MathGround · the substrate
Joules per decision
Every decision is priced in joules and carries a receipt. Cheap-deterministic before expensive-stochastic: a request resolves at the lowest tier whose grammar covers it.
Joules / decision
—
Deterministic
—
L0 · lookup (table)
L0 · retrieved (cited)
L1 · composed (cited)
L2 · model (last resort)
Every claim carries a V-class + an energy receipt. A model can't relabel itself deterministic.
The same decision, priced twice
| tier | operation | receipt | gap |
|---|---|---|---|
| lookup | 1 pJ | 0.485 mJ | 4.9e8× |
| model | 18.4 µJ | 12.8 J | 7.0e5× |
Both are true. The stream above prices the work: what the operation
itself costs, on TR-2026-25's ladder where an on-chip fetch is 1–10 pJ. A MathGround
receipt prices the device: measured latency × macmon-signed watts, so a 0.05 ms
lookup on a 9.7 W machine bills 0.485 mJ. Idle device-seconds dwarf the operation,
which is why the gap runs to nearly nine decades and is not a mistake. An energy figure is a coordinate (plane × model), never a fact.