# Diagrammatic Backpropagation and Geometric Transformers

- **Registry ID:** `catagi-db-gt`
- **Book:** Categories for AGI
- **Documentation status:** `bounded-demo-and-plot-provenance`
- **Experimental status:** executable demonstration plus archived illustrative plots
- **Canonical documentation URL:** https://categorical-ai.sridharmahadevan.com/experiments/catagi-db-gt

## Purpose

A small executable pullback/pushout energy demonstration and two archived commutator-proxy trajectories for Geometric Transformer variants.

## Book location

- Chapter 6: Diagrammatic Backpropagation
- Chapter 7: Geometric Transformers
- Chapter 8: Dynamic Compositionality

## Documented studies

- Diagrammatic pullback and pushout energy demonstration
- Two-moons commutator-proxy trajectory
- WikiText-103 early commutator-proxy trajectory
- Geometric Transformer architecture comparison

## Associated code packages

- `categories-gt-archive` — Geometric and Kan Extension Transformer archive; **local-not-public**; license decision pending. Working scripts and result directories for DB, GT, KET, language modeling, manifold, mean-field, and scaling studies. A curated public packet remains to be extracted.
- `catagi-lean` — [Categories for AGI Lean companion](https://github.com/sridharmahadevan/catagi/tree/8ce79cdc949604873aca279d6cfcafa992293eb8); **public**; MIT. Machine-checked structural companion for selected categorical statements in Categories for AGI.

## Start here

These concrete files are selected from the complete resolved source surface. They orient the reader; they are not a claim that every family is independently reproducible.

- **implementation · staged-not-public** — `categories-gt-archive:scripts/gt/geometric_transformer.py`. Locate this file in the curated companion packet; no public download is currently offered.
- **implementation · staged-not-public** — `categories-gt-archive:scripts/resmlp_gt_commutator_demo.py`. Locate this file in the curated companion packet; no public download is currently offered.
- **implementation · staged-not-public** — `categories-gt-archive:scripts/seq2seq_wiki103_prefix_suffix.py`. Locate this file in the curated companion packet; no public download is currently offered.
- **implementation · staged-not-public** — `categories-gt-archive:scripts/gt/simplicial_mp.py`. Locate this file in the curated companion packet; no public download is currently offered.

## Entry points

- `scripts/gt/`
- `scripts/resmlp_gt_commutator_demo.py`
- `scripts/seq2seq_wiki103_prefix_suffix.py`
- `Category-Theory-for-AGI-UMass-CMPSCI-692CT/notebooks/week03_db_colimit_energy.ipynb`

## Result artifacts

- `week03_db_colimit_energy.ipynb`
- `two_moons_commutator_energy.png`
- `wiki103_prefix_suffix_cech_obs.png`
- `CHAPTERS_6_8_PROVENANCE.md`

## Resolved code surfaces (8)

- **dependency** — `categories-gt-archive:scripts/datasets_linked_wt2.py`
- **dependency** — `categories-gt-archive:scripts/datasets_ptb_wt.py`
- **implementation** — `categories-gt-archive:scripts/gt/__init__.py`
- **implementation** — `categories-gt-archive:scripts/gt/geometric_transformer.py`
- **implementation** — `categories-gt-archive:scripts/gt/simplicial_mp.py`
- **implementation** — `categories-gt-archive:scripts/resmlp_gt_commutator_demo.py`
- **implementation** — `categories-gt-archive:scripts/seq2seq_gt_compare.py`
- **implementation** — `categories-gt-archive:scripts/seq2seq_wiki103_prefix_suffix.py`

## Frozen run records (0)

- No frozen run-level record is registered. Consult the result-artifact list and evidence boundary above for the exact surviving evidence; absence of a run record is not evidence that no experiment was run.

## Evidence boundary

The Chapter 6 notebook is an executable numerical illustration, not a proof that optimization computes categorical limits in general. The Chapter 8 PNGs have exact code and byte provenance but no surviving per-step raw logs, so they are archived plot-only evidence. Their residuals are task-relative order-sensitivity diagnostics, not categorical limit certificates, causal demonstrations, or general proofs of improved learning.

A code or artifact link establishes traceability. It does not by itself establish independent reproduction, statistical adequacy, correctness, or support for a claim beyond this boundary.