Track candidate Graphcal features from capability research

[shunichironomura]

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Candidate backlog derived from 30 real-world numerical-analysis and Excel-workbook migration use cases. Inclusion here does not imply that a feature should be added; each item can be converted into a dedicated issue after review.

Numerical algorithms and solver contracts

• Bounded convergence iteration (iterate_until) — Express iterative methods with explicit tolerance and maximum work.
• Bracketed scalar root finding / goal seek — Enable reverse sizing, flash calculations, and IRR without custom plugins.
• Nonlinear-system solving — Support coupled nonlinear engineering equations with explicit or automatic Jacobians.
• ODE/DAE integration and event detection — Cover transient models that need adaptive steps, algebraic constraints, or stop events.
• PDE and stencil primitives — Make grid updates and boundary policies explicit and statically checked.
• Complex reductions and linear algebra — Enable direct phasor networks, frequency-domain models, and complex solves.
• Sparse matrices, assembly, and solvers — Scale finite-element and network models beyond dense-kernel limits.
• Matrix decomposition family — Add QR, Cholesky, SVD, Schur, and standard/generalized eigen decompositions.
• Least-squares, regression, and curve fitting — Support calibration and data reduction with fit diagnostics.
• Numerical quadrature and special functions — Cover probability integrals and domain equations absent from elementary math built-ins.
• FFT/RFFT and signal-processing kernels — Support practical spectral analysis without an O(N²) manual DFT.
• Unit-aware LP/MILP modeling — Represent decisions, objectives, and constraints without erasing physical dimensions.
• Deterministic sampling and statistical analysis — Add seeded distributions, covariance, quantiles, histograms, and sensitivity metrics.

Types, shapes, indexes, and execution

• Atomic results with multiple indexed fields — Return coherent solver outputs without repeated calls or convention-based pairing.
• Richer plugin ABI value types — Allow Complex, Key, Int, Bool, algebraic values, and richer records at extern boundaries.
• Heterogeneous typed block vectors and matrices — Preserve dimensions in mixed position/velocity, observation, and covariance systems.
• Typed topology and graph operations — Model node/edge connectivity, traversal, and cycle validation without flat encodings.
• Derived axes and richer checked Nat arithmetic — Express transform output shapes such as FFT bins statically.
• Irregular coordinate and datetime indexes — Represent measured samples, ephemerides, schedules, and dated cash flows directly.
• Runtime-validity or bounded ragged results — Represent event-sized trajectories without sentinel values or invented fixed extents.
• Chunked, tiled, lazy, or streaming indexed evaluation — Process large simulations and datasets within explicit resource bounds.
• Prepared-input shape schemas — Establish checked mesh or dataset cardinalities before compilation.
• Neighborhood, lag/lead, window, and ordered search operations — Simplify stencils, time-series formulas, and first-passing-size selection.
• Masks, multi-axis reductions, sorting, ranking, and binning — Support N-D summaries, histograms, DVHs, and Pareto analyses.
• Temperature-point and temperature-interval semantics — Permit explicit affine boundary conversions while preserving safe temperature differences.
• Decimal/fixed-point quantities and rounding modes — Support accounting and other calculations requiring exact decimal policy.
• Calendar and work-period semantics — Model holidays, shifts, end-of-month rules, and financial day-count conventions.

Data and workbook migration boundaries

• Schema-checked tabular import boundaries — Validate CSV, EPW, XLSX, or database fields, units, and headers before evaluation.
• Runtime text and opaque identifiers — Carry dynamic part numbers, account codes, labels, and descriptions as data.
• Typed row datasets with keys — Represent dynamic-cardinality records with primary/foreign-key constraints.
• Join, group-by, filter, pivot, sort, and mapping operations — Cover common workbook and relational-data transformations explicitly.
• Explicit missing-data schemas and policies — Require deliberate failure, interpolation, or imputation instead of spreadsheet blank coercion.
• Versioned engineering datasets — Package property tables, catalogs, and calibrations with provenance and validity domains.
• Time-series alignment and resampling — Combine irregular sources using explicit interpolation and extrapolation policies.
• Task-network and BOM analysis — Provide checked critical-path and multi-level material-explosion operations.
• Declarative calculation reports — Generate reviewable engineering sheets, certificates, schedules, and statements from typed results.
• Additional analysis-specific plot encodings — Add interval/Gantt, histogram, control-chart, and error-bar presentations.
• Data-lineage and source-snapshot metadata — Make external inputs and refresh provenance auditable.
• Functional-core integration architecture — Define how external shells provide grids, approvals, I/O, and collaboration without weakening the pure core.