Native fitted-height assembly milestone

This implements the bounded instantaneous slice selected in fitted-height-liquid-formulation.md. FittedHeightWorkspace assembles and inspects one immutable periodic 2.5D polygonal strip. It owns no accepted velocity/pressure/liquid state, has no clock, and supplies no advancement, geometry replacement, pressure solve or transfer step. The existing advancing-viscosity refusal and prior owners are unchanged.

API and one physical geometry

FittedHeightGeometry supplies ordered cap points, independently ordered fixed bottom abscissae, extrusion width, constant density and dynamic viscosity. Both boundaries share a period and the cap closes at the same height. This permits a skewed snapshot after horizontal cap motion while keeping the bottom fixed. Each strip cell has two macrotriangles with the declared diagonal; centroids and shared-centroid/edge intersections define the six-way Powell–Sabin splits. Reject graph/order/closure, intersection, thickness or triangle-quality failure. Minimum quality and height are rejection thresholds. They never floor masses.

All three components use the same positive nodal median-dual masses. Periodic node identification and the fixed cap/bottom affine trace map R are explicit; bottom normal velocity is zero. velocity_embedding and embed_velocity expose that map. The caller’s field arrays are borrowed during inspection, rather than stored as a competing accepted flow state. Midpoint trace values must equal the checked endpoint average; bottom normal velocity must be exactly zero.

inspect accepts a full-vector periodic nodal field and coefficients in the assembled pressure basis. Each basis field is a selected column of the reduced horizontal velocity divergence, with units inverse length; pressure coefficients are therefore not per-triangle pressure samples. pressure_basis exposes the sparse reconstruction. No pressure gauge is pinned. Constant pressure remains in the image, as the native constant-mode representation checks demonstrate.

Geometry, masses, gradients, pressure basis and face topology are immutable views. triangle_stiffness returns the full 9×9 local matrix on raw geometric nodes, so affine and rigid-rotation patches can be tested without mislabeling those fields as globally periodic/bottom-admissible flows. Global diagnostics apply the full symmetric-strain operator and integrated pressure transpose to caller fields. No assembled force is applied to an accepted velocity.

Shared mass/flux/pressure/strain contracts

Within each microtriangle, masses are ρ b A/3 and the exact P1 gradients determine all velocity strain terms and the integrated negative divergence. The strain operator uses weights μ b A (2,2,1,1,1) for (∂x u,∂y v,∂y u+∂x v,∂x w,∂y w). Both out-of-plane shears are included. The pressure force is the transpose of the same integrated negative divergence. The native affine patch balances that full stress against independently integrated prescribed edge traction. This qualifies its assembly, rather than a solved homogeneous free-cap condition or pointwise stress convergence.

During inspect, bottom mesh velocity is zero and cap mesh velocity is the caller’s physical horizontal/vertical cap velocity. Centroid velocities are averages of their macro vertices. Shared edge split velocities differentiate the actual intersection construction with checked dual-number arithmetic. Area derivatives and mass rates come from those same moving microtriangles. A native central finite difference rebuilds cap/bottom geometry independently and checks these mass derivatives. It is an infinitesimal geometry consistency test, not a finite conservative material trajectory.

Dual-face pieces integrate the continuous physical velocity minus this mesh velocity. Contributions are aggregated into one oriented flux f_ij per periodic node pair before donor momentum and dissipation are formed. All three carried components use that same aggregated flux. audit_shared_flux recomputes it and requires each pair and flux bit to match; a circulation that preserves all mass marginals is rejected. There is no externally supplied accepted new height or independent cap-donor velocity.

The diagnostic ledger checks

m'_i + Σ_j f_ij = ρ b Σ_{T incident i} A_T (div u_h)_T / 3,
Uᵀ K U = Σ_T μ b A_T (2 exx²+2 eyy²+sxy²+sxz²+syz²),
Uᵀ Bᵀπ = −Σ_T b A_T π_T div u_h,
Σ_i U_i·c_i = ½Σ_i |U_i|²Σ_j f_ij + D_adv.

The first is the full Reynolds identity. Its right side is zero for a strongly divergence-free input. geometric_identity_error measures that identity; continuity_defect_max separately reports m’+Σf and divergence_max reports the actual element divergence. A deliberately divergent native example has a small geometry error and a large continuity defect. The API does not accept it as a physical incompressible step. Internal momentum-flux and strain/pressure force resultants are reported separately; wall reactions and physical external work are not hidden in an advancing update.

Pressure image and numerical limits

The strip declares 8C+1 pressure modes for C columns. Constructor elimination selects independent divergence columns and must return that dimension, or reject with PressureRank. It uses partial row pivoting and an explicit relative rank threshold; dependent columns are not silently turned into a pressure gauge. Sparse Q terms are reconstructed from the original divergence coefficients. Native tests check selected velocity columns against Q, positive pressure Gram pivots, the implied full row rank of integrated B, and constant pressure representation for C=2,3,4,6,8,12 in the tested geometry family.

This is finite numerical rank qualification. The dimension formula, rank threshold and elimination pivot ratio do not establish a uniform inf-sup bound, a spectral conditioning estimate or a mesh-family convergence theorem. Unresolved rank/geometry cases reject. The persistent dense rank scratch is bounded and counted, while Q and the element/face operators remain sparse or matrix-free. A stronger topology-derived pressure basis and stability study remain appropriate before a pressure solve is qualified.

Memory, failure and cancellation

FittedHeightPlan checks every capacity product before allocation. Constructors also enforce maximum columns, pressure-term capacity and a total payload limit. Every vector uses try_reserve_exact; actual capacities, not just logical lengths, are charged to the limit. Persistent rank scratch is included. On this qualified 64-bit target the nominal managed payload is

1056 C² + 9576 C + 208 bytes.

For C=4 this is 55,408 bytes. It includes geometry, macro edges, gradients, R, dual-face pieces/pairs, reserved sparse Q terms, pressure-column IDs, rank scratch, masses, moving-geometry scratch, candidate diagnostic rows and triangle scratch. There is no dense transfer map, dense global stiffness matrix, per-inspection heap allocation or hidden history snapshot. Fixed stack matrices and Vec headers, allocator bookkeeping, caller input/output buffers and the example’s serialization buffers are outside this managed-array payload. Caller diagnostic output alone is 96 bytes per periodic node on this target. The API exposes the managed payload so an eventual simulation facade must include it in its own total budget.

The geometry never mutates after construction. Nonfinite/nonzero subnormal inputs or checked intermediates, nonzero product/division underflow, overflow, invalid trace/shape, identity failure and cancellation reject. Scratch views may be incomplete after rejection and are explicitly named scratch. Caller output rows are copied only after every gate and the final callback, so they preserve all prior bits on failure. Native tests cancel every inspection callback and verify unchanged output and an identical retry. Constructor failure drops its partial workspace without replacing an existing object.

Qualification and next slice

The native contract suite covers mass/gradient partition, full-vector affine traction, rotation/translation null strain, pressure image/constant mode, material graph translation, changing-mass constant transport, actual rebuilt geometry derivatives, nonzero adjoint pressure work, density/width/viscosity scaling, arithmetic/shape/trace errors, capacity limits, uncertain rank and marginal-correct wrong-motion rejection. Full default/core/desktop Rust tests, formatting and strict Clippy are required, together with focused release tests. Actual debug/release example binaries produce static geometry/diagnostic arrays; independent normal/optimized Python compares them with the frozen rational research assembly and rejects altered mass, flux, third shear, pressure force and advancing-simulation scope. The figure uses those actual native arrays and is labelled instantaneous, not a temporal replay.

The frozen 15 Lean identities remain conditional exact-real algebra. Their prior compiled and negative-audited bytes are preserved. They are not Rust/IEEE, geometry-assembly, stability or physical-validation proofs. No new Lean theorem or pressure/free-surface solver is claimed by this implementation.

The next slice must select and qualify a physical space-time geometry/transport integrator. A semidiscrete pressure solve must differentiate B(t)RZ(t)=0 and include B’RZ; an endpoint pressure projection on independently changed geometry is insufficient. The same path must supply integrated dual fluxes and the GCL, and full momentum transport and force work must pass their own residual gates. Only then can candidate mesh, velocity, pressure and derived phase exports publish through one facade with a common physical time and rollback tests. Uniform pressure stability, pointwise traction, temporal accuracy, surface reconstruction/export integration, native advancing/rendered dynamics, variable density, surface tension and adhesion remain unqualified. The advancing refusal therefore remains in place.