Metadata-Version: 2.4
Name: wavefunction
Version: 0.0.3
Summary: Quantum Wavefunction with Spectral Complexity measure
Author-email: Juha Meskanen <juha@meskanen.com>
Maintainer-email: Juha Meskanen <juha@meskanen.com>
License-Expression: MIT
Project-URL: Homepage, https://github.com/juhakm/wavefunction
Project-URL: Bug Reports, https://github.com/juhakm/wavefunction
Project-URL: Say Thanks!, https://github.com/juhakm/wavefunction
Project-URL: Source, https://github.com/juhakm/wavefunction
Keywords: quantum,quantum-field-theory,information-theory,wavefunction,spinor,emergent-physics,minimal-spectral-length,computational-physics
Classifier: Development Status :: 4 - Beta
Classifier: Intended Audience :: Science/Research
Classifier: Intended Audience :: Education
Classifier: Topic :: Scientific/Engineering
Classifier: Topic :: Scientific/Engineering :: Physics
Classifier: Topic :: Scientific/Engineering :: Mathematics
Classifier: Topic :: Scientific/Engineering :: Information Analysis
Classifier: Programming Language :: Python
Classifier: Programming Language :: Python :: 3
Classifier: Programming Language :: Python :: 3.9
Classifier: Programming Language :: Python :: 3.10
Classifier: Programming Language :: Python :: 3.11
Classifier: Typing :: Typed
Classifier: Operating System :: OS Independent
Requires-Python: >=3.9
Description-Content-Type: text/markdown
License-File: LICENSE
Requires-Dist: numpy<1.27,>=1.25
Requires-Dist: scipy>=1.10
Requires-Dist: numba>=0.59
Requires-Dist: matplotlib
Dynamic: license-file

# Wavefunction

Quantum Mechanical complex valued wavefunction with Spectral Complexity measure.

## Install

```bash
pip install wavefunction
```

## Introduction

Spectral Complexity measure for complex-valued wavefunctions.

## Theory background (Meskanen 2026 — "The Wavefunction as Compression")

The central hypothesis is that the quantum wavefunction is the universe's data-compression codec. Internal observers — themselves composed of compressed structures — perceive their constituent degrees of freedom as wave-like because they are observing *compressed information*. The codec that produces this compression is the Fourier / spectral decomposition.

### Spectral Complexity $C_s$

A wavefunction $\psi(x)$ can always be written as a superposition of spectral modes, each characterised by two attributes:

- **frequency** $\omega$ — the rate of oscillation, unbounded above zero
- **phase** $\phi$ — the offset of the oscillation, bounded in $[0, 2\pi)$

The *spectral complexity* $C_s(\psi)$ is the total continuous information cost needed to specify the set of modes that materially compose $\psi$:

$$
C_s(\psi) = \sum_i \left[ \frac{\omega_i}{\Delta \omega} + \phi_{\text{cost}}(\phi_i) \right]
$$

#### Frequency cost (dominant term)

$\frac{\omega_i}{\Delta \omega}$ is the number of resolution steps $\Delta \omega$ needed to locate frequency $\omega_i$. It is unbounded, continuous, and grows linearly with frequency. This term *dominates* $C_s$ and is the reason the measure exponentially suppresses high-frequency (rough, chaotic) states.

The identification $\Delta \omega = \hbar \ln 2$ connects the minimum frequency resolution to Planck's constant.

#### Phase cost (subdominant, bounded)

Each phase $\phi_i \in [0, 2\pi)$ requires a finite amount of information to specify. The cost is *global* over all modes: it measures how much information is needed to distinguish the phases from one another.

With only two modes at phases 0 and $\pi$, very little is needed; with many modes at crowded, uneven phases, somewhat more is required. In practice this term is bounded by $\log_2(N_{\text{modes}})$ and is a second-order correction.



#### Amplitude and the fidelity engine

Amplitude does not appear as a separate encoding cost. Instead it determines *which modes are included* in the description via a power-ranked fidelity engine: modes are added in descending power order until the accumulated power reaches a target fraction of the total. Modes below this threshold are simply absent from the description — they are not part of the codec output and contribute zero complexity cost.

This correctly handles the case where many weak modes coexist with a few dominant ones: the dominant modes determine $C_s$; the weak modes are free.

#### Solomonoff suppression and the probability profile

Under Solomonoff-like induction the prior probability of a configuration is $P(\psi) \propto 2^{-C_s(\psi)}$. Because $C_s$ is a *sum* over independent modes, the probability *factorises*:

$$
P(\psi) \propto \prod_i 2^{-\omega_i / \Delta \omega}
$$

Each mode is suppressed independently and exponentially by its frequency. The resulting probability profile is Boltzmann-like with inverse temperature $\beta = \ln(2)/\Delta \omega$:

$$
P(\text{mode } i \text{ present}) \propto \exp(-\ln(2) \cdot \omega_i / \Delta \omega)
$$

Smooth, low-frequency, compressible states dominate the measure. Boltzmann brains, random fluctuations, and chaotic configurations are exponentially suppressed — not by fine-tuning, but because they require many high-frequency modes to describe.

### The conjecture $C_s \propto S_{\text{Euclidean}}$

The central open conjecture (Meskanen 2026, §9) is that the minimum spectral complexity path through configuration space coincides with the minimum Euclidean action path of standard quantum gravity. 


## Note about peformance

Implementing anything computationally heavy with pure python makes no sense. This class should be implemented in 'C'.
