Coherent paper targets give the frozen-top residual inputs

Fix head patterns, physical intervals, a ledger family, depth $d$, cutoff $W$, and rough level $K_0+1$. Assume $c,\delta_*,\beta_a>0$, $\beta_p\ge0$, $0\le\sigma\le\beta_p$, $\beta_p+\beta_a\le c/d_W$, $K_0+1\ge1/d_W$, and $2d+1\le W$. Eventually consider any bridge with the canonical sample data and guarded bank certificate. Require $\widetilde q$ equal the actual guarded smooth base mass, and require its target to be the literal barycentric target constructed from a head reserve and physical interpolation target, with reserve active mass $\widetilde q$. Its patterns must be the prime-head simplex at the reserve exponent, contain all primes up to $W$, and be head-separated. Require physical lower endpoints at least one, upper endpoints at most two and contained in the broad region $\lfloor I_\sigma^{\rm upper}n\rfloor\le2n-(K_0+1)h$, with $(K_0+1)h\le n$. Samples must avoid the guard set. Head-reserve targets at primes up to $W$ must equal the selector-tail factorizations, and the fixed exceptional charge must divide the precharged target. For the prescribed balanced alpha and total coefficient $\beta_p+\beta_a$,

The target is constrained by actual constructors and exact identities; feasibility and support are conclusions, not assumptions.