Manuscript X-B-ST@1 · X-B-ST.tex · corollary · d03c150c
Corollary: The first-order identity is independent of compatible contacts
C3: normalization and degree-one uniqueness › Contact modifications · lines 2146–2158 · proof included or linked
X-B-ST@1#cor:ward
No sheet-compatible degree-one contact changes Theorem thm:ward. Such a contact is neither needed to repair that identity nor able to break it without leaving the sheet.
Proof. The modified and original response maps have equal classes for each background and insertion. Their completed first coefficients therefore coincide.