phi-engine 1.1.2

Golden Continuum φ-Engine — An analytic compiler that computes exact calculus of black-box callables by exploiting factorial taylor structure.

φ-Engine — Exact Black-Box Calculus for Executable Systems

φ-Engine is an analytic compiler that computes exact calculus of black-box callables by exploiting factorial taylor structure.

Differentiate and integrate any callable to hundreds of digits. No computational graph. No symbolic form. No grid. No Δx.

pip install phi-engine

Quick Demo

from phi_engine import PhiEngine
from mpmath import mp

mp.dps = 200
eng = PhiEngine()

f = lambda x: mp.cos(x * x)
result = eng.differentiate(f, mp.mpf("0.25"))

print("f'(0.25):", mp.nstr(result, 12))
# Abs error: ~1e-162

What It Does

Callable ($\frac{d}{dx}$)	Order	Time	Correct Digits
GELU(x)	1	183 ms	1994
GELU(x)	3	195 ms	1088
100-layer tanh(x)	1	1.21 s	1963
100-layer tanh(x)	2	1.87 s	(no oracle exists)
sin(10¹⁰⁰·x²)	1	14 ms	1083
e^x·sin(10⁶·x)	10	43 ms	109

All orders. Parallel execution. Hybrid CPU/GPU routing. Deterministic φ-certificates.

φ-Engine knows at runtime how much precision each taylor term needs and routes to devices accordingly.

Watch φ-Engine differentiate a 724k param TANH model and route terms to CUDA as necessary:
Hybrid Self-Aware Precision Routing Example

φ-Engine evaluates your callable at factorial-spaced points using exact rational moment laws. All Taylor terms up to a predetermined degree are annihilated exactly — not asymptotically. Precision grows superfactorially with depth, and the engine knows how much precision is needed per term.

Watch AI Try to break it:

ClaudeOpus 4.5 vs φ-Engine

GPT5.2 vs φ-Engine

Click here for more adversarial AI tests

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Documentation

• WHITEPAPER.md — Full technical explanation
• examples/ — Runnable demos (differentiation, integration, loss landscape, hybrid CUDA, much more)
• LetterToCantor.pdf — Complete mathematical proof of the foundations that made φ-Engine possible

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Capability Briefs

• For AI Researchers
• For Engineers
• For Physicists
• For Mathematicians
• For Cryptographers

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Licenses

GPLv3-or-later (code) · CC BY-SA 4.0 (documents). Open forever.

Contact

Alex B — [e-mail]

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