\qquad
+from physical recovery.
 \alpha_{d,I}^{eq,(c)}=\rho_{d,I}^{(c)}
 \frac{D_{iso}}{k_{ref,I}^{(c)}}.}
 $$
 The second expression is the nodewise equivalent coefficient for a target `rho_d,I`.
 A single actual candidate coefficient may therefore generate a range of `rho_d,I`; that
 entire range is part of the calibration evidence. The dimensionally compatible
 candidate distributions carried from research are:
 1. transverse-shear/area transition family
 $$
 k_{ref,I}^{(A)}=
 \frac{GtA_{eI}}{1+qA_{eI}/t^2},
 \qquad q=2.5\times10^{-5},
 $$
 where
 $$
 A_{eI}=\int_{A_e}N_I\,dA
 \approx\sum_{g=1}^{4}N_I(\xi_g,\eta_g)
 \|\mathbf A_\xi\times\mathbf A_\eta\|_g w_g;
 $$
 2. isotropic bending rigidity
 $$
 k_{ref}^{(B)}=D_{iso},
 \qquad
 \rho_{d,I}^{(B)}=\alpha_d^{(B)};
 $$
 3. a documented positive statistic formed only from the physical rotational block
   of `K_20`, whose entries all have `force*length` units, converted by the same
   `k_ref/D_iso` ratio. A raw statistic is not comparable until this conversion is
   reported.
 The first two candidate scales differ sharply in the thin-shell limit:
 $$
 \boxed{\displaystyle \lim_{A_{eI}/t^2\to\infty}
 k_{ref,I}^{(A)}/D_{iso}=6(1-\nu)/q}.
 $$
 For `nu=0.3` and `q=2.5e-5`, this ratio is `168000`. Consequently the same raw
 coefficient, including `10^-3`, cannot represent the same small drilling stiffness
 for candidates A and B.
 The thesis rule `10^-3 min(all K_ii)` is not admissible because it can mix
 translational `force/length` and rotational `force*length` diagonals. A sweep must
 instead expand logarithmically in actual `rho_d,I` until it brackets both:
 1. a low-side scaled-rank/conditioning or factorization failure; and
 2. a high-side physical `U/N/M/Q` contamination boundary.
 A nominal value may be proposed only as the smallest point in a stable plateau, with
 the adjacent lower and higher decades and separate physical/drilling energies
 reported. The reference family, plateau, nominal value, and response/energy bounds
 remain `needs-numerical-calibration`; no common `10^-3` center is retained.
 ### 12.3 Stabilized 24-DOF matrix
@@ -963,13 +845,11 @@ Mass and damping matrices are `N/A` for this linear-static feature.
 For a valid free isolated element, the expected physical rank is 14. Embedding it in
 24 coordinates creates the six physical rigid modes plus four drilling null modes.
-Four positive independent `k_d,I` values should remove only those drilling modes,
+The positive uniform `k_d` block should remove only those drilling modes,
 giving expected stabilized rank 18 and nullity 6. These are verification targets,
-not substitutes for the scaled singular-value/rank study defined in Section 12.5.
+not substitutes for the normalized rigid-action checks defined in Section 17.1.
 The exact-arithmetic rank statement is independent of the calibrated numerical-rank
 threshold.
-### 12.4 Energy split
+### 12.4 Energy identity
 The element energies are
@@ -987,10 +867,9 @@ E_{drill}^e=\frac12\mathbf q_g^T
 =\frac12\boldsymbol\gamma^T\mathbf K_d^l\boldsymbol\gamma}.
 $$
-Both have units `force*length` and are aggregated separately in stable source order.
+Both have units `force*length`. `E_drill` is the internal quadratic identity associated
-The ratio `E_drill/E_phys` is reported only when mathematically classifiable. If
+with `K_drill`; it is not a physical shell energy and is not emitted as a required
-`E_phys` is zero or near zero, the two energies are reported explicitly; no arbitrary
+result. No drilling-energy ratio or warning threshold is defined.
 denominator clamp is used. The warning ratio remains open.
 ### 12.5 DOF scaling for rank and conditioning evidence
@@ -1032,10 +911,10 @@ $$
 \widehat{\mathbf K}_{ff}=\mathbf S_f^T\mathbf K_{ff}\mathbf S_f.
 $$
-Global condition and numerical-rank evidence uses `K_hat_ff`; a valid `0 x 0 Kff`
+Optional global condition and numerical-rank diagnostics use `K_hat_ff`; a valid `0 x 0 Kff`
 case is classified separately and is not reported as singular. Numerical
-rank/condition thresholds remain calibration decisions, but no raw mixed-unit
+condition calibration is not an implementation gate, and no raw mixed-unit matrix
-matrix may be used to choose them.
+may be used for any reported spectrum or condition estimate.
 ## 13. Numerical integration
@@ -1501,7 +1380,7 @@ for each shell element in stable source order:
 for each shell source node in stable source order:
    gather incident candidates in stable element order
    reject any nonpositive pairwise incident-normal dot product before averaging
-    reject degenerate or too-sharp incident normals
+    reject nonfinite or zero incident normals and averaged vectors
    d_I = normalize(sum(A_e * n_e))
    select least-aligned global axis with deterministic tie break
    construct right-handed (a_I, b_I, d_I)
@@ -1515,7 +1394,7 @@ build T, T_p, T_d
 initialize K20[20,20] = 0
 evaluate the complete center/Gauss/tying/recovery geometry inventory
-validate pointwise J, j_s, a_g, c_d and aggregate r_J, theta_w
+validate finite nonzero surface area and finite positive J at every required location
 evaluate and validate four midsurface tying locations
 for each 2x2 midsurface Gauss location in fixed order:
    construct and validate local frame (e1,e2,e3)
@@ -1530,20 +1409,21 @@ for each 2x2 midsurface Gauss location in fixed order:
 check K20 finite and symmetric within approved normalized tolerance
 Kphys24 = T_p^T * K20 * T_p
-construct positive Kd_local and report every k_d,I through rho_d,I = k_d,I/D_iso
+collect positive finite tangent-rotation diagonals R+ from K20
 require R+ nonempty; k_d = 1e-3 * min(R+); Kd_local = k_d * I4
 Kdrill24 = T_d^T * Kd_local * T_d
 Ke24 = Kphys24 + Kdrill24
-form S20, S24, Khat20, and Khat_e for rank/conditioning evidence only
+form S20, S24, Khat20, and Khat_e for normalized algebraic evidence only
 fint24 = Ke24 * q_g
 residual24 = fint24 - f_CLOAD
-return matrices, residual, transforms, frames, and separate energy operators
+return matrices, residual, transforms, and frames
 ```
 ### 16.3 Global linear-static lifecycle
 ```text
 assemble all Ke24 contributions with stable element-local COO ordering
-form model-length DOF scaling and Khat_ff for global rank evidence only
+form model-length DOF scaling and Khat_ff for optional normalized diagnostics only
 partition full K into Kff, Kfc, Kcf, Kcc in stable free/constrained order
 factorize Kff before load assembly
 assemble and deterministically aggregate nodal CLOAD
@@ -1551,7 +1431,7 @@ accept an exact-zero nodal moment separately; otherwise require rho_M <= 1e-12
 solve Kff * df = Ff - Kfc * dc
 reconstruct full displacement d
 compute full residual r = K*d - F
-recover shell rows and physical/drilling energies in stable source order
+recover shell rows and physical shell energy in stable source order
 validate complete finite candidate state/output, then commit
 ```
@@ -1565,7 +1445,7 @@ for each element and each 2x2 midsurface location in fixed order:
    attach exact natural coordinates, section position, frame, and source identity
 recover nodal global U/UR and full-residual RF/RM
-compute E_physical and E_drill separately; never clamp a near-zero denominator
+compute required physical shell energy; emit no drilling-specific result
 ```
 ### 16.5 Future nonlinear tangent check
@@ -1587,14 +1467,15 @@ given an approved global Phi map, objective drill potential, and load work:
 - Shape-function partition of unity, Kronecker delta, and derivative sums.
 - Nodal and integration frames orthonormal and right-handed.
- The complete `J/j_s/a_g/c_d/r_J/theta_w` inventory at center, Gauss, tying,
+- Finite nonzero surface area and finite positive `J` at every center, Gauss, tying,
-  and committed recovery points.
+  and committed recovery point.
 - Scaled `K20`, `Kphys24`, `Kdrill24`, and `Ke24` symmetry and spectrum.
 - Transformation work/energy invariance.
 - Physical rigid modes satisfy normalized scaled stiffness action.
 - Stabilized free-element nullity is exactly six; accepted non-rigid physical modes
  have positive physical energy.
- Pure drill vectors have zero physical energy and positive drilling energy.
+- Pure drill vectors have zero physical-shell energy and positive action under the
  fixed numerical drilling block.
 - Consistent force/length unit rescaling leaves dimensionless decisions unchanged.
 For any nonzero scaled stiffness under test, the approved normalized checks are
@@ -1634,41 +1515,35 @@ Independently verify:
 - pure twist and `K12/M12` convention;
 - zero strain/resultant/stress contribution from a pure drilling vector.
-### 17.3 Locking, distortion, and curved shells
+### 17.3 Nonblocking accuracy studies
- Thin and thick plate/shell mesh and thickness sequences are required; one
+Thin/thick, distorted, warped, pinched-cylinder, NAFEMS LE3 and Scordelis-Lo studies
-  displacement on one mesh is insufficient.
+remain useful for documenting the original MITC4 element's known shear- and
- Distorted and warped valid quadrilaterals must be swept through approved geometry
+membrane-locking limits. They are not required implementation-completion tests and
-  measures.
+do not authorize MITC4+ or an expanded input subset. `NR-O03` and `NR-O04` are
- Original MITC4 controls transverse-shear locking but can retain membrane locking
+explicitly removed from the acceptance scope.
  in distorted curved meshes. This is a known limitation, not permission to add
  MITC4+.
 - Preferred nodal-load-compatible curved benchmarks are the pinched cylinder and
  NAFEMS LE3 hemispherical shell. Scordelis-Lo is admissible only after an equivalent
  nodal-load adaptation is documented.
-### 17.4 Drilling sensitivity
+### 17.4 Fixed drilling checks
-For every candidate reference scale, convert candidate coefficients to the actual
+For representative valid element kernels, verify:
 nodewise `rho_d,I` inventory. Expand a logarithmic sweep until both the low-side
 rank/conditioning failure and high-side physical-response contamination boundary
 are observed, and record:
- free-element scaled rank and scaled constrained-system conditioning;
+- `R+` contains only finite positive physical tangent-rotation diagonals;
- global `U` and physical `N/M/Q` sensitivity;
+- `k_d=10^-3 min(R+)` and `K_d^l=k_d I4` exactly;
- `E_phys` and `E_drill` without denominator clamping;
+- `K_drill^24` is symmetric and positive on each pure drilling coordinate;
- invariance under consistent unit conversion, thickness ratios, and mesh sizes.
+- four nonphysical drilling null modes are removed while the six physical rigid
  modes satisfy the normalized action test;
 - physical generalized strain, resultant and stress recovery is unchanged by a
  pure drilling vector.
-Candidate runs are compared by overlapping actual `rho_d,I` ranges, never by equal
+No coefficient sweep, plateau, condition threshold, response-sensitivity criterion,
-raw `alpha_d`. The study must select the reference family, the smallest stable
+or drilling-energy warning is part of this check.
 plateau value, its adjacent-decade sensitivity, and the energy warning criterion
 before Implementation Planning.
 ### 17.5 Reference-comparison boundary
-Abaqus comparisons block only on matched global `U1/U2/U3` rows under the approved
+Abaqus comparisons block only on matched global `U1/U2/U3` rows under
-mixed tolerance decided downstream. `UR1/UR2/UR3` is fully reported and may emit a
+`tolerance_c=1e-9+1e-6*reference_scale_c`, where `reference_scale_c` is the maximum
-deterministic nonblocking large-error warning, but it does not change pass/fail.
+absolute finite Abaqus value for the same component. `UR1/UR2/UR3` uses the same
 formula but an exceedance emits only a deterministic nonblocking warning.
 FESA `S4` and `S4R` inputs must produce the same internal numerical rows for identical
 supported models while preserving distinct source metadata. Abaqus S4 and S4R are
 not expected to be numerically identical on finite meshes.
@@ -1686,16 +1561,15 @@ procedure.
 | Risk | Consequence | Required control |
 | --- | --- | --- |
-| Transverse-shear locking | overly stiff thin-shell response | exact edge-midpoint MITC projection and thickness/mesh convergence |
+| Transverse-shear locking | overly stiff thin-shell response | exact edge-midpoint MITC projection and patch/reference evidence; broader convergence is a known limitation study |
-| Membrane locking on distorted curved meshes | slow or nonuniform convergence | distortion/curvature sweeps; document original MITC4 limitation |
+| Membrane locking on distorted curved meshes | slow or nonuniform convergence | document original MITC4 limitation; optional later studies do not alter the current gate |
 | Volumetric locking | N/A for the approved plane-stress shell contract | do not infer a three-dimensional incompressible formulation |
 | Wrong tying pair or engineering-shear factor | swapped/incorrect shear and loss of patch consistency | component-level tying and patch tests |
-| Reversed or degenerate Jacobian | invalid basis, sign, or energy | common location inventory with `J/j_s/a_g/c_d/r_J/theta_w` |
+| Reversed or degenerate Jacobian | invalid basis, sign, or energy | finite nonzero surface area and finite positive `J` at every required location |
 | Discontinuous shared director | artificial coupling or undefined frame | reject; require duplicate nodes at folds |
 | Fixed-axis tangent singularity | nondeterministic rotation transform | least-aligned global-axis construction |
-| Drilling coefficient too small | rank/conditioning failure | rank and conditioning sensitivity sweep |
+| Invalid drilling reference inventory | absent or nonpositive numerical regularization | require nonempty finite positive physical rotational diagonals and fail deterministically otherwise |
-| Drilling coefficient too large | contaminated displacement/resultant | physical-output and separate-energy sensitivity sweep |
+| Mixed-unit drilling scale | unit-dependent stabilization | exclude every translational diagonal; use only the physical tangent-rotation block |
 | Mixed-unit drilling or spectrum scale | unit-dependent stabilization/rank | use `rho_d,I` and `S^T K S`; prohibit raw mixed-unit comparison |
 | Misconstructed rigid test | false drill energy in a physical mode | use rigid translation plus tangent director change with `gamma=0` |
 | Recovery/stiffness mismatch | inconsistent energy and section output | same frames, tying, material, and thickness rule |
 | Location averaging | hidden sign/identity error | preserve exact location rows; no nodal extrapolation |
@@ -1748,25 +1622,25 @@ research brief remain the project source of truth.
 | Requirement group | Formulation coverage | Remaining owner |
 | --- | --- | --- |
 | `001-004`, `030`, `037` | linear-static boundary; S4/S4R one FESA path, source identity distinct | I/O, planning |
-| `005`, `031-038` | 24 global DOFs; 20 physical plus four drill coordinates; `rho_d,I`, scaled rank, energy | Numerical Review for drill calibration |
+| `005`, `031-038` | 24 global DOFs; 20 physical plus four drill coordinates; fixed positive rotational-diagonal stabilization | Numerical Review for formula consistency |
 | `006-010` | isotropic plane stress, one centered constant-thickness layer | I/O validation |
-| `011-016` | pairwise normals, deterministic averaging/frames, complete geometry measures | Numerical Review for calibrated thresholds |
+| `011-016` | pairwise orientation, deterministic averaging/frames, basic finite/positive geometry predicates | I/O validation |
 | `017-020` | global 24-DOF virtual work; `rho_M <= 1e-12`; distributed loads excluded | I/O diagnostic/schema |
 | `024-029` | deterministic element buffers, partitioned linear lifecycle, full-residual reaction | planning |
-| `039-048` | nodal/global and shell/local recovery inventory, units, identities, energy split | I/O schema |
+| `039-048` | nodal/global and shell/local recovery inventory, units, identities, physical shell energy | I/O schema |
-| `049-057` | scaled normalized invariants, patches, locking, geometry, curved shells, drilling, equilibrium | Numerical Review/reference/physics |
+| `049-057` | normalized invariants, patches, fixed drilling, declared references and equilibrium | Numerical Review/reference/physics |
-| `058-064` | U blocking, UR warning-only comparison boundary | Numerical Review/reference model |
+| `058-064` | exact B33 mixed tolerance; U blocking and UR warning-only | reference verification |
-| `065-072` | reference immutability and displacement-only evidence boundary acknowledged | reference model |
+| `065-072` | exact existing S4/S4R paths, immutability and displacement-only boundary | reference model |
 ### 20.1 Numerical Review revision traceability
 The first review findings map to this revision as follows.
-`NR-C01` maps to Sections 9.2-9.3, 16.2, and 17.1/17.3. The geometry measures
+`NR-C01` maps to Sections 9.2-9.3, 16.2, and 17.1/17.3. Basic point inventory and
-are fixed while their thresholds still require calibration.
+finite/positive predicates remain; `NR-O03`/`NR-O04` calibration is removed.
-`NR-C02` maps to Sections 12.2 and 17.4. The common `rho_d,I` coordinate and
+`NR-C02` maps to Sections 12.2 and 17.4. The project decision replaces candidate
-candidate conversions are fixed while the stable plateau remains open.
+normalization and plateau work with the exact fixed rotational-diagonal rule.
 `NR-C03` maps to Sections 12.3/12.5 and 17.1. Element/global DOF scaling is fixed
 while the numerical-rank threshold remains open.
@@ -1781,53 +1655,45 @@ normalized algebraic metrics.
 ## 21. Open issues and downstream handoff
-### 21.1 Blocking Numerical Review decisions
+### 21.1 Current numerical-review boundary
-1. Select the dimensionally compatible drilling reference-scale family.
+No calibration decision remains open for the linear implementation. The first review
-2. Select the nodewise `rho_d,I` stable plateau, nominal value, scaled
+approved `rho_M <= 1e-12`, the normalized algebraic checks, MITC tying/component signs,
-   conditioning/rank acceptance, and physical-output contamination bound.
+constitutive law, quadrature, and recovery signs. The approved policy fixes drilling
-3. Define classification and warning behavior for `E_drill/E_phys`, including the
+and U/UR tolerance and removes drilling-energy calibration plus `NR-O03`/`NR-O04`.
-   zero/near-zero physical-energy case.
+Numerical Review shall now check internal consistency and may not treat those removed
-4. Approve `theta_smooth` after curved-mesh resolution sweeps; `20 degrees` is only
+items or an expanded reference portfolio as missing evidence.
   the initial candidate.
 5. Calibrate thresholds for the fixed `J/j_s/a_g/c_d/r_J/theta_w` geometry
   inventory using valid distortion/warp and collapsed negative sequences.
 6. Jointly with Reference Model, approve the U mixed tolerance and nonblocking UR
   large-error warning threshold.
 The first review already approved `rho_M <= 1e-12`, the normalized algebraic checks,
 the MITC tying/component signs, constitutive law, quadrature, and recovery signs.
 This revision is ready for Numerical Review rerun but not for Implementation
 Planning until the six remaining evidence-backed decisions are closed.
 ### 21.2 I/O Definition handoff
 - Preserve source `S4`/`S4R` separately from internal `FESA-MITC4`.
 - Define exact keyword subset, section/material resolution, and fail-closed
-  diagnostics for director, folds, Jacobians, unsupported loads, and recovery;
+  diagnostics for director orientation, basic topology/Jacobians, unsupported loads, and recovery;
  encode exact-zero nodal moment separately and enforce `rho_M <= 1e-12` without
  a denominator clamp.
 - Define exact HDF5 row schemas for global `U/UR`, `RF/RM`; four midsurface
  generalized-strain/resultant locations; bottom/middle/top stress positions; full
-  residual/equilibrium; and separate energies.
+  residual/equilibrium; and physical shell energy. Do not add drilling-specific datasets.
 - Preserve local frame and natural-coordinate identity without location averaging.
 ### 21.3 Reference Model handoff
- Use at least one S4 and one S4R source artifact, but compare formulation-independent
+- Record the existing `reference/shell/` S4 and `reference/shellR/` S4R input and
-  global displacement evidence rather than claiming element equivalence.
+  displacement CSV paths, but compare only formulation-independent global displacement
- Prioritize pinched cylinder and NAFEMS LE3 models compatible with nodal loads and
+  evidence rather than claiming element equivalence.
-  approved BC semantics.
+- Use the exact B33 mixed tolerance; do not add administrative metadata or portfolio gates.
 - Propose the mixed U tolerance and nonblocking UR warning threshold.
 - Do not create, repair, rename, or run reference artifacts during this formulation
  gate.
 ### 21.4 Implementation Planning handoff
- Do not begin until Numerical Review closes Section 21.1.
+- Begin after the Numerical Review, I/O contract, and lightweight Reference Model
  inventory agree with this formulation.
 - Translate the deterministic preprocessing, 24-to-20 transform, tying projection,
-  physical/drill split, quadrature, recovery, and invariant portfolio into
+  fixed physical/drill split, quadrature, recovery, and required invariants into
-  `RED -> GREEN -> VERIFY` tests before production changes.
+  Harness Step drafts with `RED -> GREEN -> VERIFY` tests before production changes.
 - Obtain user approval of the multi-Step draft before creating phase-planning files;
  Harness execution requires a separate explicit user request.
 - Keep future nonlinear state and tangent out of the current linear-static plan.
 ### 21.5 Future nonlinear formulation handoff
@@ -6,12 +6,11 @@
 - title: `Linear Static MITC4 Shell`
 - status: `approved`
 - owner_agent: `requirement-agent`
- date: `2026-08-11`
+- date: `2026-08-12`
 - approval_basis: 사용자와 확정한 선형 정적 범위, `S4`/`S4R` 매핑, 6자유도 외부 계약, drilling 안정화, 자동 director 생성, 결과 및 검증 계약
 - current_product_state: `requirements-approved-not-implemented`
- formulation_alignment: `docs/formulations/mitc4-shell-formulation.md`는 선행 draft이며 이 baseline의 6자유도 및 drilling 계약에 맞춘 후속 개정이 필요함
+- formulation_alignment: `docs/formulations/mitc4-shell-formulation.md`는 이 baseline의 6자유도 및 고정 drilling 안정화 계약과 정렬함
- declared_reference_candidate: 사용자가 `reference/shell/`에 Abaqus `S4R` 모델을 추가했다고 `2026-08-11`에 선언함
+- reference_inventory_state: `reference/shell/`의 S4와 `reference/shellR/`의 S4R input/displacement CSV를 기존 경로와 이름 그대로 사용함
 - reference_inventory_state: 요구조건 작성 시점의 workspace에서는 `reference/shell/`이 관찰되지 않아 exact artifact inventory는 `needs-reference-artifacts`로 유지함
 ## Purpose
@@ -51,7 +50,7 @@ Formulation, Numerical Review, I/O, Reference Model, Implementation Planning 및
 - Abaqus source element type `S4`와 `S4R`의 동일한 FESA MITC4 매핑
 - 절점당 전역 자유도 `[UX, UY, UZ, URX, URY, URZ]`
 - 3개 병진과 director 접평면 회전 2개로 구성된 물리 MITC4 kernel
- 비물리 local drilling 회전 1개에 대한 작은 scale-aware 수치 안정화
+- 비물리 local drilling 회전 1개에 대한 고정 수치 안정화
 - 막, 굽힘, 횡전단 및 이들의 coupling
 - 단일층, 균질 등방성 선형 탄성
 - element set별 일정한 양의 두께와 하나의 material을 갖는 `*SHELL SECTION`
@@ -60,7 +59,7 @@ Formulation, Numerical Review, I/O, Reference Model, Implementation Planning 및
 - DOF 1~6의 nodal `*BOUNDARY`와 nodal `*CLOAD`
 - deterministic assembly와 기존 linear-static partition/factorization/substitution lifecycle
 - HDF5 nodal displacement/reaction, shell generalized strain/resultant, in-plane stress, residual 및 energy output
- element invariant, patch, locking, distortion, curved-shell, reference 및 physics verification
+- element invariant, patch, 현재 S4/S4R displacement reference 및 physics verification
 ## Out Of Scope
@@ -115,9 +114,9 @@ Formulation, Numerical Review, I/O, Reference Model, Implementation Planning 및
 - **FESA-REQ-LSMITC4-011** — The initial nodal director shall be a dimensionless unit vector in the positive thickness direction; scalar thickness shall remain a separate property and shall not be encoded in the director magnitude.
 - **FESA-REQ-LSMITC4-012** — The positive element normal candidate shall be derived deterministically from the source node order and midsurface covariant tangent cross product.
 - **FESA-REQ-LSMITC4-013** — At a smooth shared node, consistently oriented incident element normal candidates shall be combined by deterministic area-weighted averaging and normalized to form the common nodal director.
- **FESA-REQ-LSMITC4-014** — Zero/near-zero normal candidates, a zero/near-zero averaged director, opposing incident orientations, and a fold sharper than the approved smooth-patch criterion shall fail model validation.
+- **FESA-REQ-LSMITC4-014** — Nonfinite or zero normal candidates, a nonfinite or zero averaged director, and opposing incident orientations shall fail model validation; this feature does not introduce a calibrated smooth-patch angle.
 - **FESA-REQ-LSMITC4-015** — A physical fold or hinge shall be represented with duplicated source nodes so each smooth shell patch owns a separate director; the solver shall not silently average a discontinuous director field.
- **FESA-REQ-LSMITC4-016** — Element geometry validation shall reject duplicate nodes, self-intersection, nonfinite coordinates, degenerate area, and nonpositive or near-singular Jacobians at every formulation-required Gauss and tying location.
+- **FESA-REQ-LSMITC4-016** — Element geometry validation shall reject duplicate nodes, self-intersection, nonfinite coordinates, zero area, and nonpositive or nonfinite Jacobians at every formulation-required Gauss and tying location; this feature does not introduce calibrated distortion or warp thresholds.
 - **FESA-REQ-LSMITC4-017** — The solver shall support nodal `*BOUNDARY` targets resolved by source node label or node set for global DOFs 1 through 6, including existing zero and nonzero prescribed-displacement semantics.
 - **FESA-REQ-LSMITC4-018** — The solver shall support nodal `*CLOAD` forces on DOFs 1 through 3 and nodal moments on DOFs 4 through 6 after deterministic aggregation in global coordinates.
 - **FESA-REQ-LSMITC4-019** — The aggregated nodal moment component parallel to the approved nodal director shall be rejected as `unsupported-drilling-load`; a drilling-direction moment shall not be carried only by numerical stabilization.
@@ -140,10 +139,10 @@ Formulation, Numerical Review, I/O, Reference Model, Implementation Planning 및
 - **FESA-REQ-LSMITC4-031** — The physical MITC4 kernel shall use three translations and two director-tangent rotations per node and shall not treat the drilling rotation as a physical strain variable.
 - **FESA-REQ-LSMITC4-032** — The six-DOF element embedding shall transform global nodal rotations into two director-tangent components and one director-parallel drilling component using deterministic right-handed orthonormal frames.
- **FESA-REQ-LSMITC4-033** — The drilling contribution shall be symmetric, positive, scale-aware, sufficiently small to remain numerical, and sufficient to remove the nonphysical drilling null modes of otherwise valid models.
+- **FESA-REQ-LSMITC4-033** — The drilling contribution shall be a symmetric positive numerical stabilization of the four director-parallel coordinates and shall not define a physical drilling strain or load channel.
- **FESA-REQ-LSMITC4-034** — The drilling scale shall be derived from dimensionally compatible physical rotational stiffness; the implementation shall not apply `10^-3 * min(all Kii)` across mixed translational and rotational diagonal entries without an approved dimensional derivation.
+- **FESA-REQ-LSMITC4-034** — Let `R+` be the finite strictly positive diagonal entries of the physical local stiffness belonging only to the eight director-tangent rotational DOFs. The element shall use `k_ref=min(R+)`, `k_d=10^-3*k_ref`, `K_drill_local=k_d I4`, and the documented drilling transformation `T_d`; translational diagonals shall never enter `R+`.
- **FESA-REQ-LSMITC4-035** — Drilling stabilization shall not contribute to physical membrane, bending or transverse-shear generalized strain/resultant or section-point stress; its energy shall be recovered separately.
+- **FESA-REQ-LSMITC4-035** — Drilling stabilization shall not contribute to physical membrane, bending or transverse-shear generalized strain/resultant, section-point stress, or separately reported result quantities.
- **FESA-REQ-LSMITC4-036** — Exact drilling reference scale, dimensionless coefficient and acceptable artificial-energy ratio shall be approved through Research and Numerical Review before Implementation Planning; no implementation-selected default may close this decision silently.
+- **FESA-REQ-LSMITC4-036** — An otherwise accepted element with no finite strictly positive entry in `R+` shall fail numerical validation deterministically; coefficient sweeps, plateau selection, conditioning calibration, artificial-energy ratios, and drilling-specific result datasets are outside this feature.
 - **FESA-REQ-LSMITC4-037** — Source `S4R` shall not select reduced integration or Abaqus hourglass control; all accepted `S4` and `S4R` inputs shall use the single quadrature and MITC tying contract approved by the FESA formulation.
 - **FESA-REQ-LSMITC4-038** — The stabilized element shall retain exactly six physical rigid-body modes within the approved normalized tolerance, preserve stiffness symmetry and coordinate-transformation energy, and have positive energy for every accepted non-rigid physical deformation mode.
@@ -156,7 +155,7 @@ Formulation, Numerical Review, I/O, Reference Model, Implementation Planning 및
 - **FESA-REQ-LSMITC4-043** — The same shell locations shall output local section resultant components `[N11,N22,N12,M11,M22,M12,Q13,Q23]`, where `N` and `Q` have dimension `force/length` and `M` has dimension `force` as moment resultant per unit edge length.
 - **FESA-REQ-LSMITC4-044** — Each required shell location shall output local in-plane stress `[S11,S22,S12]` at bottom, middle and top section positions with dimension `force/length^2`; `S33` shall be documented as the plane-stress assumption and `S13/S23` point stress shall not be emitted.
 - **FESA-REQ-LSMITC4-045** — Result rows shall identify source element, integration/tying or recovery location, natural coordinates, section position, local frame/director and component order without averaging mismatched locations.
- **FESA-REQ-LSMITC4-046** — The output shall include free-DOF residual evidence, total force/moment equilibrium metrics, physical strain energy and drilling stabilization energy with dimension `force*length` and deterministic aggregation order.
+- **FESA-REQ-LSMITC4-046** — The output shall include free-DOF residual evidence, total force/moment equilibrium metrics and physical shell strain energy with dimension `force*length` and deterministic aggregation order; no drilling-specific stiffness, ratio or energy dataset is required.
 - **FESA-REQ-LSMITC4-047** — Abaqus output requests shall neither suppress nor expand the mandatory HDF5 quantity inventory; any deterministic FESA CSV projection shall remain a debugging/review view rather than official solver output.
 - **FESA-REQ-LSMITC4-048** — Nonfinite recovery values, inconsistent component/location inventory or failure to finalize required HDF5 rows shall fail the analysis without committing a partial successful state.
@@ -166,10 +165,10 @@ Formulation, Numerical Review, I/O, Reference Model, Implementation Planning 및
 - **FESA-REQ-LSMITC4-050** — Element invariant tests shall cover frame orthonormality/handedness, Jacobian sign, stiffness symmetry, coordinate-transformation energy invariance, six physical rigid modes, deformation-mode positivity and deterministic repeatability.
 - **FESA-REQ-LSMITC4-051** — Normalized algebraic acceptance shall use `1e-12` for symmetry, frame orthonormality and transformation-energy invariance and `1e-10` for rigid-mode action, linear-system residual and global equilibrium unless Numerical Review approves and documents an evidence-backed scale-aware replacement before Implementation Planning.
 - **FESA-REQ-LSMITC4-052** — Patch verification shall independently cover constant membrane strain/stress, pure bending, transverse shear and twist, including sign and component-order checks for generalized strain, resultant and recovered in-plane stress.
- **FESA-REQ-LSMITC4-053** — Locking/convergence verification shall include thin- and thick-shell or plate sequences over documented thickness ratios and mesh refinements and shall demonstrate the approved MITC4 transverse-shear behavior rather than judge one displacement on one mesh.
+- **FESA-REQ-LSMITC4-053** — The implementation shall pass the formulation-defined element invariants and patch/manufactured tests plus the two declared S4/S4R displacement reference cases; an expanded locking, distortion or curved-shell benchmark portfolio is not an implementation-completion gate for this feature.
- **FESA-REQ-LSMITC4-054** — Geometry verification shall include planar, smoothly curved, distorted and warped valid elements plus negative tests for degenerate, inverted, self-intersecting, opposing-normal and sharp-fold topologies.
+- **FESA-REQ-LSMITC4-054** — Geometry validation tests shall cover the exact accepted/rejected conditions defined by the formulation and I/O contract; `NR-O03` smooth-director calibration and `NR-O04` distortion/warp threshold sweeps are not required tests.
- **FESA-REQ-LSMITC4-055** — Curved-shell verification shall include at least one nodal-load-compatible pinched-cylinder, hemispherical-shell or equivalently justified benchmark; Scordelis-Lo may be included only with documented equivalent nodal loading inside the approved input subset.
+- **FESA-REQ-LSMITC4-055** — Additional pinched-cylinder, hemispherical-shell, Scordelis-Lo or mesh-convergence studies may be added later as nonblocking research or release evidence, but are not required for Implementation Planning or feature completion.
- **FESA-REQ-LSMITC4-056** — Drilling verification shall vary the approved stabilization coefficient around its nominal value, confirm stable equation rank, report physical displacement/resultant sensitivity and enforce the approved drilling-to-physical energy warning criterion.
+- **FESA-REQ-LSMITC4-056** — Drilling verification shall check the fixed formula in Requirement 034, symmetry, positivity, deterministic assembly, removal of the four nonphysical local drilling null modes, and exclusion from physical recovery; coefficient sweeps and drilling-energy checks are not required.
 - **FESA-REQ-LSMITC4-057** — Physics verification shall check load/reaction balance, global moment balance, displacement direction, symmetry, energy positivity, result sign and consistency between assembled residual and recovered shell resultants.
 ## Verification Quantities
@@ -180,31 +179,29 @@ Formulation, Numerical Review, I/O, Reference Model, Implementation Planning 및
 - shell_section_resultant: required, local `N/M/Q` eight components at documented locations
 - stress: required, local bottom/middle/top `[S11,S22,S12]`; Abaqus equality comparison N/A
 - residual: required, free-DOF and normalized global equilibrium evidence
- energy: required, separate physical strain and drilling stabilization energies
+- energy: required for the physical shell strain energy; drilling-specific energy output is not required
 - modes_and_invariants: required, six physical rigid modes, symmetry, transformation invariance and positive deformation energy
 ## Tolerance Policy
- **FESA-REQ-LSMITC4-058** — Abaqus reference pass/fail shall apply only to matched global `U1/U2/U3` rows using `tolerance_c = absolute_floor_c + relative_coefficient_c * reference_scale_c`.
+- **FESA-REQ-LSMITC4-058** — Abaqus reference pass/fail shall apply only to matched global `U1/U2/U3` rows using `tolerance_c = 1e-9 + 1e-6 * reference_scale_c`, exactly reusing the approved B33 displacement rule.
 - **FESA-REQ-LSMITC4-059** — `reference_scale_c` shall be computed only from finite Abaqus values in the same model, step/frame, quantity and component group; reference values shall not be zero-clamped and row-specific relative denominators shall not replace the group scale.
- **FESA-REQ-LSMITC4-060** — MITC4 displacement absolute floors and relative coefficients shall not silently inherit the B33 numerical values; Reference Model shall propose dimensioned floors and coefficients from benchmark evidence and Numerical Review shall approve them before reference comparison implementation.
+- **FESA-REQ-LSMITC4-060** — The `1e-9` absolute floor is expressed in the model's user-consistent length unit for U; no additional MITC4 tolerance calibration is required.
- **FESA-REQ-LSMITC4-061** — Global `UR1/UR2/UR3` rows shall be compared and fully reported but shall not affect pass/fail; errors beyond the approved large-error threshold shall emit deterministic nonblocking warnings and remain visible in known limitations.
+- **FESA-REQ-LSMITC4-061** — Global `UR1/UR2/UR3` rows shall use the same component-scale formula as Requirement 058 and shall be fully reported; an exceedance emits a deterministic nonblocking warning and never changes pass/fail.
- **FESA-REQ-LSMITC4-062** — The UR large-error threshold and drilling-energy warning ratio are `needs-downstream-decision` owned jointly by Reference Model and Numerical Review and shall be fixed before Implementation Planning.
+- **FESA-REQ-LSMITC4-062** — The `1e-9` UR floor is dimensionless. No separate UR large-error or drilling-energy threshold is required.
 - **FESA-REQ-LSMITC4-063** — Missing, extra, duplicate, nonfinite, schema-mismatched or source-identity-mismatched rows shall fail artifact/schema validation before numeric tolerance evaluation for both U and UR inventories.
 - **FESA-REQ-LSMITC4-064** — The comparison report shall record each U/UR row decision, maximum absolute error, component-scale normalized error, RMS error, vector-norm error and worst source row/component; nonblocking UR warnings shall not be omitted from an otherwise passing report.
 ## Reference Artifact Requirements
-The user-declared first candidate is `reference/shell/` and is said to contain an Abaqus
+The approved lightweight inventory uses the existing S4 and S4R paths below. These files
-`S4R` model. At requirements-authoring time that directory was not visible in the shared
+remain read-only; their names are identities, not canonical/legacy-policy decisions.
 workspace, so no exact filename, schema, units, generator, step/frame or row inventory is
 asserted here. The bundle shall remain read-only when it becomes observable.
- **FESA-REQ-LSMITC4-065** — Reference Model shall inventory `reference/shell/` without creating, renaming, rewriting or repairing files and shall classify a missing/unobservable candidate as `needs-reference-artifacts` rather than fabricate its content.
+- **FESA-REQ-LSMITC4-065** — The S4 case shall use `reference/shell/shell.inp` and `reference/shell/shell displacements.csv` without creating, renaming, rewriting or repairing either file.
- **FESA-REQ-LSMITC4-066** — A usable new reference bundle shall contain `model.inp` and `<model-id>_displacements.csv`, or shall receive an explicitly approved legacy-alias contract that records its exact existing filenames without rename; `metadata.json` is optional and its absence shall not make the bundle unusable.
+- **FESA-REQ-LSMITC4-066** — The S4R case shall use `reference/shellR/shellR.inp` and `reference/shellR/shellR displacements.csv` without creating, renaming, rewriting or repairing either file.
- **FESA-REQ-LSMITC4-067** — The approved Reference Model Contract shall record Abaqus generator/version, creation provenance, source element type, model/step/frame identity, user unit system, global coordinate convention, section/material/thickness data, CSV schema and tolerance policy; if `metadata.json` exists, it shall be inventoried read-only and checked against that contract and the stored artifacts.
+- **FESA-REQ-LSMITC4-067** — Reference readiness requires only the declared input and required displacement CSV, FESA `results.h5`, deterministic source-node/component mapping, and Requirements 058-063 tolerance/precheck rules. README, `metadata.json`, canonical naming, provenance, Abaqus version, duplicated model semantics, and a schema version are not required gates; a present `metadata.json` is optional read-only context.
- **FESA-REQ-LSMITC4-068** — Artifact validation shall confirm an approved single `*STEP, *STATIC` model, expected `S4` or `S4R` source type, supported keyword subset, unique finite displacement rows and exact source-node/component identity before comparison.
+- **FESA-REQ-LSMITC4-068** — Artifact validation shall require unique finite displacement rows and deterministic source-node/component identity before comparison; it shall not attempt to establish Abaqus internal formulation equivalence.
- **FESA-REQ-LSMITC4-069** — End-to-end mapping evidence shall cover at least one `S4` input and at least one `S4R` input; the declared `reference/shell/` S4R model may satisfy only the S4R side after inventory validation, so separate S4 evidence remains required.
+- **FESA-REQ-LSMITC4-069** — The two declared cases satisfy the required source-label coverage: `reference/shell/` covers S4 and `reference/shellR/` covers S4R. No expanded reference portfolio is required for this feature.
 - **FESA-REQ-LSMITC4-070** — Reference verification shall compare FESA HDF5 global nodal displacement rows directly against Abaqus displacement CSV rows by model, step/frame, source node and component identity; a FESA-generated CSV view shall not become the authoritative comparison source.
 - **FESA-REQ-LSMITC4-071** — Abaqus reaction, stress, strain and shell force/moment output may be retained as review evidence if present but shall not change the approved `U1/U2/U3` pass/fail boundary or become an undeclared equality gate.
 - **FESA-REQ-LSMITC4-072** — FESA agents shall not execute Abaqus or another reference solver and shall not generate, modify, restore or normalize reference artifacts during requirements, research, formulation, implementation or verification unless a later phase explicitly authorizes that operation.
@@ -221,72 +218,61 @@ without gaps or overlap.
 | `002-004` | `S4`/`S4R` mapping and identity | input/model | User approval | must | Parser/semantic/HDF5 metadata tests | Both source types map to one MITC4 path and preserve distinct source metadata and four-node identity | Exact element/type identity | I/O Definition; Implementation Planning | approved |
 | `005` | Six global nodal DOFs | model | User approval; project DOF convention | must | DofManager and HDF5 schema tests | Exact component order and no distributed equation ownership | Exact ordering | Formulation; I/O Definition; Implementation Planning | approved |
 | `006-010` | Isotropic material and single-layer section | input/model | User approval | must | Parser, mapping and validation tests | Valid `E,nu,t` resolve once per element; excluded section/material meanings fail | Exact inequalities; finite values | Research; I/O Definition; Implementation Planning | approved |
-| `011-016` | Initial director and geometry validity | geometry | User approval; MITC director kinematics | must | Geometry/unit/property-based tests | Deterministic unit directors for smooth valid meshes; every invalid topology fails | Smooth-angle and scale-aware Jacobian thresholds: Research + Numerical Review | Research; Formulation; Numerical Review; I/O Definition | approved-with-downstream-decision |
+| `011-016` | Initial director and geometry validity | geometry | User approval; MITC director kinematics | must | Geometry/unit/property-based tests | Deterministic unit directors for supported valid meshes; explicitly invalid mappings fail | Exact formulation/I/O predicates; no `NR-O03`/`NR-O04` calibration gate | Formulation; I/O Definition; Implementation Planning | approved |
-| `017-020` | Boundary and nodal-load subset | input/load | User approval | must | Parser/semantic/load tests | Global BC/CLOAD works; director-parallel moment and distributed loads fail | Drilling projection threshold: Numerical Review + I/O Definition | Formulation; I/O Definition; Implementation Planning | approved-with-downstream-decision |
+| `017-020` | Boundary and nodal-load subset | input/load | User approval | must | Parser/semantic/load tests | Global BC/CLOAD works; director-parallel moment and distributed loads fail | Exact-zero/projection rule from Formulation and I/O | Formulation; I/O Definition; Implementation Planning | approved |
 | `021-023` | Parser subset, wrappers and no-op policy | input | User approval; ADR-003/013/018 | must | Parser diagnostic and semantic identity tests | Only approved meanings affect Domain; excluded meanings fail closed | Exact keyword/diagnostic inventory | I/O Definition; Implementation Planning | approved |
 | `024-030` | Ownership, deterministic assembly and linear-static execution | architecture/execution | PRD; ADR-004/007/008/009/016/017 | must | Unit, orchestration and repeated-thread-count tests | Ownership boundaries, event order, residual reaction and deterministic bytes/rows match | `1e-12` deterministic numeric target where applicable | Numerical Review; Implementation Planning | approved |
-| `031-038` | 5-DOF physics embedded in 6-DOF with drilling stabilization | numerical boundary | User approval; MITC literature and thesis 6-DOF discussion | must | Formulation review, element invariant, rank and energy tests | Physical outputs exclude drilling; stable system retains six physical rigid modes | Scale/coefficient/energy ratio: Research + Numerical Review | Research; Formulation; Numerical Review | approved-with-downstream-decision |
+| `031-038` | 5-DOF physics embedded in 6-DOF with fixed drilling stabilization | numerical boundary | User approval; MITC literature and thesis 6-DOF discussion | must | Formulation review, invariant and rank tests | Exact `10^-3` positive rotational-diagonal rule; physical outputs exclude drilling | Fixed by Requirements 033-036 | Formulation; Numerical Review; Implementation Planning | approved |
 | `039-048` | Mandatory HDF5 output and failure atomicity | output | User approval; ADR-005/016/018 | must | Recovery, schema, identity, nonfinite and atomicity tests | Every quantity/location/unit/identity exists; failure commits no partial success | Exact component/location inventory; I/O Definition owns schema | Formulation; I/O Definition; Implementation Planning | approved |
-| `049-057` | TDD, invariants, patch, locking, geometry, curved shell and physics | verification | User approval; shell benchmark evidence; project process | must | CTest evidence, analytical/patch/convergence reports and physics review | Every verification family has passing evidence before release | `1e-12` symmetry/frame; `1e-10` rigid/residual; convergence targets by Numerical Review | Research; Numerical Review; Reference Model; Implementation Planning | approved-with-downstream-decision |
+| `049-057` | TDD, invariants, patch, declared references and physics | verification | User approval; shell formulation evidence; project process | must | CTest evidence, analytical/patch tests, two reference cases and physics review | Required tests pass; removed calibration/portfolio checks are not reintroduced | `1e-12` symmetry/frame; `1e-10` rigid/residual | Numerical Review; Implementation Planning | approved |
-| `058-060` | Translational displacement pass/fail tolerance | tolerance | User approval | must | Comparator unit/integration tests and report review | Every matched U row uses the approved mixed tolerance without clamp/omission | Floors/coefficient: Reference Model + Numerical Review | Reference Model; Reference Verification | approved-with-downstream-decision |
+| `058-060` | Translational displacement pass/fail tolerance | tolerance | User approval; B33 baseline | must | Comparator unit/integration tests and report review | Every matched U row uses `1e-9 + 1e-6*reference_scale_c` without clamp/omission | Fixed by Requirements 058-060 | Reference Verification | approved |
-| `061-062` | Rotational warning and drilling-energy warning | tolerance/warning | User approval | must | Comparator/diagnostic tests and report review | UR never changes pass/fail; large error and energy ratio produce deterministic visible warnings | Thresholds: Reference Model + Numerical Review | Numerical Review; Reference Model; Reference Verification | approved-with-downstream-decision |
+| `061-062` | Rotational warning-only comparison | tolerance/warning | User approval; B33 baseline | must | Comparator/diagnostic tests and report review | UR never changes pass/fail; same mixed-tolerance exceedance emits a deterministic warning | Fixed by Requirements 061-062 | Reference Verification | approved |
 | `063-064` | Row/schema failure and report completeness | reference verification | User approval; ADR-005/014/018 | must | Negative comparator and report-schema tests | Invalid inventory fails before numeric comparison; all U/UR metrics remain visible | No ignored invalid rows | I/O Definition; Reference Verification | approved |
-| `065-068` | `reference/shell` inventory and artifact validity | reference | User declaration; project artifact policy | must | Read-only inventory and schema/provenance review | Candidate becomes usable only after exact files, S4R type, provenance and row schema are validated | Current state `needs-reference-artifacts` | Reference Model | needs-reference-artifacts |
+| `065-068` | Exact S4/S4R reference-case inventory and row validity | reference | User declaration; ADR-019 | must | Read-only inventory and source-row/component precheck | Four declared paths exist; required rows are unique, finite and deterministically mapped | Requirements `058-063` | Reference Model; Reference Verification | approved |
-| `069-071` | S4/S4R coverage and displacement-only comparison | reference | User approval | must | Portfolio coverage and HDF5-to-CSV comparison | At least one model per source type; only U is blocking and UR is warning-only | Requirements `058-064` | Reference Model; Reference Verification; Physics Evaluation | approved-with-downstream-decision |
+| `069-071` | S4/S4R coverage and displacement-only comparison | reference | User approval | must | HDF5-to-CSV comparison | Declared S4/S4R cases; only U blocks and UR only warns | Requirements `058-064` | Reference Verification; Physics Evaluation | approved |
 | `072` | Reference solver/artifact immutability | governance | User/project policy; ADR-010 | must | Process audit and Git diff | No unapproved execution or artifact mutation | Exact zero mutations | All downstream agents | approved |
 ## Open Questions and Required Downstream Decisions
-No additional user scope decision is pending. The following technical values must remain visible
+No user or numerical calibration decision remains before Implementation Planning. Formulation
-and be approved by their named downstream owners before Implementation Planning:
+shall retain exact quadrature, tying interpolation, local-axis, sign and recovery definitions.
-
+Future geometric-nonlinear execution remains separately unauthorized even though its residual
-1. Research and Numerical Review shall define a dimensionally consistent drilling reference stiffness, dimensionless coefficient range and nominal value.
+and tangent derivation may remain in the formulation document.
 2. Numerical Review shall approve the maximum drilling-to-physical strain-energy warning ratio and the displacement/resultant sensitivity criterion for coefficient variation.
 3. Research and Numerical Review shall define the smooth-patch director angle criterion and scale-aware degenerate/Jacobian thresholds without an arbitrary `max(1, ...)` clamp.
 4. Reference Model and Numerical Review shall define MITC4 U component absolute floors and relative coefficients in the approved mixed-tolerance form.
 5. Reference Model and Numerical Review shall define the nonblocking UR large-error threshold and reporting severity.
 6. Formulation shall fix quadrature, tying-point interpolation, shear correction, local axes, sign conventions and recovery locations consistent with this baseline.
 7. `reference/shell/` shall be re-inventoried when visible. Until then its exact filenames, units, provenance and CSV schema are not established evidence.
 8. Separate `S4` end-to-end evidence remains required even if the declared `S4R` candidate is valid.
 9. The existing formulation draft's 5-DOF-only and no-drilling statements conflict with this approved baseline and shall be revised during the Formulation gate, not patched silently during implementation.
 ## Downstream Handoff
 ### Research Agent
 - Establish source-backed MITC4 linear kinematics, tying, quadrature, shear correction and benchmark applicability.
- Research dimensionally consistent 6-DOF drilling stabilization alternatives and sensitivity/energy criteria; distinguish the thesis's printed `10^-3 min(Kii)` rule from a FESA-approved scale-aware rule.
+- Record the thesis drilling rule and the approved dimensional restriction to positive physical rotational diagonals; do not reopen coefficient calibration.
- Research nodal-director generation, smooth-patch angle handling and distorted/warped geometry limits.
+- Preserve nodal-director and geometry evidence as implementation guidance without creating `NR-O03`/`NR-O04` calibration gates.
 - Identify nodal-load-compatible flat, locking, distorted and curved-shell benchmark families.
 ### Formulation Agent
 - Revise `docs/formulations/mitc4-shell-formulation.md` to align with global 6-DOF input/output and a physical 5-DOF MITC4 kernel plus numerical drilling embedding.
 - Keep current-product equations strictly linear static; retain geometric-nonlinear residual/tangent only as clearly separated future formulation.
- Define local frames, transformations, generalized component order, quadrature/tying, stress/resultant recovery, energy split and consistent units/signs.
+- Define local frames, transformations, generalized component order, quadrature/tying, stress/resultant recovery and consistent units/signs.
 - Do not introduce distributed-load product support or make `S4R` select reduced integration.
 ### Numerical Review Agent
- Independently review the revised formulation for rigid modes, rank, symmetry, invariance, locking, distortion, Jacobian/director validation and drilling contamination.
+- Independently review the revised formulation for dimensions, rigid modes, rank, symmetry, invariance, Jacobian/director handling and separation of fixed drilling stabilization from physical recovery.
- Approve every downstream numerical threshold listed above before Implementation Planning.
+- Treat drilling calibration/energy-ratio checks and `NR-O03`/`NR-O04` as removed scope, not missing evidence.
 - Require coefficient sensitivity and artificial-energy evidence rather than accepting a small coefficient by assertion.
 ### I/O Definition Agent
 - Define the exact Abaqus keyword/data subset for `S4`, `S4R`, single-layer `*SHELL SECTION`, material, BC and CLOAD semantics.
- Define source identity, auto-director metadata, unsupported-drilling-load projection, diagnostics and exact HDF5 dataset/row schemas.
+- Define source identity, auto-director data, unsupported-drilling-load projection, diagnostics and exact HDF5 dataset/row schemas without drilling-specific result datasets.
 - Preserve source element type separately from FESA formulation and define bottom/middle/top stress location identity.
 ### Reference Model Agent
- Re-inventory the user-declared `reference/shell/` candidate read-only and report exact files, S4R identity, provenance, units, step/frame and CSV row schema or `needs-reference-artifacts`.
+- Record the exact existing S4 and S4R input/displacement CSV paths from Requirements 065-066 and keep them read-only.
- Do not rename or repair noncanonical files; propose an explicit legacy alias only if retaining them is justified.
+- Define only the HDF5-to-CSV source-node/component projection and the already approved B33 mixed tolerance; do not add bundle administration or portfolio gates.
 - Prepare coverage for both S4 and S4R, flat/thin/thick/distorted/curved response and the approved displacement-only blocking comparison.
 - Propose evidence-backed U tolerance coefficients/floors and UR warning thresholds for Numerical Review approval.
 ### Implementation Planning Agent
- Do not start until Research, revised Formulation, Numerical Review, I/O and Reference Model contracts have resolved every named downstream decision.
+- Do not start until Research, revised Formulation, Numerical Review, I/O and lightweight Reference Model inventory are mutually consistent.
 - Trace every `must` requirement to RED/GREEN/VERIFY tests and preserve current solver ownership, deterministic assembly and failure-atomic HDF5 boundaries.
- Include independent tests for source-type mapping, auto directors, drilling rank/energy/sensitivity, all recovery quantities, schema failures and U-versus-UR comparison behavior.
+- Use the project Harness skill to propose self-contained implementation Steps for user approval, then write only the approved phase-planning files; do not execute Harness without a separate explicit request.
 - Include tests for source-type mapping, auto directors, fixed drilling rank/separation, required recovery quantities, row failures and U-versus-UR comparison behavior; exclude coefficient sweeps, drilling energy and `NR-O03`/`NR-O04`.
@@ -4,12 +4,12 @@
 - feature_id: `linear-static-mitc4-shell`
 - source_requirement: `docs/requirements/linear-static-mitc4-shell.md`
- status: `research-complete-awaiting-approval`
+- status: `approved`
 - owner_agent: `research-agent`
- date: `2026-08-11`
+- date: `2026-08-12`
 - product_scope: small-displacement, small-rotation, single-step linear static analysis
 - evidence_route: local papers in `docs/reference-papers/MITC4/`, the configured FEM wiki, original peer-reviewed papers, and official Abaqus documentation
- reference_inventory_state: `reference/shell/` was not observable during this research; no filename, schema, provenance, unit, or result value is asserted for that user-declared candidate
+- reference_inventory_state: existing read-only S4 case at `reference/shell/` and S4R case at `reference/shellR/`; exact comparison paths are fixed by the approved requirements
 - source_policy: each external claim below is assigned a reliability tier; FESA decisions are labeled `Project contract`, and derived recommendations are labeled `Inference` or `Research recommendation`
 This brief supplies evidence to the Formulation, Numerical Review, I/O Definition, and
@@ -22,10 +22,10 @@ formulation-equivalent to Abaqus S4 or S4R.
 1. What kinematics and degrees of freedom define the original four-node continuum-mechanics-based MITC4 element in the linear regime?
 2. How are the transverse shear components tied, and what evidence supports the quadrature and homogeneous-isotropic section behavior?
 3. How can the physical five-DOF kernel be exposed through six global rotational components without treating drilling rotation as a physical MITC4 strain?
-4. Which drilling-stiffness scales are dimensionally defensible, and which coefficient, sensitivity, and artificial-energy decisions remain unsupported?
+4. What evidence and dimensional restriction support the approved fixed drilling stabilization without turning it into a physical strain or load channel?
 5. What evidence supports connectivity-derived thickness directions, nodal-normal smoothing, local tangent frames, and geometry rejection?
 6. What may and may not be inferred when Abaqus S4 and S4R input types are both mapped to one FESA MITC4 formulation?
-7. Which patch, locking, distortion, curved-shell, and source-solver benchmarks fit the approved nodal-load-only scope?
+7. Which element-level checks and the declared S4/S4R source-solver cases fit the approved implementation scope?
 ## Source Reliability Tiers
@@ -87,20 +87,20 @@ navigation aid. No key numerical decision relies on them.
 - **F-12 — Verified transformation, Tier 2 (S3):** The nodal rotation projection can be written `[alpha,beta,gamma]^T = [t1^T;t2^T;n^T] theta_global`, followed by `K_global=T^T K_local T`. An orthonormal right-handed frame preserves virtual work and strain energy.
 - **F-12A — Kinematic inference requiring explicit review:** A physical rigid rotation of a five-DOF director shell is represented by rigid midsurface translations plus the tangent-plane change of each director; the director-parallel drilling coordinate is a gauge and can be zero. A rigid-mode test must construct those director changes explicitly. Blindly assigning the full spatial rotation vector, including its normal projection, to every six-DOF shell rotation would excite the numerical penalty and test a different quantity.
 - **F-13 — Verified thesis implementation, Tier 2 (S3):** The thesis fills each otherwise zero local drilling diagonal with `d=10^-3 min(Kii)`. It does not provide a dimensional restriction on which diagonals enter the minimum.
- **F-14 — Dimensional inference:** Translational stiffness diagonals have units `force/length`, while rotational stiffness diagonals have units `force*length`. Taking a minimum across all of them is not unit invariant and can change meaning under a length-unit conversion. The unqualified S3 rule is therefore not acceptable as the FESA rule and is already prohibited by P1.
+- **F-14 — Dimensional inference and approved restriction:** Translational stiffness diagonals have units `force/length`, while rotational stiffness diagonals have units `force*length`. Taking a minimum across all of them is not unit invariant. P1 therefore applies the thesis coefficient only to finite strictly positive physical director-tangent rotational diagonals, all of which have `force*length` units.
 - **F-15 — Verified precedent, Tier 1 (S9):** Abaqus states that a small drill penalty is proportional to transverse shear stiffness. Its small-strain shell theory presents a rotational constraint scale of the family `G h A_node / (1 + q A_node/h^2)`, multiplied by a small dimensionless factor, with `q=2.5e-5`. The base quantity has units `force*length` and transitions toward a thickness-cubed scale for thin shells. Abaqus says the small factor was selected numerically but does not disclose a general FESA-ready value.
- **F-16 — Research recommendation:** Carry at least two dimensionally compatible candidates into Numerical Review: (A) the S9 transverse-shear/area transition family and (B) the isotropic bending rigidity `D_iso=E t^3/[12(1-nu^2)]`. A statistic formed only from the physical rotational block is a third implementation-dependent comparator. Do not silently choose among them in code.
+- **F-16 — Historical alternatives, not current gates:** A transverse-shear/area transition scale and `D_iso=E t^3/[12(1-nu^2)]` are dimensionally compatible alternatives. The project has instead approved the implementation-local statistic `k_ref=min(R+)`, where `R+` contains only positive physical rotational diagonals; no comparison among these alternatives is required in this feature.
- **F-17 — Research recommendation with explicit evidence limit:** `10^-3` may be used only as the center of a logarithmic sensitivity experiment because S3 supplies that order of magnitude; it is not an approved nominal coefficient. Numerical Review must examine lower and higher orders, equation rank/conditioning, physical `U/N/M/Q` sensitivity, and separate drilling energy before fixing a nominal value and range.
+- **F-17 — Approved project decision with evidence limit:** P1 fixes `k_d=10^-3 k_ref` and `K_drill_local=k_d I4`. The `10^-3` value is a project choice informed by S3, not a claim of universal optimality or Abaqus equivalence. Coefficient sweeps, plateau/conditioning calibration, and response-sensitivity studies are outside the approved implementation gate.
- **F-18 — Verified evidence gap, Tier 1 (S13):** Abaqus exposes artificial strain energy associated with singular-mode and drill constraints but gives no drill-specific acceptable percentage. Guidance for kinetic energy or dynamic hourglass energy is not transferable to this static drilling penalty. A numerical `E_drill/E_physical` warning limit remains a blocking Numerical Review decision.
+- **F-18 — Scope consequence:** S13 supplies no drill-specific acceptable artificial-energy percentage. P1 therefore defines no `E_drill/E_physical` threshold and requires no drilling stiffness, ratio, or energy result dataset. This absence is an explicit scope decision, not missing numerical evidence.
 - **F-19 — Verified boundary, Tier 1 (S7/S8):** MITC4/D and independent-rotation membrane formulations give drilling rotation physical/variational content. FESA's approved diagonal regularization is not MITC4/D, must not carry a director-parallel applied moment, and does not justify intersecting-shell, sharp-fold, hinge, or shell–beam drilling transfer.
 ### Initial director, tangent frame, and geometry evidence
 - **F-20 — Verified precedent, Tier 1 (S10):** Abaqus computes normals from adjacent shell midsurfaces and uses order-independent grouping; its default averaging heuristic requires all normals in a smooth group to remain within 20 degrees. The manual warns that a coarse mesh can create a false fold or smooth a real fold.
 - **F-21 — Project contract, informed by F-20:** FESA uses one deterministic area-weighted unit director at a smooth shared node and fails discontinuous/opposed incident directions, requiring duplicated source nodes at a physical fold. It does not adopt Abaqus's ability to retain multiple normals at one source node.
- **F-22 — Research recommendation:** Use 20 degrees as the first Numerical Review candidate for the maximum incident-normal deviation in a smooth patch, not as a proven theorem. Because it becomes a hard FESA rejection rather than an Abaqus grouping choice, it must be tested against curved benchmark mesh densities and documented as a mesh-resolution limit before approval.
+- **F-22 — Evidence limit and project decision:** The 20-degree value is an Abaqus modeling heuristic, not a universal MITC4 constant. P1 does not adopt or calibrate a smooth-patch angle in this feature; `NR-O03` is removed. Supported inputs still require finite nonzero, consistently oriented incident normals.
 - **F-23 — Research recommendation:** Build each tangent frame by selecting the global basis least aligned with the unit director, projecting or crossing it into the tangent plane, normalizing, and forming the second tangent by a cross product. This avoids the near-parallel fixed-axis singularity seen in simpler source examples and is deterministic, but the exact sign/axis rule belongs in Formulation.
- **F-24 — Research recommendation:** Geometry acceptance should use dimensionless or geometry-scaled measures, such as positive Jacobian at every Gauss and tying location, `J_min/J_max`, and `J/L_char^2`; it must not use `max(1,geometry_scale)`. No reviewed source establishes a universal numerical cutoff for all valid warped shells, so the constants remain a Numerical Review decision supported by distortion sweeps.
+- **F-24 — Evidence limit and project decision:** No reviewed source establishes a universal distortion/warp cutoff. P1 therefore requires only the formulation/I/O finite, nonzero-area, topology, and positive-Jacobian predicates and removes `NR-O04`; a distortion/warp threshold sweep is not an implementation-readiness gate.
 ### Abaqus S4/S4R mapping and comparison meaning
@@ -115,9 +115,9 @@ navigation aid. No key numerical decision relies on them.
 ## Candidate Benchmarks
-Exact acceptance tolerances are intentionally not assigned here. Published values are
+This catalog records useful future evidence, not the minimum implementation-completion
-source targets whose geometry, units, boundary conditions, and loading must be reproduced
+portfolio. The approved blocking source-solver cases are only the existing S4 and S4R
-and independently checked before becoming a Reference Model contract.
+input/displacement pairs named in P1. Published values below do not create additional gates.
 | benchmark_id | source/evidence | configuration and target quantities | verifies | does not verify / adaptation limit |
 | --- | --- | --- | --- | --- |
@@ -131,8 +131,8 @@ and independently checked before becoming a Reference Model contract.
 | `MITC4-PINCHED-CYLINDER` | S1/S3/S12 | thin cylinder with end diaphragms and concentrated pinching load; radial displacement and mesh convergence. S12 cites `1.825e-5`; S3 uses `L=600`, `R=300`, `t=3`, `E=3e6`, `nu=0.3`, `P=1` and reports `1.8248e-5` | nodal-load-compatible inextensional bending, complex membrane response, curvature, convergence, regular/irregular mesh sensitivity | one response point cannot certify stresses or drilling; diaphragm semantics must fit approved BCs without rigid elements |
 | `MITC4-NAFEMS-LE3` | S12 | radius-10 hemispherical shell, `t=0.04`, `E=68.25 GPa`, `nu=0.3`, opposite radial `2 kN` point loads; target `Ux(A)=185 mm`; S4 and S4R official cases exist | positive Gaussian curvature, point load, symmetry, automatic directors, S4/S4R source-label coverage candidate | official decks use explicit nodal normals and shorthand symmetry/perturbation semantics; FESA adaptation and mesh refinement are required, and the target is not a tolerance |
 | `MITC4-SCORDELIS-LO` | S1/S2/S4/S5 | quarter cylindrical roof, mesh convergence of free-edge displacement and preferably field/resultant evidence | mixed-dominated shell behavior and classical convergence comparison | original dead-weight loading is outside P1; only a documented deterministic equivalent nodal CLOAD version may enter FESA product tests |
-| `MITC4-DIRECTOR-GEOMETRY` | S10 plus P1 | connectivity reversal, smooth curved patches around the candidate angle, opposed normals, duplicated-node fold, valid warp, bow-tie, inversion, degeneracy, and Gauss/tying Jacobian sweeps | deterministic director generation and fail-closed geometry policy | physical shell accuracy |
+| `MITC4-DIRECTOR-GEOMETRY` | S10 plus P1 | connectivity reversal, opposed normals, bow-tie, inversion, degeneracy, and Gauss/tying Jacobian checks | deterministic director generation and fail-closed basic geometry policy | `NR-O03`/`NR-O04` calibration and physical shell accuracy |
-| `MITC4-DRILL-SENSITIVITY` | S3/S9/S13 plus inference | dimensionally compatible scale candidates; logarithmic coefficient sweep around the S3 order; unconstrained rank, constrained solve, `U/N/M/Q`, condition evidence, `E_physical`, and `E_drill` | regularization sufficiency and physical contamination risk | no source supplies an automatic passing coefficient or energy ratio |
+| `MITC4-DRILL-FIXED` | S3 plus P1 | exact positive physical-rotational-diagonal selection, fixed `10^-3` factor, free-element rank, symmetry, and physical-recovery exclusion | implementation of the approved numerical regularization | coefficient optimality, sensitivity plateau, or energy ratio |
 | `MITC4-S4-S4R-SAME-PATH` | S11 plus P1 | identical supported model written once as S4 and once as S4R; FESA HDF5 numeric rows equal while source metadata differs | approved semantic mapping and deterministic internal path | Abaqus S4/S4R equivalence; their reference displacements are expected to differ on finite meshes |
 The local S3 hemispherical example with target displacement `0.0924` and its reported
@@ -143,10 +143,10 @@ problems must not be mixed.
 ## Verification Relevance
 - **Element code verification:** rigid modes, stiffness symmetry, tangent-frame orthonormality, transformation-energy invariance, quadrature cross-checks, individual tying values, and patch fields isolate algebraic mistakes before a source-solver comparison.
- **Locking and convergence:** thin/thick cantilevers, pinched cylinder, LE3, and optional Scordelis–Lo must be run as mesh/thickness sequences. Underpredicted displacement on a single thin mesh is evidence of possible locking, not a complete diagnosis.
+- **Locking and convergence:** thin/thick cantilevers, pinched cylinder, LE3, and Scordelis–Lo remain useful future studies. They are not additional completion gates for the approved two-case implementation scope.
 - **Geometry verification:** tests must evaluate every formulation-required Gauss and tying location, not only the element center. Director smoothing and Jacobian quality are separate checks; a smooth director cannot rescue a self-intersecting or inverted mapping.
- **Drilling verification:** rank success alone is insufficient. Numerical Review must compare physical outputs across the coefficient sweep and examine separate artificial energy. Drilling stabilization must remain absent from `E/N/M/Q/stress` recovery.
+- **Drilling verification:** verify the fixed formula, dimensional family, symmetry, positivity, four-mode regularization, and absence from physical `E/N/M/Q/stress` recovery. Sensitivity and artificial-energy evidence are excluded.
- **Reference comparison:** a valid S4 and S4R artifact portfolio can test source mapping and global displacement. It cannot prove formulation identity. Schema, node/component identity, units, and finite values fail before P1's mixed displacement tolerance is evaluated.
+- **Reference comparison:** the declared S4 and S4R cases test source mapping and global displacement. They cannot prove formulation identity. Missing, extra, duplicate, nonfinite, or source-node/component-mismatched required rows fail before P1's mixed displacement tolerance is evaluated.
 - **Physics sanity:** force and global moment balance, symmetry, displacement direction, reaction sign, positive physical energy, free residual, and consistency of recovered resultants remain mandatory even when all reference displacement rows pass.
 - **Validation boundary:** the identified sources provide analytical, benchmark, and source-solver verification. No experimental dataset was established for the approved homogeneous linear-static feature; physical validation remains N/A unless separately added.
@@ -172,72 +172,65 @@ problems must not be mixed.
 2. Use a single documented `2x2` midsurface integration path for source S4 and S4R, subject to independent Formulation derivation and Numerical Review rank/patch checks.
 3. Use homogeneous-isotropic plane-stress resultants with `5/6` transverse-shear correction as the formulation candidate, and recover linear in-plane stress at `-t/2,0,+t/2`.
 4. Project global rotations with deterministic right-handed nodal frames and keep drilling stiffness and energy algebraically separate from all physical shell results.
-5. Reject the unqualified `10^-3 min(all Kii)` rule. Compare the dimensionally compatible F-16 candidates before selecting a scale.
+5. Apply `10^-3` only to the minimum finite positive physical director-tangent rotational diagonal and use the resulting scalar uniformly for the four local drilling coordinates.
-6. Treat 20 degrees as a documented smooth-normal candidate requiring mesh/benchmark calibration, not as a self-justifying universal threshold.
+6. Do not adopt a calibrated smooth-normal angle or distortion/warp threshold in this feature; retain finite, orientation, topology and positive-Jacobian validation.
-7. Make pinched cylinder and NAFEMS LE3 the preferred nodal-load-compatible curved tests; retain Scordelis–Lo only as a documented equivalent-nodal-load auxiliary case.
+7. Keep pinched cylinder, NAFEMS LE3 and Scordelis–Lo as optional future evidence rather than implementation-completion requirements.
-### Blocking numerical decisions before Implementation Planning
+### Closed decisions and nonblocking evidence limits
-1. **Drilling reference scale:** choose between or formally combine the F-16 candidates after unit-rescaling, thickness, mesh-size, rank, and conditioning studies.
+1. **Drilling:** P1 fixes the positive physical-rotational-diagonal scale and `10^-3` factor. Alternative-family comparison, coefficient sweep, conditioning plateau and artificial-energy threshold are not required.
-2. **Drilling coefficient:** define the tested logarithmic range and nominal dimensionless value. S3 supports only considering `10^-3` as an experiment center, not approving it.
+2. **Director/geometry:** `NR-O03` and `NR-O04` are removed. The absence of a calibrated smooth angle or distortion/warp cutoff is not missing evidence.
-3. **Drilling acceptance:** define physical displacement/resultant sensitivity and an `E_drill/E_physical` warning rule. If physical energy is zero or near zero, the ratio must not be hidden by an arbitrary denominator clamp; the two energies need explicit classification.
+3. **Reference tolerance:** P1 reuses the B33 formula `1e-9 + 1e-6*reference_scale_c`; U exceedance fails and UR exceedance only warns.
-4. **Director angle:** approve the hard smooth-patch criterion after checking representative curved mesh densities. The consequence of rejection versus mesh refinement must be documented.
+4. **Reference cases:** the existing `reference/shell/` S4 and `reference/shellR/` S4R input/displacement pairs are the complete required inventory. Administrative bundle metadata and an expanded portfolio are not gates.
 5. **Geometry scale:** approve dimensionless Jacobian/warp measures and constants at Gauss and tying locations. No universal source value was identified.
 6. **Reference tolerances:** P1 assigns U floors/coefficients and UR warning thresholds to Reference Model and Numerical Review; this Research brief supplies no invented values.
 7. **Artifact inventory:** re-inventory `reference/shell/` read-only when it becomes visible. Until then the user-declared S4R candidate provides no auditable benchmark evidence, and separate S4 evidence is still required.
-These issues do not require a new user scope choice, but Items 1–5 must be closed by
+No research-owned numerical decision remains blocking for Implementation Planning.
 Numerical Review before implementation planning can truthfully claim a complete numerical
 contract.
 ## Requirement Traceability
 | requirement area | research evidence | downstream result |
 | --- | --- | --- |
 | `006-010` material/section | F-09–F-11 | homogeneous isotropic plane-stress and section recovery candidate; exact I/O remains downstream |
-| `011-016` director/geometry | F-20–F-24, `MITC4-DIRECTOR-GEOMETRY` | 20-degree and scale-aware geometry candidates; constants remain blocking Numerical Review decisions |
+| `011-016` director/geometry | F-20–F-24, `MITC4-DIRECTOR-GEOMETRY` | basic deterministic validity rules; `NR-O03`/`NR-O04` calibration removed |
-| `031-038` 5-to-6 DOF/drilling | F-12–F-19, `MITC4-DRILL-SENSITIVITY` | dimensional rejection of mixed diagonals; scale/coefficient/energy decisions carried forward |
+| `031-038` 5-to-6 DOF/drilling | F-12–F-19, `MITC4-DRILL-FIXED` | fixed dimensionally compatible rotational-diagonal rule; calibration and energy output excluded |
 | `037` S4/S4R common path | F-25–F-27, `MITC4-S4-S4R-SAME-PATH` | source mapping supported only as a FESA product decision, never an Abaqus formulation claim |
-| `039-048` shell outputs | F-09–F-11/F-18 | physical/drilling energy split and bottom/mid/top stress-location evidence |
+| `039-048` shell outputs | F-09–F-11/F-18 | physical shell output and bottom/mid/top stress locations; no drilling-specific dataset |
-| `049-057` element verification | F-28/F-29 and Candidate Benchmarks | invariant, patch, locking, distortion, curved, drilling, equilibrium, and energy portfolio |
+| `049-057` element verification | F-28/F-29 and Candidate Benchmarks | required invariant/patch/fixed-drill checks; broader portfolio remains optional |
-| `058-064` U/UR tolerance | F-25–F-27 | displacement comparison is meaningful but numerical tolerance/UR warning values remain with Reference Model/Numerical Review |
+| `058-064` U/UR tolerance | F-25–F-27 plus P1 | exact B33 mixed tolerance; U blocking and UR warning-only |
-| `065-072` reference artifacts | S11/S12 and current inventory state | official public S4/S4R candidates identified; local user artifact remains `needs-reference-artifacts` and immutable |
+| `065-072` reference artifacts | S11/S12 and current inventory state | exact existing S4/S4R paths, source-row/component mapping, and immutability |
 ## Downstream Handoff
 ### Formulation Agent
 - Re-derive the exact bilinear geometry, physical `20x20` kernel, local component order, edge-midpoint shear tying, `B` matrices, plane-stress section matrices, `2x2` quadrature, and bottom/middle/top recovery from S1/S2 rather than copying OCR text blindly.
- Revise the existing formulation draft to expose global six-DOF input/output while keeping only two tangent rotations in physical strains. Define `T`, signs, frame construction, physical/drilling energy split, and all units explicitly.
+- Revise the existing formulation draft to expose global six-DOF input/output while keeping only two tangent rotations in physical strains. Define `T`, signs, frame construction, the fixed drilling embedding, and all units explicitly.
 - Keep any geometric-nonlinear residual/tangent material in a clearly marked future-only section; it is not part of the approved executable analysis.
- Present drilling scales as candidates pending Numerical Review, not as an implementation default.
+- State the approved fixed drilling rule exactly and do not reintroduce candidate sweeps or drilling-specific recovery.
 ### Numerical Review Agent
 - Independently check six physical rigid modes, non-rigid rank, symmetry, transform energy, patch consistency, and every Gauss/tying Jacobian.
- Resolve all seven blocking decisions above. Require consistent-unit rescaling and thickness/mesh sweeps for drilling, not only a successful factorization.
+- Confirm the fixed drilling rule's dimensions, symmetry, positivity and physical-recovery separation without reopening coefficient calibration.
 - Audit the original MITC4 distortion/membrane-locking limitation and set convergence expectations that do not imply MITC4+ behavior.
- Approve benchmark mesh densities compatible with the hard director-angle policy.
+- Treat `NR-O03`/`NR-O04` and expanded benchmark portfolios as removed/nonblocking scope.
 ### I/O Definition Agent
 - Preserve source S4/S4R identity separately from `FESA-MITC4`, while mapping both to one quadrature/kernel path.
- Define automatic director metadata, the exact unsupported-drilling-load projection rule, and fail-closed diagnostics for folds, normals, Jacobians, section/material data, and excluded loads.
+- Define automatic director data, the exact unsupported-drilling-load projection rule, and fail-closed diagnostics for normals, topology, Jacobians, section/material data, and excluded loads without calibrated `theta_smooth`.
 - Distinguish Gauss, tying, and section positions in HDF5 identities; do not average mismatched result locations.
 ### Reference Model Agent
- Prefer pinched-cylinder and NAFEMS LE3 adaptations for curved nodal-load coverage, and explain every change from the published model needed to fit the approved FESA keyword subset.
+- Record the exact existing S4 and S4R input/displacement paths without creating, renaming, repairing, or normalizing artifacts.
- Provide at least one S4 and one S4R model, but never use their different Abaqus algorithms to select different FESA kernels.
+- Define deterministic HDF5-to-CSV source-node/component mapping and the fixed B33 tolerance; do not require provenance, naming policy, README/metadata, duplicated model descriptions, or an expanded portfolio.
 - Re-inventory `reference/shell/` without creating, renaming, repairing, or normalizing artifacts. Establish provenance, units, node/component identity, and supported semantics before using any row.
 - Propose U mixed-tolerance values and nonblocking UR warning thresholds from actual artifact scales and mesh/convergence evidence for Numerical Review approval.
 ### Implementation Planning Agent
- Do not start until revised Formulation, Numerical Review, I/O, and Reference Model contracts close the blocking decisions.
+- Start after revised Formulation, Numerical Review, I/O, and lightweight Reference Model inventory are mutually consistent.
- Translate every selected benchmark and negative geometry case into TDD `RED -> GREEN -> VERIFY` work while preserving the project linear-static lifecycle and deterministic assembly/output rules.
+- Use the project Harness skill to draft self-contained RED/GREEN/VERIFY Steps, obtain user approval before writing `phases/` planning files, and never run the executor without a separate explicit request.
 ### Coordinator Agent
- Treat Research as evidence-complete once this brief is approved, but track drilling scale/coefficient/energy, director/Jacobian constants, U/UR tolerance, and missing reference artifacts as downstream blockers.
+- Treat Research as approved and do not track removed drilling calibration, `NR-O03`/`NR-O04`, tolerance calibration, bundle administration, or portfolio expansion as downstream blockers.
 - Reopen Requirements only if physical drilling loads, fold/intersection coupling, explicit normals, distributed loads, MITC4+, or nonlinear execution is proposed.