← MCC-OE: Measured-Construct Closure and Observable Exhaustion / MCC-OE-05 · Certificate-relative task sufficiency

MCC-OE: Measured-Construct Closure and Observable Exhaustion MCC-OE-05 · Certificate-relative task sufficiency Neo.K (as signed)

Exact-Root Monotonicity Probe and Certificate-Relative Task Sufficiency: Canonical 18-Piece Continuum Root Ordering, the B01 Chart Collision, and the First Real Coupling with the Chart-Free HSL Certificate

Exact-root interval probing orders the declared canonical roots strictly (gap lower bound ≥ 1.78775629508683e-8 at ρ = 1e-4); the first genuine B01 leaf spans four support-chart regimes, yet its chart-free HSL certificate still passes (margin ≥ 1.0219e-9). The author calls this 'certificate-relative task sufficiency'.

For this one certificate route, a structural difference (spanning four chart regimes) did not produce a task difference (the certificate still passes). The slogan 'Structural Difference does not imply Task Difference' is scoped by the paper itself to this one certificate route; it is not a general proof of task sufficiency.

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PreviousMCC-OE-02 · Task-sufficiency collision protocol · Task-Sufficiency Collision Protocol and Transition-Threat Compiler: Red-Teaming the Observable Basis with Numerical Probes and Compiling Unclassified Transition States into Measurable Threat Boundaries

NextMCC-OE-06 · B01 chart-free boundary cover · B01 Chart-Free Boundary Threat Cover: The Hausdorff–Steiner Leaf Certificate, a Prototype HSL Cover of Over Half the Volume, and Adaptive Multi-Route Certificate Closure

This is a full-text translation of the Chinese source, which remains authoritative for its research claims. Translation is not independent mathematical verification and does not upgrade the original evidence level.

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