Emergent Stochasticity from Serialized Concurrency

A Constructive Theory of Uniform Measure on Interleaving Space.

Record type: Thesis (paper + proofs + executable simulations) — published v2, April 3, 2026 DOI: 10.5281/zenodo.19571762 Record URL: https://zenodo.org/records/19571762 All-versions DOI: 10.5281/zenodo.19564056 License: CC-BY-4.0 Authors / Creators: Sethurathienam Iyer (Researcher) — ORCID: 0009-0008-5446-2856

Description#

This repository contains the preprint, mathematical proofs, and executable simulations for a novel physical and computational ontology that completely reformulates the nature of randomness.

Rather than treating stochasticity as an axiomatic primitive of the universe, this paper postulates that uniform randomness is an emergent artifact — the invariant measure generated when a massively concurrent, deterministic system is forced through a sequential, capacity-limited interface (the serialization bottleneck).

Talk / Video: YouTube

Key Contributions#

1. Theoretical Framework#

Formulates the Interleaving Space representing concurrent tie-blocks of simultaneous events as products of symmetric groups:

\Omega \;=\; \prod_{i} S_{n_i}

Each tie-block is a maximal set of events that occur “simultaneously” in the concurrent system. When forced through a serializing interface, these tie-blocks become interleavings — and the space of all possible interleavings is $\Omega$ .

2. Formal Proofs#

Implements the Kendall tau distance and the Perron-Frobenius theorem to mathematically prove that minimal-change transport over these tie-blocks induces an irreducible, aperiodic Markov chain whose unique invariant measure is strictly uniform.

The mixing time bounds are exponential in the size of the tie-block:

t_{\text{mix}} \;\leq\; O(n \log n)

and the total-variation distance between the empirical distribution and the uniform distribution vanishes at exactly the rate predicted by coupling arguments.

3. Berry Holonomy#

Demonstrates that stochastic shuffling is geometrically equivalent to the phase shift accumulated over constraint permutations, proving that the limiting Boltzmann entropy converges exactly to

\lim_{N \to \infty} \frac{S_N}{N} \;=\; \log 2

This is the same entropy as a fair coin — but derived constructively from a deterministic system, not postulated axiomatically.

4. Algorithm Instantiation (BAHA)#

Establishes that BAHA (Branch-Aware Holonomy Annealing) — a core module of the NitroSAT solver — is a direct, physical realization of this concurrency theory. By traversing thermodynamic fractures on NP-hard landscapes using the Lambert W function, BAHA achieves linear-time optimization in the number of fractures, turning a known exponential bottleneck into a tractable one.

The Central Claim#

Randomness is not fundamental. It is the invariant measure of a deterministic dynamical system viewed through a serializing interface.

Concretely:

Classical view	This paper’s view
Stochasticity is axiomatic	Stochasticity is emergent
Random processes require randomness	Deterministic processes on concurrency space produce uniform measure
Entropy is postulated	Entropy is derived from constraint-permutation holonomy
Mixing time is empirical	Mixing time has a provable bound

Included Files & Artifacts#

File	Size	MD5
`emergent_stochasticity.pdf`	383.9 kB	`a35c8d114e45a1cdd94c5f10593ea292`
`toy_simulation.py`	30.5 kB	`d9f303e42c8215569cf7f7ca7ea1053c`
`emergent_stochasticity_numpy.py`	27.0 kB	`3e9981da0333c3b105b9b72730e680ec`

Total: 441.4 kB across 3 files.

emergent_stochasticity.pdf — The complete academic paper detailing the mathematical proofs, mixing time bounds, and the formal theory.
toy_simulation.py — An executable Python environment that successfully validates the emergence of uniform measures (total variation distance → 0) from strictly deterministic, exchangeable constraints.
emergent_stochasticity_numpy.py — Vectorized NumPy implementation of the same simulation at scale.

Validation#

The paper ships executable proofs, not just formal ones. Running toy_simulation.py confirms:

The empirical distribution over tie-block orderings converges to uniform.
The total-variation distance decays as $O(1/\sqrt{n})$ — exactly as predicted by concentration bounds.
The Berry holonomy phase shifts reproduce the fair-coin entropy $\log 2$ in the limit.

License & Attribution#

License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Author: Sethurathienam Iyer (ShunyaBar Labs)

Citation#

BibTeX#

@article{EmergentStochasticity2026,
  author    = {Iyer, Sethu},
  title     = {{Emergent Stochasticity from Serialized Concurrency: A Constructive Theory of Uniform Measure on Interleaving Space}},
  year      = {2026},
  publisher = {Zenodo},
  version   = {v2},
  doi       = {10.5281/zenodo.19571762},
  url       = {https://doi.org/10.5281/zenodo.19571762},
  license   = {CC-BY-4.0}
}

APA#

Sethurathienam Iyer. (2026). Emergent Stochasticity from Serialized Concurrency: A Constructive Theory of Uniform Measure on Interleaving Space (Version v2). Zenodo. https://doi.org/10.5281/zenodo.19571762

Versions#

Version	DOI	Date
v2	10.5281/zenodo.19571762	Apr 3, 2026
v1	10.5281/zenodo.19564057	Apr 14, 2026

Cite-all DOI (always resolves to latest): 10.5281/zenodo.19564056

Indexed In#

OpenAIRE
Zenodo (publisher)
CERN Data Centre (infrastructure)

Metadata#

Field	Value
Resource type	Thesis
Publisher	Zenodo
Language	English
Created	April 14, 2026
Modified	April 14, 2026
License	CC-BY-4.0