Introduction to 5D Link Naming for Matheology

1. What is this and why should I care?

Imagine hundreds of axioms, theorems, objections, and responses spread across multiple models and worldviews. Some are written for experts, some for beginners. Some present an axiom from a Jewish perspective, others from a secular one. How do you find anything? How do you know what connects to what? How do you make sure nothing gets lost as the system grows from dozens of elements to thousands?

The BEST Names system is the answer. It gives every piece of content a short, consistent label that humans can read and machines can parse. BEST stands for Brief, Explicit, Summarizing, Title — four naming layers, from a compact code (pet-ax1) to a full display title (ax1 — Containment). If you can read a postal address, you can read a BEST label.

2. A label in 60 seconds

Take pet-ax5. Three pieces, separated by hyphens:

• pet = the model. Pet stands for Pan-En-Theistic — the foundational axiom system (ax1–ax14) that formalizes the claim “all is in God, but God exceeds all.”

• ax = the type. This is an axiom — a statement assumed true without proof.

• 5 = which one. Axiom number 5: Necessary Divine Existence.

That is the whole label. Model, type, number. Now watch it extend:

• pet-ax5-easy = the same axiom, explained for beginners

• pet-ax5-vjud = the same axiom, seen through a Jewish lens

• pet-ax5-oov2 = the same axiom, frozen at version OOv2

You build up from simple to specific, one hyphen at a time. The core label (pet-ax5) always points to the canonical, most comprehensive page for that element. Everything else is a suffix that narrows the view.

A few more examples to build your intuition:

• pet-ax5-logic = what logic framework does axiom 5 use?

• jub-th8 = Jub Theorem 8 (from the Jubilee extension model)

• jub-con11 = the 11th objection registered in HELL

• pet-ax-ff = FeedbackFlow collection for all Pet axioms

3. The five dimensions

Every label can be located in a five-dimensional space. Not every combination exists as a page, but any valid combination gets a unique, collision-free address.

D1 — Model: Which axiom system?

A model is a registered set of axioms. pet is the Pan-En-Theistic foundation (ax1–ax14). jub is the Jubilee extension (ax15–ax25), which adds axioms about human agency and divine delegation. 4be is a future model, reserved but not yet active. Without this dimension, you could not tell which system an axiom belongs to — and systems can overlap, extend, or diverge. (See the full model registry in the AHA doc, Section 4.)

D2 — Element: What is it, and what about it?

This is the heart of the label. ax means axiom. th means theorem. con means objection. pro means response. You can chain types to ask specific questions: pet-ax5-logic chains ax5 with logic to ask “what logic does axiom 5 use?” Without this dimension, you would have names but no way to say what kind of thing you are naming. (See the full D2 registry.)

D3 — Version: Which frozen snapshot?

When the system reaches a milestone, it freezes a version. oov1 is Original Objections Version 1. oov2 is Version 2. A versioned label like pet-ax5-oov2 will never change — it is an immutable record. Without this, you could not cite a specific state of the system with confidence that it will still say the same thing next year.

D4 — Depth: For which audience?

The same axiom can be presented at different levels. The default is expert (full synthesis for researchers). easy is for beginners. prod is for teachers and communicators. math is a formal extraction for mathematicians. Without this, a beginner would always land on the expert page, and an expert would wade through simplified explanations.

D5 — View, Source, and Language: Which perspective?

Three prefixes partition this dimension. v + 3 letters = a worldview tradition (vjud for Judaism, visl for Islam, vsec for secular philosophy). s + 3 letters = a source text (stor for Torah, squr for Quran). l + 2 letters = a language-specific cultural insight that resists translation (lde for German, lhe for Hebrew). Without this, you could not systematically explore how different traditions and languages illuminate the same axiom.

4. The PoR — one axiom, fully dressed

Behind every short label is a rich, structured page called a PoR (Place of Reasoning). Think of the label as a street address and the PoR as the house behind it.

Here is what the house looks like for pet-ax1 — the foundational axiom “Containment” (“The world is part of God”):

• BriefName (id): pet-ax1 — the compact label you use in links and code.

• Title: “ax1 — Containment” — the display heading.

• SummarizingName (sum): “The world is part of God” — a one-line statement of what the axiom claims.

• FormalMathLatex (latex): \(W \leq G\) — the mereological parthood relation, saying W (world) is part of G (God).

• LogicsUsed (logic): Mereology + S5 modal logic — what formal framework applies and what it can express.

• SupportTorah (stor): Deut 4:39 (“God in heaven above and earth beneath”) — a citation with a hint explaining why the passage matters.

• ViewSecular (vsec): “We are parts of a whole that exceeds any part” — how secular philosophy frames the same idea.

• AnyAim (aa): current tasks and next steps for this axiom.

Each PoR can hold 40+ fields like these. You do not need to read them all. The system shows different subsets depending on your audience depth: at easy depth, you see the summary and a single strong citation; at expert depth, the full technical apparatus appears.

For the complete field list, see the PoR Fields Registry.

5. How content flows: Seed, Feed, Grow, Reap

Matheology grows by iterative cultivation, not by decree. The audit cycle follows an agricultural rhythm:

Seed — Prepare the ground. Define the scope of a review: which axioms, which models, what kind of scrutiny. Write it down before anyone starts, so the intent is on record.

Feed — Expose the work to challenge. Let critics, colleagues, and adversarial agents test the axioms. Every objection is nourishment, not attack — it shows where the roots are shallow. You do not need expertise in modal logic to notice that an argument feels wrong or that a tradition has been misrepresented. Those observations are among the most valuable nutrients in the field.

Grow — Extract the findings. Each genuine objection gets a permanent con number; each response gets a pro number. Assess honestly: mark each finding HELD (the system withstood the challenge) or BREACH (something must change). A BREACH is not failure — it is the system getting stronger.

Reap — Gather what you have learned. Walk through the objections and responses, decide what changes are justified, and identify scope for the next cycle. Each season builds on the last.

For the full lifecycle description, see Section 16 of the AHA doc.

6. HELL is not what you think

HELL stands for Historically Experienced Lessons Learned. It is a public register of bugs found in theological reasoning — modeled after software engineering’s bug databases. The idea: when one tradition discovers a flaw, every other tradition should be able to learn from it without repeating the pain.

Objections are treasured here, not feared. Every con (objection) gets a permanent address and a matched pro (response). For example, Con-A.1 — th8 Is Not a Theorem; Bistability Is Asserted, Not Derived challenges whether Theorem 8’s claim of bistability is actually proven or merely asserted — a serious mathematical gap. The matched Pro-A.1 — Response to Con-A.1 (th8 Bistability) responds with a formal dynamical-systems argument showing why oscillations cannot persist in finite systems. The pair stays linked forever, so future readers can see both sides and judge for themselves.

If you find something wrong, that observation has a permanent home.

7. How to contribute

You do not need a PhD to help. Three entry points:

1. Read and react. Pick any axiom, read it, and if something feels wrong or unclear, that observation is valuable. Use the FeedbackFlow (ff) link at the bottom of most pages to send your reaction directly.

2. Check a source. If you know a tradition well — Torah, Quran, Buddhist sutras, secular philosophy — check whether the citations are accurate and whether better ones exist. Source accuracy is where deep knowledge of a tradition makes a direct difference.

3. Ask a hard question. The most valuable contributions to HELL are honest objections. The system is designed to welcome them. A good objection, clearly stated, strengthens everything it touches.

8. Where to go next

• The full 5D Link Naming doc — the complete technical reference for the naming architecture.

• Pet axioms (A1–A14) — start reading the foundational axiom system.

• Jub axioms (A15–A25) — the Jubilee extension covering agency and delegation.

• HELL register — see objections and responses in action.