Source code and Mathematical Proof: https://github.com/Purrplexia/LettersToMyHeroes

PyPI package: https://pypi.org/project/phi-engine

Hi HN,

You are the first public audience to see this project. It has not been posted anywhere else yet. I chose to release it here first because Hacker News consistently rewards rigor, originality, and open-source tools built for ideas rather than for marketing.

This project contains entirely original mathematics. The core theory is proven in a rigorous 34-page proof titled "LetterToCantor.pdf" included in the repository. It builds a constructive continuum and a gridless analytic calculus from factorial moment laws and golden-ratio scheduling.

Derivatives and integrals of any analytic function can be computed *exactly* by a *frozen*, function-agnostic operator composed of exact rational coefficients (a "β-stream"). No grids, no step size, no limits, no symbolic math. Once synthesized, these operators work globally for every analytic function. β-streams can be synthesized on-the-fly in milliseconds for thousands of digit accuracy, precompute is only needed if you want to push the boundaries of digits to comical scale. Once a β-stream is synthesized or loaded, it is cached and reused on all future functions. No recompute, no wasted cycles, no dependency on the function.

To make this reproducible and verifiable, the project includes phi-certificates: canonical JSON/gz files that store these global calculus operators as exact rationals, sealed with canonical SHA-256. Anyone can load a certificate, verify its key material, and use the operator forever on any analytic function. The certificate is the calculus rule itself. A phi-certificate is a canonical, global, arbitrary-precision analytic instruction, sealed by a 32-byte hash.

All code is GPLv3-or-later. All math documents are CC-BY-SA 4.0. Everything is permanently free and open.

The repo includes: - the full mathematical proof (LetterToCantor.pdf) - the phi-engine (exact rational contraction engine) - phi-certificates (deterministic, hash-verifiable analytic operators) - demos of extreme derivatives and integrals (sin(googol x^2) in 400ms to 6000 digits) - demos of engine logic - demos of certificate loading and emission - full reproducibility scripts and PGP verification

Every artifact in this repo is hashed and PGP signed, ensuring bit-for-bit reproducibility.

If you want to see the math, start with: Cantor_GoldenContinuum/LetterToCantor.pdf!!! It is a crafted experience for those who love mathematics.

If you want to try the engine immediately: pip install phi-engine (see examples/ after install)

If you care about reproducible, verifiable mathematics and globally reusable analytic operators, I hope you enjoy exploring this. I welcome questions, critique, and adversarial tests from the HN community — you are the first eyes on it — I will post it elsewhere later.