Learn the Framework

Non-Newtonian calculus, scheme composition, and spectral gap theory.

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What is Meta-Calculus?

A gentle introduction requiring only basic calculus. Understand the big idea in 5 minutes.

No prerequisites | 5 min read

Recommended Reading Order

  1. 1.

    What is Meta-Calculus?

    The big idea, why it matters, key concepts

  2. 2.

    Failures and Pivots

    What we tried that did not work (and why)

  3. 3.

    Core Framework

    Generators, derivatives, integration, weights

  4. 4.

    Proofs and Derivations

    Step-by-step mathematical proofs with no skipped steps

  5. 5.

    Complete Textbook

    9 chapters, full treatment with code examples

Built on Non-Newtonian Calculus

This framework extends the mathematical foundations established by Michael Grossman and Robert Katz.

Grossman, M., & Katz, R. (1972). Non-Newtonian Calculus. Lee Press.

Grossman, M. (1983). The First Nonlinear System of Differential and Integral Calculus. Mathco.

CASCADE Toy Benchmark

The CASCADE suite is a synthetic toy benchmark: it measures the reduction in distance to a singular point of one 2-D test function. It is labeled non-citable and is not a physics result.

View the synthetic toy benchmark →

Quick Reference

D_BG[x^n] = e^n

Power-law identity (x > 0)

D_G[e^x] = e

Geometric derivative of an exponential

L_BG[1/r]=-1

Bounded log-slope on r > 0; 1/r itself still diverges