Why large tasks need it

Parent: stages-and-gates

Stage-gating isn't bureaucracy for a big task — it's necessary, and five independent arguments converge:

• Near-decomposability (Simon, 1962; the watchmaker parable) — Hora builds in stable sub-assemblies and finishes; Tempus builds monolithically and is destroyed by every interruption. A gate = where you stabilize a sub-assembly.
• Error compounding — a long autonomous run has P(success) ≈ pⁿ, decaying with horizon; gates bound / reset it before it snowballs.
• Real options under uncertainty (Dixit–Pindyck; Gompers 1995) — the bigger / more irreversible / more uncertain the task, the higher the option value of abandoning; staging buys that option.
• Cost-of-defect curve (Boehm) — a defect costs ~exponentially more the later it's found; gates catch it early.
• Cooper's NPD benchmarking — disciplined stage-gate processes show higher success rates empirically.

→ A "large task" = long-horizon + uncertain + irreversible + error-compounding + (often) an untrusted executor. Each clause independently demands stages + gates.

Formal derivations

The above are the claims; the rigorous backing — each written to stand as an independent paper (precise setup, explicit hypotheses, complete proofs, cited-vs-proved separated, honest scope) — lives in derivations:

• adaptive-commitment-value — option value = information value (the value of a gate), via measure-theoretic convex analysis
• reliability-and-checkpointing — pⁿ decay + the exact optimal checkpoint interval √(2δM)
• simon-ando — near-decomposability ⇒ spectral gap ⇒ two-timescale aggregation (degenerate perturbation)
• holmstrom-informativeness — gate an untrusted executor where the interim signal is informative about effort