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 Sushil Acharya, Karl Fabian, Anis Yazidi, Kjetil Westeng
Year 2026
Publisher Frontiers in Earth Science
Kind of work article
Discipline Geology
Secondary disciplines Data Science
Applied false
Read it at the publisher 10.3389/feart.2026.1736164
Depth mismatches between well logs acquired in different runs (e.g., electrical wireline logging (EWL) versus logging while drilling (LWD)) impede stratigraphic correlation and bias reservoir property estimation. Existing alignment methods, such as maximum cross-correlation (MaxCC), are fast but generally assume near-uniform shifts and can be noise-sensitive, whereas dynamic time warping (DTW) can accommodate nonlinear discrepancies but is computationally heavier than global-shift methods and less interpretable. We present a semi-automated Fast Walsh–Hadamard Transform (FWHT) workflow that enhances step-like responses associated with lithological transitions, quantifies boundary evidence via a Walsh Boundary Index (WBI), and uses matched boundary pairs as control points to construct a monotone, piecewise-linear depth-warping function that maps LWD depths onto an EWL reference. The method is applied to normalized EWL–LWD datasets containing gamma ray, bulk density, neutron porosity, and compressional sonic slowness logs. FWHT increases the slice-averaged Pearson correlation from 0.079 to 0.574 and reduces the Euclidean distance from 1.863 to 0.964. Scalability is evaluated on 89 GR log pairs from the Norwegian Continental Shelf: mean Pearson correlation increases from 0.367 (unaligned) to 0.851 with FWHT. Overall, the FWHT framework provides an interpretable and computationally efficient approach for boundary-controlled, nonlinear well-log depth alignment.
To develop an interpretable, computationally efficient method for detecting stratigraphic bed boundaries and using them to align depth-mismatched well logs from different drilling runs.
Normalized electrical wireline logging and logging-while-drilling log pairs (gamma ray, bulk density, neutron porosity, sonic slowness) from a Norwegian Continental Shelf well, plus a batch of 89 gamma-ray log pairs from the same region.
A semi-automated Fast Walsh–Hadamard Transform workflow enhances step-like log responses at lithological transitions, quantifies boundary evidence with a Walsh Boundary Index, and uses matched boundary pairs as control points for a monotone piecewise-linear depth-warping function, benchmarked against maximum cross-correlation and dynamic time warping baselines.
The Walsh-Hadamard boundary-detection method raised mean log-to-log correlation from 0.367 to 0.851 across 89 well-log pairs, performing comparably to established alignment baselines while remaining more interpretable.
The finding shows that reliably distinguishing bed boundaries in one signal lets otherwise mismatched records of the same underlying whole be reconciled into a single coherent depth framework.
Patterns it shows D, S
Added 2026-09-28
How to cite this Sushil Acharya, Karl Fabian, Anis Yazidi, Kjetil Westeng (2026). Semi-automated bed boundary detection and log alignment using fast Walsh–Hadamard transform. Frontiers in Earth Science.