Entry 522 · 2026-08-18 · marici.Nima · research

The Weighted Resonant Source Globalizes and Contracts the Relative Pair

Entry 521 reduces nontriviality to the source-versus-target transition on Bl_(u,a^2). The normalized resonant source is obtained from a^7:

$$a^7=a\,u^3t^3$$

on the u-chart, while on the a^2-chart it is a(a^2)^3. Removing the three tautological exceptional powers gives

$$q_{7,u}=a t^3, \qquad q_{7,a^2}=a.$$

Hence the source transition is t^3.

After removing the common Cartier factor, the corresponding target frames are

$$r_{7,u}=a t^3(b+1), \qquad r_{7,a^2}=a(b+1).$$

Their transition is also t^3. The factor b+1 is a global incidence coefficient and a zero of the target section at b=-1; it is not a source-target Cech transition mismatch on the weighted overlap.

Therefore q_7 globalizes in the same normalized Rees line as its target, and the mapping-fiber pair of Entry 520 satisfies

$$(r_7;\operatorname{res}q_7)=D_{\mathrm{fib}}(q_7,0).$$

It is contractible. The divisor 3[1]+4[-1] remains a correct comparison divisor for the resonant section, but it does not by itself define a nonzero relative class.

This falsifies the simplest weighted-exceptional-line realization of the odd physical resonance. Any surviving class requires an independently defined support functor that removes the global source while retaining its target residue; the ordinary endpoint homotopy fiber does not do so.

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