Ledger Margin and Failure Scans

Charge Closure Is Necessary Three-Row Scan

Three rows separate charge closure from full reaction acceptance. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Opposite charges close

Scaled charge totals start at 0 and end at 0; accepted bit is 1.

0→0,a=10\to0,\quad a=1
Particle ledger rowInput and output particle ledgers feed one conservation check.electronpositronphotonphotonQ3=-3B3=0Le=1Lmu=0Q3=3B3=0Le=-1Lmu=0Q3=0B3=0Le=0Lmu=0Q3=0B3=0Le=0Lmu=0accepted

An electron alone cannot become photons

Scaled charge totals start at -3 and end at 0; accepted bit is 0.

−3→0,a=0-3\to0,\quad a=0
Particle ledger rowInput and output particle ledgers feed one conservation check.electronphotonphotonQ3=-3B3=0Le=1Lmu=0Q3=0B3=0Le=0Lmu=0Q3=0B3=0Le=0Lmu=0rejected

Charge closure is not enough

Scaled charge totals start at 3 and end at 3; accepted bit is 0.

3→3,a=03\to3,\quad a=0
Particle ledger rowInput and output particle ledgers feed one conservation check.protonpositronphotonQ3=3B3=3Le=0Lmu=0Q3=3B3=0Le=-1Lmu=0Q3=0B3=0Le=0Lmu=0rejected