* fix(formulas): replace hardcoded ~/gt/ paths with $GT_ROOT
Formula files contained hardcoded ~/gt/ paths that break when running
Gas Town from a non-default location (e.g., ~/gt-private/). This causes:
- Dogs stuck in working state (can't write to wrong path)
- Cross-town contamination when ~/gt/ exists as separate town
- Boot triage, deacon patrol, and log archival failures
Replaces all ~/gt/ and $HOME/gt/ references with $GT_ROOT which is
set at runtime to the actual town root directory.
Fixes#757
* chore: regenerate embedded formulas
Run go generate to sync embedded formulas with .beads/formulas/ source.
Defines the state machine that Dogs execute for death warrants:
- 3-attempt interrogation with escalating timeouts (60s, 120s, 240s)
- PARDON path when session responds with ALIVE
- EXECUTE path after all attempts exhausted
- EPITAPH step for audit logging
Key design decisions documented:
- Dogs are goroutines, not Claude sessions
- Timeout gates close on timer OR early response detection
- State persisted to ~/gt/deacon/dogs/active/ for crash recovery
Implements specification for gt-cd404.
Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
