Scope boundaries
This is the most important page in this section. omnibias is powerful within a precise scope, and overstating that scope is the failure mode we most want to prevent.
What omnibias does claim
- Closed-form
σⁿ(z)for the smooth (Riccati) activation family, at any order, with oneσevaluation — bit-identical across backends. - Exact derivatives of one-layer fields and exact propagation of Taylor jets through compositions (Faà di Bruno), to float64 round-off.
- Rigorous enclosures (interval / affine / Taylor-model) that provably contain the true value, outward-rounded.
- Tamper-evident certificates, and a
theorem_prover_verifiedflag earned only by a genuine Lean kernel pass.
What omnibias does not claim
Read this before quoting any result
- It is not a PDE solver and does not prove existence, uniqueness, or regularity of true PDE solutions. It bounds the residual of a given trained surrogate over a given box.
- It does not close the infinite analytic obligations of hard problems. The
Yang–Mills mass-gap scaffold in
formal/keeps those obligations honestlysorry. Do not represent it otherwise. - "Exact" always carries a category. Numerical / grid-based pieces (fractional calculus, spectral methods) are not closed form and are labelled so.
- A
theorem_prover_verified = falseflag means not proven by the kernel — it must not be reported as if it were proven.
The three exactness categories
Full detail: Exactness & scope.
A one-line honesty test
Before publishing a number, can you name its exactness category and point to the command (and, if rigorous, the certificate) that produced it?
If not, it is not ready to publish.