Phase Differential Theory
Phase Differential
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R12

Joint closure and the realisation boundary

The requirements for a common physical model and the distinction between physical closure and the adopted actuality boundary.

Current foundationsPaper overview and reading guideManuscript PDF availableReview draft 1.0
Document version
Review draft 1.0
Date printed on the document
24 September 2026
Public release date
Not confirmed

This page is a reading guide written for the website. It is not the manuscript and does not reproduce its proofs. The manuscript PDF is linked below. It is a review draft and carries its own review notice. Authorship is not stated in the document and has not been confirmed. The public release date on this website has not been confirmed; the date shown is the date printed on the document. “Current foundations” does not by itself mean peer reviewed or experimentally confirmed.

Purpose

The question addressed

R12 states what a common physical model requires and separates physical closure from the adopted actuality boundary.

Mathematical starting point

Objects and premises used

  • The physical modules of R04 to R11 and the A6 realisation commitment of R01.

Main results

What the paper establishes

  • Requires one common model with compatible observations, records and stress accounting.
  • Separate solutions in different sectors do not by themselves establish a shared physical solution.
  • Distinguishes physical closure from the adopted realisation boundary.

Explanation

One history, not several

A quantum record model, a matter model and a gravitational solution each satisfying their own equations are not yet one physical history. R12 states what must be shown for them to be combined.

More on the mathematics page: Physical geometry and gravity →

Physical interpretation and scope

What connects this to physics

This is the PDT U layer: the requirement that physical modules belong to a common realised history.

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Using this paper

View the R12 manuscript (PDF)Download PDF

R12. “Joint closure and the realisation boundary.” Phase Differential Theory current foundations. Review draft 1.0, document dated 24 September 2026. https://www.phasedifferentialtheory.com/foundations/r12

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Reading order is expository and is not a claim that each premise is derived in the preceding paper.