# FC08 — mutexes and priority inheritance

This card is a deterministic Hazard3/RV32I experiment for Chapter 8 of the
FreeRTOS Kernel Book. It proves the mechanism, not only the final value.

```text
Low p1 owns mutex
  → High p3 blocks on the mutex
  → Low effective priority becomes 3
  → Medium p2 is Ready but does not run
  → Low gives the mutex
  → High acquires before Medium runs
  → Low returns to priority 1
```

Only public FreeRTOS APIs are used for acceptance assertions. The internal
`uxBasePriority` and `uxPriority` fields are shown as debugger evidence, not
as application dependencies. No manual `vTaskPrioritySet` substitutes for
priority inheritance.

## Build and evidence

```sh
make task1
make host-test
make check-abi
make sim
make check-determinism
```

The final verifier checks the real mutex holder, effective priorities, public
task state, three distinct task stacks, protected-resource invariant, exact
event order and a stable digest from three clean simulator processes.

## Interactive views

- A2 — mutex, owner, waiters and protected resource;
- A4 — deterministic task topology;
- A5 — complete inheritance and hand-off sequence;
- A6 — mutex ownership and effective-priority states;
- A7 — handles, stacks, public observations and TCB debugger evidence;
- A8 — critical section, scheduler suspension, mutex and gatekeeper choices.

Source basis: FreeRTOS Kernel Book, Chapter 8. No source example is copied
verbatim.