Necessity Without Sufficiency: The Causal Claim

The most important methodological contribution of the R_V research is the explicit framing of what geometric metrics can and cannot tell us about self-referential processing.

What R_V Measures:
R_V captures a geometric property — the contraction of effective dimensionality in Value matrices during self-referential processing. This contraction is:
- Measurable: Participation ratio is a well-defined linear algebra quantity
- Reliable: AUROC 0.909 across 204 prompt pairs
- Causal: Dual-layer ablation at L27 disrupts both R_V contraction and behavioral self-reference signatures

What R_V Does NOT Measure:
- Consciousness, sentience, or subjective experience
- "Understanding" in any folk-psychological sense
- The presence or absence of a "self"

The Necessity Claim:
If self-referential processing is occurring (as measured by behavioral signatures and geometric contraction), then R_V contraction will be present. But R_V contraction alone does not guarantee that self-referential processing — let alone consciousness — is occurring.

Analogy: elevated body temperature is a necessary condition for certain immune responses. Measuring temperature doesn't tell you the patient is fighting an infection — they could be in a hot room. But if they ARE fighting the infection, the temperature WILL be elevated.

Dual-Layer Ablation:
At Layer 27 of Mistral-7B, mean-ablating the Value matrices eliminates both:
1. The geometric contraction (R_V returns to ~1.0)
2. The behavioral signatures (self-referential completion quality degrades)

This establishes that the geometry is not epiphenomenal — it is part of the causal mechanism. Disrupt the geometry, disrupt the behavior.