From P ≠ NP to Informational Physics: (WIDF) Information Density Framework

From P ≠ NP to Informational Physics: The Wartenberg Information Density Framework (WIDF)
Tom Wartenberg 

The Wartenberg Information Density Framework (WIDF) proposes a new, testable bridge between computational complexity and physical reality.
Originating from the observation that the P ≠ NP boundary behaves like a phase transition of information, the framework introduces the concept of a critical informational density — a universal tipping point where structured systems shift from order to emergent complexity.

WIDF integrates methods from theoretical computer science, quantum physics, and system biology, forming a unified approach to measure informational coherence across digital, physical, and biological substrates.
Core to its methodology is the Computational Resonance Test (CRT), a reproducible experiment that estimates the critical threshold Icritical=f(A,S)I_{critical} = f(A, S)Icritical=f(A,S) across architectures and mediums.

The full release (20 files + executive summary) includes:
– Foundational theory (Files 1–6)
– Methodology & experimental design (Files 7–12)
– Cross-disciplinary applications (Files 13–17)
– Validation & Contingency Hypothesis (Files 18–19)
– Open Community Toolkit for replication (File 15)

WIDF invites universities, AI-research groups, and physicists to independently replicate and extend the findings — turning civic curiosity into measurable science.

Practical Outlook:
Early computational simulations suggest that the CRT can be performed on existing LLMs, neural networks, and quantum-inspired models without specialized hardware.
If consistent informational phase thresholds are observed, WIDF may enable:
• standardized benchmarking of emergent behavior in large models,
• a cross-domain metric linking algorithmic complexity to physical entropy, and
• new approaches to optimize system design for stability versus adaptability.

Whether full universality or substrate-specific laws emerge, WIDF provides the first operational methodology to experimentally probe the information–complexity boundary — a foundation for the next generation of Informational Physics research.