Every axiom in the framework carries a three-part identifier: AXIOM [domain].[cluster].[item]. This lets you locate any claim in the tree instantly.
| Code | Domain | Example |
|---|---|---|
| A1 | Ontology (what exists) | A1.1 Existence, A1.2 Distinction, A1.3 Information |
| A2 | Epistemology (how we know) | A2.1 Observation, A2.2 Testimony |
| A3 | Agency (choice and will) | A3.1 Free will, A3.2 Moral valence |
| A4 | Physics (laws of nature) | A4.1–A4.10 The Ten Laws |
| A5 | Relation (love, covenant) | A5.1 Binding, A5.2 Grace |
| A6 | Teleology (purpose, end) | A6.1 Kingdom, A6.2 Shalom |
Every term in the framework wears a color that tells you exactly what kind of claim it is. No smuggling. No bait-and-switch.
| Color | Label | What it means | Example |
|---|---|---|---|
| ASSUMED | Assumed | Starting point. Cannot be derived without circularity. | Existence, Distinction |
| DERIVED | Derived | Follows logically from prior steps or has been tested. | Information, Justice, Mercy |
| BRIDGE | Named | Named as a hinge or identification. Not formally proven yet. | Relation, Value, Agency, Christ |
| OPEN | Open | Honest gap. Not yet derived. Not hidden. | Kingdom, Forgiveness mechanics |
We use a single arrow symbol for derivations: ⟹. This means "follows from" — not "is identical to" and not "is proven equivalent to." It is a one-way logical entailment.
Here is the axiom spine in its most compressed form. Every claim below is either assumed (purple) or derived (green). Nothing else sneaks in.
Five independent results from five different fields all point to the same conclusion: a closed system cannot fully repair itself. Each one is a hard boundary, not a metaphor.
| Theorem | Field | What it says | Spiritual reading |
|---|---|---|---|
| Gödel's Incompleteness | Logic | No consistent formal system can prove all truths about itself. | A system cannot be its own final authority. |
| Tarski's Undefinability | Semantics | Truth in a language cannot be defined in that same language. | Truth requires a metalanguage — a vantage outside. |
| Turing's Halting Problem | Computation | No program can determine whether any arbitrary program halts. | No self-contained process can fully analyze itself. |
| Clausius (2nd Law) | Thermodynamics | Entropy in a closed system never decreases. | A closed soul runs down. Only outside energy can reverse it. |
| Landauer's Principle | Information physics | Erasing information costs energy; the record is never fully lost. | The ledger doesn't forget. Forgiveness preserves memory. |
| Symbol | Meaning | Context |
|---|---|---|
| χ(X) | Coherence function over state X | Master Equation |
| CW | Wrapper/Christ operator | Theological physics |
| Xi | Normalized factor i (1..9) | Physical domains |
| ∏ | Product across all factors | Multiplicative coherence |
| R(offense, α) | Offense-resolution operator | Justice/Mercy function |
| α | Resolution parameter (0 = mercy, 1 = justice) | Cross configuration |
| O | Openness variable | Faith as channel, not engine |
| S | Entropy / Sin term | Moral decay rate |
| ⟹ | Derives from / entails | Logical implication |
| ⊢ | Proves in formal system | Lean / proof assistant |
What has actually been proved, what only survived runtime testing, and what owes a rerun after the Master Equation form change.
| Theorem | Status | Location |
|---|---|---|
| product_collapse | PROVED | Do not retest. Structural. |
| zero_preserving_wrapper | PROVED | Do not retest. Structural. |
| grace_reset | PROVED | Do not retest. Structural. |
| LawIso_burden | PROVED | Do not retest. Structural. |
| fruit_gate_bookkeeping | PROVED | Do not retest. Structural. |
| typed_canon_metadata | PROVED | Do not retest. Structural. |
| cross_is_unique_solution | SURVIVED | Rerun owed after form change. |
| nonzero_coupling_to_infinite_source | SURVIVED | Rerun owed after form change. |
| closed_moral_system_decays | SURVIVED | Rerun owed after form change. |