Exact global R4.T2 context theorem
The context rule behind the V14 affine cases can be promoted from sampled observation to an exact fixed-context theorem.
Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.
What was tested?
The context rule behind the V14 affine cases can be promoted from sampled observation to an exact fixed-context theorem.
Why the test is meaningful
V15 promotes the local V14 observation only after deriving a context selector and checking the entire declared low-bit domain. Fresh nTime values test whether the rule is bound to the intended header context rather than memorizing the original sample.
selector q(header context) → affine formula fqtheorem scope: ∀x∈{0,1}⁴, T2_low4(x,q)=fq(x)reuse allowed only when q_new=q_certifiedHow it was tested
Derive the selector, test 100,000 registered samples, perform fresh-nTime checks and exhaust the relevant low-bit context domain.
What happened
The contextual handoff and fresh-test gates passed; selector use remains restricted to its matching nTime context.
Exactness and statistical controls
The selector was tested on 100,000 registered samples, fresh-nTime cases and exhaustive low-bit contexts. Handoff and fresh-context errors were zero; cross-context reuse is explicitly forbidden.
What the result means
The theorem formalizes exact local behavior. Cross-job or cross-nTime reuse is forbidden without a separate theorem.
Limitations
- The theorem is context-bound.
- It covers low four bits, not full T2.
- No cost advantage follows from theorem status alone.
Evidence trail
Deterministic selector derivation plus exhaustive context checks and fresh-context validation.
Canonical variants
SUBENGINE-V15ASUBENGINE-V15BSUBENGINE-V15CSUBENGINE-V15DSUBENGINE-V15ESUBENGINE-V15FSUBENGINE-V15GSource: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.