R07: Spatial carriers metric and orientation

Purpose

The question addressed

R07 gives conditional constructions of internal spatial carriers, their metric structure and the persistence of orientation.

Mathematical starting point

Objects and premises used

The phase plane and transport structure of R02.
A supplied comparison seed and a physical displacement interpretation.

Main results

What the paper establishes

Constructs internal spatial carriers under stated conditions.
Separates an internal positive metric from a physical Lorentzian spacetime.
States conditions for orientation persistence.

Explanation

Internal metric and physical spacetime

An internal positive metric on a mathematical carrier measures size inside that carrier. A physical spacetime is a common four-dimensional Lorentzian metric, a separate premise introduced as G1 in R10.

More on the mathematics page: Physical geometry and gravity →

Physical interpretation and scope

What connects this to physics

The link from internal carrier to physical space is carried by the comparison seed and the displacement interpretation, which are supplied premises.

Dependencies and related reading

Mathematical dependencies

R02: Phase transport and complex structure
Uses the phase plane and transport structure

Physical premises introduced or used

A comparison seed.
A physical displacement interpretation.

Historical background

PTG 2Related current treatment
Transport geometry and curvature are treated currently through loop phase in R02 and conditional carrier constructions in R07.
PTG 3Related current treatment
Metric selection is treated currently by separating internal metrics (R07) from the declared physical metric premise and action class (R10).
PTG 4Related current treatment
Sector structure and chirality relate to orientation persistence in R07 and to matter models in R09.
PTG IIHistorical background
Focusing in a transport congruence relates to carrier geometry (R07) and gravitational dynamics (R10).
PTG IIIHistorical background
Transport capacity and completeness relate to transport structure (R02) and conditional carrier constructions (R07).
QM IISpecific claim corrected
Field structure and a constructed metric relate to internal carriers (R07) and the physical metric premise (R10).

Topic: Internal spatial carriers and orientation.

Read, download and cite

Using this paper

View the R07 manuscript (PDF)Download PDF

R07. “Spatial carriers metric and orientation.” Phase Differential Theory current foundations. Review draft 1.0, document dated 24 September 2026. https://www.phasedifferentialtheory.com/foundations/r07

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Spatial carriers metric and orientation