topographo 0.1.0rc1

Reusable Cayley-Dickson and sedenion settlement math for Topographo.

Occurrence Theory

This repository contains a draft research paper and verification script for Occurrence Theory (OT), defined as an oriented form of Sedenion Settlement Dynamics (SSD).

The central object is the Aut-invariant settlement channel on the sedenion zero-divisor crack. The paper separates theorem, exact computation, measurement, interpretation, and conjecture using explicit ledger tags:

• [T] theorem
• [C] computation
• [M] measurement
• [I] interpretation
• [X] conjecture

Files

• topographo/ - reusable Python package for Cayley-Dickson algebra, validation gates, operators, and SSD helpers.
• occurrence-theory.md - main paper draft.
• occurrence_theory_audit.py - numerical audit and verification script for the algebraic claims.
• exceptional_algebras_lab.py - supporting exceptional algebra reproduction module used by the audit.
• occurrence_theory_prompt.md - source prompt and writing constraints used to generate the paper.
• .github/workflows/audit.yml - CI workflow that compiles and runs the audit scripts.
• LICENSE - MIT license.

Requirements

The audit script requires Python 3.11 or newer and NumPy. The verified exceptional_algebras_lab module is included in this repository and is used by the audit at runtime.

uv is the preferred runner for local audit work:

uv run python occurrence_theory_audit.py

For editable package installation:

uv pip install -e .

After installation, the core math layer is importable without running the Occurrence Theory audit narrative:

from topographo.core import CayleyDicksonAlgebra, verify_gates
from topographo.ssd import SedenionAlgebra

API documentation is generated with pdoc and published to GitHub Pages: https://theswanfactory.github.io/occurence/

To build it locally:

uv run pdoc \
  topographo \
  topographo.core \
  topographo.core.algebra \
  topographo.core.cayley_dickson \
  topographo.core.gates \
  topographo.ssd \
  topographo.ssd.channel \
  topographo.ssd.sedenion \
  -o site

Run the Audit

From the repository root:

uv run python occurrence_theory_audit.py

To save the output:

uv run python occurrence_theory_audit.py > audit_results.txt

After installation, the same audit is also available as:

occurrence-theory-audit

CI runs the audit workflow on pull requests and pushes to main.

Status

This is a research workspace, not a packaged library. The paper is the primary artifact; the script is included to reproduce the computation-backed claims.

License

MIT. See LICENSE.