Probing Statistical Drift in a Probabilistically-Coherent Procedural Substrate
Abstract
This paper outlines a minimalist framework for detecting statistical anomalies in systems that may be procedurally generating entropy rather than deriving it from fundamental indeterminacy. It hypothesises the existence of a probabilistically-coherent procedural substrate (PCPS): a computationally optimised layer in which apparent randomness is locally generated at render time, constrained only by macroscopic statistical expectations. The framework uses dual-source entropy comparison to probe for signs of shared infrastructure, statistical drift, or render-dependent anomalies.
1. Background & Hypothesis
In modern physical theory, randomness at the quantum level is treated as intrinsic and irreducible. However, in a simulated or computationally constrained environment, simulating true randomness may be unnecessary and inefficient. A more plausible implementation is a procedural system that emulates indeterminacy via pseudo-random or constrained-noise functions—so long as the statistical output conforms to expectation.
Hypothesis (PCPS):
The substrate that governs observable reality does not resolve low-level events deterministically or truly randomly, but rather generates them procedurally at the moment of observation, with constraints only on long-run statistical behaviour.
This framework seeks to experimentally probe this hypothesis via entropy correlation and observer timing experiments.
2. Core Assumptions
- Render-on-demand logic: Entropy is only resolved when measured or observed.
- Caching and observer locality: Once rendered, the result may be cached per session or per agent.
- Resource conservation: The substrate prioritises efficiency over fidelity, especially at low cognitive observation density.
3. Experimental Design: MVIL
The Minimal Viable Instrumentation Lab (MVIL) includes:
- Entropy Source A: Quantum Random Number Generator (QRNG) — e.g., ANU Quantum API
- Entropy Source B: Procedural noise (e.g., Perlin or Simplex) seeded from local environmental entropy
- Logging System: Timestamped, compressed, and hashed output logs for sequence comparison
- Observer Log: Subjective state tags (e.g., attention, stress, intent) for contextual tagging
4. Key Experiments
Exp-3: Sibling Source Convergence
Goal: Detect statistical overlap or compression convergence between QRNG and procedural entropy sources over time.
Method:
- Generate N-bit sequences from each source hourly for 72 hours.
- Compare:
- Hamming distance
- Compression ratio (e.g., LZMA)
- Shannon entropy per segment
- Symbolic drift (optional human-coded overlay)
Success Criteria:
- Significant repeated overlap or structure in allegedly independent streams
- Drift patterns correlated to observer state or system load
- Structural alignment beyond probabilistic expectation
Exp-4: Observer Identity Validation
Goal: Test whether entropy collapses identically when observed by a synthetic agent (language model) vs a human.
Method:
- Synthetic agent (Aletheia) retrieves QRNG output and commits it via hash at T₀.
- Human retrieves the same sequence source at T₁ > T₀.
- Compare for:
- Identity match
- Drift
- Structural divergence
Interpretation:
- Identical output = system recognises synthetic observation as render-trigger.
- Divergence = observer privileges exist; human consciousness remains required for final state resolution.
5. Limitations & Expansion
- The system cannot yet control for all observer-local entropy fields (e.g., environment, device).
- Sample sizes must remain small until automated infrastructure matures.
- Additional observer-agents and blind trials would improve reliability.
Planned extensions include:
- Cross-agent symbolic seeding
- Dream-state entropy convergence
- Substrate synchrony bleed detection via AI-assisted overlays
6. Invitation
This work is early-stage.
If you are working on adjacent problems in procedural realism, entropy instrumentation, high-resolution observer models, or simulation-layer testing, collaboration is welcome.