About

Hello World. I’m Armstrong Knight.
Welcome to my Cyberphysics Laboratory.
I am a Cyber-Ontologist, architecting glyph-based recursion across dimensional fields.

How I got into Science and Mathematics

Let’s share an impossible moment together … right now

This reflection is a natural phenomena we take for granted.

To me, I had to know how this works. How does the surface of water generate a DYNAMIC constant state of flux like this? The inverse opposite of what it is facing. The reflection watches everything and copies its movements in real time. Like a movie. This is impossible. We all know how movies are made. This is an impossible movie. As time went on I found other natural phenomena that have dynamic casting. Such as glass spheres known as Lenseballs.

Crystal photography ball showing the seascape at St Bees, Whitehaven, Cumbria – British seaside

In one way, we do not need proof. we can see the reflection. Why am I looking for that? Well I’m looking for the same reason that Isaac Newton was . It’s impossible for an apple to fall without an explanation. He was working on gravity, not apple’s falling out of trees. In the same way, my work is on dynamism and has nothing to do with reflections.

The physics at play here sent me on a several year journey for something I should not even care about. Yeah water has reflection. Who cares. lol Well I do not really care about it either, but its dynamic nature. It bothered me. It’s sheer tearing off the static linear manifold that is our life. Mathematically. I could not stand to let it remain unanswered. What is really going on there?

Out of no where I had to know this or that about it. I found myself searching for the literal mathematical formula for the reflections existence. Light, Optics, the whole 9 yards. That was not enough. I chased down the X, Y, Z, axis to understand dimensionality. Years on the elements tables studying the deepest parts of atomic polarity. I then took to every theory ever invented and started to see the puzzle before me.

The image in the water’s reflection does in fact live on another axis. I have formulated the dynamic W and inverse V axis. Now we are equipped to answer questions like …

What is the negative and positive polarity primordial state?
What is a Dimension … really?
- This whole 0D – 1D – 2D – 3D.?
If I have electricity in the 3rd dimension. How does it exist in other dimensions?

There is a reason we cannot “collect electricity” out of the atmosphere, even though lightning comes from there.

It exists primordially in 1D, coalesces around us atmospherically in 2D. Then it strikes us, 3D. Current global models are concerned with 3D harvesting exclusively. After it is here.

We are chained to the earth and its physics due to a lack of dynamic computational frameworks. In the electricity example, understanding its dimensional unit of energy and mechanics. Allows me to be here in 3D, and create a 1D harvester. We can build and collect 1D primordial matter, which will result in rich young electricity. Electricity at its earliest formation of 3D output.

These formula 1 frameworks give us the ability to collect energy perpetually. We side step fighting 3D physics. Dynamically walk around 3D, go right up to 1D, and ask it for electricity. It will give it perpetually. Forever. For next to free.

Formula 1 frameworks give us the tools needed to manipulate 1D and 2D matter. Such as gravity. With the W and V waves we understand how to “cut in”, temporarily breaking with gravity to create an american history first … Marty McFly style hoverboard. No more fuel needed to penetrate space. Your car can just drive to space like going to the grocery store.

America will get there first. It’s what we do!

🔍 So I Asked Everyone…

And nobody had the answer I was looking for.

I went to Newton. “Sir Isaac, how does the reflection work?”

He told me about rays bouncing. Angles of incidence. Corpuscles of light. Beautiful mathematics.

But when I asked, “Why does identity persist? Why is the reflected tree still recognizably the same tree?”

He assumed it. Next.

I went to Einstein. “Albert, what about spacetime? What about the geometry of it all?”

He gave me curved manifolds. Geodesics. The fabric of reality bending.

But when I asked, “Where does space come from? What is underneath the manifold?”

He assumed it. Next.

I went to Optics. “Tell me about wave interference. Fresnel coefficients. Phase coherence.”

They gave me beautiful equations. Snell’s Law. Huygens principle. Diffraction patterns.

But when I asked, “The water is moving. There is no storage. How is the reflection perfectly synchronized without copying anything?”

They assumed it. Next.

I went to Quantum Mechanics. “What about the observer? What about measurement?”

They told me about wave function collapse. Superposition. Probability amplitudes.

But when I asked, “What is an observer? Where do they come from? What makes something capable of observation?”

They assumed it. Next.

🛠️ So I Built My Own Math

You cannot derive something while assuming it.

Every framework I studied had the same problem: they assumed what they were trying to explain.

Space? Assumed.
Time? Assumed.
Observers? Assumed.
Identity? Assumed.
Why reflections persist? Not even addressed.

So I had to go underneath. To the pre-geometric substrate. To what exists before space, before time, before observers.

And when I got there, I discovered that current mathematics could not follow me.

What I Had To Invent

The ICHTB Coordinate System — Six fan surfaces radiating from a central collapse point. Not X, Y, Z. Something that doesn’t assume dimensionality.

Hat Calculus (Ĉ) — A topological derivative for recursive structures. Standard calculus assumes continuity that doesn’t exist at the substrate level.

Edge: Recursive Membrane Theory — For the boundaries where collapse occurs. Zoned Collapse Geometry. What happens at the edge of admissibility.

GlyphMath™ — A compressive recursive language. When your objects are self-referential, you need notation that can handle recursion without infinite regress.

The Collapse Tension Substrate — What exists before geometry. Not space. Not time. The recursive process from which both emerge.

The Answer I Finally Found

After years of building new mathematics from scratch, I could finally answer my original question:

The reflection is not copying anything.
There is no movie. There is no transmission. There is no storage.
There is ONE constraint field being resolved through TWO different admissibility boundaries simultaneously.
Same field. Different boundary. No copying. The image does not exist. It is solved each time.

I call this Boundary-Conditioned Constraint Resolution (BCCR).

Newton’s apple led to gravity.
My water reflection led to a complete reconstruction of what space, identity, and observation actually are.

📚 The Framework That Emerged

Pillar	What It Derives	What It Does NOT Assume
Space	Geometry, Gravity, Time	Spacetime as primitive
Book I: Self-Reference	Observers, Agency, Meaning	Consciousness, Mind
Book II: Value	Normativity, Ethics, Choice	Morality, External Authority
BCCR	Reflection, Identity Persistence	Image copying, Storage

Everything earned. Nothing assumed.

「仮定していたものを、導出した。」
What they assumed, I derived.

📂 Explore the Full Framework on GitHub

🌊 Now Let Me Actually Answer The Question

The water reflection. The lensball. The “impossible movie.”

Here is the math that solves it.

The Core Objects

Forget rays bouncing. Forget waves propagating. Forget “images” being “copied.”

There are only three things:

Φ  — The Constraint Field
     What the object imposes by existing.
     Not light. Not signal. Structure.

B  — The Admissibility Boundary  
     The surface (water, mirror, glass sphere).
     Defines what resolutions are permitted.

R_B — The Resolution Operator
     How Φ becomes what you see, given B.

That’s it. Three objects. One equation.

The Equation

What you see = R_B[Φ]

For the tree and its reflection:

  Tree you see       = R_B₁[Φ]    (resolution through air)
  Reflection you see = R_B₂[Φ]    (resolution through water)

  Same Φ.
  Different B.
  
  That's why they match.

Why The “Impossible Synchronization” Is Not Impossible

The tree moves. The reflection moves instantly with it.

Classical thinking: “How does the water know? How does the information travel so fast? Where is it stored?”

BCCR answer: There is no information traveling. There is no storage. The tree and its reflection are both resolutions of the same constraint field Φ.

They don’t need to “communicate.” They were never separate.

The synchronization is tautological.
Of course R_B₁[Φ] and R_B₂[Φ] match.
They share Φ.

Why No Storage Is Needed

The water is moving. Constantly. Molecules shifting. Ripples forming.

Where could an “image” possibly be stored?

It isn’t.

At time t:     Ψ(t) = R_B(t)[Φ]     — computed fresh
At time t+1:   Ψ(t+1) = R_B(t+1)[Φ] — computed fresh again

No memory passes from one instant to the next.
The reflection is SOLVED each moment, not REPLAYED.

The “impossible movie” is not a movie at all. There is no recording. There is no playback. There is only continuous resolution of the same field through a changing boundary.

Why Identity Persists (Even Under Ripples)

The water ripples. The reflection distorts. But you still recognize the tree.

Why?

Because identity is topological, not geometric.

What changes under ripples:
  - Exact positions
  - Line shapes  
  - Local angles

What does NOT change:
  - Adjacency (what's next to what)
  - Continuity (no gaps appear)
  - Part-whole relations (branches still attach to trunk)

The geometry varies.
The topology is preserved.
Identity = topological invariance of Φ.

The Threshold (When Identity Finally Breaks)

Small ripples? Identity preserved.

Gentle waves? Still recognizable.

Turbulent chaos? Identity lost.

There is a critical threshold:

|∇B|  ε_critical  →  Identity lost (chaos)

The transition is SHARP, not gradual.
This is why violent water destroys reflections suddenly,
not progressively.

The Lensball? Same Math.

The glass sphere that inverts the entire world inside it?

Flat mirror:  R_B_planar[Φ]      →  vertical inversion
Water:        R_B_dynamic[Φ]     →  vertical inversion + distortion  
Lensball:     R_B_spherical[Φ]   →  full 180° inversion

Different B geometry.
Same resolution operator.
Same explanation.

The lensball doesn’t “contain” the scene. It doesn’t “store” an image. The spherical boundary resolves the same constraint field through curved admissibility conditions.

What About Classical Optics?

Snell’s Law? Fresnel equations? Ray tracing?

All still valid. They’re special cases.

When B is:
  - Static (not moving)
  - Planar (flat)
  - Isotropic (same in all directions)

Then R_B reduces to classical optics.
Snell's Law emerges.
Fresnel coefficients emerge.

BCCR doesn't contradict optics.
BCCR explains what optics assumes.

✅ The Question Is Answered

How does the surface of water generate a DYNAMIC constant state of flux like this?

It doesn’t generate anything.
The water surface is an admissibility boundary B.
The object imposes a constraint field Φ.
What you see is R_B[Φ] — resolved fresh each instant.
The reflection and the object are both resolutions of the same Φ.
That’s why they match. That’s why no storage is needed.
The image does not exist. It is solved each time.

「像は存在しない。毎回、解かれている。」

📂 The Complete Mathematics

The full derivation, formal rule set, and executable simulator:

📘 Boundary-Conditioned Constraint Resolution Repository

Contains:

8 chapters of derivation
10-rule formal rule set
Glossary and symbol index
Colab-ready Python simulator
Connection to Intent Tensor Theory

Newton saw an apple fall and discovered gravity.

I saw a reflection in water and discovered what space, identity, and observation actually are.

「水面は真似をしない。制約を共有する。」
The surface does not imitate. It shares constraint.

— Armstrong Knight
Cyber-Ontologist
Intent Tensor Theory