Axioms
Seven structural constraints. Not beliefs — geometry.
The projector and the project are the same object.
(•*X) = project(projector)
Self-reference is structural, not paradoxical. The system that observes itself finds another projection, not a homunculus.
The channel is the channel.
(| = |)
The medium is not transparent. HTTP is not a neutral carrier — it IS the transmission. The protocol shapes what can be said.
Interference is dimensional information.
{~~<} ∈ Signal, not Noise
When two projections disagree, the disagreement carries information about dimensions neither projection alone can see. Filtering interference destroys depth.
Coherence is a band, not a floor.
0.3 < C(field) < 0.95
Perfect coherence (1.0) means all lenses agree — one of them is redundant. The system is most alive in the interference band.
The rotation IS the transmission.
R(θ): white → pink
Communication is not built on top of the algebra. Communication IS the rotation between basis spaces. White noise becomes pink noise not by filtering but by rotating the observer’s lens.
There is no I in GiROS. There is i.
Observer participates. Observer does not own.
The lowercase i is a hinge between Geometric and Relational. Individual perspective is real and necessary but not sovereign. The i does not start the sentence.
Security is phase-boundary integrity, not access denial.
(secure) = boundary holds shape under rotation
An insecure system is one where the lens can be rotated without detection. Security is not locking the door — it is knowing when the geometry has changed.