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docs: clarify configured vs effective half-life

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Rewrote simulation section explaining why effective half-life differs
from configured half-life:

1. Decay is CONTINUOUS (24/7 in calendar time)
2. Work is SPARSE (only during work hours)
3. Decay during BREAKS (overnight with no new work)

Added single table showing effective half-life for work patterns
(12h, 10h, 8h, 6h, 4h, 2h) vs configured half-lives (24h, 48h, 72h).

Key insight: 72h configured = 18h effective for 8h/day worker.
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.claude/JOURNAL.md
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@@ -255,3 +255,6 @@ This journal tracks substantive work on documents, diagrams, and documentation c
84. **Task - Half-life simulation tables**: Added detailed simulation results to documentation<br>
**Result**: Ran Python simulation for different work patterns (10h, 8h, 4h per day) across calendar half-lives (24h-168h). Added three tables to docs/activity-tracking-methodology.md showing "Work Hours at 50%" and "Work Days at 50%" for each combination. Key finding: 72h calendar half-life consistently yields ~2.9 work days at 50% point regardless of daily work hours. Activity scores correctly reflect work fraction (10h=41.6%, 8h=33.3%, 4h=16.6%)
85. **Task - Configured vs Effective half-life documentation**: Rewrote simulation section with clearer explanation<br>
**Result**: Replaced multiple tables with single effective half-life table showing work patterns (12h, 10h, 8h, 6h, 4h, 2h) vs configured half-lives (24h, 48h, 72h). Added explanation that difference is NOT about sampling but about: (1) decay is continuous 24/7, (2) work is sparse, (3) decay continues during overnight breaks. Added example showing overnight decay: 16h sleep causes ~15% weight loss. Key insight: 72h configured = 18h effective for 8h/day worker (~2.25 work days)

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docs/activity-tracking-methodology.md
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@@ -11,57 +11,52 @@ Our current approach uses **exponential decay scoring**:
### Why 72-hour Half-life?
The decay applies to **wall-clock time**, not working time. Users work only a fraction of each 24-hour period, creating a mismatch between calendar decay and effective working activity decay.
The decay applies to **wall-clock time**, not working time. Users work only a fraction of each 24-hour period, creating a mismatch between configured (calendar) half-life and effective (working hours) half-life.
#### Simulation Results
#### Configured vs Effective Half-life
The following tables show how different calendar half-lives translate to effective working-time decay for various work patterns. "Work Hours at 50%" indicates how many actual working hours contribute 50% of the weighted activity score.
**The difference is NOT about sampling** - sampling just measures activity at discrete intervals.
**10h/day work pattern** (intensive)
The difference comes from:
1. **Decay is CONTINUOUS** - applies to calendar time 24/7
2. **Work is SPARSE** - only happens during work hours
3. **Decay during BREAKS** - overnight/weekend decay continues with no new work
| Calendar Half-life | Work Hours at 50% | Work Days at 50% | Activity Score |
|:------------------:|:-----------------:|:----------------:|:--------------:|
| 24h (1d) | 10.0h | 1.0 days | 41.0% |
| 48h (2d) | 19.8h | 2.0 days | 41.5% |
| 72h (3d) | 28.5h | 2.9 days | 41.6% |
| 96h (4d) | 35.3h | 3.5 days | 41.6% |
| 168h (7d) | 47.7h | 4.8 days | 41.7% |
Example with 72h configured half-life and 8h/day work:
**8h/day work pattern** (typical)
| Event | Calendar Age | Weight | Work Added |
|:------|-------------:|-------:|:----------:|
| Day 0: Work 9am-5pm | 0h | 1.000 | +8h |
| Day 0: Sleep overnight | 16h | 0.857 | -- |
| Day 1: Work 9am-5pm | 24h | 0.794 | +8h |
| Day 1: Sleep overnight | 40h | 0.680 | -- |
| Day 2: Work 9am-5pm | 48h | 0.630 | +8h |
| Day 2: Sleep overnight | 64h | 0.540 | -- |
| Day 3: Work 9am-5pm | 72h | 0.500 | +8h |
| Calendar Half-life | Work Hours at 50% | Work Days at 50% | Activity Score |
|:------------------:|:-----------------:|:----------------:|:--------------:|
| 24h (1d) | 8.0h | 1.0 days | 32.7% |
| 48h (2d) | 16.0h | 2.0 days | 33.2% |
| 72h (3d) | 22.8h | 2.9 days | 33.3% |
| 96h (4d) | 28.3h | 3.5 days | 33.3% |
| 168h (7d) | 38.2h | 4.8 days | 33.3% |
At 72h calendar age, weight = 0.500 (half-life by definition). But only 24 work hours occurred in those 72 calendar hours. Each overnight break (16h) causes ~15% decay with no new work added.
**4h/day work pattern** (part-time)
#### Effective Half-life Table
| Calendar Half-life | Work Hours at 50% | Work Days at 50% | Activity Score |
|:------------------:|:-----------------:|:----------------:|:--------------:|
| 24h (1d) | 4.0h | 1.0 days | 16.3% |
| 48h (2d) | 8.0h | 2.0 days | 16.6% |
| 72h (3d) | 11.5h | 2.9 days | 16.6% |
| 96h (4d) | 14.2h | 3.5 days | 16.6% |
| 168h (7d) | 19.2h | 4.8 days | 16.7% |
The following table shows **effective half-life in working hours** for different work patterns and configured half-lives. Simulation: 7 days, 10-minute sampling intervals.
#### Summary: 72-hour Half-life Across Work Patterns
| Work Pattern | Work Hours at 50% | Effective Work Days | Activity Score |
|:------------:|:-----------------:|:-------------------:|:--------------:|
| 10h/day | 28.5h | 2.9 days | 41.6% |
| 8h/day | 22.8h | 2.9 days | 33.3% |
| 4h/day | 11.5h | 2.9 days | 16.6% |
| Work Pattern | Configured 24h | Configured 48h | Configured 72h |
|:------------:|:--------------:|:--------------:|:--------------:|
| 12h/day | 12.0h | 21.3h | 26.8h |
| 10h/day | 10.0h | 17.8h | 22.3h |
| 8h/day | 8.0h | 14.3h | 18.0h |
| 6h/day | 6.0h | 10.8h | 13.5h |
| 4h/day | 4.0h | 7.2h | 9.0h |
| 2h/day | 2.0h | 3.7h | 4.5h |
#### Key Insights
With a 72-hour calendar half-life:
- **Consistent ~3 work days** at the 50% point regardless of daily work hours
- Activity score reflects actual work fraction (8h/24h ≈ 33%, 4h/24h ≈ 17%)
With a 72-hour configured half-life:
- **8h/day worker**: effective half-life is 18 working hours (~2.25 work days)
- **4h/day worker**: effective half-life is 9 working hours (~2.25 work days)
- **Consistent ~2.25 work days** at the 50% point regardless of daily work hours
- Overnight breaks don't aggressively penalize scores
- A 24-hour half-life would be too aggressive - yesterday's work already at 50% weight before today starts
- A 24-hour configured half-life gives exactly 1 work day effective half-life
## Industry Approaches