An Observer-Centric, Metric-Agnostic Universe from Spectral Compression

1. Foundational Postulates: The State-Space

Based on observational evidence the universe web observe is finite, informational, timeless, and static. Given a state space of $n$ bits, there exist $2^n$ possible configurations. Ontologically, all configurations are entirely equal. Binary system is not fundamental, it it chosen for convenience only.

No physical laws, geometric properties, or native metrics are prescribed at this foundational level. Time is not a fundamental property; rather, it emerges strictly as a random walk through these configurations. To maintain absolute typicality without relying on fine-tuned algorithms, this walk is modeled as a fair bit-flip process (an Ehrenfest process) moving through increasing states of entropy.

2. The Spacetime Fabric: Chains and Knots

The system is initially analyzed as a 1+1 dimensional model (one emergent spatial dimension and one temporal dimension) whose structure is dictated purely by entropy:

• The Chain (Spacetime Fabric): The individual links of the chain represent the minimal units of the spacetime fabric—the raw bits within a bitstring. Spatial dimension is defined as the ordinal sequence of the walk through these chains, with the fundamental minimal temporal resolution being a single bit change between consecutive configurations.
• The Knots (Microstructures): Emergent microstructures within the bitstring manifest as specific substring patterns (e.g., repeating localized sequences). These knots represent the physical building blocks of the universe, including the macroscopic observer and everything the observer is capable of observing.

The Mechanics of Spacial Contraction and Time Dilation

Because a knot consists of multiple bits, its formation inherently consumes bits from the string, thereby reducing its total apparent length, as observed from internal emergent observer. This derives a natural concept of spatial density and distance. Furthermore, a complex microstructure consisting of many bits cannot appear or disappear instantaneously after a single fair bit-flip; it requires a sequence of multiple flips to form or alter. This restrictions dilates the temporal resolution observable to a macroscopic entity constructed from these very knots.

3. The Structural Hump-Curve and Cosmic Expansion

The model does not rely on a pre-programmed or assumed algorithms. Instead, everything emerges out of statistical typicality.

It can be mathematically demonstrated that during an Ehrenfest random-walk process starting from zero entropy, the probability of any given substring pattern (a knot) typically follows a distinct hump-curve:

1. Early Phase (Low Entropy): The bitstring is highly ordered (e.g., all zeros); knot probability is zero.
2. Mid Phase (Rising Entropy): Random flips inevitably construct structured clusters by sheer statistical typicality. The hump-curve peaks here, yielding maximum structural density.
3. Late Phase (Equilibrium/Heat Death): The system approaches maximum entropy, causing complex microstructures to dissolve back into a uniform, white-noise plateau residual value.

When you subtract this structural hump-curve (which dynamically reduces spacetime resolution via knotting) from a standard relaxed, unguided increasing entropy curve, it naturally yields a three-fold expansion profile (characteristic of cosmic inflation, deceleration, and dark energy acceleration). This naturally resolves the cosmological fine-tuning problem.

       ▲
       │        /  Relaxed Entropy Curve
       │       /
Value  │      /     _..---.._   Structural Hump-Curve (Knots)
       │     /    .'         `.
       │    /    /             `-.____
       │   /    /
       └───┴───────────────────────────►
         Low Entropy       High Entropy (Equilibrium)

4. The Observer and Geometric Dimensionality

So far model is thoroughly metric-agnostic. A 1D chain of knots possesses no native geometry and can be mapped or interpreted geometrically in nearly infinitely many ways. This raises a fundamental question: What dictates the topology and the observed dimensionality (3D) of our universe?

The answer is Observer Selection governed by Algorithmic Information Theory (Solomonoff Induction).

The macroscopic observer is defined as a geometry (observational fact). Out of all the mathematically possible ways the underlying chain of knots can be arranged to describe the observer and their environment, the metric that dominates the measure is the one that compresses best.

The Spatio-Temporal "MPEG" Codec

Crucially, this compression does not operate over an isolated, instantaneous horizontal slice of time (like a static JPEG frame). Compression is evaluated over the entire spacetime history block—the entire "movie" of the universe (like an MPEG video file).

A sequence of chaotic, disconnected spatial states cannot be compressed temporally. Therefore, the trajectories through the $2^n$ state-space that survive Solomonoff selection are those that possess deep temporal redundancy.

┌─────────────────────────────────┐
│ Temporal Slice T_n              │ ◄── High Spatial Randomness
├─────────────────────────────────┤     (Fails JPEG/Spectral Compression)
│ Temporal Slice T_2              │
├─────────────────────────────────┤
│ Temporal Slice T_1              │
└─────────────────────────────────┘
                ▲
                │ Evaluated globally as a 2D/3D Spacetime Block 
                │ via Spatio-Temporal "MPEG" Compression

We choose Spectral Complexity over standard Kolmogorov complexity for two main reasons. First, because of a glaring observational fact: the micro-cosmos waves everywhere. Waves, periodic functions, and continuous smooth movements are the ultimate compression codec. We perceive a smooth, wavy, 3D geometric reality because it represents the most highly compressed, informationally efficient representation of the underlying bit-string walk. Universes that do not compress spectral-temporally have a massive "file size" and are heavily suppressed by the measure, leaving the wavy, geometric paths to dominate reality. Second, 'sin' function is the simplest continuous closed function. It's Kolmogorov complexity is constant, and compared to the spectral data (modes, frequencies and phases), its informational cost is vanishingly small.