E3: overlap equations and ordered values

The automatic identity

on a triple overlap is only a consistency condition. It does not prove solvability within the restricted spectator, jet, and normal-order class.

Moreover, before E1 is completed, local prescriptions may differ on noncoincident characteristic sets. Such a difference is not made contact-supported by the gluing notation.

The ordered values that must survive are

These are the inherited values for full functional supports, not a statement using $\mathrm{supp}f$ alone.

Every allowed interaction–observable contact vanishes on a strictly ordered, disjoint attachment region, by Lemma lem:rigidity. Thus contacts cannot change its prescribed off-collision value. This establishes the support part of the ordered-value audit, not the complete overlap construction.

For the common-frequency attempt, agreement with the canonical product on the admissible ordered attachment domains follows from Proposition prop:good-limit. No exact causal factorization is asserted at finite $\tau$: Gaussian damping has noncausal tails.