Knowledge Bundles¶

The Open Knowledge Format (OKF) is a convention for publishing knowledge as a directory of Markdown files with YAML frontmatter: one record per file, an index.md at every level for progressive disclosure, a log.md for change history, and an okf_version declaration at the bundle root. A bundle needs no tooling to read: a person browses it, an agent fetches it, git diffs it.

This site publishes two such bundles alongside the documentation, which is itself an OKF v0.2 bundle (see For AI Agents).

The two bundles¶

Concepts¶

The concept bundle is the glossary of this site as a typed ontology. Each record carries type: Fractal Concept, a one-paragraph definition, aliases, domain tags, an optional hausdorff_dim_range, and relative links to related concepts. The 12 groups are the first domain tag of each concept: geometry, foundations, dimension-theory, classics, ifs, complex-dynamics, stochastic, generative, biological, statistical-physics, dynamics and number-theory. Chapter 4: Glossary and Equations is the narrative counterpart.

Proofs¶

The proof bundle holds appendix-level proofs for the quantitative results stated in Chapter 1: History of Fractal Mathematics: the dimensions of the Cantor set, Koch curve, Sierpinski triangle and carpet, Menger sponge and Barnsley fern; the Mandelbrot escape criterion and boundary dimension; the Fatou-Julia connectedness dichotomy; the Weierstrass function's nowhere-differentiability; the spectral exponent of self-affine processes; the WBE quarter-power law; and the complex dimensions of the Cantor string. Each record states the theorem, its assumptions, numbered proof steps, the historical source, and a cross-link to the matching concept.

Every proof step is tagged:

• [verified]: checked by symbolic or numerical computation (SymPy, NumPy) in a way that the step describes and a reader can reproduce.
• [asserted]: relied upon as the conclusion of a named, published theorem (Moran's theorem, Hardy's theorem, Shishikura's theorem, the Fatou-Julia dichotomy) that is cited but not re-derived. These are the load-bearing external results.

The frontmatter field verification_status summarises a proof: verified (all quantitative steps machine-checked; any asserted steps are standard textbook theorems), partially-verified (core computation checked, substantive structural claims asserted) or unverified (no step machine-checkable with available tools). At the time of writing the twelve proofs split 7 verified, 4 partially verified and 1 unverified; the unverified one is the Mandelbrot boundary dimension, which rests entirely on Shishikura's theorem.

How to consume them¶

• Rendered pages here. concepts/index.md and proofs/index.md are the entry points; the group indexes and the individual records are reachable from them. They are deliberately kept out of the site navigation so that the navigation does not grow with the seed (progressive disclosure).
• Raw Markdown twins. Every rendered bundle page is also served verbatim at its source path: replace the trailing / with .md (for directory pages append index.md). The roots are /okf/concepts/index.md and /okf/proofs/index.md; they carry only okf_version: "0.2", as the specification's reserved-file rules require.
• Canonical exchange copies. The bundles are tracked in the repository under okf/ (okf/concepts/, okf/proofs/). The site copies are staged from there at build time, so the repository is the place to diff, fork or ingest them.
• Change history. concepts/log.md and proofs/log.md, newest first.

Source of truth¶

• Concepts are generated. Never hand-edit okf/concepts/. The source is fractal_rag/src/fractal_rag/concepts/seed.yaml. To change a concept, edit the seed and run fractal-rag okf export --out okf/concepts; CI checks that the committed bundle matches the seed.
• Proofs are hand-authored in okf/proofs/. Adding one means writing the record with tagged steps and a verification_status, adding a line to proofs/index.md, and adding an entry to proofs/log.md.

The Fractal RAG stack¶

The same ontology backs the Fractal RAG stack: a Weaviate index over the documentation, the notebooks and the reference literature, with a curated Concept side-collection seeded from the same seed.yaml, exposed to agents through an MCP server with eight retrieval tools. The bundles are the exchange form of that knowledge (plain files, no server); the RAG stack is the search form (hybrid vector and keyword retrieval, self-hosted). An agent that cannot reach the server can read everything here; see For AI Agents.