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.
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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 Julian De Vuyst, Stefan Eccles, Philipp A. Höhn, Josh Kirklin
Year 2025
Publisher Journal of High Energy Physics
Kind of work article
Discipline Physics
Applied false
Read it at the publisher 10.1007/JHEP07(2025)063
A significant step towards a rigorous understanding of perturbative gravitational entropy was recently achieved by a series of works showing that a proper accounting of gauge invariance and observer degrees of freedom converts the Type III algebra of QFT observables in a gravitational subregion to a Type II crossed product, whose entropy reduces to the generalised entropy formula in a semiclassical limit. The observers thus used are also known as quantum reference frames (QRFs); as noted in our companion work, using different QRFs result in different algebras, and hence different entropies — so gravitational entropy is observer-dependent. Here, we provide an in-depth analysis of this phenomenon, with full derivations of many new results. Using the perspective-neutral QRF formalism, we extend previous constructions to allow for arbitrarily many observers, each carrying a clock with possibly degenerate energy spectra. We consider a semiclassical regime characterized by clocks whose energy fluctuations dominate over the fluctuations of the energy of the QFT. Unlike previous works, we allow the clocks and fields to be arbitrarily entangled. At leading order the von Neumann entropy still reduces to the generalised entropy, but linear corrections are typically non-vanishing and quantify the degree of entanglement between the clocks and fields. We also describe an 'antisemiclassical' regime as the opposite of the semiclassical one, with suppressed fluctuations of the clock energy; in this regime, we show how the clock may simply be 'partially traced' out when evaluating the entropy. Four explicit examples of observer-dependent entropy are then given, involving a gravitational interferometer, degenerate clock superselection, a semiclassical approximation applying to some clocks but not others, and differences between monotonic and periodic clocks.
To extend the perspective-neutral quantum-reference-frame formalism to multiple observers with entangled clocks and analyze how gravitational entropy depends on the observer's reference frame.
Not an empirical sample; a formal/theoretical derivation with four worked examples (a gravitational interferometer, degenerate clock superselection, a mixed semiclassical case, and monotonic versus periodic clocks).
Analytic derivation within the crossed-product/Type II algebra framework for gravitational subregions, extended to arbitrarily many observers with possibly entangled clocks, computing von Neumann entropy in semiclassical and 'antisemiclassical' regimes.
Extending the quantum-reference-frame formalism to multiple observers with entangled clocks, the study found that the gravitational entropy assigned to a system depends on which observer's quantum reference frame is used, with corrections beyond the leading-order generalized entropy formula that scale with the degree of clock-field entanglement.
Demonstrates that perspective is not incidental to but constitutive of the physical quantity measured, since the same gravitational system's entropy differs by observer or reference frame.
Patterns it shows P
Added 2026-09-28
How to cite this Julian De Vuyst, Stefan Eccles, Philipp A. Höhn, Josh Kirklin (2025). Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy. Journal of High Energy Physics.