Assembly

The ledger P13_ch_dependency_rows.json has three surviving rows:

• $R_{hh}$, $(S_0,{{\Gamma }_1}^{[2]})$$s_{2}K:K.c$, inputs D01+D02+D03+D11+D12, with $X_{hh}=\int (s_{0}h)G_{hh}h$;

• $R_{Kc}$, $(S_0,{{\Gamma }_1}^{[2]})$$s_{1}h:h^2$, input D13, with $X_{Kc}=\int G_{Kc}cEh$, where $E$ is the $h^2$-monomial operator of $S_0$;

• $R_{1pt}$, $(S_1,{{\Gamma }_1}^{[1]})$, inputs D14a–c.

Every input is evaluated; none is Missing, and a Missing input is refused rather than set to zero (control). The defect is computed for seven external assignments, including “c hat, h tilde”. For each it is given as the exact $d$-dependent value times MB, its pole, its coefficient of $L$ and its MS-bar local part.

{Result: the defect is zero, exactly in $d$, in every part and every assignment.} Why it is zero. Each surviving row vanishes separately in the projected slot. No counterterm cancellation is involved, and no cancellation between rows.

• (i)

  hh row: full-row transverse decoupling. D01 and D03 are each nonzero in the slot and cancel each other (the p17/p18 transverse sum). D11 is transverse by itself, and D02 = D12 = 0.

• (ii)

  K.c row: D13 reaches the ch slot only through $T_1$ and $E_1$ ($T_2$, $T_3$ and $E_2$ are longitudinal; $E$ is transverse), and $A_{T_1}=A_{E_1}=0$ exactly in $d$.

• (iii)

  One-point row: the tadpoles D14a–c vanish under the declared prescription.

This rests on:

• M2 / the D11 matching, verified on the 4D components only (the D11 matching for the evanescent components is not applicable and not verified);

• the evanescent decoupling proofs (P16 E2; P17/P18 hh evanescent and full-row decoupling);

• the frozen P.3 projection and the P13 ledger;

• the declared prescription.

Evanescent decoupling in the assembly. The evanescent parts of both rows were assembled explicitly and are zero for all seven assignments. The evanescent poles themselves are nonzero; they are regulated and not subtracted.