ORDINATIVE SCIENCES EDUCATION · Repository ufficiale

Ordinative Sciences Ecosystem Map

Fabio Ghioni · Copia del 2026-09-18

Ordinative Sciences Ecosystem Map

This file explains how the four public repositories of the Ordinative Sciences programme connect.

Four Repositories, Four Roles

Repository Role Function
ordinative_sciences_framework Theory Defines the TE foundations, ontology, and full module architecture (Bootloader, Core, SVP, SCIMS, VERT, LENS, PPRO, OBSERVER).
te-ordinative-lora Practice Implements TE principles in model fine-tuning workflows; LoRA dataset and training pipeline.
te-oct-framework-en Validation Publishes the English mirror of the core framework, plus the OCT (Ordinative Category Theory) corpus with reproducibility assets and validation cycles.
te-ordinative-algebras-en Algebras Publishes the SA (Semantic Algebra) and PA (Proportional Algebra) frameworks — the analytical operators and the proportional space they live in.

Conceptual Flow

  1. Theory (ordinative_sciences_framework) defines the principles.
  2. Practice (te-ordinative-lora) applies the principles in training pipelines.
  3. Validation (te-oct-framework-en) documents and tests formal/empirical consistency through OCT.
  4. Algebras (te-ordinative-algebras-en, this repo) provides the formal operator-level grammar — the analytical tools that connect theory, practice, and validation.

The four repositories are not redundant. Each addresses a distinct layer of the same underlying programme.

ASCII Map

                    ORDINATIVE SCIENCES ECOSYSTEM
                              |
      ----------------------------------------------------------
      |                |                  |                    |
      v                v                  v                    v
   THEORY           PRACTICE          VALIDATION             ALGEBRAS
   ordinative_      te-ordinative-    te-oct-                te-ordinative-
   sciences_        lora              framework-en           algebras-en
   framework
      |                |                  |                    |
      |                | <---- trains --- |                    |
      | <--- defines - |                  |                    |
      |                |                  | <--- formalises -- |
      | ----- provides invariants ------> |                    |
      |                                                        |
      | ---------------- analytical grammar --------------- >  |

How the Algebras Repository Relates

  • To Theory: SA and PA operate on the structures defined by the TE framework. The Collapse Function E = Φ(C, I, K) (TE equation 1.1) is upgraded in PA to a formal algebraic operator with falsifiable properties.
  • To Practice: The SA invariant library and the operators (S, π) are the structural primitives that the LoRA training pipeline aims to teach a model to recognise and apply.
  • To Validation: PA's Extended Round-Trip and falsification criteria provide the structural-test layer that complements OCT's category-theoretic validation cycles.

Suggested Reading Order

For a complete tour of the ecosystem:

  1. ordinative_sciences_framework — read the Bootloader and Core to understand the foundations.
  2. te-ordinative-algebras-en (this repo) — read SA first (operational entry), then PA (formal grounding).
  3. te-oct-framework-en — read OCT for the category-theoretic and validation-cycle layer.
  4. te-ordinative-lora — read the dataset and training pipeline to see the practical implementation.

For first-time readers of this repository specifically, start with START_HERE_FIRST_TIME.md.