Module solvers 

Zero-Allocation Solver Library

This module provides mathematical solvers designed for the #![no_std] zero-allocation environment of Qualia-DB. All solvers operate on fixed-size stack arrays and maintain strict memory constraints.

Enabled:

• All native and WASM solver kernels
• qpu — QPU problem formulation + in-process job queue (non-WASM only)

(Note: this module is not actually #![no_std] — the qpu submodule pulls in std + tokio. The individual solver kernels are written to be no-std-compatible, but the attribute only has effect at the crate root, so it is not applied here.)

Re-exports

pub use calculus::BVPState;

pub use calculus::IntegralChunk;

pub use calculus::ODEState;

pub use calculus::RungeKutta4Static;

pub use calculus::ShootingMethodBVP;

pub use calculus::SimpsonsIntegratorChunked;

pub use linear_algebra::ConstTensorContractor;

pub use linear_algebra::FixedLanczosEigensolver;

pub use linear_algebra::Matrix4x4;

pub use linear_algebra::StaticLuDecomposition;

pub use linear_algebra::Tensor3x3x3;

pub use linear_algebra::Vector4;

pub use optimization::BoundedNewtonRaphson;

pub use optimization::CurveFitState;

pub use optimization::LevenbergMarquardtStack;

pub use optimization::NelderMeadSimplex;

pub use optimization::OptimizationState;

pub use optimization::RootFindingState;

pub use quantum_optimizers::QAOAAngleOptimizer;

pub use quantum_optimizers::QAOAAngles;

pub use quantum_optimizers::QuantumOptimizerState;

pub use quantum_optimizers::SpsaGradient;

pub use quantum_optimizers::SpsaOptimizer;

pub use symbolic_logic::BoundedSatSolver;

pub use symbolic_logic::DefeasibleState;

pub use symbolic_logic::ForwardChainingDefeasible;

pub use symbolic_logic::SatState;

Modules

activation

Activation & normalization functions — the STEM definitions of the element-wise and reduction operations a transformer forward pass is built from.

attention

Scaled dot-product attention — the STEM definition of the transformer’s attention operation, as the composition it actually is:

calculus

Calculus & Differential Solvers - Zero-Allocation Implementation

exact

Exact / arbitrary-precision arithmetic — the §3.1 “exact computation” foundation.

feed_forward

Feed-forward network (SwiGLU) — the STEM definition of the transformer FFN block as the composition it is:

fuzzy_query

f-SPARQL — degree-aware querying over the semantic graph.

geometric_algebra

Geometric Algebra Module

graph_match

Fuzzy RDF graph matching (Ma, Li & Ma) — degree-aware similarity and the approximate subgraph match that is the identity-reconciliation primitive.

graph_opt

Graph optimization & propagation (Graph corpus / Vector Semantics).

grounding

KG↔LLM grounding evaluation — does a model’s asserted claim actually trace to the graph facts it cited?

interpolation

Interpolation & function approximation (Gap analysis §3.7).

learning

Statistical learning (ISL) — predictive estimators built on the engine’s existing foundation, never duplicating it (see stats_plan.md).

linear_algebra

Linear Algebra & Matrix Solvers - Zero-Allocation Implementation

number_theory

Number theory & combinatorics (Gap analysis §3.2-NT).

ontology_align

Ontology alignment (CI-SKM ch 4) — the engine behind “machine proposes closeMatch, signed human ratifies exactMatch”. Given two ontologies’ entity similarity, it proposes a graded correspondence set as review-required closeMatch — never an asserted exactMatch (the human-ratification invariant, enforced by correspondence).

optimization

Optimization & Root Finding - Zero-Allocation Implementation

polynomial

Polynomial & complex algebra — the engine’s home for complex arithmetic, real quadratic solving, and dependency-free polynomial root finding.

qpu

QPU (Quantum Processing Unit) solver integration.

quantum_optimizers

Hybrid Quantum Optimizers - Zero-Allocation Implementation

rope

Rotary Position Embedding (RoPE) — the STEM definition: a 2-D rotation.

special_functions

Special functions (Gap analysis §3.5) — beyond the Gamma/erf/incomplete family already in crate::solvers::statistics::distributions::special.

statistics

Statistics solver — the single, canonical home for numeric statistics.

symbolic_logic

Symbolic & Logic Solvers - Zero-Allocation Implementation

transforms

Integral & discrete transforms (Gap analysis §3.4) — Fourier, Laplace, Z.

units

Units, physical constants & dimensional analysis (Gap analysis §3.6).

vector_calculus

Vector calculus (Calculus plan §4.3) — the differential operators (grad, div, curl, Laplacian) symbolically over the CAS, and the integral side (line integrals, surface flux) numerically, with the divergence/Green theorems as validation.

Structs

SolverConfig

Common solver configuration

SolverState

Common solver state — includes all fields referenced by disabled sub-modules so they can be re-enabled without structural changes.

Enums

SolversError

Unified error type for solver operations.

Type Aliases

SolverResult

Result type for solver operations