# Kuhnian Dimensions -- Stage 1 Overlap Rules

**Owner:** frame-divergence-gate (E8). **Scope:** the three dimensions compared in Stage 1 and the overlap-counting rule. Combining logic in `TWO_STAGE_HYBRID_SPEC.md`. Index computation in `DIVERGENCE_INDEX_CALCULUS.md`. Zero overlap.

## Source anchor

Kuhn's mature position (SEP; Sankey, "Kuhn's Changing Concept of Incommensurability"; "Incommensurability: An Overview") treats incommensurability as a **multi-dimensional relation**. Feyerabend's methodological incommensurability reinforces that rival frameworks may employ standards that cannot be mapped in any neutral language. The three dimensions below are the defensible partition of declared-axiom identity.

## The three dimensions

### Methodological

**What it answers:** "What counts as evidence, and by what procedure is evidence admitted?"

Includes: admissibility rules, warrant standards (e.g., "replicated RCT" vs "triangulated ethnographic reading"), procedural commitments (double-blinding, member-checking), and the ranking order over evidence types.

**Overlap test:** Evaluator and RAM overlap on methodological dimension iff their declared admissibility rule AND their declared warrant standard AND their procedural commitment align on the active question.

### Semantic

**What it answers:** "Which taxonomic terms are core, and how do they partition the question-relevant domain?"

Includes: the core lexicon for the question, taxonomic primitives, and the partition structure over the domain (what counts as the same kind of thing).

**Overlap test:** Evaluator and RAM overlap on semantic dimension iff their core lexicons share dominant taxonomic terms AND those terms partition the domain identically on the active question. A lexicon sharing one term without structural partition match does NOT count as overlap.

### Ontological

**What it answers:** "What entities are primitive? What is reducible to what?"

Includes: primitive-entity list, reducibility claims (e.g., "mental states reduce to neural states" vs "mental states are irreducible"), and causal primitives.

**Overlap test:** Evaluator and RAM overlap on ontological dimension iff their declared primitives and reducibility commitments align on the active question.

## Overlap-counting rule

Count dimensions where BOTH axioms are present AND declared aligned on the active question. Missing axioms do not count as overlap. Declared-divergent axioms do not count as overlap.

```
overlap_count = |{ d in {methodological, semantic, ontological}
                 : axioms_align(evaluator_d, ram_d, active_question) = true }|
```

**Decision:**
- `overlap_count >= 2` -> Stage 1 **FAIL** (frames too similar).
- `overlap_count < 2` -> Stage 1 **PASS**.

## Recording rules

In the Frame Registry record, write:

- `stage1_binary_verdict`: PASS or FAIL.
- `stage1_failing_dimensions`: the dimensions that overlapped (not the ones that diverged). If Stage 1 PASS, this may be empty or contain fewer than two dimensions.

## Anti-patterns

- Never rewrite a dimension to manufacture an overlap difference. The three are fixed.
- Never infer a missing axiom. Escalate as `RAM_FRAME_UNPARSEABLE` or `FRAME_HOST_NOT_LOADED`.
- Never weight the dimensions. The test is unweighted dimension count.
- Never fold Stage 2 concepts into Stage 1. Shared-concept surface is Stage 2 only.
