Mathematics Core Semantics

The language and structures the theory must earn in mathematics before it can answer.

Mathematics Core Semantics includes recovery targets for formal checkability, finite syntax and proof objects, finite arithmetic and algebraic calculation, Euclidean geometry, representation of standard formal systems as object theories, and explicit bridge criteria into standard mathematics.

Core Semantics does not require reproducing established semantics unchanged. It requires carrying what works, retyping what breaks, and making any semantic transformation explicit.

Why Core Semantics differs from open problems

The Mathematics Structural Challenge Ledger asks whether the kernel can express or re-ground Clay- and Langlands-scale stress tests. Mathematics Core Semantics asks which mathematical capacities must be earned before those stress tests can even be handled responsibly.

The recovery burden is not to import standard foundations wholesale. It is to recover formal checkability, finite syntax and proof objects, finite arithmetic and algebraic calculation, Euclidean geometry, representation of standard formal systems as object theories, and explicit bridge criteria into standard mathematics.

Mathematical refusals

These recovery targets must be read together with the Mathematical Refusals. The tau-kernel does not recover mathematics by silently importing unrestricted classical background assumptions.

Recovery targets

Relation to Verify

Mathematics Core Semantics connects directly to formal verification, bridge verification, TauLib, and the meta-verification frontier. The page fixes the public burden; the Verify lane records how much of that burden has actually been discharged.