A final audit binds delay, launch, reflection, echo, and bounce ledgers. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The audit cites finite travel and launch power

The delay is 4 seconds, current is 3 amperes, and launch power is 36 watts.

4 s,3 A,36 W4\ \text{s},\quad 3\ \text{A},\quad 36\ \text{W}
Transmission audit sourcesDelay, current, and power are cited from source checks.sourceloadlineforwardincidentreflectedoutechoincidentreflectedlinew0w1w2w3length 12 mspeed 3 m/sdelay 4 sstep 12 Vline 4 ohmcurrent 3 Apower 36 Wline 4 ohmload 2 ohmGamma -1/3in 12 Vback -4 Vlaunch 0 sone way 4 sround trip 8 secho 8 sline 4 ohmload 4 ohmGamma 0in 12 Vback 0 Vload Gamma 1/2source Gamma -1/2load total 9 Vdelay 4 scurrent 3 Aecho 8 sload total 9 Vaccepted

The audit keeps both mismatch and match claims visible

The mismatch coefficient is -1 over 3, while the matched reflected voltage is 0 volts.

Γmismatch=13,V,match=0 V\Gamma_{\text{mismatch}}={-1\over 3},\quad V_{-,\text{match}}=0\ \text{V}
Mismatch and match auditA nonzero echo and a zero matched reflection are both checked.sourceloadlineforwardincidentreflectedoutechoincidentreflectedlinew0w1w2w3length 12 mspeed 3 m/sdelay 4 sstep 12 Vline 4 ohmcurrent 3 Apower 36 Wline 4 ohmload 2 ohmGamma -1/3in 12 Vback -4 Vlaunch 0 sone way 4 sround trip 8 secho 8 sline 4 ohmload 4 ohmGamma 0in 12 Vback 0 Vload Gamma 1/2source Gamma -1/2load total 9 Vdelay 4 scurrent 3 Aecho 8 sload total 9 Vaccepted

The final accepted bit depends on every cited source

The echo arrives at 8 seconds and the bounce partial load total is 9 volts, so the audit accepts.

techo=8 s,Vload=9 Vt_{\text{echo}}=8\ \text{s},\quad V_{\text{load}}=9\ \text{V}
Transmission-line auditThe accepted label is tied to every source reference.sourceloadlineforwardincidentreflectedoutechoincidentreflectedlinew0w1w2w3length 12 mspeed 3 m/sdelay 4 sstep 12 Vline 4 ohmcurrent 3 Apower 36 Wline 4 ohmload 2 ohmGamma -1/3in 12 Vback -4 Vlaunch 0 sone way 4 sround trip 8 secho 8 sline 4 ohmload 4 ohmGamma 0in 12 Vback 0 Vload Gamma 1/2source Gamma -1/2load total 9 Vdelay 4 scurrent 3 Aecho 8 sload total 9 Vaccepted