The Universal & Atomic Elements of Organization
A falsifiable scientific theory proposing that the same irreducible structures organize both thought and reality — from the quantum to the social scale.
O-Theory proposes that four irreducible structures — Distinctions, Systems, Relationships and Perspectives (DSRP) — form the universal grammar of organization. Rather than being merely useful ways of thinking, these structures are hypothesized to be the atomic elements from which every organized phenomenon emerges, whether in cognition, biology, physics, mathematics, society, or the cosmos.
| D | S | R | P |
| Distinctions | Systems | Relationships | Perspectives |
| Identity ↔ Other | Part ↔ Whole | Action ↔ Reaction | Point ↔ View |
| D := (i ↔ o) | S := (p ↔ w) | R := (a ↔ r) | P := (ṗ ↔ v) |
This is a living scientific evidence compendium: an open, continually evolving collection of independent empirical research, formal theory, mathematical proofs, cross-disciplinary analyses, applications, critiques, and proposed falsifications. Every entry is included because it supports, refines, challenges, or attempts to falsify the theory.
Scientific theories are strengthened not only by evidence that confirms their predictions, but also by surviving attempts to falsify them. This compendium brings both together: independent evidence from researchers who were not testing DSRP and proposed counterexamples evaluated against the formal theory.
One counterexample is enough to falsify O-Theory. Until then, the question remains: do the same four structures organize everything from quantum systems to human thought?
Independent convergence is one of the strongest forms of scientific evidence because researchers arrive at the same conclusion while investigating different questions for different reasons.
The number is not the point. Researchers in different fields, studying different questions with different methods, repeatedly arrived at the same structural predictions—almost always without testing DSRP or using its language.
Try a different term or clear the filters.
This compendium began as the peer-reviewed literature review “A Literature Review of the Universal and Atomic Elements of Complex Cognition,” published in the Journal of Systems Thinking with 109 studies. That paper is the peer-reviewed foundation. What you see here is its living, continuously updated version . New studies are checked before they are added, and the collection now holds and keeps growing. Open any card to see what the researchers found, why it bears on DSRP, and where the original review discusses it, the fuller account.
The collection is updated continuously, so the citation carries the date you consulted it rather than a study count — the count changes weekly, and putting it in the reference would make the same collection look like a different work to everyone who cites it. To cite a single claim or study, use its own address: every one has a permanent link.
This is the adversarial half of the compendium. Where the evidence track asks what converges on DSRP, this one asks what would end it: a single organized phenomenon whose structure needs a fifth pattern, a ninth element, or a fifth structural dynamic. It holds written up from candidates across territories, and resolutions — the general answers those cases settle against. Every case is published whether it held or failed, including the ones still open.
Cite this rather than the evidence collection when the point is what survived attack. The two are separate works with separate addresses: one asks what converges on the theory, the other asks what would end it, and a reference to the first does not support a claim about the second. Case and resolution numbers change when the record is revised, so cite a case by its own permanent link rather than by number.
This collection is meant to keep growing. Send us a study, paper, book or critique that bears on DSRP, whether it supports the theory or cuts against it, and we will read it and decide whether it belongs.
Authors Chris Huntingford, Paul D. L. Ritchie, Joseph Clarke
Year 2026
Publisher Nonlinear Processes in Geophysics
Kind of work article
Discipline Climatology
Secondary disciplines Mathematics
Applied false
Read it at the publisher 10.5194/npg-33-385-2026
The risk that the climate system may contain tipping points remains a concern. Firstly, a level of global warming may be reached at which relatively small additional warming could cause major parts of the Earth system to transition to a new state. Depending on the location and specific Earth system component, this could disproportionately impact large sectors of society. Secondly, the Earth system component may exhibit hysteresis effects, and therefore, if global temperatures are subsequently lowered after triggering a jump in state, a return to earlier conditions may not occur until warming is substantially reduced. Earth System Models (ESMs) are numerical frameworks that operate at fine spatial scales. Such models are designed to estimate how all components of the climate system will evolve in response to changes in atmospheric greenhouse gas concentrations caused by human activity. Many ESM projections suggest that various parts of the climate system are capable of tipping. Yet, these models are computationally demanding and have therefore been operated only over a small range of scenarios. Very few "overshoot" simulations with ESMs exist, where climate change is reversed, resulting in limited understanding of hysteresis effects following a tipping event. Advances in nonlinear mathematics include developing dynamical systems whose equations frequently contain a bifurcation parameter. These equations can accurately replicate tipping points, jumps in state, and hysteresis as the bifurcation parameter changes. Recent progress in ESM development often introduces higher spatial resolution, enhancing process representation and increasing accuracy in predicting local changes. However, mapping the broad behaviour of the components of ESM projections onto simpler dynamical system models may also offer many advantages, including the overall characterisation of climate models and a method to rapidly extrapolate their projections to a wider range of forcing scenarios. The bifurcation parameters in such equations may represent changing forcings, such as an increasing warming level that leads to a tipping event. Progress has already been made in mapping many components of the Earth system onto large-scale variables for representation as dynamical systems. Most advances to date have focused on understanding whether tipping events can be avoided if systems possess substantial inertia, i.e. respond over long timescales, allowing climate change to temporarily exceed thresholds that might otherwise trigger major nonlinear change. However, potential hysteresis effects in the context of climate change are less well represented in equation form. Achieving such a mathematical formulation requires a dynamic system to describe a climate system component not only at the point of tipping but also for substantial periods before and after. This behaviour corresponds to a bifurcation parameter that first increases and then decreases, with the modelled behaviours differing significantly during the return phase. To support such necessary developments, we present a parameter-sparse dynamical system model that can exhibit hysteresis following a tipping occurrence, offering the potential for characterising Earth system components with this feature. We place particular emphasis on presenting in full the algebra needed to map known or modelled key attributes of a system that can tip onto the simplified dynamical system equation. We drive the equation with a time-evolving forcing representing an "overshoot" trajectory of global warming that exceeds a threshold for potential tipping. Calculations are performed over a range of system inertia values, illustrating a threshold inertia above which full tipping and hysteresis can be avoided. We use scale analysis to relate this threshold to those reported in existing climate research on behaviour near potential tipping points. In some instances, a basic equation may be too simple to capture the dominant qualitative be
To develop a mathematically simple dynamical-system model that captures both the sudden state change ("tipping") and the hysteresis that can follow it in components of the Earth's climate system, as a fast alternative to full Earth System Models.
Not an empirical sample; the study develops and analyzes a five-parameter dynamical-system equation representing generic tippable Earth-system components under a warming-then-cooling ("overshoot") forcing trajectory.
Mathematical modeling: derivation of a bifurcation-parameter equation, algebraic mapping of Earth-system attributes onto the model, and calculation of system behavior across a range of inertia values under an overshoot warming scenario, compared against known climate-tipping thresholds using scale analysis.
The five-parameter model shows that a climate-system component driven past a tipping threshold and then back down avoids permanent state change only above a threshold level of system inertia, below which the return path differs systematically from the path that caused tipping, producing hysteresis.
The finding shows that whether a system crosses a threshold into a new state depends on a directional, history-dependent relationship between rising and falling forcing (hysteresis) together with the system's own part/whole properties such as inertia and extent, illustrating distinctions, relationships, and systems together.
Patterns it shows D, S, R
Added 2026-09-26
How to cite this Chris Huntingford, Paul D. L. Ritchie, Joseph Clarke (2026). A simple dynamical system for representing climate tipping points with hysteresis. Nonlinear Processes in Geophysics.