A Recursive, Prime-Gated Framework for Self-Emergent Information Processing
Abstract
This paper introduces the Self-Emergent Processor (SEP), a novel framework positing that reality is a recursive, information-theoretic system. We redefine fundamental physical concepts: identity emerges from inverse recursive referencing, energy from phase imbalance, entropy from recursive alignment, and information acts as a cohesive force analogous to gravity. The system's dynamics are governed by a discrete, prime-gated iteration, formalized through a novel Lagrangian.
We present the SEP Engine, a high-performance C++ implementation that operationalizes these principles through quantum-inspired algorithms (QBSA, QFH) operating on raw data streams. Through a series of computational simulations and applications in complex systems analysis, we demonstrate the framework's capacity to quantify emergent properties like coherence and stability. The implications of this work for quantum computing, cosmology, and the theory of information are discussed, presenting a new paradigm for understanding computation and physical reality as a unified, self-emergent process.
Core Postulates
1. Identity is Recursion
Identity is not a static property but an emergent process defined dynamically through continuous inverse recursive references.
2. Energy is Phase Imbalance
Energy is the potential for change arising from misalignment of complex phases between interacting informational units.
3. Entropy is Recursive Alignment
Entropy measures the system's progress toward equilibrium through recursive interactions and phase alignment.
4. Information is Gravitational Coherence
Information acts as a cohesive force, binding disparate units into stable structures through correlational attraction.
5. Measurement is Historical Reference
Quantum measurement collapses potentiality into discrete historical facts that condition subsequent interactions.
Mathematical Formalism
Prime-Gated Time
The evolution of the universe is governed by discrete "update events" occurring at prime-numbered intervals (2, 3, 5, 7, 11, ...). This ensures:
- Irreducible, fundamental time steps
- Non-periodic, non-repeating dynamics
- Inherent incommensurability preventing trivial loops
Discrete Lagrangian
The SEP Lagrangian at prime step p is defined as:
L_SEP(p) = C(p) - I(p)
Where:
- C(p): Computational cost (analogous to kinetic energy)
- I(p): Information gain (analogous to negative potential energy)
Phase-Based Definitions
Energy as Phase Imbalance
E(Δφ) ∝ Σ|Δφₖ|
Energy proportional to cumulative phase differences
Informational Gravitation
G_I = (I_m × I_n) / r²
Information acts with inverse-square law attraction
Recursive Update Rule
ε_{n+1} = ε_n + λδρ_n
Coherence evolution driven by information gradients
SEP Engine Architecture
Design Principles
- Datatype-Agnostic: Processes any data as raw byte streams
- Modular Architecture: Clear component boundaries with unidirectional dependencies
- High Performance: C++/CUDA backend for real-time processing
Core Algorithms
Quantum Fourier Hierarchy (QFH)
The Phase Aligner
Establishes fundamental periodicities and phase alignments within data streams, decomposing patterns into constituent frequencies.
Quantum Bit State Analysis (QBSA)
The Coherence Prober
Performs differential comparison between consecutive states, identifying persistent coherence and critical ruptures.
Informational Quantum Electrodynamics
The interplay between QFH and QBSA generates "emergent informational forces" mediated by "virtual informational photons". The system naturally evolves to minimize ruptures and maintain phase coherence.
Empirical Validation
| Proof of Concept | Description | Source Code |
|---|---|---|
| POC 1: Datatype Agnosticism | Distinguishes random, structured, and repetitive files | tests/pattern_metric_engine_test.cpp |
| POC 2: Stateful Coherence | Coherence remains stable across iterations | examples/pattern_metric_example.cpp |
| POC 3: Executable Analysis | Operates on compiled binaries as byte streams | examples/pattern_metric_example.cpp |
| POC 4: Performance | High speed with predictable complexity | examples/pattern_metric_example.cpp |
| POC 5: Compositionality | Metrics aggregate consistently over chunks | tests/pattern_metric_engine_test.cpp |
Applications and Implications
Complex Systems Analysis
SEP Engine quantifies informational quality in financial markets, distinguishing stable trends from chaotic noise through coherence metrics.
Cosmological Modeling
The framework proposes that cosmic acceleration can be described by a massive spin-2 field representing SEP manifold coherence, utilizing the Fierz-Pauli Lagrangian.
Artificial Intelligence
SEP provides a unifying theory for AI scaling laws and neural efficiency, reframing intelligence as achieved informational coherence.
Falsifiable Predictions
- Cosmology: Observable deviations from General Relativity in environments of extreme information density
- Complex Systems: Coherence metrics as leading indicators of phase transitions
- Computation: Superior energy efficiency for SEP-based architectures in optimization problems
Conclusion
The Self-Emergent Processor framework offers a novel paradigm for understanding information, computation, and physical reality as a unified, self-organizing system. By operationalizing these principles in the SEP Engine, we demonstrate that theoretical concepts can be translated into practical tools for analyzing complex systems. This work invites further collaboration to explore the algorithm of reality itself.