Edition 2: Add Theorem 6.1 — aged-task abandonment incentive

New Section 4.5 proves that completing old tasks is actively punished
by the unweighted mean: a single 26-day-old task hurts the average
more than 26 one-day tasks help it (same total wait resolved, worse
metric). The rational response is not starvation (Theorem 3) but
abandonment — closing aged tasks as "won't fix" to protect the average.

Changes:
- New Section 4.5 with Theorem 6.1 and Corollary 6.2
- Old Section 4.5 (Compound Effect) renumbered to 4.6, table updated
- Conclusion updated with new item 3, subsequent items renumbered
- Edition 1 backed up to .backup/README.md.v1

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

README.md

@@ -255,9 +255,63 @@ $\blacksquare$
 will observe an improvement in unweighted mean completion time with **zero
 change in actual throughput**. The metric improves. The output does not.
 
-### 4.5 The Compound Effect
+### 4.5 The Aged-Task Abandonment Incentive
 
-Combining Theorems 4, 5, and 6:
+Theorems 3–5 show that SPT deprioritizes large tasks. But the metric
+creates a second, more destructive incentive: **completing old tasks is
+actively punished**.
+
+**Theorem 6.1 (Aged-Task Penalty).** Completing a single task with
+completion time $C_{\text{old}}$ increases the running mean by more than
+completing $C_{\text{old}}$ tasks with completion time 1 each.
+
+**Proof.** Let the team have completed $m$ tasks with running sum
+$S = \sum_{i=1}^{m} C_i$ and running mean $\bar{C} = S/m$.
+
+**Case 1:** Complete one task with completion time $C_{\text{old}}$:
+
+$$\bar{C}_1 = \frac{S + C_{\text{old}}}{m + 1}$$
+
+**Case 2:** Complete $C_{\text{old}}$ tasks each with completion time 1:
+
+$$\bar{C}_2 = \frac{S + C_{\text{old}}}{m + C_{\text{old}}}$$
+
+Both cases add the same value ($C_{\text{old}}$) to the numerator. But
+Case 2 adds $C_{\text{old}}$ completions to the denominator, while Case 1
+adds only 1. Therefore:
+
+$$\bar{C}_1 - \bar{C}_2 = \frac{S + C_{\text{old}}}{m + 1} - \frac{S + C_{\text{old}}}{m + C_{\text{old}}} = (S + C_{\text{old}}) \cdot \frac{C_{\text{old}} - 1}{(m+1)(m + C_{\text{old}})}$$
+
+For $C_{\text{old}} > 1$, this difference is strictly positive: the old
+task produces a **worse average** than the equivalent volume of fresh
+work. $\blacksquare$
+
+**Example.** A team has completed 100 tasks with a running mean of 2 days
+($S = 200$). They can either:
+
+- Complete one 26-day-old task: $\bar{C} = 226/101 = 2.24$ days
+- Complete 26 tasks at 1 day each: $\bar{C} = 226/126 = 1.79$ days
+
+Same 26 days of total wait resolved. The metric says the second team is
+better — 1.79 vs 2.24 — despite resolving the same total wait time.
+
+**Corollary 6.2 (Abandonment Incentive).** Under the unweighted mean,
+the rational response to an aged task is not to deprioritize it (SPT,
+Theorem 3) but to **remove it from the system entirely** — close it as
+"won't fix," transfer it to another team, or let it expire. This removes
+the task from both numerator and denominator, protecting the average.
+
+This goes beyond starvation. Theorems 3–5 prove that the metric
+*delays* large and old tasks. Theorem 6.1 proves that the metric
+*punishes completion of them* — meaning the incentive is not merely to
+defer but to abandon. A metric that penalizes resolving the hardest
+problems is not measuring performance; it is measuring avoidance.
+
+---
+
+### 4.6 The Compound Effect
+
+Combining Theorems 4, 5, 6, and 6.1:
 
 | Measure | Effect of optimizing unweighted mean |
 |---------|--------------------------------------|
@@ -265,6 +319,7 @@ Combining Theorems 4, 5, and 6:
 | Delay for small tasks | Minimized — approaches zero (SPT) |
 | Delay for large tasks | **Maximized** — bears all queuing burden (Theorem 5) |
 | Completion time of largest task | **Maximum possible**: $\sum p_i$ (Theorem 4) |
+| Incentive for aged tasks | **Abandon rather than complete** (Theorem 6.1) |
 
 The net effect on perceived quality is negative because:
 
@@ -996,11 +1051,13 @@ The unweighted average completion time is a **biased statistic** that:
 1. **Can be gamed** by scheduling policy (Theorem 1), unlike work-weighted
    completion time which is schedule-invariant (Theorem 2).
 2. **Incentivizes starvation** of large tasks (Theorem 3).
-3. **Degrades client satisfaction** with zero compensating productivity
+3. **Punishes completion of aged tasks**, incentivizing abandonment
+   over resolution (Theorem 6.1).
+4. **Degrades client satisfaction** with zero compensating productivity
    gain (Theorem 7).
-4. **Actively contradicts priority systems** by carrying zero information
+5. **Actively contradicts priority systems** by carrying zero information
    about business-impact classification (Theorem 9).
-5. **Ignores priority entirely** in its scheduling recommendation,
+6. **Ignores priority entirely** in its scheduling recommendation,
    producing suboptimal priority-weighted delay whenever priority and
    size are not perfectly inversely correlated (Theorem 10).