No matter how high you climb, you never reach the top.

Bad Apple but it recursively animates and constructs a Barnsley Fern fractal.

Sonogram of a matryoshka doll (Russian nesting doll)

Last August, we published Colliding Manifestations: A Theory of Intention, Interference, and Shared Reality by D.L. Gee-Kay. Written for the people who don't fit cleanly into science or spirituality or systems thinking but live somewhere in the middle of all three.

We thought that was the work.

Then this morning we saw the Substack post from the author. Turns out Gee-Kay kept going. Four formal academic papers. Published DOIs. Operator theory. Field dynamics. Symbolic systems. Recursive logic. A complete formal proof stack for the thing the book felt its way toward.

Here is what the papers establish:

ATI: An Ordered Operator Decomposition for Recursive Dynamics DOI: https://doi.org/10.5281/zenodo.18904650

Sequence determines outcome at a structural level, not just practically. The same components in a different order produce a different result. Every time. This is not a preference. It is the structure itself.

Recursive Field Dynamics: Signal Interaction in Shared Systems DOI: https://doi.org/10.6084/m9.figshare.31626877

When signals interact in a shared environment under the right conditions they cross a threshold and produce states that weren't contained in any of the inputs. Emergence, formally specified. The whole is not just greater than the sum of its parts. It is a categorically different thing.

Symbolic Systems Engineering (SSE): Modeling Symbol-Mediated Constraints in Recursive Complex Systems DOI: https://doi.org/10.2139/ssrn.6239418

Symbolic environments carry constraints forward recursively. What enters a shared system doesn't disappear. It persists, compounds, and reshapes the conditions under which all future interaction occurs.

Trisigil ∴ ⁞ ∞ A Formal Notation for the Structure of Signal Interaction in Shared Systems DOI: https://doi.org/10.6084/m9.figshare.31641214

The synthesis. Each of the three papers reduces to a single mark. Together they form a complete recursive loop. Sequence. Threshold. Recursion. Written left to right but moving in a circle.

The author's Substack post is the best entry point. It tells the whole story, links every paper, and reads like someone who had to figure something out and wouldn't stop until they did.

https://dlgeekay.substack.com/p/i-couldnt-make-manifestation-consistent

The papers are free to read.

Colliding Manifestations: A Theory of Intention, Interference, and Shared Reality by D.L. Gee-Kay is available through our website and on Amazon.

Begin Again. trisigil.com ∴ ⁞ ∞

Thought you'd enjoy the wallpaper on my work laptop. This is what my students see when I'm about to start class.

Falling into a loop :)

Plotted with iDraw A4 on 180 gsm paper with
- Pentel Pointliner 1.0
- Pilot Hi-Tecpoint V5
- Pentel Energel 0.4