Theorem: Oai282-B release

For the free massless scalar and the original Weyl net specified in this paper:

1. Physical membership of $L=-Q/2$, including mixed products, a common invariant domain containing the benchmark's old domain, and compact affiliated realizations, is proved.

2. Translation, Lorentz, dilation, and special-conformal contacts are explicitly calculated. Their local currents act on the complete ordered Wick-field algebra and obey the stated Lie compatibility.

3. A complete stress-tensor classification and two actual separating probes prove coverage in the declared homogeneous polynomial class.

The following are not constructed:

1. an interacting improvement scalar;

2. a global integration theorem for the conformal generators;

3. a complete arbitrary time-ordered stress-insertion normalization scheme;

4. the inherited six-branch characteristic map and its admitted quantum coefficient;

5. a gravitational or spacetime-emergence dictionary.

O.1 remains NOT_CLOSED.

Proof. The positive assertions are Propositions prop:domain and prop:physicalL, Proposition prop:elementarycontact, Theorem thm:localaction, Proposition prop:brackets, and Theorems thm:classification and thm:coverage. The listed exclusions are outside their objects, domains, or prescription classes. No construction of those objects has been inserted into their proofs.