# The Oversight Yield Curve

Source: https://dinand.com/research/oversight-yield-curve/
Author: Dinand Tinholt
Published: 2026-09-05

> With reviewers who tire, the reviewer capacity lever falls from +1.46 to +0.93 below 0.8 sustained utilisation, and above 0.8 the margin goes negative.

The Oversight Yield Curve

Simulation study · 90,568 units · four slices · zero error units

# The Oversight Yield Curve

"Pricing Agent Autonomy" reported reviewer capacity as the largest positive lever an AI-agent organisation can pull, at +1.46. Capacity was a dial in that model, so reviewers could never tire. Here we make them tire. The lever survives, at +0.93, until sustained utilisation passes 0.8. Past that the margin crosses zero and keeps falling.

Pre-registered 2026-09-04 · campaign complete 2026-09-05 · certificate 200/200 pairs, p95 0.0137 · adversarially verified from the raw ledger

Dinand Tinholt · executive brief: [Staff Before You Escalate](https://dinand.com/research/staff-before-you-escalate/) · earlier study: [the Delegation Cliff campaign](https://dinand.com/research/campaigns/delegation-cliff/)

90,568

units run, zero error units

+1.4595

pub-slice capacity coefficient; the published campaign said +1.456

+0.927

capacity lever below sustained utilisation 0.8, still the largest positive one

−0.593 vs +1.148

escalation swept against fixed capacity, then with staffing scaled in lockstep

200/200

revalidation pairs passed, p95 difference 0.0137

## Why this experiment

The published article carried its own to-do list. Its limitations section said reviewer capacity was a parameter, so saturation could never arise from inside the model, and it named the interaction with endogenous fatigue as the obvious next experiment. A circulating preprint pressed on the same spot from the other side: oversight follows an inverted-U, because reviewers fatigue, so adding review can make a system less safe. The published result moved reviewer capacity; the preprint moved escalation rate against a queue of fixed size, a different lever. This campaign puts both in one design space and sweeps them together.

## Pre-registration, and what happened to it

Three hypotheses were registered on 2026-09-04, before any unit ran. The first one failed as plainly written, and we score it failed. The registered text, verbatim:

>

H1 (yield shape): With endogenous fatigue, margin against capacity is concave: positive slope at low load, flattening past a knee near sustained utilisation ~0.8. It does not go negative anywhere in the swept space.

H2 (inverted-U placement): The preprint's reversal appears only when escalation RATE is swept against FIXED capacity, and disappears when capacity scales with rate. Both studies are right in their own coordinates; the reversal is a projection artefact of holding capacity fixed.

H3 (coefficient survival): The band-only capacity coefficient falls from +1.46 but stays the largest positive lever below utilisation 0.8.

| Hypothesis | Verdict | What the data did to the wording |
| --- | --- | --- |
| H1 | Refuted as written | The yield curve is concave and its slope stays positive everywhere. The margin itself goes to −0.93 at sustained overload, which the registered sentence said would never happen. There is no flat-then-knee shape. |
| H2 | Supported in direction, corrected in statement | Escalation rate is −0.593 at fixed capacity and +1.148 when capacity scales with it. The registered "both studies right in their own coordinates" overclaims: the preprint's inverted-U failed to appear even in its own coordinates. |
| H3 | Supported | Capacity is +0.927 below utilisation 0.8, the largest positive lever there. Only the restricted quantity fell; the unrestricted coefficient rose to +1.601 and cannot back the registered "falls" clause. |

## Methods

### The 15-dimensional extension

The published campaign swept twelve organisational dimensions and scored each configuration on the delegation margin, the signed distance between delivered quality and a 0.95 quality floor, clipped to [−1, +1]. We keep all twelve dimensions with identical ranges and replace the static `human_capacity` ceiling with a reviewer pool. Escalations land in a queue. Reviewers drain it at a service rate that degrades under sustained load through a two-parameter fatigue curve: service is full below a threshold τ, then falls linearly to a floor of (1 − s) as the 7-day EMA of utilisation approaches the clip at 2.0. Three new swept dimensions result: escalation rate (0 to 0.60 of agent tasks routed to review by policy), τ (0.40 to 0.95) and s (0 to 0.85). The queue caps at 5,000 items per path; overflow would be recorded as coded drops.

### Four slices, and why the pub slice is the identification strategy

The campaign ran 90,368 primary units in four pre-planned Sobol slices with disjoint skips, 384 stochastic paths each, horizon 365 days.

| Slice | Units | Pinning | Role |
| full | 41,024 | all 15 dimensions swept | the extended space |
| pub | 16,448 | escalation rate = 0, fatigue strength = 0 | the published generating process |
| pre | 16,448 | capacity pinned mid-range | the preprint's coordinates |
| scl | 16,448 | capacity moves in lockstep with rate | the staffed alternative |

The extended kernel passes a bitwise reduction test: with escalation rate and fatigue strength at zero, it reproduces the published kernel's `simulate_quality` exactly, to the bit. The pub slice therefore contains the published experiment inside this one. If the pub slice recovers the published coefficients, every cross-slice difference is attributable to endogenising capacity and to nothing else. That is the identification strategy, and Table 1 shows it held.

### Guards

The campaign carried the binding rules from the Delegation Cliff pre-publication review. Margins of ±1 are censoring bounds; every quotable fit uses only units strictly inside the band. Every unit carries an error code and none were dropped: 90,368 primary units, zero errors. Escalations conserve per unit (arrived = served + queued + coded drops), with zero residual across all units checked. After completion, 200 randomly chosen configurations were re-run from scratch: median absolute difference 0.0, 95th percentile 0.0137, maximum 0.0244, against a tolerance of 0.05.

## Results

### Table 1. The pub slice recovers the published campaign

| Dimension | Published (n=4,948) | Pub slice (n=10,068) | Δ |
| Delegation depth | −1.499 | −1.5103 | −0.0113 |
| Reviewer capacity | +1.456 | +1.4595 | +0.0035 |
| Task coupling | −0.958 | −0.9658 | −0.0078 |
| Model capability | +0.949 | +0.9655 | +0.0165 |
| Self-check calibration | +0.915 | +0.9020 | −0.0130 |
| Rework cost | −0.803 | −0.7971 | +0.0059 |
| Verification depth | +0.413 | +0.4117 | −0.0013 |
| Verification coverage | +0.308 | +0.3034 | −0.0046 |
| Detection lag | −0.259 | −0.2560 | +0.0030 |
| Workload volatility | −0.147 | −0.1445 | +0.0025 |
| Trust response | +0.102 | +0.1070 | +0.0050 |
| Escalation latency | −0.007 | −0.0053 | +0.0017 |
| Fatigue threshold (placebo, inert here) | n/a | +0.006 |  |

Reviewer capacity reproduces to the third decimal on a fresh Sobol draw through a rebuilt kernel. Fatigue threshold, swept in this slice while fatigue strength is pinned at zero, is inert by construction and lands at +0.006, a passed placebo. The extension changed nothing it should not have.

### The margin against sustained utilisation

One curve carries the finding. Take the full slice, all 15 dimensions swept, and bin the band-only margin by each configuration's mean sustained reviewer utilisation.

Figure 1 · Delegation margin vs sustained reviewer utilisation

*Full slice, 41,024 units. Band-only bin means (censoring bounds excluded); equal-width utilisation bins, thinly populated bins below utilisation 0.2 omitted. Shaded: the zero crossing lands between sustained utilisation 0.8 and 1.0, near 0.9 on this binning. The terminal point pools the 23,703 units pinned at the utilisation clip of 2.0, where the band-only mean is −0.72, 66% of units are fragile-clamped at −1, and the deepest fine-grained bins reach −0.93.*

Below utilisation 0.8 the margin is positive and falls smoothly as load rises. The crossing sits in the registered 0.8 to 1.0 window. Beyond it the decline continues without a floor in the swept space: the deepest overload bins reach −0.93. The concave half of H1 survives on the capacity axis, Figure 3, where the slope stays positive across the whole swept range and flattens as capacity grows. The data refuted the clause about the margin never going negative, and refuted the flat-then-knee shape with it.

### The same lever with opposite signs

The pre slice sweeps escalation rate against a reviewer pool of fixed size, which is the preprint's experiment rebuilt inside our space. The scl slice sweeps the identical rate range while capacity scales in lockstep, which is what an organisation does when it staffs the review function it is loading.

Figure 2 · Margin vs escalation rate, fixed vs scaled capacity

*Band-only bin means, 12 bins across the swept range. Fixed capacity (pre slice, n=11,325 in band): monotone decline, slope −0.593 over the swept range. Capacity scaled with rate (scl slice, n=10,133 in band): monotone rise along the diagonal, +1.148 over the swept range. Same kernel, same rate axis.*

Route more work into a review queue of fixed size and the margin falls in every bin: −0.03 at the lowest rate down to −0.34 at the highest, slope −0.593. When the reviewer pool grows in lockstep with that same routing decision, the identical sweep pays +1.148 along the diagonal. The sign of "more oversight" lives in whether the capacity underneath it moves.

A number this report will never quote as a lever. A naive per-dimension fit on the scl slice prints "+0.574" for capacity and the same for rate. That is a rank-deficiency artefact. Capacity and rate are the same column of the design matrix in that slice, one identified quantity, and least squares splits it in half. The identified diagonal coefficient is +1.148 (SE 0.008). The verifier found this by attacking the metric; the half-value would have understated the staffed lever by a factor of two.

### Does the capacity coefficient survive? (H3)

Below sustained utilisation 0.8, on 11,179 full-slice units, the band-only capacity coefficient is +0.927 (SE 0.010). It is the largest positive lever in that region: bootstrap probability 1.000 of ranking first among positive coefficients over 1,000 resamples, with agent capability next at +0.654. In magnitude it is statistically tied with delegation depth (−1.26 in the same region), so the claim it supports is "largest positive lever" and no more. The unrestricted full-slice coefficient is +1.601, above the published +1.46. That number pools the overload region, where high capacity separates surviving configurations from clamped ones, and it measures a different quantity than the published band fit. It rose, so the registered clause that the coefficient "falls from +1.46" can only be scored against the restricted quantity, which fell to +0.927.

Figure 3 · Margin vs reviewer capacity, full slice

*Band-only bin means across the swept capacity range (0.05 to 0.50 of daily arrivals reviewable). The slope is positive in every bin and the curve flattens as capacity grows: the concave yield H1 registered. Nowhere does added capacity reduce the margin.*

### The preprint contrast, stated honestly

The registered H2 offered the preprint a diplomatic reading: each study right in its own coordinates. The data declined to sign it. In the pre slice, which is the preprint's own coordinate system, the margin declines monotonically across all 12 rate bins and all 24 bins of a finer cut. There is no interior maximum. No inverted-U appeared anywhere in the swept space. What survives of the preprint's position is one sign: at fixed capacity, more oversight does harm. The rise-then-fall shape that carries its safety argument did not reproduce. The fixed-capacity projection of this space is monotonically harmful from the first bin.

### Mechanism: fatigue and backlog, with the drop channel silent

The kernel has one coded way to lose an escalation: queue overflow past 5,000 items. That code never fired. Across all 90,368 units the maximum queue depth observed was 2,454, and zero units recorded drops. Every escalation that arrived was eventually served or was still queued at horizon. The harm at fixed capacity therefore runs through two channels only: fatigued reviewers serving slower, and backlogs delaying service while contaminated work compounds downstream. Any narrative in which overloaded reviewers "drop" escalations would be wrong about this space.

## Verification

Under the lab's standing protocol, findings do not ship until an independent verification subagent reproduces them from the raw ledger, and the verifier is instructed to attack the metric itself, since an arithmetically correct summary can still measure the wrong thing. The verifier recomputed every number in this paper from the raw ledger alone: unit counts and slice pinning (the pub slice's escalation-rate coordinate is exactly zero on all units), the band-only fits per slice, the conservation identity at zero residual, the certificate pairs, covariate balance across slices, and the utilisation curves. Two of its findings shaped this write-up: the scl rank deficiency behind the never-quote "+0.574", and the confirmation that the fixed-capacity decline holds with no interior maximum at both binnings. The figure data here was then recomputed a second time, independently, from the same ledger.

## Limitations

The fatigue curve is an assumption. Service degrades along a linear ramp parameterised by a threshold swept 0.40 to 0.95 and a strength swept 0 to 0.85, and the shape of the overload well inherits that form. An empirically calibrated curve, convex collapse or recovery dynamics, would move the crossing location and the depth of the well. The reproduction in Table 1 and the sign contrast in Figure 2 do not depend on the ramp, since the pub slice disables it entirely and the pre/scl contrast holds at every swept strength. The kernel is synthetic and unanchored to field data; coefficients are descriptive band-only slopes on a Sobol sample, and configurations outside the band are excluded by construction, so the fits describe where a margin exists rather than whether one does. Everything here is one quality floor, θ = 0.95. The full slice runs hot: 58% of its units saturate the utilisation clip, and 27% sit below utilisation 0.8, which still leaves 11,179 units under the H3 restriction. The preprint contrast is a reconstruction of its coordinates inside our kernel, and says nothing about its empirical setting.

## Reproducibility

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