Super Simple FAQ

1) What is this project?

A research repository containing two formal frameworks (SA and PA) developed within the Technology of Expressions / Ordinative Sciences programme.

2) Are SA and PA the same thing?

No. They are distinct frameworks that share a structural relationship.

• SA (Semantic Algebra) was developed first, to extract universal structural patterns from natural language for AI training and cross-domain translation.
• PA (Proportional Algebra) was announced in the foundational TE text and formalises the space, metric, and operations that govern collapse across all domains — not only language.

PA Theorem 9.1 shows that SA is mathematically a restriction of PA to the decoherent space D. This does not make them the same project — SA has independent development, applications, and an established invariant library.

3) Should I read SA or PA first?

Most readers should start with SA — it has lower formal entry barrier and concrete operational examples. Then PA gives the deeper theoretical structure.

If your background is mathematical or physical, you can also read PA first.

4) Is this a code project I can run?

Partially. PA/pa_engine/ contains a small Python reference engine (~700 lines) implementing PA's operators and metrics for experimentation. It is not production software. The rest of the repository is documentation-first.

5) Is this proof of cross-domain unity / a "theory of everything"?

No. Both SA and PA explicitly state their limits and falsification criteria. They are research frameworks with operational tests and falsifiable claims, not metaphysical pronouncements.

6) Where should I start as a first-time reader?

1. START_HERE_FIRST_TIME.md
2. README.md
3. INDEX.md

For SA-specific entry: SA/START_HERE_SA.md. For PA-specific entry: PA/START_HERE_PA.md.

7) Where is the formal definition of the operators?

• SA operators (S, π): SA/SA_BOOK/06_the_strip_operator.md and SA/SA_BOOK/07_the_recontextualization_operator.md
• PA operators (Φ, S, ⊗, τ): PA/PA_BOOK/08_collapse_operator.md through PA/PA_BOOK/12_pulsation_temporal_generator.md

8) Where is the validation evidence?

• SA: SA/SA_BOOK/08_the_seven_text_experiment.md (positive) and SA/SA_BOOK/09_the_discrimination_test.md (negative)
• PA: PA/PA_BOOK/13_chemistry.md through PA/PA_BOOK/17_artificial_intelligence.md (cross-domain) and PA/PA_BOOK/18_limits_and_open_questions.md (falsification criteria)

9) Can I cite this work?

Yes. Please cite with author Fabio Ghioni, the relevant framework name (Semantic Algebra or Proportional Algebra), the version tag from this repository, and the URL.

10) What if I do not understand a term?

Open SIMPLE_GLOSSARY.md first, then the formal vocabularies:

• SA/SA_BOOK/appendix_a_vocabulary.md
• PA/PA_BOOK/appendix_a_symbol_register.md