Start Here (First Time)

This guide is written for people with zero background. No technical knowledge is required.

In One Sentence

This repository contains two distinct formal frameworks — Semantic Algebra (SA) and Proportional Algebra (PA) — that come from the Technology of Expressions research programme. They give you tools to extract, classify, and re-express structural patterns across any field.

If You Have 5 Minutes

1. Read README.md (what is in the repository).
2. Read SIMPLE_GLOSSARY.md (plain words for the key terms).
3. Read SUPER_SIMPLE_FAQ.md (short answers to common confusion).

If You Have 20 Minutes

1. Read README.md.
2. Open SA/README.md and SA/START_HERE_SA.md.
3. Read SA/SA_BOOK/00_prologue.md and SA/SA_BOOK/01_the_lossy_channel.md.
4. Then look at the operators: SA/SA_BOOK/06_the_strip_operator.md.

If You Want the Formal Theory

1. Read PA/README.md and PA/START_HERE_PA.md.
2. Read PA/PA_BOOK/01_why_the_sciences_cannot_speak.md through PA/PA_BOOK/03_what_is_needed.md for motivation.
3. Read PA/PA_BOOK/04_the_proportional_space.md for the formal space definition.
4. Read PA/PA_BOOK/08_collapse_operator.md, 09_strip_and_recontextualisation.md, and 10_resonance_operator.md for the three operators.
5. Read PA/PA_BOOK/11_extended_round_trip.md for the integrity test.

If You Want Validation Evidence

• SA positive validation (7-text experiment): SA/SA_BOOK/08_the_seven_text_experiment.md
• SA negative validation (discrimination): SA/SA_BOOK/09_the_discrimination_test.md
• SA self-correction case study (Ungaretti): SA/SA_BOOK/10_the_self_correction.md
• PA cross-domain demonstrations: PA/PA_BOOK/13_chemistry.md to PA/PA_BOOK/17_artificial_intelligence.md
• PA falsification criteria: PA/PA_BOOK/18_limits_and_open_questions.md

If You Want to Run Code

The PA reference engine is in PA/pa_engine/. It is a small Python package (~700 lines) implementing the resonance metric, the Remir structure, the collapse and strip operators, and a simulation orchestrator.

Entry script: PA/pa_engine/simulation_orchestrator.py.

The engine is for experimentation — not production software.

Do Not Confuse This Project With

1. A "theory of everything" that claims cross-domain unity without falsification — both frameworks include explicit falsification criteria.
2. A finished AI product — this is research material, including reference code, not a deployed system.
3. A purely philosophical text — both frameworks contain operational procedures and replicable tests.
4. A medical or biological project — PA/PA_BOOK/16_medicine.md discusses medicine as a domain of application, not as a clinical recommendation.

If You Feel Lost

Use this recovery path:

1. Return to README.md.
2. Read SIMPLE_GLOSSARY.md.
3. Read INDEX.md and follow only one section at a time.

Two Frameworks, One Repository

This repository deliberately bundles SA and PA in the same place because the cross-references between them are tight. They remain distinct projects — not two halves of one — and each can be read on its own. See ECOSYSTEM.md for how they relate to the other repositories in the Ordinative Sciences programme.