decoy_q_one

Module Wave C2 R0+R1 treats the dynamic structure-function bracket on a two-site discrete phase space. R0 is the decoy residual: the naive lookalike that plugs $g,x$ into the frozen HamW slot and reuses frozen partials fails, because the configuration partial picks up an uncompensated $\partial g/\partial q$ term. R1 then shows the honestly differentiated candidate inhabits the phase-space-dependent Hamiltonian construction and recovers the target bracket.

The decoy phase point is the explicit witness: unit configuration and unit momentum at site $0$, zero at site $1$, chosen so that both the gradient and $\partial g/\partial q$ are nonzero at site $0$. Configuration and momentum are functions $\mathbb{Z}/2\mathbb{Z}\to\mathbb{R}$. This lemma records the configuration value at the complementary site.

One-line wrapper: simp unfolds the definition of the decoy phase point. The configuration component is the piecewise map that returns $1$ at site $0$ and $0$ elsewhere, so evaluation at $1:\mathbb{Z}/2\mathbb{Z}$ reduces to $0$ by definitional simplification.

Feeds the R0 decoy theorem TypedResidual_naive_dynamic_HamW_decoy_fails, which states that at this witness, with the decoy lapse and site $0$, the honest configuration partial of the dynamic Hamiltonian differs from the frozen HamW partial by the uncompensated $\partial g/\partial q$ term. Closing R0 (and R1) is the first block of the Gap-5 residual DAG; continuum and HKT residuals stay open, and gap5_constraint_recovery is not flipped. The lemma is pure bookkeeping on the witness, not a physics claim about gravity itself.