optimality contracts: what a certified result guarantees

Every solver in the suite carries a contract class: the strongest claim its result is allowed to make. The class is part of the result itself, delivered in a typed _contract block beside the native output, with status, diagnostics, certificates, and warnings.

The audit is per solver, not per family. An iterative solve and an exact search sit in the same toolbox but are permitted entirely different sentences.

class	meaning	safe claim	solvers
exact_optimal	The method provably returns the global optimum for the declared model.	global optimum, when native status confirms completion	12
exact_decision	Complete decision, feasibility, or equivalence answer with a witness for the declared model.	proved SAT, UNSAT, feasible, or equivalent	4
optimal_to_tolerance	Numerical optimizer with residual, KKT, Bellman, or constraint diagnostics under stated model assumptions.	optimal to tolerance under assumptions	6
solve_to_tolerance	Equation, root, spectral, or linear solve with residual diagnostics.	solution to tolerance	14
local_convergence	Local nonlinear optimization or fixed-point convergence.	local converged result, no global proof	9
heuristic_best_so_far	Stochastic or local search with a best-so-far output and no global certificate.	best found within the search budget	6
stochastic_estimate	A statistical estimate, delivered with sample-count and error diagnostics.	estimate with sampling diagnostics	4
policy_decision	Deterministic rule, contract, selection, or control decision.	validated policy decision, not an optimum	10
computed_not_optimizer	Deterministic numeric, symbolic, or transform primitive with no optimization objective.	validated computation, not an optimum	32
total			97

class

meaning

safe claim

solvers

exact_optimal

The method provably returns the global optimum for the declared model.

global optimum, when native status confirms completion

exact_decision

Complete decision, feasibility, or equivalence answer with a witness for the declared model.

proved SAT, UNSAT, feasible, or equivalent

optimal_to_tolerance

Numerical optimizer with residual, KKT, Bellman, or constraint diagnostics under stated model assumptions.

optimal to tolerance under assumptions

solve_to_tolerance

Equation, root, spectral, or linear solve with residual diagnostics.

solution to tolerance

local_convergence

Local nonlinear optimization or fixed-point convergence.

local converged result, no global proof

heuristic_best_so_far

Stochastic or local search with a best-so-far output and no global certificate.

best found within the search budget

stochastic_estimate

A statistical estimate, delivered with sample-count and error diagnostics.

estimate with sampling diagnostics

policy_decision

Deterministic rule, contract, selection, or control decision.

validated policy decision, not an optimum

computed_not_optimizer

Deterministic numeric, symbolic, or transform primitive with no optimization objective.

validated computation, not an optimum

total

Last audited 2026-06-06 against the wired roster. Caps and native status flags always take precedence: a node-limit result is an incumbent, never an optimum, whatever the class says.