madmatrix: squared split orders, so the interference syntax stops returning the total

[oliviermattelaer]

Stacked on #60 — please merge that first. Base is claude/dixon-maltoni-gluon-basis-69e1d7, not main.

The bug

madmatrix ignored the ^2 (interference) syntax and returned the full amplitude squared.

Every C++ exporter contracted one jamp vector per helicity with the colour matrix once, so the |M|^2 it returned was the sum over every squared-order component. That is the requested number whenever the constraint keeps all of them, and it is silently wrong when it drops one — which is exactly the interference case, since a cross term cannot be reached by dropping diagrams at generation.

u u~ > u u~ QED^2==2 asks for the QCD-EW cross term alone (-5.58e-02) and got the whole +2.7756 back, from generated code that differed from the unconstrained process by one comment line.

The fix

jamp_sv becomes njampso = ncolor * nampso long — one vector per amplitude split order — and the colour sum pairs them, mirroring the Fortran GET_MATRIX(JAMP(NCOLOR,NAMPSO) -> RES(NSQAMPSO)) contract. The pairing lives in a dedicated color_sum_splitorders.cc because the sum changes shape rather than gaining a hole; everything else is a hole whose empty fill is the text that was already there.

The trap, for reviewers: the loop over amplitude-order pairs runs over all ordered pairs, never a triangle. The colour contraction keeps its triangular matrix with the off-diagonal doubled — for a single jamp vector that is just the statement that the (i,j) and (j,i) terms are conjugates, but for two different vectors they are not. Only (m,n) and (n,m) together equal the truth. Masking stays safe because sqSoIndex is symmetric (a squared order is the sum of the two amplitude orders), so a pair and its transpose are always kept or dropped together.

Switched off while the jamps are split: the jamp CSE/orbit (its shared partial sums would mix amplitudes of different orders into one vector) and the BLAS colour sum (it takes a single jamp vector). Colour choice is deliberately not split or masked — jampso_sv[icol] = sum_M jamp_M[icol] only picks which flow to write out.

GPU refuses at compile time: the device jamp buffers are sized ncolor, not njampso, and the backend is a make-time flag, so color_sum_splitorders.cc #errors under MGONGPUCPP_GPUIMPL. The exporter also says so at generation, rather than letting a GPU build be the first the user hears of it.

Why it is stacked on #60 rather than main

Only #60 carries the jamp CSE/orbit and the BLAS colour sum that this has to switch off. On main those do not exist, so the port would drop half its own safety logic and then silently mis-sum once #60 landed.

The third commit is the port adaptation, kept separate: the formats renamed to standalone/standalone_fortran, and the colour reflection folding (ncolorfold/colorFoldRep[]) that #60 removed, so the sum runs over ncolor directly.

Worth flagging: an unrecognised format name on the output line is not an error — it is taken as the directory name. The original test drove output standalone_mg7, which after the renaming silently exercised the default format instead.

Validation

u u~ > u u~, FPTYPE=d, standard RAMBO point:

component	madmatrix	output standalone_fortran
QED=0	2.8276928588371750e+00
QED=2	-5.5828746494657258e-02	-5.5828746494657265e-02
QED=4	3.7810076327210495e-03
sum	2.7756451199752387e+00
QED^2<=4	2.7756451199752394e+00	(computed independently)

The interference now matches Fortran to 1.3e-16, and the sum rule closes to 3 ulp. u u~ > d d~ g (ncolor=4) reproduces its three components too, with the sum rule at 2.8e-16.

The sum rule is the check that pins the pair loop: it is internal to one backend, so momenta and parameters cancel and it sees the interference algebra alone. A triangle over the pairs gives roughly 2x.

Regressions:

• Byte-identical output to the base commit for u u~ > u u~, g g > t t~ and p p > j j QCD^2==4 (PYTHONHASHSEED=0, ignoring *.pkl/*.gz). The last one carries a ^2 constraint that resolves to a single amplitude order, so the new path correctly stays off.
• Unit suite unchanged: 1581 tests, 2 failures, 94 errors on both the base commit and this branch, and diffing the failure names shows no difference. All 96 are pre-existing on Cheaper colour sum: DDM colour basis, Kleiss-Kuijf flows, and the same for madmatrix #60.
• New acceptance test test_standalone_split_orders_interference passes.

🤖 Generated with Claude Code