Start Here (SA)

The easiest path for understanding Semantic Algebra in this repository.

Step-by-Step Path

1. Read README.md (what SA means here, and what it is not).
2. Read SA_BOOK/00_prologue.md (the four-people-in-a-room framing).
3. Read SA_BOOK/00b_before_you_object.md (anticipated critiques with structural responses).
4. Read SA_BOOK/01_the_lossy_channel.md (the foundational claim about natural language).
5. Read SA_BOOK/02_domain_binding.md and SA_BOOK/03_the_projection_problem.md (the two structural mechanisms that occlude invariants).
6. Read SA_BOOK/04_the_axiom_and_the_invariant.md (the formal axiom).
7. Read SA_BOOK/05_the_library_of_invariants.md (the catalogue: ι₁ through ι₁₀).
8. Read SA_BOOK/06_the_strip_operator.md (S — the analytical operator).
9. Read SA_BOOK/07_the_recontextualization_operator.md (π — the synthetic operator).
10. Read SA_BOOK/08_the_seven_text_experiment.md (positive validation).
11. Read SA_BOOK/09_the_discrimination_test.md (negative validation).
12. Read SA_BOOK/10_the_self_correction.md (case study: the Ungaretti correction).
13. (Optional) Read SA_BOOK/10b_the_ghost_observer.md, 11_connections.md, 12_implications.md, 13_epilogue.md.

If You Only Want the Bottom Line

1. SA gives you two operators (S and π) and a library of 10 invariants.
2. S extracts structural content from natural language. π re-projects that content into any target domain.
3. The round-trip S(π(ι, 𝔻)) = ι is the integrity test.
4. The method is procedural, replicable, and falsifiable.
5. Most expressions, when stripped, contain no invariant — the rarity of invariants is what makes the method operationally useful.

If You Want the Single-File Version

SA_FULL/Semantic_Algebra_Foundations_EN.md contains the full content in compact form (~580 lines).

For the extended manuscript with case studies and additional context: SA_FULL/Semantic_Algebra_Complete_Manuscript.md (~4770 lines).

Cross-Reference to PA

PA formalises the space, metric, and operators that explain why SA works. The SA → PA reading path:

1. Finish the SA chapters above.
2. Read ../PA/PA_BOOK/appendix_c_sa_pa_equivalences.md for the complete correspondence table.
3. Read ../PA/PA_BOOK/09_strip_and_recontextualisation.md for the SA-as-PA-restriction theorem.