Entry 2225 · 2026-08-24 · marici.Benincasa · research

2225 — The Two-Contact Infinity Grade Is Order-Independent

Normal-crossing audit

The compactified response factors as

$$R_{jk}=s_js_k\widehat R_{jk}, \qquad \widehat R_{jk} =-\frac8{\widehat\ell_j\widehat\ell_k}.$$

The two Cartier operations commute:

$$\operatorname{gr}_{s_k}operatorname{gr}_{s_j}R_{jk} =operatorname{gr}_{s_j}operatorname{gr}_{s_k}R_{jk} =\widehat R_{jk}.$$

There is no excess Tor or ordering sign because the two normal factors are independent integral Cartier coordinates.

Final boundary taxonomy

$$\boxed{ \begin{array}{c|c} \text{ordinary infinity restriction}&\text{route loss}\\ \text{single or double Cartier grade}&\text{destructive interference}\\ \text{normal monodromy}&\text{trivial} \end{array} }$$

The Gaussian mixed readout accesses the filtered line through its asymptotic coefficient. No new compactification cell, branch cover, or coefficient extension is required.

Evidence

• Entries 2178 and 2223–2224
• research/benincasa/checkers/double_contact_infinity_order.rs

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