Project: Kairos

Computational Physics & Applied Game Systems

Buffered entropy architectures, 1/f noise coherence, and spectral integrity metrics for non-equilibrium systems.

entropy.occybyte.com   Visualizations   /lab

The Tool and the Paper

Kairos was built in 2025 as a 1/f-coherent entropy API. The ErisAPI layer powers randomness in Gatcha Gauntlet, Numbers, and Soulforger. The raw output passes the Dieharder test suite at 1GB (1 weak result). A full whitening pipeline (XOR cascade + Toeplitz) conditions the output for cryptographic suitability.

The research pitch deck for Kairos was awarded the 1517 Fund Medici Grant after due diligence.

Sparkle Kurtosis

During development, the raw FFT spectrum of ERIS output exhibited strong diagonal banding with distinct energy bands at ~0.8 entropy, while the core sat at ~0.92. The visual effect was unmistakable: the spectrum glittered like stars across the frequency bands. This was internally named "sparkle kurtosis" — a bicoherence signature in the raw output indicating persistent phase coupling across frequencies.

The whitening pipeline suppresses these energy bands by driving their amplitude toward zero (more leading zeros before the 0.8), but it does not destroy the underlying phase relationships that produce them. The phase coupling persists through whitening and HTTP transport. This means the randomness that reaches game clients still carries the 1/f phase structure that distinguishes it from pseudorandom sources like Math.random().

Connection to the Preprint

The sparkle kurtosis observation from the tool (2025) directly informed the central thesis of Phase Coherence, Not Spectral Slope, Determines Recovery in Noise-Driven Bistable Systems (2026, Research Square). The paper formalizes what the FFT spectrum showed empirically: that structural coherence in complex systems depends on phase coupling (bicoherence), not amplitude distribution (spectral slope). The whitening pipeline's behavior — suppressing amplitude while preserving phase — is a concrete demonstration of this principle.

The tool came first. The paper came from understanding what the tool was already doing.

Artifacts

Design memos and case studies from the Kairos / ERIS research line. PDFs under /downloads; die-roller case study on /lab/dieroller-demo.

Applied Metaphysics of Game Design — Entropy & Information Systems

TL;DR: Randomness becomes visible when fair PRNGs settle into attractors (local minima) that feel stuck. Treat games as applied metaphysics of state and entropy; favor temporally aware (1/f) randomness with memory so long sequences stay fair, exploratory, and surprising.

What to look for:

  • Where randomness shows up: loot scarcity and long-run perception vs statistical fairness
  • PRNG attractors / local minima: seeds + play history can lock into safe patterns
  • Rare events need scale: sub-1% drops may require 7k–500k trials to observe
  • Temporal memory: stateful RNG and pink-noise (1/f) processes for evolving surprise
  • Physics as rules: games instantiate causality; micro–macro inversion yields emergence; design is HCI/information

Download PDF

Case Study: Die Roller Demo

TL;DR: 100k+ d20 rolls. ERIS preserves variance and resists local minima; PRNG stabilizes into uniform mimicry. Exploration vs fairness.

Open case study · Die Roller Demo PDF

Technical Papers