ORDINATIVE SCIENCES EDUCATION · Repository ufficiale

SA — Semantic Algebra

Fabio Ghioni · Copia del 2026-09-18

SA — Semantic Algebra

A formal method for extracting universal structural invariants from natural language and re-projecting them into any target domain.

Scope

This folder contains the Semantic Algebra corpus in English for:

  • GitHub public repository content
  • Zenodo / OSF deposits
  • Hugging Face documentation/dataset cards
  • AI training material (the SA invariant library and operators serve as structural primitives in the TE LoRA training pipeline — see te-ordinative-lora repository)

What SA Is

Semantic Algebra operates on natural-language expressions through two operators:

  • S (Strip): extracts whatever structural content is present in an expression — or certifies its absence — by removing field-specific vocabulary.
  • π (Re-contextualization): takes a structural pattern and re-expresses it deliberately in a chosen target domain.

The objects produced by S are called invariants — structural patterns that do not change under change of domain. The current invariant library contains 10 validated invariants (ι₁ through ι₁₀).

What SA Is Not

  • Not a numerical algebra in the high-school sense; "algebra" here means a structured grammar with formal operators and tests.
  • Not a claim that all wisdom traditions or scientific disciplines say the same thing — most expressions, when stripped, contain no invariant at all. The invariants that survive are rare.
  • Not deployed software — the formal method is procedural and human-replicable; AI implementations are downstream applications.

Relationship to Proportional Algebra

PA Theorem 9.1 establishes that SA is mathematically a restriction of PA to the decoherent space D. This connects them formally without collapsing them into a single project. SA was developed first, has independent applications, and has its own validation track. See ../PA/PA_BOOK/appendix_c_sa_pa_equivalences.md for the complete correspondence table.

Start Here

  1. START_HERE_SA.md — orientation and reading paths
  2. SA_BOOK/00_prologue.md — the four-people-in-a-room framing
  3. SA_BOOK/00b_before_you_object.md — anticipated critiques and structural responses
  4. SA_BOOK/01_the_lossy_channel.md — the foundational claim about natural language
  5. SA_BOOK/06_the_strip_operator.md — the S operator definition and procedure
  6. SA_BOOK/07_the_recontextualization_operator.md — the π operator definition and procedure

Validation

  • Positive validation (SA_BOOK/08_the_seven_text_experiment.md): 7 texts from 7 maximally distant domains. Result: 5 distinct invariants, 1 unprogrammed convergence (Shakespeare's King Lear and Lao Tzu's Tao Te Ching both yielding ι₁).
  • Negative validation (SA_BOOK/09_the_discrimination_test.md): 4 expressions that simulate depth. Result: 0 false positives, 3 different diagnostic types correctly identified.
  • Self-correction case study (SA_BOOK/10_the_self_correction.md): documented procedural correction of an initial projection error in the analysis of Ungaretti's M'illumino d'immenso.

Editorial Note

Two single-file manuscripts are provided in SA_FULL/:

  • Semantic_Algebra_Foundations_EN.md — concise reference (~580 lines)
  • Semantic_Algebra_Complete_Manuscript.md — extended manuscript (~4770 lines) with prologue, "Before You Object" critiques, and case-study chapters
  • Semantic_Algebra_What_Language_Hides_UNIFIED.md — unified compilation

Use the concise version for orientation and the complete manuscript for full study. The chapter-level files in SA_BOOK/ are the canonical source of truth.