# 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.