← NS-X72 / X72-57 · Viscosity Continuation and the Adjoint-Positivity Bifurcation Map
Building on Round 56's rigorous closure at a single normalized viscosity, this round restores viscosity to a continuous parameter and investigates whether the regular central coefficient can change sign as viscosity varies. Proves that the tail contraction coefficient admits an exact scaling decomposition in viscosity, so that any fixed positive viscosity can push the onset of strict contraction out to a sufficiently deep sideband — meaning that if positivity were to fail, it could only happen at the finite-core matching or at some isolated zero, never out at the tail's infinity; a logarithmic sweep across eight orders of magnitude in viscosity shows the coefficient staying positive on both source fibers, exhibiting a positive linear asymptotic law as viscosity tends to zero and an inversely proportional asymptotic law as it tends to infinity. Route halts at STOP-C61 (viscosity-uniform positivity / endpoint-continuation gap): the absence of a zero across the entire interval is for now supported only by a high-resolution numerical sweep, not a proven theorem, handed to the next round to treat the singular endpoint at small viscosity; this round also includes a numerical-verification script and CSV data.
Relationship to the rest of the series, stated as closely as possible in the document's own words, not my interpretation.
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