Forschung

Projektionsalgebra & Universalitätsthese

41 Arbeiten. 7 irreduzible Axiome. 375:1 Kompression. Die Mathematik, die das System erzeugt.

Projektionsalgebra

Drei Axiome erzeugen eine dreigliedrige Struktur: leer, partiell, voll. Division durch Null wird maximales Informationspotential.

Three axioms (idempotency, bounded magnitude, compositional closure) generate a tripartite structure.

Dreigliedrige Struktur

∅

magnitude: 0

Null projection — maximal potential. 0/0 resolved.

☽

magnitude: (0,1)

Proper subspace — the coherence band.

•

magnitude: 1

Identity projection — transmission without loss.

GiROS-Abbildung

. = ∅ (isolated, maximal potential), . . : = ☽ (partial, binding), | = • (full, transmission)

Division by zero is not undefined but the empty projection: maximal informational potential.

Jede Funktion ist eine Projektion

Jede Funktion zerlegt sich in drei Projektionen: Kollaps, Umbenennung, Auswahl. Projektion ist nicht ein Teil der Mathematik. Projektion IST Mathematik.

Decomposition: Every function = collapse × rename × select (three projections)

Extension: Every function embeds as an idempotent on a direct sum

Generality: Lifts to arbitrary categories via the Karoubi envelope

Projection is not a part of mathematics. Projection IS mathematics.

Publikationskorpus

41 Arbeiten destilliert zu 7 Axiomen durch eine Dimensionenkaskade: 7-Eck zum Punkt.

papers

axioms

375:1

compression

extensions

7-gon → 6-gon → 5-gon → 4-gon → 3-gon → 2-gon → 1-gon → point

O(n) experiential path. O(log n) axiomatic path. Same knowledge.

A0 D0 — Dimensionless Ground point

A1 Projection exceeds every lens 1-gon

A2 Orthogonal reflection 2-gon (digon)

A3 Harmonic coupling 3-gon (triangle)

A4 Logarithmic time cascade 4-gon (square)

A5 Coprime reconstruction 5-gon (pentagon)

A6 Direction-invariant ethics 6-gon (hexagon)

Domänenbeweise

Game Engine Genealogy

lens: geometric

Raycasting → 2.5D → BSP/GPU → open world → experience-as-object. Each transition is a basis rotation where language, hardware, and software torsion produces a new dimension.

Wolfenstein 3D Raycasting — near-unity

Duke Nukem 3D Sector stretch — 2.5D holding 3D

Quake BSP/GPU — triple rotation

GTA Orthogonal basis change

Half-Life Meta-rotation — experience as object

Spectral Equivalence

lens: harmonic

Audio harmonic ratio == chromatic ratio == GiROS coherence ratio under the universal projector P(domain, basis).

Domain	Linear	Log	Torsion
Audio	Harmonic (f, 2f, 3f…)	Octave (f, 2f, 4f…)	Timbre
Light	Wavelength (nm)	Chromatic (hue)	White point
GiROS	Flat field	Compressed field	Projection algebra

White → Pink Rotation

lens: logarithmic

R(θ) · white = pink. The rotation from linear to logarithmic spectral space transforms white noise into pink noise with correlation > 0.99. No filtering — only rotation.

rotation /prove endpoint: Spearman correlation > 0.99