Runtime Approximation Graphs

Backend-independent composition theorems for approximation bounds over typed SSA/tape graphs.

The leaf modules define forward graph composition, reverse-mode/backward graph composition, and the bridge from proof-level graphs to the executable autograd-algebra GraphData representation. Concrete numeric backends instantiate these graph theorems by supplying local per-op approximation lemmas. Architectures are compositions of those nodes; there is no MLP, convolution, or attention case in the graph induction. NumericalCertificate complements the analytic error bounds with an operation-keyed IEEE-754 range registry and the backend audit for the selected kernel capsules. Its coverage pass names every unsupported primitive before certificate propagation begins.