Worked examples: a ledger that closes, and one that does not
Two illustrative ledgers for a rack of AI inference servers over 24 hours. The figures are invented to teach the method; they are not a measurement of any real system.
Illustrative only
Every figure on this page is illustrative, chosen to show how the method works. None is a measurement of a real system.
Example A: the ledger closes
| Account | kWh over 24 hours | Label |
|---|---|---|
| Intake (M4) | 1,200.0 | Measured |
| ΔReserve (UPS battery) | +4.0 | Measured |
| Work | 690.0 | Measured |
| Overhead | 410.0 | Measured (sub-metered) |
| Waste | 96.0 | Estimated |
| Sum of accounts | 1,200.0 | — |
| Closure residual r | +0.00% | Pass if |r| ≤ 1.5% |
The accounts add up to the intake, so the residual is +0.00%, inside the 1.5% combined uncertainty. Overhead is sub-metered, which satisfies the rule that one account besides Intake is measured independently. Waste is Estimated, so the whole result is labeled Estimated, not Measured.
The ratios from Example A
- Rack energy at M3 over the same 24 hours: 980 kWh (illustrative).
- Overhead Ratio: OR(M4/M3) ↓ 1.22.
- Decision Yield with 2,400,000 passing decisions: DY(M3) ↑ 2,449 decisions per kWh.
Example B: the ledger does not close
| Account | kWh over 24 hours | Label |
|---|---|---|
| Intake (M4) | 1,140.0 | Measured |
| ΔReserve (UPS battery) | +4.0 | Measured |
| Work | 690.0 | Measured |
| Overhead | 410.0 | Measured (sub-metered) |
| Waste | 96.0 | Estimated |
| Sum of accounts | 1,200.0 | — |
| Closure residual r | -5.26% | Pass if |r| ≤ 1.5% |
Here the accounts exceed the intake by 60 kWh, a residual of -5.26%. That is outside the uncertainty, so the result is reported as not closed.
Diagnosing the residual
- Check that every meter covers the boundary it claims. Here, the intake meter sits after the uninterruptible power supply (UPS).
- Check that the accounts sit inside that boundary. The UPS conversion losses, 60 kWh, were booked to Overhead, but they happen upstream of the intake meter.
- Fix the boundary, not the numbers: move the intake meter upstream of the UPS, or remove upstream losses from Overhead and report them separately.
- Re-run the closure check. With the boundary fixed, the ledger matches Example A and closes.
What this shows
Most ledgers that fail do so because of a boundary error, not arithmetic. That is why JL-26 makes the meter point part of every result.
Questions
Why publish an example that fails?
Because a check that never fails proves nothing. Showing how a failure is found and fixed is the clearest way to show the rule is enforced.
Keep reading
Take the next step.
Two illustrative Joule Ledgers for an AI inference rack: one that closes within uncertainty and one that fails, with the residual diagnosed step by step.