Published July 19, 2026 | Version 2.2.0
Software documentation Open

Recurrence Dynamics Study: Predictive-State Quotient and Hidden-State Ambiguity Framework

Authors/Creators

Description

The Recurrence Dynamics Study develops a reproducible framework for analyzing complete-state recurrence, observational recurrence, predictive equivalence, finite observability, and hidden-state ambiguity in deterministic dynamical systems.

The framework distinguishes equality of complete predictive states from equality of reduced observations. It provides a finite-state partition-refinement procedure for determining whether a chosen observation map is predictively sufficient, whether hidden-state ambiguity resolves after a finite observation history, and whether distinct microscopic states remain permanently observationally equivalent.

The exact benchmark is an exhaustive analysis of the four-particle, zero-momentum sector of a reversible (3 \times 3) Hardy-Pomeau-de Pazzis lattice gas under sitewise-density observation.

The benchmark contains:

  • 9,153 microscopic states

  • 9,126 predictive classes

  • 9,099 singleton classes

  • 27 predictive doubletons

  • 54 permanently ambiguous microscopic states

  • 18 collision-free microscopic cycles of period 3

  • 9 time-reversal-related orbit pairs

The exceptional structure is:

54 = 18 × 3 = 9 × 2 × 3

Density records particle occupancy but omits velocity information. In the exceptional collision-free cycles, reversing every particle velocity produces a distinct microscopic orbit whose density history is identical after the correct phase alignment.

Version 2.2.0 adds the Recurrence Dynamics Framework, including:

  • a general finite-state diagnostic protocol

  • formal recurrence and ambiguity classifications

  • predictive-state quotient construction

  • a time-reversal ambiguity module

  • observability and finite-history reconstruction procedures

  • reporting standards for future applications

  • extension guidance for AI systems, robotics, sensors, coarse-grained physics, scientific model discrimination, and quantum diagnostics

The release includes the manuscript, source code, exact datasets, figures, independent verification procedures, validation scripts, integrity manifest, citation metadata, and the general framework document.

The framework does not claim that the physical universe is finite, that reality exactly recurs, that all systems contain unknown hidden physical variables, or that the result establishes a hidden-variable interpretation of quantum mechanics. Its exact conclusions are limited to the declared finite dynamical system, state sector, and observation map.

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Additional details

Related works

Is version of
Software documentation: https://github.com/scottasundy/recurrence-dynamics-study/releases/tag/v2.2.0 (URL)

Software

Repository URL
https://github.com/scottasundy/recurrence-dynamics-study
Programming language
Python
Development Status
Active

References

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