Phase Differential Theory
Phase Differential
A Framework for Reality
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R13

Mathematical audit and reproducibility

The verification record, mathematical provenance and reproducibility of the suite.

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

R13 is the verification record of the suite: its mathematical provenance, its audit and the means of reproducing its results.

Mathematical starting point

Objects and premises used

  • The results stated in R01 to R12 and the standard mathematical results they rely on.

Main results

What the paper establishes

  • Records the provenance of each result, including attribution to standard mathematics.
  • Sets out how the stated results and examples can be reproduced.

Explanation

What verification here means

Checking a worked example by direct calculation verifies that example only. It is not experimental confirmation and not formal proof-assistant verification.
The website examples, such as the six exclusion histories summing to 1, were checked in this sense.

More on the mathematics page: Sources and verification →

Physical interpretation and scope

What connects this to physics

R13 makes no new physical claim. It supports review by recording where each result comes from.

Read, download and cite

Using this paper

View the R13 manuscript (PDF)Download PDF

R13. “Mathematical audit and reproducibility.” Phase Differential Theory current foundations. Review draft 1.0, document dated 24 September 2026. https://www.phasedifferentialtheory.com/foundations/r13

BibTeX will be offered when verified authors, version and release date are available. All citations

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