GRADANTIR

also known as Grade Exchange. The product name is Gradantir; the code, the store key, and the export format still say grade-exchange, and stay that way for now.

A risk-adjusted pricing engine for academic performance under severe small-sample constraints.

A student's transcript is a sparse, heteroscedastic, non-stationary time series with a hard boundary at both ends and no guarantee of a trend. Report cards summarize it with an arithmetic mean, which is the one statistic that discards everything decision-relevant: whether the student is drifting, whether they are erratic, whether their edge over the cohort is closing, and whether the low-stakes work predicts the high-stakes work.

This engine estimates two distinct quantities and refuses to conflate them:

	question	answer
Fair value (FV)	What is this subject probably worth?	A Bayesian capability estimate over every print, with Student-t credible intervals.
The MARK	What would a risk-averse market pay for it today?	Fair value minus an itemized, attributable risk discount.

The gap between them is the object of interest. Fair value is an unbiased estimator and is used for every forecast. The mark is deliberately, defensibly biased downward in proportion to the pathologies present in the tape — drift, instability, shock, coursework divergence, alpha erosion — and is what the interface displays as the price. A subject that oscillates between 52 and 85 and a subject that prints 68 every time have the same mean; they do not have the same mark.

The presentation layer is a trading terminal because the metaphor is load-bearing, not decorative: a price falls when the position deteriorates, the deepest discounts mark where effort has the highest return, and the discount is always decomposed into the charges that produced it. Static single-page app, no backend, localStorage only.

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1 · The estimation problem

Grade data violates nearly every assumption that standard forecasting machinery relies on:

property of the data	what breaks
$n \approx 5\text{–}12$ prints per subject	asymptotics; least-squares extrapolation; any CLT appeal
heterogeneous instruments (exam / test / assignment / quiz)	i.i.d. observation noise
irregular spacing — 3-day gaps and 200-day breaks	discrete-time state-space models
bounded support $[0,100]$ with ceiling effects	symmetric predictive intervals of any family
difficulty varies between sittings	comparability of raw scores
a single catastrophic print is common and uninformative	mean- and OLS-based estimators

Four design constraints follow, and every component below is answerable to them:

1. Produce an honest estimate from $n = 1$. No component may be undefined at small $n$; it must degrade to a defensible prior instead.
2. Never hallucinate a trend from noise. A slope must pass a significance gate before it may forecast, and is damped by how weakly it passed. This is a bound on how much noise can become trend, not a guarantee that none does — see §5, which states the limit precisely rather than overclaiming it.
3. Uncertainty must widen when data is thin, not silently vanish. Student-t throughout, never Gaussian. (Student-t is an answer to thin data, not to the $[0,100]$ boundary — §23 is explicit about what the intervals do at the ceiling.)
4. No single print may hijack the line. Medians, MAD, winsorizing — not means.

A fifth constraint governs Part II specifically: every point of discount must be attributable. A risk model that outputs a scalar "quality score" is unfalsifiable and unactionable. Each charge names its factor, its magnitude in points, and its evidence.

flowchart LR
    E[prints<br/>score · type · date] --> D["difficulty detrend<br/>score − λ(ref − ref̄)"]
    D --> K[Kalman<br/>local-level]
    D --> W[EWMA<br/>recency × signal]
    D --> S["shrunk mean<br/>empirical Bayes"]
    D --> T[Theil–Sen<br/>τ-gated slope]
    K --> V{{walk-forward<br/>validation}}
    W --> V
    S --> V
    T --> V
    V --> EN["ensemble<br/>moment-matched t"]
    EN --> FV["FAIR VALUE<br/>ci50 · ci90 · p10"]
    D --> FA["factor panel<br/>vol · drift · shock<br/>streaks · alpha · cw"]
    D --> CU["CUSUM<br/>drift detector"]
    FV --> MK
    FA --> MK["MARK<br/>FV − Σ premia"]
    CU --> MK
    E --> DP["depth model<br/>π class · β desk · σ"]
    DP --> OB["order book<br/>field rank"]
    MK --> CO["GX COMPOSITE"]
    D --> NX["next-exam oracle<br/>exam side ⊕ (cw side + δ̂)"]
    EN --> RT["analyst desk<br/>4 views → consensus"]
    NX --> RT
    MK --> AD[advisor<br/>urgency]

Loading

The factor panel and the CUSUM hang off the detrended tape, not the raw prints, and both run their own walk-forward pass rather than reading the ensemble's — they answer different questions and must not inherit its weights.

Notation

Subject $s$ has prints $y_1,\dots,y_n$ (scores, 0–100) at calendar days $x_1 \le \dots \le x_n$, each of type $c_i \in \{\text{Exam},\text{Test},\text{Assignment},\text{Quiz}\}$, optionally carrying a class average $a_i$, year-level average $g_i$, and placement $(r_i, N_i)$. "Today" is $x_\ast$. Detrended scores are $\tilde y_i$.

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Part I · Fair value — the measurement model

1b · The school calendar — two clocks, and the settlement lag

Every figure in this document is bucketed by term, so being wrong about terms is being wrong about everything downstream. A school year is not four calendar quarters: terms open and close on dates the school publishes, those dates drift by a week or two each year, and — the part that breaks every naive implementation — results arrive after the term they measure. A Term 1 paper sat in late March is handed back in the April holidays one year and two days into Term 2 the next; the mid-year paper is marked over the July break and published a fortnight into Term 3. Bucketing by "which term is this date in" files the same round under a different term every year.

So the calendar keeps two clocks:

clock	question	used by
teaching term	where is the school physically today?	session chrome, week numbers, holiday-aware ageing
reporting term	which term does this result report on?	every bucket, tape, index and average

The reporting grid is the teaching grid shifted forward by a settlement lag $L$ (default 28 days), anchored to the next term's opening rather than the previous term's close so the seven-week summer cannot swallow a December round into February:

$$\text{term}(d) \;=\; \max\{\,T : \text{start}(T) + L \le d \,\}$$

On the reference book this files all three April rounds as T1 and both August rounds as T2, across three years whose term dates differ by up to a fortnight. Published dates live in src/lib/calendar.ts and are editable per year in Settings; a year the school has not published yet is projected off the nearest one it has, weekday-aligned, which is accurate to within a few days. Any single result can also be filed by hand (entry.term), which always wins — the calendar is inferring, and the person holding the paper knows.

Rounds are then read off the book rather than assumed: a term with prints is a round, a term without one never existed and is never drawn. Their names come off the book too — the shared stem of the titles inside a round ("Mid-Year 2025", "Course work · Mid-Year 2025") is what the axis reads, so the tape says MID 25 rather than the anonymous T2 25. Which terms a school examines in is likewise learned: the recurring pattern of terms that have printed exams is what PREDICTION targets next, and it adopts a new term the first time one is sat.

One consequence runs through Part II: silence is measured in school days. A subject cannot print over the summer, so the summer must not age it — on calendar time every desk in the book drifts toward caution every January for no reason anyone chose. Ability drift (Kalman, EWMA) deliberately stays on calendar time, because you really do forget things over the holidays.

2 · Difficulty detrending

A 60 on a paper the class averaged 50 is not the same event as a 60 when the class averaged 75. Where a reference $\rho_i = a_i$ (else $g_i$) exists over $m$ prints, scores are recentred against the subject's usual reference level $\bar\rho$:

$$\tilde y_i \;=\; y_i - \lambda\,(\rho_i - \bar\rho), \qquad \lambda = \frac{m}{m+2}$$

$\lambda < 1$ keeps a single reference point from over-correcting. Prints without a reference pass through untouched. Every within-subject quantity runs on $\tilde y$ — the price, the factor panel, the CUSUM, the oracle. The one deliberate exception is the cross-subject pool of §3, which needs a shared centre rather than each subject's own and so runs on $y - \rho + \bar\rho_{\text{book}}$. Two transforms, two jobs; §3 says why.

3 · Cross-subject shrinkage (empirical Bayes)

With two prints a subject's own mean is a poor estimator; James–Stein prescribes partial pooling. From per-subject means we estimate between-subject variance $\tau^2$ (floored — subjects always differ) and within-subject noise $\sigma^2$ (pooled, floored), then trust local data by

$$B \;=\; \frac{\tau^2}{\tau^2 + \sigma^2/n}, \qquad \hat\mu_{\text{shrunk}} \;=\; B\,\bar{\tilde y} + (1-B)\,\bar\mu_{\text{book}}$$

$B \to 0$ as $n \to 0$ (a new subject opens at the book's level); $B \to 1$ as evidence accumulates. If subjects genuinely spread far apart ($\tau^2$ large), even one print earns real trust — the formula decides, not a heuristic.

Pooling is only valid between comparably-scaled measurements, and marks are not: a subject whose year-level mean is 70 would drag one whose year-level mean is 55 toward it for no reason but the marking. So the pool runs on difficulty-corrected scores $y_i - \rho_i + \bar\rho_{\text{book}}$, centred on the book's mean reference so the correction is genuinely cross-subject and the scale stays a percentage.

4 · Local-level Kalman filter

Ability is modeled as a random walk observed through noisy assessments:

$$\alpha_t = \alpha_{t-\Delta} + w, \quad w \sim \mathcal N(0,\; q\,\Delta) \qquad\qquad \tilde y_i = \alpha_{t_i} + v_i, \quad v_i \sim \mathcal N(0,\; R_{c_i})$$

with $q = 0.06\ \text{pts}^2/\text{day}$ and per-type observation noise built from the reliability standard deviations

$$R_c = \{\text{Exam } 5,\ \text{Test } 6.5,\ \text{Assignment } 8,\ \text{Quiz } 10\}\ \text{pts}$$

so the Kalman's observation variance is $R_c^2$. $R_c$ is a standard deviation everywhere in this document and everywhere in the code (RELIABILITY_SD in params.ts); it is squared only here, inside the filter. Per print — predict, then update:

$$P \leftarrow P + q\,\Delta t, \qquad K = \frac{P}{P + R_c^2}, \qquad m \leftarrow m + K(\tilde y - m), \qquad P \leftarrow (1-K)\,P$$

Real day-gaps matter: a print after a 200-day break meets an honestly wider prior than one three days after the last. The prior is the pooled book mean with variance $15^2$, so the filter is well-defined from the first print.

5 · Robust trend — Theil–Sen under a Kendall-τ gate

The trend member takes the median of pairwise slopes (29% breakdown point), but a slope may only forecast if the ordering of the data supports it. Kendall's $\tau$ over $(x, \tilde y)$ yields a normal-approximation two-sided $p$, and the slope is gated:

$$\hat\beta \;=\; \begin{cases} \beta_{TS}\,(1-p)^2 & n \ge 4 \text{ and } p \le 0.5\\[2pt] 0 & \text{otherwise} \end{cases}$$

What this does and does not guarantee. Under the null — no monotone relationship at all — $p$ is approximately uniform, so roughly half of shuffled series will clear $p \le 0.5$ and report a nonzero slope. The gate is not a proof of flatness and this document should not claim one. What it is, is a hard bound on how much noise can become trend:

• a slope that only just passes is damped by $(1-p)^2 \le 0.25$ — at most a quarter of an already-spurious slope survives, and the damping goes to zero continuously as $p \to 0.5$;
• the surviving slope is a median of pairwise slopes, so it is unbiased in expectation under the null — the spurious trends point up as often as down and do not accumulate;
• below $n = 4$ it is hard zero, no exceptions;
• and the ensemble (§8) then scores the member on prints it did not see, so a member that keeps inventing trends loses its weight to the ones that do not.

Four defences, none of them a guarantee, and the design is honest about which it is. Both $p \le 0.5$ and the $(1-p)^2$ exponent are chosen constants — the gate is where the judgement lives, not a place it was avoided. robust.test.ts demonstrates the behaviour on a worked noise series rather than asserting a distributional property it cannot assert from one draw.

This is still the engine's answer to the classic small-$n$ failure of least squares, which will cheerfully extrapolate a line through four random points at full strength and with no gate at all.

Damped extrapolation. The $\tau$-gate fixes how fast the trend member drifts; damping fixes how far. Rather than ride the fitted line straight to the target, the member holds its fitted value at the last print and adds a saturating drift over the horizon $h$ (days):

$$\Delta(h) \;=\; \hat\beta\,\tau_d\,\bigl(1 - e^{-h/\tau_d}\bigr), \qquad \tau_d = 90\ \text{days}$$

For a one-step gap $h \ll \tau_d$ this is $\approx \hat\beta h$ — the same straight line — so short-horizon forecasts are untouched; but the total drift can never exceed $\hat\beta\tau_d$, so a slope that fit a hot streak stops paying out a full rating horizon later. This is the structural cure for the forecaster optimism the post-mortem measured (§26): an undamped upward slope over-predicts every exam it is extrapolated past. On the synthetic fixture the effect is near-nil — its slopes are mostly $\tau$-gated to zero, so there is little drift to bleed off — but on a tape that genuinely trends it caps the runaway. robust.test.ts pins the saturation.

6 · Recency EWMA, and the two weight tables

A 60-day half-life crossed with per-type signal weights:

$$w_i = 2^{-(x_\ast - x_i)/h} \cdot u_{c_i}, \qquad \hat\mu_{\text{EWMA}} = \frac{\sum w_i \tilde y_i}{\sum w_i}, \qquad u = \{\text{Test/Asgn } 1.6,\ \text{Exam } 1.25,\ \text{Quiz } 0.7\}$$

Note the deliberate asymmetry against the Kalman's $R_c$. Reliability asks how precisely does one print measure ability? — exams win, under controlled conditions. Signal asks how much should this print move the day-to-day capability estimate? — coursework wins, being frequent, recent, and diagnostic of current work. The two tables answer different questions and both are correct. This distinction is the formal statement of the project's central empirical claim about coursework, developed in §10 and §21.

7 · Predictive distribution — NIG → Student-t

Mean and variance are unknown, so a conjugate Normal-Inverse-Gamma prior $(\mu_0, \kappa_0, \alpha_0, \beta_0) = (\bar\mu_{\text{book}},\, 1,\, 1.5,\, \sigma^2_{\text{book}})$ updates on the data:

$$\kappa_n = \kappa_0 + n,\quad \mu_n = \frac{\kappa_0\mu_0 + n\bar y}{\kappa_n},\quad \alpha_n = \alpha_0 + \tfrac n2,\quad \beta_n = \beta_0 + \tfrac S2 + \frac{\kappa_0 n(\bar y - \mu_0)^2}{2\kappa_n}$$

giving the posterior predictive

$$y_{n+1} \;\sim\; t_{2\alpha_n}\!\left(\mu_n,\ \sqrt{\tfrac{\beta_n(\kappa_n+1)}{\alpha_n \kappa_n}}\right)$$

The degrees of freedom $2\alpha_n = 3 + n$ are the honesty mechanism: at $n=2$ the tails are heavy and the 90% interval is wide. Certainty is earned print by print. Quantiles are exact — regularized incomplete beta via Lentz's continued fraction, inverted by bisection — because series approximations fail precisely at the small df where this engine operates.

8 · Ensemble stacking by walk-forward validation

Four members with orthogonal failure modes — Kalman (adapts, but chases), EWMA (recent, but jumpy), shrunk mean (stable, but slow), gated trend (directional, but only when provable) — are combined by how well each actually forecast prints it had not seen. For each of the last $k \le 8$ prints every member is refit on strictly earlier prints and scored on its one-step-ahead error; weights follow inverse regularized MSE:

$$w_m \;\propto\; \frac{1}{\text{MSE}_m + \varepsilon}, \qquad \varepsilon = 4\ \text{pts}^2$$

Below $n=3$ there is nothing to validate against, so fixed priors apply $(0.35, 0.25, 0.30, 0.10)$. The blend is moment-matched as a mixture, so member disagreement itself widens the band:

$$\hat\mu = \sum_m w_m \hat\mu_m, \qquad \hat\sigma^2 = \sum_m w_m\!\left[\hat\sigma_m^2 + (\hat\mu_m - \hat\mu)^2\right]$$

Dispersion markup. That mixture variance carries member disagreement and each member's in-sample residual scatter, but not the members' own estimation uncertainty, and it runs systematically too tight out-of-sample — the walk-forward 90% intervals covered only ~0.79. The published sd is therefore marked up, $\hat\sigma \leftarrow \rho\,\hat\sigma$ with $\rho = 1.15$, a factor swept against walk-forward CRPS (not coverage): the score bottoms across a flat $\rho \in [1.1, 1.3]$ basin, so widening lowers a proper score — the shortfall was genuine over-confidence, not sacrificed sharpness. Coverage rises to ~0.84; the degrees of freedom are left untouched, since the tail shape is the NIG posterior's job (§7) and $\rho$ only rescales the width. See §26 for the sweep and the gate. A boundary-aware likelihood for the $[0,100]$ ceiling (§23) is the next refinement of the interval's shape.

On clean trending data the trend member wins the weights and the blend rides it (ensemble.test.ts); on a series with no monotone structure the gate closes and the member degrades to the running median (robust.test.ts). Both are verified behaviour rather than intention — with the caveat §5 sets out about what "no monotone structure" can be proven to mean at $n \approx 8$.

9 · Fair value

$$\text{FV} = \mathrm{clip}_{[0,100]}(\hat\mu)$$

with $t_{3+n}(\hat\mu, \hat\sigma)$ credible intervals (50%, 90%) and a 10th-percentile downside $p_{10}$. Fair value is the unbiased estimate and the basis of every forecast in this document. It is not what the terminal displays as the price.

10 · The next-exam oracle — exam calibration $\hat\delta$

Coursework predicts exams; exams pay differently. The raw gap between winsorized exam and coursework means is shrunk toward zero by $\kappa = 3$ pseudo-observations:

$$\hat\delta = \frac{n_E}{n_E + \kappa}\, \left(\overline{y}^{\,w}_{\text{exam}} - \overline{y}^{\,w}_{\text{coursework}}\right)$$

One exam moves the offset a quarter of the way; a track record moves it almost fully. This converts "your assignments say 84 but exams print 78" into a calibrated forecast, and it is what makes coursework a leading indicator without ever being a grade: $\hat\delta$ is a bridge, not a weight.

A bridge is crossed once. $\hat\delta$ carries the coursework side into exam terms, so it may be added to a coursework-only level and nowhere else. The tempting shorthand $\hat\mu + \hat\delta$ — capability plus the offset — crosses it one and a half times, because $\hat\mu$ already contains the exams. With effective exam weight $w$ inside the ensemble, that shorthand lands $w\,(E - C)$ past the exam level, always away from the exams and in proportion to how much the two disagree. On this book it forecast ENG's next paper at 71.1 against a recency-weighted exam level of 58.9 — above every exam ENG had sat in two years.

So the oracle blends two estimates of the same quantity, each produced by the full ensemble of §8 on its own slice of the tape:

$$\hat\mu_E = \text{ens}(\text{exams}), \qquad \hat\mu_C^{\to E} = \text{ens}(\text{coursework}) + \hat\delta, \qquad w_E = \frac{\sigma_E^{-2}}{\sigma_E^{-2} + \sigma_C^{-2}}$$ $$\widehat{\text{exam}}_{n+1} = \mathrm{clip}_{[0,100]}\!\big(w_E\,\hat\mu_E + (1-w_E)\,\hat\mu_C^{\to E}\big)$$

Because both sides run through the ordinary ensemble, both inherit shrinkage toward the book, the Kalman's honest gap handling, the $\tau$ gate and the small-$n$ degradation — a subject with one exam is never asked to forecast from one exam. The blend is moment-matched as a mixture, exactly as §8's is, so when the exam tape and the coursework tape disagree about where the next paper lands, the band widens rather than quietly averaging. The degrees of freedom are the thinner side's: a forecast leaning on two exams is not made confident by a long coursework tape it only half trusts.

A subject with only exams is answered by $\hat\mu_E$ alone; one with only coursework has $\hat\delta = 0$ by construction and is answered by its coursework level. The forecast is a convex combination of its two sides, so it can never land outside them — which is precisely the invariant $\hat\mu + \hat\delta$ violated (oracle.test.ts).

The carry. What the analyst desk of §19 earns from the next print being an exam is $c = \widehat{\text{exam}}_{n+1} - \text{FV}$, not $\hat\delta$ itself. The ensemble members have already priced part of the exam-coursework gap; charging $\hat\delta$ on top would pay the subject twice for it. On ENG that distinction is +1.9 points rather than +8.6.

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Part II · The MARK — risk-adjusted pricing

11 · Why fair value is not a price

Fair value is the conditional mean of a capability distribution. It is the right answer to "what is your best guess?" and the wrong answer to "what is this position worth?", because it is invariant to properties that any risk-bearing party cares about:

• Two subjects with identical means, one steady and one oscillating ±18 points.
• Two subjects at the same level, one flat and one having bled 4 points a term for a year.
• Two subjects at 70, one whose coursework implies 78 and one whose coursework implies 61.
• Two subjects at 70, one holding a +12 edge over the cohort and one whose edge just closed.

In each pair the second subject is strictly worse to hold, and fair value prices them identically. Financial markets solved this by discounting for risk; the same construction applies here, with an explicit behavioral asymmetry (§14) because the decision this number supports — where should effort go tonight? — is genuinely asymmetric in its payoffs.

The mark is therefore

$$\text{MARK} \;=\; \mathrm{clip}_{[0,100]}\big(\text{FV} - \mathcal{D}\big), \qquad \mathcal{D} \ge 0$$

where $\mathcal{D}$ is a credibility-weighted, soft-capped sum of itemized risk premia. $\mathcal{D} \ge 0$ is structural: the market never pays above fair value. Positive evidence can at most return a subject to par. This is not pessimism — it is the recognition that fair value already incorporates good news through the mean, and that counting it twice would let a strong recent print paper over a chronically unstable tape.

12 · The factor panel

One cross-sectional pass (quant/factors.ts) computes, per subject, the diagnostic quantities the premia are charged from. Small-$n$ honesty is enforced factor by factor: a factor that cannot be estimated returns null and its premium contributes nothing, rather than defaulting to zero and silently asserting health.

factor	definition	gate
$\hat\beta_{30}$	τ-gated slope on the detrended tape, pts/30d	$n \ge 4$, $p \le 0.5$
$\hat\beta_{30}^{\text{rel}}$	$\hat\beta_{30}$ minus the book median slope	$\ge 2$ eligible subjects
$\text{RMSSD}$	$\sqrt{\frac{1}{k-1}\sum (y_i - y_{i-1})^2}$ over the last 10 prints on the vol basis	$k \ge 4$
$\text{volRatio}$	RMSSD over the book median RMSSD	$\ge 2$ eligible
$\text{semiDev}$	$\sqrt{\frac1k \sum \min(0,\, y_i - \mu)^2}$ — downside only, last 10	$k \ge 3$
$z_{\text{shock}}$	latest exam vs winsorized trailing exam mean, over $\max(\text{MAD}, R_{\text{Exam}})$	$\ge 3$ prior exams
missStreak	consecutive prints under the estimate that stood before each of them	$n \ge 4$
$\Delta\alpha$	latest edge over cohort minus trailing mean edge	$\ge 3$ referenced
$z_{\text{cw}}$	$(\text{cwMean} + \hat\delta - \text{examAnchor})\ /\ \sqrt{s_{cw}^2/n_{cw} + R_{\text{Exam}}^2}$	both sides non-empty

$R_{\text{Exam}} = 5$ pts is the reliability standard deviation of §4, used here as a floor on a scale estimate and not as a variance. MAD is the $1.4826$-scaled median absolute deviation, so both terms of $\max(\text{MAD}, R_{\text{Exam}})$ are in the same units.

The vol basis is exams once four exist. A mixed tape conflates instability with coursework-exam divergence, which the panel already prices separately as $z_{\text{cw}}$; below four exams the basis falls back to all prints. Both the swing and the semideviation are measured over the last ten prints on that basis, so a subject is judged on its current tape rather than on a crash three years ago it has since grown out of.

RMSSD rather than standard deviation is a deliberate choice. A tape that whipsaws 70 → 85 → 70 → 85 has a perfectly ordinary standard deviation about its median; it cannot disguise itself from its own first differences. Successive-difference variance is the statistic that distinguishes inconsistency from spread, which is exactly the distinction the user asked the price to make.

The miss streak is measured against a walk-forward estimate, not against a fixed threshold: each print is compared to the forecast that stood before it, so the streak counts failures to meet the standard the subject itself had set, not failures to hit an arbitrary number. That forecast is deliberately the crude one — an ordinary least-squares line over the last ten prints (regression.ts), the estimator §5 spends a page arguing against. It is admissible here and nowhere else because a miss streak is a detector, not a forecast: it never reaches the price directly, only the count of consecutive shortfalls does, and a jumpy standard makes that count harder to trip, not easier. §23 states the asymmetry plainly rather than leaving it implied.

$z_{\text{cw}}$ is not self-cancelling, but it is not clean either. $\hat\delta$ appears inside $z_{\text{cw}}$ and also defines the quantity it is compared against, which invites the objection that the statistic collapses to a measure of how much $\hat\delta$ was shrunk. It does not, because the two sides are estimated over genuinely different windows: $\text{examAnchor}$ and $\text{cwMean}$ are recency-weighted EWMAs of the detrended tape, while $\hat\delta$ comes from winsorized raw means over the whole history. On MATH those disagree by a factor of 2.3 — a 25.7-point recency-weighted gap against an 11.1-point winsorized one — which is why $z_{\text{cw}} = +2.8$ rather than the $+0.8$ a collapse would produce. What remains true is that the two estimators share data and would partly cancel on a subject whose recent form matches its history. Read $z_{\text{cw}}$ as "the coursework tape is diverging from the exam tape faster than the long-run bridge accounts for", which is what it measures, rather than as a clean divergence in levels.

13 · CUSUM drift detection

A slope answers how fast is the tape falling? It answers slowly, because $\hat\beta_{30}$ is τ-gated and the gate needs several prints in agreement before it opens. The question a student needs answered earlier is have I been printing under my own forecast long enough that the misses stopped being noise? That is a change-point problem, and Page's CUSUM is its classical solution.

Over standardized walk-forward residuals $z_i = (y_i - \hat y_{i|<i}) / \max(\text{MAD},\, R_{c_i})$ — same units convention as §12, $R_{c}$ an sd in points — winsorized to $\pm 2.5$:

$$S_i \;=\; \max\big(0,\; S_{i-1} - z_i - k\big), \qquad k = 0.4, \qquad \text{alarm} \iff S_i \ge h = 2.5$$

Three properties make this the right instrument here:

• Upside residuals drain the statistic. A whipsaw accumulates nothing, because its recoveries subtract as fast as its drops add. Verified: an eight-print 70/80 oscillation never alarms.
• Per-step winsorization separates shock from drift. One catastrophic print is capped at $2.5\sigma$ and cannot alone breach $h$ — it is an earnings shock, priced by its own premium. It takes a second bad print to declare drift. Verified: 75,75,75,75,49 is silent; 75,75,75,75,49,49 alarms.
• Recovery forgives, but the peak remembers. $S$ decays back toward zero as the subject recovers, while peak retains the worst excursion.

14 · Loss aversion, and why it is defensible here

Charges bill at full weight; credits are damped by $\eta = 0.35$. The reference point is the loss-aversion coefficient $\lambda \approx 2.25$ of Tversky and Kahneman, whose reciprocal is $0.44$ — so $\eta$ is deliberately harsher than the literature, not an approximation of it. $1/\eta \approx 2.9$ is the effective asymmetry. The extra severity is a choice, made for the reason the rest of this section gives, and §23 lists it among the constants that are chosen rather than fitted. This is a modeling choice that requires justification, since deliberately biasing an estimator is normally a defect.

The justification is that the mark is not an estimator — it is a decision variable. It exists to allocate a scarce resource (study time) under an asymmetric loss function. The cost of under-attending a subject that is quietly deteriorating is a compounding deficit across a term; the cost of over-attending a subject that was actually fine is a few displaced hours. When the loss function is asymmetric, the Bayes-optimal action is not the one that maximizes the posterior mean, and an unbiased input produces a biased-toward-harm decision. Fair value remains available, unbiased and unmodified, for every question where estimation rather than allocation is the goal.

15 · The premium schedule

Each premium is a bounded function of one factor group, in points, with its evidence string carried alongside for display. $H = \text{horizon}/30$ where the horizon is the subject's own median print gap, clamped to $[14, 90]$ days — a subject that prints monthly is charged over a month.

key	charge	cap
unc	$0.6\,(\hat\sigma - 5)^+$ — error bars beyond one clean exam's reliability	6
vol	$0.55\,(\text{RMSSD} - 2)^+ \cdot \mathrm{clip}_{[0.6,1.6]}(\text{volRatio}) \;+\; 1.5\min(\text{volExp}-1.3,\,1)^+$	7
mom	$(-\hat\beta_{30})^+ \cdot H$ — points bled over one horizon	7
lag	$0.8\,(-\hat\beta_{30}^{\text{rel}})^+ \cdot H$ — trailing the book while nominally flat	4
shock	$1.6\,(-z_{\text{shock}})^+ \cdot \text{decay}(\text{prints since},\ \text{age})$	6
down	$0.4\,\text{semiDev} + 0.7\min(\text{miss},4) + 0.5\min(\text{downStreak},4)$	6
cw	$z_{\text{cw}} < 0$: $1.4\,\lvert z_{\text{cw}}\rvert + 0.5\min(-\hat\beta^{cw}_{30},3)^+$ — else $-\eta\min(1.4 z_{\text{cw}},3)$	6 / −1.05
alpha	$0.5\,(-\Delta\alpha)^+ + 0.35\,(-\alpha_{\text{latest}})^+$	5
cusum	$1.2\min(S - h + 1,\ 4)$ when alarmed	5
stale	$(\text{staleDays} - 65)^+/30$, in school days	4
effort	$4\,(1-\rho_a)^+$ — measured spend under an even share — else $-4\eta\min(\rho_a-1,1)$	6 / −1.4
plan	$1.25\,(1-\rho_p)^+$ — planned spend under an even share — else $-1.25\eta\min(\rho_p-1,1)$	2.5 / −0.44
steady	$-\min(2,\ 1 + 0.3(3.5 - \text{RMSSD})^+)$ when the consistency gate passes	−2

The credit cap reads −1.05 rather than −3 because the 3 binds before $\eta$: the raw credit is capped at 3 points and then damped, so the most a coursework upgrade can ever return is $3\eta = 1.05$. The asymmetry is therefore $3.92 : 1.05$ — a factor of 3.7 — at the $\lvert z_{\text{cw}}\rvert = 2.8$ that MATH actually prints.

Two schedule details carry the design's intent. Shock decays on market time, not calendar time — $\text{decay} = 2^{-\text{prints}/2} \cdot 2^{-(\text{age}-120)^+/60}$ — because on a termly cadence the April sitting is the current state in July; it is superseded by newer prints, not by the calendar turning. And staleness is counted in school days and free for 65 of them for the same reason (§1b): a term gap is the normal rhythm of the instrument, a holiday is not neglect, and a subject silent through two terms of teaching genuinely has gone dark. Sixty-five session days is the old 120-day calendar window converted at this school's rhythm of ≈55 teaching days to a term, so behaviour across a normal gap is unchanged; what disappears is the book ageing over holidays nobody could print in.

15b · Effort weighting, and what it is careful not to claim

The last two lines are the only place the effort spider (D1, lib/allocate.ts) touches a price. Each desk's holding on a ring is read as its share of an even share of the same week,

$$\rho \;=\; \frac{n\,x_i}{T},\qquad n = \text{desks in the plan},\quad T = \text{the token budget},$$

so $\rho = 1$ is a fair share, $\rho = 0$ is starvation, and the shortfall $(1-\rho)^+$ is charged linearly to the cap. The two rings are deliberately unequal — 4 points against 1.25, roughly 3 : 1 — because what you measured yourself doing is evidence and what you merely intended is not. Both are loss-averse like the rest of the sheet: over-resourcing a desk earns back only $\eta$ of what starving it costs, and the surplus is capped at one even share, so tipping the whole week into one desk is worth no more than doubling it.

Three constraints keep this honest, and each rules out a tempting alternative:

• The reference is an even share, never the model's own recommendation. The recommendation is water-filled from priority, which is downstream of the advisor, which is downstream of this mark. Marking a desk against it would close a feedback loop and make the board a function of its own previous render. An even share is an input, so the pass stays pure.
• The actual ring is divided by the planned total, not by its own sum. A week you meant to spend 14 hours on and spent 7 on should starve every desk, not renormalize itself back to "perfectly balanced".
• Only the shape of the week is priced, never its size. The plan sums to the budget by construction, so its shares average exactly one: doubling hoursPerWeek moves nothing. This is the constraint that stops the feature from quietly becoming an effort→grade coefficient. §1 is explicit that one student's book cannot identify that response, and nothing here estimates it. What is claimed is the weaker thing a risk desk actually says: a subject you are visibly under-resourcing this term is worth less today than one you are not.

A desk absent from the plan has no effort read at all — unbudgeted is not starved — and a desk absent from the actual record gets a null, not a zero. Both premia are exactly absent on a book that has filed no allocation, which is why the committed fixture, §21 and the walk-forward gate are untouched by this section's existence. The EFFORT BUDGET card carries the switch that removes both lines from every mark, and a one-tap clear actual hours — because the effort line is priced as hard on a half-remembered figure as on a measured one, and most people never time themselves at all.

15c · Readiness weighting — an ordinal input, priced ordinally

The duel arena (D2, lib/duel.ts) asks one question — which are you more ready to sit? — and fits an Elo rating to the pile. What that pile contains is ordinal: it says this desk is readier than that one and says nothing at all about level. The premium is built so that it cannot claim otherwise.

Elo is read as what it is actually estimating, Bradley–Terry log-strength. A rating difference of 400 points is 10 : 1 odds by construction, so

$$\lambda_i \;=\; \frac{r_i - \bar r}{400/\ln 10},\qquad \textstyle\sum_i \lambda_i = 0$$

is a log-odds you can read directly: $\lambda = 0.4$ means you would pick this desk over an average one about 60% of the time, $\lambda = 1$ about 73%. Dividing by the sample spread instead — a z-score — would make three duels and thirty look identical, which is exactly the error the credibility factors below exist to avoid. The charge is then the familiar loss-averse pair, capped at 2.5 points, the same ceiling as the PLAN line and well under the ACTUAL one: a gut call is softer evidence than hours you measured yourself keeping.

Because $\lambda$ is centred, the line is a tilt: what it charges one desk it credits another, so a readiness pile can decide which desks carry the risk and cannot mark the whole book down. The one exception is deliberate. Credits are damped by $\eta$ like everything else on the sheet, so a book whose desks are unevenly prepared nets a small charge that an evenly prepared one does not. Dispersion in readiness is itself a risk, and a loss-averse desk prices it.

The multiplier on all of it is two credibilities in series:

$$c \;=\; \underbrace{\frac{n_d}{n_d + 8}}_{\text{how much you answered}} \times \underbrace{w_{\text{ready}}}_{\text{how well it predicted}}$$

The second is earned. For every round in which two or more desks sat an exam, the ordering the pile implied before that round — duels dated strictly earlier; one recorded afterwards knows the answer — is scored by pairwise hit-rate against the realized exam ordering, and the register's as-of forecast (§26) is scored on the same pairs. Both losses $1-h$ go through the shared credibility rule in quant/earned.ts.

Unlike the §27 pool, $w_{\text{ready}}$ shrinks toward a prior of 0.4 rather than toward zero, and the difference is the point. The pool makes a forecast, and a forecaster with no record has earned nothing. Readiness reports a state — how prepared you feel — which this engine already charges the moment it exists everywhere else it appears: a difficulty tag, a reliability tag, a plan that starves a desk. What the record buys is the right to be charged more or less than that baseline. A pile that has out-read the desk over two rounds rises above it; one the desk has beaten falls below it.

Exactly absent on a book that has never duelled, which is why the committed fixture, §21 and the walk-forward gate are untouched by this section's existence — the ablation prints ready: 0.00 on it. The READINESS DUELS card carries the switch that removes the line from every mark, and every answer on record is individually removable, because a pile you can only wipe wholesale is not correctable.

16 · Aggregation, credibility, and the soft cap

$$\mathcal{D} \;=\; C\,\tanh\!\left(\frac{1}{C}\cdot\frac{n}{n+\kappa}\sum_j \pi_j\right), \qquad C = 25,\quad \kappa = 2,\quad \textstyle\sum_j \pi_j \ \text{floored at } 0$$

The Bühlmann credibility factor $n/(n+\kappa)$ means a subject with two prints cannot be marked down hard on evidence it does not have — the same exposures charge a 10-print subject roughly 1.7× what they charge a 2-print one. The $\tanh$ envelope is a smooth ceiling: it is approximately linear for small totals and saturates below $C$ for pathological ones, so no subject is ever marked to zero and the ordering among distressed subjects is preserved rather than collapsing at a hard clip. "Approximately" is doing real work — at the $\mathcal{D} \approx 11$ this book's subjects actually carry, the curve has already compressed the total by 6.6%, so an ordinary discount is not exactly the sum of its parts, and that is exactly why the rescale step below exists.

Attribution is exact. The total is a nonlinear function of its parts, so after shrinkage and saturation every displayed line is rescaled by $\mathcal{D}/\sum\pi_j$ and the rounding remainder is assigned to the largest line. The waterfall shown in the interface therefore sums to the displayed discount to the last decimal — not because the compression was negligible but because it is allocated proportionally rather than swept up. A risk model whose explanation does not reconcile with its own output is not an explanation.

Regime is read off $\mathcal{D}$ — PRIME $< 2.5 \le$ STABLE $< 6.5 \le$ STRESSED $< 12.5 \le$ DISTRESSED — with an active CUSUM alarm forcing at least STRESSED regardless, since a confirmed drift is a qualitative state, not a quantity.

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Part III · Cross-sectional structure

17 · Market depth — the field behind the class

A placement describes the room you sat in. Where classes are streamed, that room is a biased slice of the year level, and the same placement means different things in a strong set and a weak one. Worse, a student can hold their placement while the room changes underneath them, and a plain percentile reports no change.

For every print carrying $(r_i, N_i)$ and a year-level mark $g_i$, write the placement as a within-class $z$ and decompose the remainder:

$$z_i = \Phi^{-1}\!\left(1 - \frac{r_i - 0.5}{N_i}\right), \qquad y_i - g_i \;=\; \underbrace{\pi_{t(i)}}_{\text{class}} + \underbrace{\beta_{s(i)}}_{\text{subject}} + \sigma_{\text{cls}}\, z_i + \varepsilon_i$$

$z_i$ absorbs where the student sits inside the class, so what remains is a property of the class: $\pi_t$ is the form class's strength over the year level in period $t$ — the peer premium — and $\beta_s$ is a subject whose own class differs from it.

$\pi$ and $\beta$ are collinear alone, so the subject block carries a ridge penalty $\kappa\sum_s\beta_s^2$. That both identifies the system (a common shift belongs to the class, not the subjects) and stops a subject with one placement absorbing its whole residual. It is one penalised least-squares solve over the book: a period's class strength is separable only when every subject is read together.

Converting a class position to a field position needs the year-level spread, which one student's reports cannot identify. It comes from three adjustable settings — parallel classes $S$, year size, streaming tightness $\rho$:

$$\sigma_{\text{cls}} = \sigma_{\text{yr}}\sqrt{1 - \rho^2\,(1 - v_S)}, \qquad v_S = 1 - \tfrac{1}{S}\sum_j m_j^2, \quad m_j = S\big(\varphi(a_j) - \varphi(b_j)\big)$$

$v_S$ is the within-band variance left when a normal is cut into $S$ equal-probability bands. The defaults assert nothing about the school: $S = 1$ or $\rho = 0$ both give $\sigma_{\text{yr}} = \sigma_{\text{cls}}$, reproducing the plain Hazen percentile $p = 100(1 - (r-0.5)/N)$ exactly. The engine additionally reports whether $\bar\pi$ clears its own standard error, so a streamed book announces itself rather than being assumed.

The order book renders the resulting distribution head-by-head: $N_{\text{yr}}(\Phi(z_{hi}) - \Phi(z_{lo}))$ students per mark band with open-ended outer rungs, your own class overlaid as $N(g + \pi + \beta, \sigma_{\text{cls}})$ — a soft band, not a hard slice, because loose streaming genuinely spills a class across levels.

18 · Book-level instruments

AGGREGATE is the one number in this document with no model behind it: the straight sum of each subject's most recent exam, out of 100 apiece. No detrending, no shrinkage, no coursework. An exam is carried forward however old it is; subjects that have never sat one leave the sum and the denominator, so a new listing shows as pending rather than as a drag. The move is measured over subjects holding two exams, so a first exam cannot fake a rally.

PREDICTION is its forward twin, $\sum_s \widehat{\text{exam}}_{s,n+1}$ with errors in quadrature — built on fair value, because a forecast must be unbiased. It is pinned to a named round (§1b), not to an anonymous "next": on the reference book, standing in Term 3 with the mid-year papers still out, it forecasts MID 26.

Adding the errors in quadrature assumes the subjects' forecast errors are independent, and they are not: §17 exists precisely because a common period effect $\pi_t$ is real and measurable. A term that goes badly tends to go badly across the board. The point estimate is unaffected — expectations add regardless of correlation — but the PREDICTION band is too tight, by exactly the cross-subject covariance term, and the same applies to the COMPOSITE's. §23 says why the honest fix is not available from one student's book.

GX COMPOSITE is the mean mark across priced subjects. Its history reprices and re-marks the whole book at each past round using only the prints that existed then, so the line is what the engine would have said at the time, not today's model painted backwards.

Both tapes are struck at rounds, never at term-ends. A term the school did not examine in draws no point, because carrying April's exams forward and stamping a later term on them is how a board ends up claiming a result it does not have. The composite tape then closes with a single live mark at today, since a price — unlike a result — really does keep moving between rounds.

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Part IV · Direction and urgency

19 · The analyst desk

The four ensemble members are four analysts, weighted by the walk-forward record of §8. Each is re-evaluated one horizon out and publishes an expected total return:

$$r_m \;=\; \underbrace{(T_m - M_m)}_{\text{momentum}} \;+\; \underbrace{\varphi\,(M_m - \text{FV})}_{\text{convergence}} \;+\; \underbrace{c}_{\text{carry}}, \qquad \varphi = 0.35, \qquad c = \widehat{\text{exam}}_{n+1} - \text{FV}$$

Convergence is an error-correction term: an analyst that thinks the subject is mispriced expects a share $\varphi$ of its own gap to close. The gap is measured against fair value, and that choice is load-bearing rather than incidental: fair value is the weighted member mean, so $\sum_m w_m(M_m - \text{FV}) = 0$ exactly and the term makes the analysts disagree honestly without moving the consensus. Measured against the mark the identity fails — the gaps would sum to the discount $\mathcal{D}$ instead of to zero, silently paying every damaged subject $\varphi\mathcal{D}$ of expected return for the crime of being cheap, and inflating the dispersion that scores the analysts against each other by $(\varphi\mathcal{D})^2$. Price targets are still quoted off the mark, because a target price is a marked price; only the convergence gap is measured off fair value.

Ratings are relative: each subject's consensus is measured against the book benchmark $b = \mathrm{median}s \bar r_s$, since a term in which everything rises is not a book full of buys. Write $D{\text{core}}$ for the weighted spread of the momentum-plus-carry part — the part the consensus is actually made of — and $n_{\text{eff}} = (\sum w_m^2)^{-1}$ for Kish's effective analyst count:

$$s = \sqrt{q\,H_d + \frac{D_{\text{core}}^2}{n_{\text{eff}}}}, \qquad z = \frac{\bar r - b}{s}, \qquad \boxed{\;z^\ast = z \cdot \frac{n}{n+3} \cdot 2^{-\text{stale}/35}\;}$$

Two notational cautions, since both symbols are overloaded elsewhere in this document. $H_d$ here is the horizon in days, not §15's $H = \text{horizon}/30$, because $q$ is quoted in $\text{pts}^2$ per day. And the staleness half-life is 35 school days (§1b's clock, RATING_FRESH_HALF_SESSION_DAYS) — a rating cannot decay over a holiday nobody could have printed in. The full dispersion $D$, which does include the convergence spread, scores the individual analysts against one another and is reported separately; only $D_{\text{core}}$ enters $s$, since a term that contributes nothing to $\bar r$ cannot be error in $\bar r$.

Disagreement is priced as estimation error, not as a wider goalpost. Credibility and information decay follow. Buckets at $|z^\ast| \ge 0.35$ (BUY/SELL) and $\ge 1.05$ (STRONG), $n < 2$ → N/A.

Conviction is an edge, not a probability. The number reported is

$$100\big(2\Phi(|z^\ast|) - 1\big) = 100\big(P(\text{right}) - P(\text{wrong})\big)$$

which is the margin over a coin flip, not $P(\text{correct sign})$ — that is $\Phi(|z^\ast|)$, and at $z^\ast = 0$ it is 50%, not 0. Reporting the edge is the deliberate choice: a HOLD should read 0, because a HOLD has no edge, and a headline "50% confident" on a coin flip would be worse than useless. A conviction of 50 here means 75/25.

20 · The advisor

Urgency, not direction, from four normalized stress factors, each clipped to $[0,1]$ before weighting:

$$\text{priority} = 100\cdot\mathrm{clip}_{[0,1]}\!\Big( 0.35\,\tfrac{\text{gap}}{15} + 0.30\,\tfrac{\text{FV}-p_{10}}{12} + 0.20\,\tfrac{-\hat\beta_{30}}{5} + 0.15\,\tfrac{\text{stale}-12}{30} \Big)$$

gap is the distance under the user's own target, $\text{target} - \text{MARK}$, counted only when positive and contributing nothing when no target is set. It is the one place the advisor reads the mark rather than fair value, and deliberately: a target is a decision about what you will accept, so it should be measured against the number the terminal quotes.

Tail width, by contrast, is measured from fair value, since $p_{10}$ is drawn around FV; measuring it from the mark would net the discount against the tail it already charged for.

stale is school days again (§1b) — free for a fortnight of teaching, saturating at six weeks of silence. Those are the calendar-day thresholds of an earlier draft converted to the session clock, which is why they are 12 and 30 rather than 21 and 45. Note that the three staleness scales in this document are deliberately different quantities on one shared clock: the mark charges nothing for 65 session days (§15, a term gap is normal), a rating's information half-life is 35 (§19, a call ages faster than a price), and the advisor starts nagging at 12 (here, because nagging is the cheap action).

Three orthogonal axes, deliberately. The mark is level — what it is worth. The rating is direction — where it is headed relative to the book. The advisor is urgency — what to do tonight. A subject can be marked DISTRESSED and rated STRONG BUY simultaneously; that combination means badly damaged and turning, which is precisely the position worth working on. §21 contains two live examples.

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Part V · Empirical results

21 · The engine on a full book

The committed fixture src/lib/__fixtures__/book.json is a three-year tape (2024–2026; six active subjects, 66 prints, exam + coursework, with cohort placements) anonymised from the author's real export — identical structure and trajectory shapes, synthetic marks, so the real transcript never enters the public repo. Every figure below is the engine's actual output on that fixture at 2026-07-21 and every one in the table is asserted in mark.book.test.ts under §21 · the published table, so a retune that rewrites this section fails the build rather than quietly disagreeing with it. That is not decoration: an earlier draft of this table drifted several tenths away from the engine and nothing caught it, because nothing was checking.

	$n$	FV	MARK	$\mathcal D$	regime	RMSSD	$z_{\text{shock}}$	$\Delta\alpha$	largest charge
BUS	6	81.7	69.8	11.9	STRESSED	19.8 (1.8×)	+1.7	+23.0	instability 4.8
ECON	6	71.7	57.8	13.9	DISTRESSED	20.4 (1.8×)	−0.9	−7.0	instability 4.5
MATH	11	70.8	60.1	10.7	STRESSED	7.1 (0.6×)	−1.0	−13.5	alpha erosion 3.9
PHYS	11	70.8	52.8	18.0	DISTRESSED	12.6 (1.1×)	−5.9	−25.2	instability 4.2
GEO	11	64.8	50.0	14.8	DISTRESSED	9.0 (0.8×)	−3.5	−15.0	exam shock 4.1
ENG	11	60.3	48.8	11.5	STRESSED	5.2 (0.5×)	−1.8	−11.0	alpha erosion 3.8

Fair value ranks the book; the mark re-ranks the whipsaw. Fair value spreads the six subjects across 60.3–81.7 (population sd 6.61) in the order above — BUS sits 10.0 clear of ECON, while MATH and PHYS share a fair value outright at 70.8. The mark does not merely widen that spread (to sd 7.15, +8%); it reorders it. ECON prices second on capability but is the book's most violent desk, and once its instability discount is charged it drops below MATH — the harsh mark holds that a subject which can print 80 and can print 54 is not the second-best asset on the book regardless of where the mean lands. The pair fair value could not separate, MATH and PHYS at 70.8 each, is 0 points apart before risk and 7.3 points apart after it. That separation is the engine's entire purpose: the difference between "these two are about the same" and "one of these is in trouble."

Instability is charged even when the latest print is excellent. BUS enters with the book's highest fair value (81.7), a positive shock ($+1.7\sigma$ — its latest exam beat its own trailing mean), and a $+23$ point widening of its edge over the cohort. It is nonetheless marked down 11.9 points, essentially all of it from instability (RMSSD 19.8, 1.8× the book median) and downside semideviation (14.2). Its exam history is 80, 54, 74, 84 — a subject that can print 80 and can print 54 is not an 82-point asset regardless of which one it printed most recently. This is the behaviour the loss-aversion asymmetry of §14 exists to produce, and it is the single clearest demonstration that the mark measures something the mean cannot.

Coursework moves the price without touching the grade. MATH's coursework tape implies a next exam of 76.4 against a recency-weighted exam anchor of 61.9 ($z_{\text{cw}} = +2.7$), and earns a credit of exactly −0.8 points — the raw signal capped, damped by $\eta$, then shrunk by credibility. Its contribution to the projected grade remains zero. The asymmetry is built into the same column by design: a coursework tape talking the exam down by that margin is charged several times as hard as the credit it would earn talking it up, because the cap on credits bites before the $\eta$ damping and so compounds with it.

Note that 61.9 is the anchor $z_{\text{cw}}$ is measured against — a recency-weighted EWMA of the detrended exam tape, which sits under MATH's winsorized exam mean because its recent papers (72, 65) are among its weakest. The two are different estimators by design, and §12 explains why the difference is what keeps $z_{\text{cw}}$ from collapsing.

The most distressed desk is a BUY; the highest-priced is a SELL. PHYS carries the deepest discount on the book (17.6, DISTRESSED after a 78→50 crash) and is nonetheless rated BUY, while BUS — highest fair value of all six — is the book's clearest SELL. This is not the discount leaking into the rating: §19's convergence term is measured off fair value precisely so that it cannot, and no term in $z^\ast$ depends on the mark. (The price targets are quoted off the mark and so move down with it; the call itself is untouched.) It is that the rating is relative and forward: an oversold desk turning faster than a book whose median expected return is itself negative reads as a buy, while a desk priced for perfection with a violent tape reads as a sell. Read together the statements are coherent and actionable, and exactly the reading a single blended "score" would have destroyed.

No subject is clean. Every one of the six pays some premium; the minimum discount on the book is 10.1 points. This is a full tape in a genuinely weak period (its median 30-day slope sits at or below flat, and its median staleness is 57 school days — 104 calendar days, but the engine only counts the ones anyone could have printed in), and a risk model that returned "everything is fine" for it would be broken.

22 · Behaviour at small $n$

$n$	fair value	intervals	trend	mark	rating
0	unpriced, excluded from indices	—	—	—	N/A — no coverage
1	shrunk hard toward the book mean	df 4 — very wide	off	credibility 0.33	N/A — coverage initiated
2	mostly book + recency	df 5	off	credibility 0.50	live
3	walk-forward weights engage	df 6	off (needs 4)	0.60	credibility 0.50
4–5	data-driven	tightening	τ-gated	0.67–0.71	0.57–0.63
10+	fully local	earned	fully damped by $p$	0.83+	0.77+

Note the double protection at small $n$: the factors individually refuse to report (RMSSD needs 4 prints, shock needs 3 prior exams, CUSUM needs 4), and the aggregate discount is credibility-shrunk. A thin subject is not marked down for pathologies nobody could yet have measured.

23 · Limitations

• $\eta$, the premium weights, and the caps are chosen, not fitted. There is no ground truth to fit them against — no observable "correct price" for a subject exists. They are calibrated so that the resulting discounts on real books land in an interpretable range and the ordering they induce is defensible. The claims that are empirically testable are the invariants (mark ≤ fv, exact waterfall reconciliation, monotonicity in each factor, determinism), and those are asserted in tests.
• The depth model needs school geometry it cannot observe. Streams, year size, and tightness are user settings; the defaults are the assumption-free choice, and the engine reports whether the data supports the streamed reading.
• Detrending assumes the class/year reference is a difficulty signal. Where a reference moves because the cohort itself changed, the correction is partly misattributed.
• The intervals do not know about the ceiling. §1 lists bounded support as a property that breaks standard machinery, and Student-t does not fix it — t is unbounded and its tails past 100 are heavier than a Gaussian's, not lighter. Every quoted interval is a symmetric t-interval truncated to $[0,100]$ for display, which is a presentation convention and not a boundary-aware likelihood. For a subject printing in the 90s the interval is asymmetrically wrong: it under-states how much probability is really piled against the ceiling and over-states the room above the last print. A beta or censored-t likelihood would fix this properly and is the clearest unclaimed improvement in the model. The input side of that fix is already in place: a print can be tagged censored (a maxed or floored paper), which for now widens its observation noise so a boundary mark pulls the level less; the one-sided likelihood that reads it as a true bound is the pending core change.
• PREDICTION and the COMPOSITE add their errors in quadrature, which assumes the subjects' forecast errors are independent. §17 is direct evidence against that assumption — it fits a common period effect $\pi_t$ because one exists. Both bands are therefore too tight by the cross-subject covariance term, and a term that goes badly across the board will fall outside them more often than 1-in-10. Sizing the correction needs a covariance one student's book cannot identify: with six subjects and eleven rounds there is no way to separate "a hard term" from "a bad term" without a second student to compare against. The point estimates are unaffected — expectations add regardless of correlation.
• The miss-streak detector uses the estimator §5 argues against. Its walk-forward reference is an ordinary least-squares line over the last ten prints, with no $\tau$ gate and no robustness, because it is a detector rather than a forecast and a noisier standard makes a streak harder to trip rather than easier. That is a defensible asymmetry but it is an asymmetry, and it is the one place in the engine where a single wild print can move an internal reference line.
• The credibility pool weights one unaudited forecaster against another on very few sittings. §27 shrinks hard and caps at 0.45 precisely because the share is barely identified from four or five papers — but "barely identified" is not "identified", and a student who guesses well twice will carry real weight on the third call. The pool is also blind to why the desk was off: it reads the symptom (persistent error) and never the cause, so a run of easy papers is credited to the student's judgement exactly as a genuine insight would be.
• The effort premia are self-reported inputs priced as if they were measurements. §15b is careful about what the charge claims — resourcing risk, not an effort→grade response — but it cannot be careful about the number you typed. A study-hour figure is unaudited, unverifiable and reported by the person it prices; the effort line charges a remembered figure exactly as hard as a stopwatched one, which is why the card offers to clear it outright and why the whole section can be switched off. Nothing else in the engine takes an input the book cannot check.
• Everything here is estimation from a handful of numbers. The intervals are honest about that; the point estimates should be read with them, and none of it is advice.

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24 · The derivation layer — the paper, inside the terminal

Everything above is invisible to someone looking at the running interface, which shows 70.7, STRESSED and a conviction percentage, and no reason to believe any of them. So every model-generated figure on the board is inspectable: hover it, focus it, or tap it, and a research note opens carrying

• the equation as this document writes it, typeset in KaTeX;
• the same equation with that desk's live values substituted, the numbers picked out in amber against the algebra;
• the gates that had to open for the quantity to be defined at all, each marked passed or failed — so "why is there no number here" is answerable, not merely observable;
• the primary literature the method comes from, in full;
• the source file and function that computed it.

Charges drill into their factors (INSTABILITY → RMSSD, EXAM SHOCK → z_shock) through chips that swap the panel in place, so the waterfall can be read all the way down to the first differences without ever stacking a popover on a popover.

The layer covers every board, not only the quote. Seventy figures are registered, and the ones outside D1 are the ones a reader has least other way to check:

board	what opens	the mathematics behind it
D2 · charts	the dashed estimate, the smoothed line, the composite overlay	OLS on the last ≤10 points with its residual sd and an explicit extrapolation warning; the Slutsky–Yule caveat and the half-window lag a trailing mean induces; the cross-sectional spread behind the index point
D3 · compare	either lens, when it is NOW · MARK or ORACLE · NEXT EXAM	the mark and the oracle's own derivations, per spoke
D5 · scoreboard	CRPSS, aggregate MAE, optimism bias, 90% coverage, each ablation Δ	the proper scoring rules themselves — why CRPS and not MAE, the closed form for the Student-t, the walk-forward protocol, Murphy's bias/variance split, the binomial band on a coverage proportion, and why a premium is judged by low-τ pinball rather than by absolute error
D5 · you vs the desk	your MAE, your range CRPS, your coverage, your chip Brier, the teacher's error	the accuracy/sharpness kernel decomposition, why absolute error asks for a median, Murphy's reliability–resolution partition, and the standing finding that people's 90% intervals contain the truth nearer half the time
D5 · priced channels	each earned weight, each Elo rating, the scored aggregate call, the readiness charge	one shared credibility rule written out with each channel's own κ, cap and shrinkage target; Elo read as Bradley–Terry log-strength; Spearman's ρ with its standard error
D5 · effort	the model allocation and the plan-vs-practice drift	the concave objective and the KKT water-filling condition that solves it, plus the water level λ this week actually cleared

Ordinary arithmetic is still deliberately left alone. The last print, term averages, the spread, ATH, the AGGREGATE, a lens that is a term column, a candle's open/high/low/close, and every figure the student typed in themselves carry no derivation — because a dotted underline has to mean there is real machinery here, and decorating a mean, or explaining a number back to the person who entered it, would spend that signal on nothing. ⇧D lights every inspectable figure at once for anyone who would rather see the extent of the model than hunt for it.

The layer is pure (src/lib/derive/, React-free, built lazily on hover) and reads engine traces rather than recomputing anything, so a research note cannot drift from the number it explains. The quant modules publish their intermediates through quant/trace.ts; the scoreboard and the chart board assemble their figures from several engines at once and have no single module to trace, so the view hands down what it computed through derive/facts.ts — which is why addForecast returns its fit rather than letting a note refit the line.

derive.book.test.ts asserts all of it against the full fixture book: every derivation's stated result equals the figure the interface displays, every LaTeX string parses, every citation in the bibliography is actually used, and every registered id builds somewhere. A derivation that disagrees with its own output would be worse than none. The elicited channels price inputs the tape-only fixture deliberately does not carry, so that test synthesizes a duel pile, a register, a staked calendar and a filed budget against the fixture's own dates — otherwise the readiness charge would ship with an unparsed formula and nobody would find out until it opened on a real book.

That test pins the result, not the algebra above it, and the gap is real: a panel could in principle display a correct number under a formula that does not produce it. It did, once — the analyst-returns panel showed $r_m$ carrying a convergence term while reporting a consensus computed without one, and asserted an identity $\sum_m w_m(M_m - \text{PX}) = 0$ that was false for the PX it named on the same screen. §19 now measures that gap off fair value, which makes the identity true rather than merely stated, and the panel carries the $\bar r = \sum_m w_m r_m$ step that reaches its own reported result.

25 · Reproduction

npm install
npm test           # every calculation path, the real-book calibration including
                   #   §21's published table, the derivation layer's reconciliation
                   #   against it, and the skill scoreboard's verdict (§26)
npm run gate       # the merge gate: walk-forward CRPS must not regress (§26)
npm run gen:table  # regenerate §21 + the skill baseline (never hand-typed)
npm run dev
npm run build      # type-check + production build → dist/

The calculation layer (src/lib/) is pure and React-free; views consume precomputed SubjectStats and never do their own math. The engine lives in src/lib/quant/: robust · shrinkage · kalman · bayes · calibration · ensemble · price (fair value) · oracle (the next exam) · factors · cusum · mark (the discount) · depth · aggregate · ratings · advisor. Constants are centralized in params.ts with their justifications, and every module hands its intermediates out through trace.ts so §24 can quote them rather than recompute them. The derivation catalogue itself is src/lib/derive/, equally pure — and so is src/lib/wire/, the AI intake desk's prompt engine (§29).

Data lives in localStorage under grade-exchange:v3; exports are a versioned JSON envelope validated field-by-field on import — the same validator that receives an AI reply through the wire (§29). Archived subjects leave every board, index, and — deliberately — the shrinkage pool, so this year's thin subjects borrow strength only from this year's book. Deployment is any static host; .github/workflows/deploy.yml builds and publishes to GitHub Pages on push.

Terms come from the school's published dates, and results file against the term they examined rather than the date they landed (§1b). Scores are 0–100. AGGREGATE is arithmetic; everything else is a model estimate with honest intervals.

---

26 · The skill scoreboard, the register, and the change protocol

Everything above estimates from a handful of numbers; §22–§23 are honest that the point estimates are weak. This section is the machinery that keeps them honest over time and stops a retune from quietly making them worse.

The objective is CRPS, walk-forward — not MAE

src/lib/quant/eval/ grades the engine against itself. For every print past a short warm-up it refits the ensemble on strictly-earlier prints (the cross-subject pool rebuilt as-of, so nothing leaks) and scores its predictive with proper rules — CRPS and pinball, closed-form on the location-scale Student-t — against the realized score, beside a probabilistic last-value naive. MAE is reported but is never the gate: it rewards overconfidence, and calibration is the deliverable. The scoreboard reports per-subject skill ($1 - \text{CRPS}/\text{CRPS}_{\text{naive}}$), the far-more-forecastable all-subject mean beside it, the optimism bias, realized 50/90 coverage, and a leave-one-out verdict on every ensemble member and every premium: each must beat its own absence out-of-sample or it is dead weight. On the committed fixture the verdict reproduces the post-mortem's own finding — a modest per-subject edge (skill ≈ 0.26), a mean that is easier to forecast than its parts, honest under-coverage, a positive optimism bias, and at least one member the ablation flags for pruning.

The forecast/bias register — derived, never stored

The register was originally a log: the app recorded its own live forecast on every render and persisted the pile, exported it, imported it and merged it. That is derived state kept as though it were evidence, and it rots in all the ways derived state does — it records only the days somebody happened to open the app, it survives a recalibration that invalidates it, and a merged book inherits a stranger's model runs.

So src/lib/quant/eval/replay.ts rebuilds it from the tape instead, on the one discipline that makes a forecast register mean anything: walk-forward, no leakage. For each exam round a desk has printed in, the engine is refit on the prints strictly earlier than that round — with the cross-subject pool rebuilt as-of, or a desk borrows strength from results that had not happened — and asked for its next-exam call, dated at the last print it could have seen. That call is then scored against the mark the round actually printed. Ids stay the deterministic composite subjectId|roundKey|exam|version, so the replay is idempotent and two runs over the same book agree exactly.

src/lib/quant/biascal.ts then fits a shrunk-hierarchical correction — a pooled global offset plus per-subject offsets shrunk hard toward it (barely-identified offsets barely leave the pool, which is what stops the correction oscillating) — and a width recalibration toward realized coverage. It is exactly the identity on an empty register, applied as a post-process in computeStats, so the live board and the §21 lock are untouched until a book has resolved rounds to replay.

Two consequences are worth stating plainly. The register is now reproducible: two people holding the same book get the same bias correction, and nothing about it depends on when either of them was looking. And it is what lets the elicitation channels (§15c, §28) ask "did you beat the desk?" honestly, because it hands them the desk's call as of the day the call was made rather than one made with the answer already sitting on the tape. The export (v8) therefore carries inputs only; a v6/v7 file carrying forecasts still imports cleanly and the key is ignored. The "now" enters only at the App edge, where the replay is deferred past first paint like the skill backtest; the calculation layer stays pure.

The change protocol

Core numbers are generated, never hand-typed, and a change ships only if it does not regress skill:

1. Branch. State the hypothesis as a skill claim (e.g. "damping the drift lowers CRPS").
2. Change one equation or constant — params.ts is the preferred surface.
3. npm run gate — walk-forward CRPS must not regress vs eval/__snapshots__/baseline.json. If it does, revert; never retune to chase §21.
4. npm run gen:table — regenerate the §21 rows and the skill baseline.
5. Paste the regenerated numbers into README §21 and mark.book.test.ts in the same commit.
6. Update any affected derivation builder's LaTeX/substitution (src/lib/derive/*).
7. npm test — §21, the derivation reconciliation, the determinism guards and the scoreboard verdict all green. Update baseline.json deliberately, in the same commit, with the before/after skill in the message.

A "phase" of the ongoing model work is a sequence of these commits; each is independently gated, so a bad step cannot hide behind a good one and §21 can only ever state something the build proves.

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27 · The credibility pool — the desk versus the person sitting at it

Everything above §26 estimates ability from prints. Prints are the only thing the book can audit, and §22 is blunt that there are few of them. But the student knows things the tape cannot: which fortnight they actually worked, whether the topic finally landed, that this is the paper they have been dreading. When the engine is persistently off — §23 lists several reasons it might be, and a term-to-term swing in effort (§15b) is a plausible one — that private knowledge is the only genuinely new information in the room, and declining to price it is a choice rather than neutrality.

So the next-exam call becomes a performance-weighted linear pool of the desk's predictive and the student's own, on the sitting they staked a call on:

$$\mu \;=\; (1-w)\,\mu_m + w\,\mu_y, \qquad \sigma^2 \;=\; (1-w)\,\sigma_m^2 + w\,\sigma_y^2 + w(1-w)\,(\mu_y-\mu_m)^2 .$$

The weight is not asserted, it is earned from how the two forecasters have actually scored against each other on resolved sittings:

$$\text{share} \;=\; \frac{S_m}{S_m + S_y}, \qquad w \;=\; \min\!\left(\text{share}\cdot\frac{n}{n+\kappa},\; w_{\max}\right), \qquad \kappa = 4,\; w_{\max} = 0.45 .$$

Three properties are what make this shippable rather than a licence to overrule the engine with a wish.

It shrinks toward the desk, not toward a draw. $\kappa$ pseudo-sittings pull $w$ to zero, so a student with no record changes nothing and one who has been worse than the desk gets nothing at all. Four flawless calls buy half the share the record nominally justifies. The cap is strictly under a half, so the desk always owns the majority of its own forecast — a self-report is the one input in the engine the book cannot audit, and a forecast the student can move further than the tape can is a wish with an interval around it.

Both sides are scored by a proper rule, matched within each sitting. CRPS against CRPS where a 90% range was stated, absolute error against absolute error where only a point was. Charging a bare point call the CRPS of a degenerate predictive would bill the student for a certainty they never claimed; scoring the desk on location alone for that sitting keeps the comparison fair. Only the ratio is ever used, so a mixed record is still legitimate.

Disagreement widens the band. The between-component term $w(1-w)(\mu_y-\mu_m)^2$ is the whole safety argument: a student who confidently contradicts the desk does not get a confident forecast, they get a wide one. Being pulled toward a contested mean while keeping the old precision is the one version of this feature that would actually be dangerous.

The pool is fitted and applied strictly downstream of the register. App keeps two boards: the raw one, which is what forecastlog scores and what "you vs the desk" (§D3) compares against, and the pooled one, which is what the interface draws. A forecaster cannot be allowed to grade a paper it half-wrote — without that separation the measured gap between you and the desk would close on its own, and the weight would feed on its own output. It is exactly the identity on an empty record, so the fixture, §21 and the walk-forward gate are untouched, and the switch on the YOU VS THE DESK card removes it entirely.

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28 · The aggregate pool — your call on the book

§26 is explicit that the aggregate is the level this engine can genuinely forecast: per-desk calls are noisy, the sum of them is not. That cuts both ways, and this is the other edge of it. If the overall average is where the model has skill, it is also where a student's own read is worth the most — one number about the whole term, elicited once, instead of six point forecasts nobody can calibrate.

So the forward AGGREGATE (§18) becomes a performance-weighted pool of the desk's and yours, by the same moment-matched mixture as §27:

$$\mu \;=\; (1-w)\,\mu_m + w\,\mu_y, \qquad \sigma^2 \;=\; (1-w)\,\sigma_m^2 + w\,\sigma_y^2 + w(1-w)\,(\mu_y-\mu_m)^2 ,$$

with $w$ earned from how the two of you have actually scored: your absolute error on the average against the register's as-of aggregate error over the same rounds, shrunk by $\kappa = 4$ pseudo-rounds and capped at $w_{\max} = 0.45$. The between-component term is retained for the same reason it is in §27 — disagreeing with the desk widens the band rather than sharpening it, so a contested aggregate is an uncertain one.

Three limits keep the claim inside what the elicitation actually supports:

• It touches the book-level forecast and never a per-desk mark. Your call is about the average. Allocating it back across the desks would invent per-desk opinions you never stated.
• The forced ranking is scored and shown but weighs nothing here. Level and ordering are separate claims priced by separate channels — the ordering channel is the duel pile (§15c), which is built for it. Letting the ranking also tilt the marks would charge one opinion twice.
• A call is only ever scored against a round it was made before. A call logged after the marks landed is a memory, not a forecast, and meanCallSkill skips it.

Every call is kept rather than overwritten. The card seeds its draft from your standing call and files a revision as a new row, so a call made after the desk printed its number sits in the record beside the one it revised — which is the comparison worth having, and the reason the card shows the desk's own number while you type rather than hiding it. Anchoring that is visible in the record is better than anchoring the record cannot see.

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29 · The wire — the AI intake desk

Hand-typing a book is the tax every other section quietly charges. The wire removes it: the terminal writes a prompt (Settings → Data → The Wire, or IMPORT VIA AI from the palette), the student carries it to any external AI beside their report cards, portal screenshots or plain memory, and the AI answers with one JSON payload the terminal validates, itemizes and merges. Four properties make this safe enough to ship against a book that §26 spends a whole section defending:

• One validator. The reply lands in the very same parseImport → sanitizeBook pipeline as a file import — the wire adds charity (fence-stripping, prose-trimming, a meta back-channel for the AI's warnings and questions) but never a second trust path. The prompt's schema tables render from src/lib/wire/schema.ts, whose satisfies Record<keyof T, FieldSpec> locks make the prompt and the data model one compile unit: add a field to types.ts and the build fails until the prompt can describe it. The worked example inside the prompt is pushed through the real importer by the tests, so the prompt cannot teach a shape the validator would refuse.
• Provenance is priced, not asserted. Every extracted mark carries a reliability tag on the ladder the Kalman already prices (official ▸ returned ▸ remembered ▸ estimated ▸ partial), so a half-remembered quiz enters the book as a half-remembered quiz. The sections that score the student's forecasting skill (§15c, §27, §28) are transcribe-only: the prompt forbids the AI to invent them, undocumented calls are filed createdAt = today so hindsight cannot masquerade as foresight, and the review step flags them for the student's own confirmation before anything lands.
• The echo cannot cost the book a field. Merge replaces subject rows wholesale, so the prompt orders a lossless roster echo — every row verbatim: color, target, coursework split and formerly lineage included. And because the sanitizer cannot tell "the model said null" from "the model dropped the key", the modal re-hydrates every same-desk echo from the current book before filing (rehydrateSubjects): explicit incoming values win, silence falls back to what the book already holds, and an id collision that is a different desk passes through untouched for the §26 re-listing.
• The AI's opinions are quarantined into one field. With the forecast module opted in, the AI may file its own call per pending sitting — aiPred: {point, lo, hi, basis} on upcoming, nowhere else. It is scored beside yours and the teacher's on the scorecard (AI ERROR), and — unlike the teacher's — it can be priced, on the terms below.

The wire's seat in the forecast

The channel obeys the §27 credibility rule with one term changed: an outside desk is even less auditable than the student, so it pays more for less. Its weight is fitted by the same matched proper scoring (CRPS against CRPS when it stated a range, absolute error otherwise), shrunk by $\kappa = 4$ pseudo-sittings toward zero, and capped at $w_{\max} = 0.35 < 0.45$ — an outside forecaster earns a smaller maximum seat than the person whose book it is. The next-exam call then pools three ways by the same moment match as §27,

$$\mu \;=\; \sum_i w_i\,\mu_i, \qquad \sigma^2 \;=\; \sum_i w_i\big(\sigma_i^2 + (\mu_i - \mu)^2\big), \qquad i \in \{\text{desk},\ \text{you},\ \text{wire}\},$$

under one new constraint, the joint ceiling: $w_{\text{you}} + w_{\text{wire}} \le 0.6$, enforced by proportional scale-down so the two outside channels keep their relative standing — and the house model keeps at least 40% of every call it makes, however good both records look. The between-component terms carry §27's safety argument unchanged: any forecaster who contradicts the pool widens the band.

Two guardrails complete the integrity story. The switch (aiWeighting) is the inverse of the other four — absent means off, stored only when true — so a book exported before the wire existed can never import with an outside desk already priced in. And aiPred lives on upcoming, outside the register's inputs (subjects, entries, settings), so filing a wire call cannot re-run the replay that scores it: the wire is graded by a record it structurally cannot touch. On the committed fixture the channel is an exact identity — no sittings, no calls, no seat — which is why §21 and the gate are unmoved by its existence.

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30 · Life signals — the state desk

§27–29 price what the student and an outside desk know that the tape cannot. This layer prices a third kind of private information: state — how many hours actually went in this fortnight, whether last night was a six-hour night before the paper, which topics the last marked script proved shaky, whether the syllabus is the kind where a shaky prerequisite caps everything built on it. src/lib/quant/signals/ reads five logged inputs — sessions, rest, disruptions, topics/topicMarks, and a subject's own traits/mix/belief/attendancePct plus a person-level profile — and turns them into one small shift on the desk's own nextExam call and a widening on its bands: a fifth priced channel beside bias, self, aggregate and wire, but seated differently from all three — it moves the house's own read, not a member of a pool.

The doctrine

Every term is deviation-shaped, not level-shaped. stock.ts's hours-logged term measures a decayed 14-day study stock against the desk's own decayed 42-day norm, never against an assumed-ideal hour count. mastery.ts compares the book's own topic-weighted prediction against the model's own modelMean, never against 100. rest.ts's chronic term fires only on a recent-vs-baseline worsening — a desk that has always run a steady six hours a night prices at zero, same as one that has always run nine. A student who studies, sleeps and sits exactly the way they always have gets adj ≈ 0 on every desk. That is what stops the channel double-counting against biascal.ts (§26): bias correction already absorbs a subject's steady-state miscalibration, so a signal term is only ever entitled to claim the change on top of it.

The channel sits house-side, not pool-side. applySignals (apply.ts) shifts the desk's own nextExam before the §27/§29 self/wire pool runs, in the same seat biascal.ts occupies — so it is not a member competing for the POOL_CEIL = 0.6 those two channels share. App.tsx runs the three in one fixed order: stats = applyBias(rawStats, bias), then signalled = applySignals(stats, signalReads, signalFit.w, on), then pooled = poolBoardJoint(signalled, …). rawStats and the forecast register stay untouched by any of it, so every fit — including the channel's own walk-forward scorer below — still reads strictly-earlier, unadjusted history.

The variance claim is ungated; the level claim is earned. traits.ts's sdMult — marker noise from low determinism, sampling noise from low breadth compounded by uneven topic mastery — applies at full strength whenever signalWeighting is on, with no earnedWeight shrinkage in front of it. A widening is a humility claim, not a directional bet, the same precedent §27 sets for the pool's own disagreement term $w(1-w)(\mu_y-\mu_m)^2$, which is never earned-gated either. The level shift (w · adj) is the one piece of this channel that has to be earned — see the credibility rule below.

A state prior, not a zero prior. At zero scored rounds, signalSkill returns w = SIGNAL_PRIOR = 0.3 — the same "charged from the day it exists" treatment §15c's READINESS_PRIOR gets, but lower, because a signal read makes a level claim on the forecast where readiness only tilts a premium. SIGNAL_PRIOR multiplies an adj of 0 on an empty book, so the prior is real but inert until there is a book to read.

Identity on the committed fixture, everywhere, by construction. book.json carries no signal slices, so signalBoard returns adj=0, sdMult=1, terms:[] on every desk, applySignals hands back the same array reference, and signalSkill returns the identity object at enabled: false — npm run gate, README §21 and mark.book.test.ts are all unmoved. Settings.signalWeighting follows the other student-input switches' polarity (absent ⇒ ON, stored only when false) — the inverse of the wire's aiWeighting (§29), so a book exported before this feature existed imports with the channel already on, exactly as it would have read had the feature always been there.

The formulas

Every constant below is quoted from src/lib/quant/signals/params.ts (package-local, the pool.ts Z90/SELF_DF precedent) or src/lib/quant/params.ts's life-signals block, never hand-typed. That claim was false for a whole release — rest.ts, mastery.ts, signalread.ts, disrupt.ts and traits.ts each typed knobs inline, and the layer carried a second, invisible short-sleep threshold — so it is now asserted by params.test.ts, which reads the module sources back and fails if a lifted literal reappears in the body that spends it.

Stock (stock.ts) — a decayed 14-day effective-study read against the desk's own decayed 42-day baseline, both projected through the subject's own knowledge/procedure/skill half-life $H$ (halfLifeOf, log-domain blend of 14/45/120 days, default 45 when the mix is unset):

$$\text{term}_{\text{stock}} = \text{STOCK\_W} \cdot \tanh\!\left(\frac{k_{14} - \text{baseline}}{\max(\text{baseline}, \text{STOCK\_FLOOR})}\right), \qquad \text{STOCK\_W} = 2.0,\ \text{STOCK\_FLOOR} = 240 \text{ min}.$$

Mastery (mastery.ts) — the one measured channel, everything else here is a self-report. A whole-paper prediction $P\cdot 100$ blends covered-topic EWMA mastery (decayed, prereq-gated in a cumulative subject) with the model's own mean on the uncovered share, then prices only the deviation from that same model mean, gated on enough marked topics and dampened while the count is thin:

$$\text{term}_{\text{mastery}} = \text{MASTERY\_W} \cdot \tanh\!\left(\frac{100P - \text{modelMean}}{\text{MASTERY\_SCALE}}\right) \cdot \min\!\left(1, \frac{\text{totalMarks}}{\text{MASTERY\_FULL\_CREDIT\_MARKS}}\right),$$

The prereq gate is a cap on the weakest prerequisite, in the subject's own cumulativeness $C$:

$$m_{\text{eff}} = (1-C)\,m_{\text{eff}}^{0} + C\cdot\min\!\Big(m_{\text{eff}}^{0},\ \min_j m_{\text{eff},j}^{0} + \text{PREREQ\_HEADROOM}\Big)$$

— the minimum over the named prerequisites, not their mean. A mean would let one failed prerequisite hide behind two strong ones, which is not a cap; the code averaged them for a whole release while this section and PREREQ_HEADROOM's own comment both described the cap, and the gate now has a test (mastery.test.ts, "caps on the WEAKEST prerequisite").

The term is zero unless covered mass $\ge$ MASTERY_MIN_COVERAGE = 0.3 and marked topics $\ge$ MASTERY_MIN_MARKS = 3, with MASTERY_W = 3.0 and MASTERY_SCALE = 8 — the largest single weight in the layer, because it is the only term reading a measurement rather than a report.

Rest (rest.ts) — three deterioration-only sub-terms, each $\le 0$, needing REST_MIN_NIGHTS = 7 nights before pricing (14 for the baseline window):

$$\text{chronic} = -\min\!\big(\text{REST\_CHRONIC\_W}\cdot\text{clamp}(\overline{h}_{56}-\overline{h}_{14},\,0,\,2),\ \text{REST\_CHRONIC\_CAP}\big), \qquad 0.75,\ 1.5$$ $$\text{reg} = -\text{REST\_REG\_W}\cdot\text{clamp}\!\left(\frac{\text{regSd}-60}{60},\,0,\,1\right), \qquad \text{REST\_REG\_W} = 0.5$$ $$\text{acute} = -\min\!\big(\text{REST\_ACUTE\_W}\cdot(\text{SHORT\_SLEEP\_H}-h_{\text{night before}}),\ \text{REST\_ACUTE\_CAP}\big), \qquad 0.8,\ 2.0$$

— chronic on a widening 56-vs-14-day sleep gap, reg on bedtime irregularity beyond REST_REG_FREE_SD_MIN = 60 min of sd, acute on a night under SHORT_SLEEP_H = 6.0h immediately before the sitting. That is the same threshold stock.ts's encoding penalty uses: the layer has exactly one definition of a short night. It used to have two — the acute term gated on a hardcoded 6.5h — so a 6.2h night was short for one term and full for the other, and only one of the two thresholds was visible in params.ts. An absolute sleep level is never priced, only these three deviations — see the caveat below on why.

The chronic term is also disjoint from the encoding penalty. A night under SHORT_SLEEP_H that was followed by a logged study session has already docked that session inside $k_{14}$, so it is dropped from the recent window before the baseline comparison — the chronic term prices $\overline{h}_{56} - \overline{h}_{14}^{\,\text{uncharged}}$, not $\overline{h}{56} - \overline{h}{14}$. A short night is therefore charged once: mechanistically against the session it degraded, or as a sustained baseline shift, never both. mean14 itself stays unfiltered, because the absolute deficit is still worth showing even where it is not priced.

Disruption (disrupt.ts) — a decaying shock, not a flat deduction, only priced against a live sitting to recover against:

$$\text{term} = -\min\!\left(\sum_i \text{DISRUPT\_SEV}[k_i]\cdot\Big(0.5+\tfrac{0.5\min(d_i,7)}{7}\Big)\cdot e^{-\Delta_i/\text{DISRUPT\_TAU}},\ \text{DISRUPT\_CAP}\right),$$

severity illness/family = 1.5, event = 0.75, other = 1.0, duration credit capped at a week, recovery time constant DISRUPT_TAU = 10 days, whole-channel cap DISRUPT_CAP = 2.5.

Anxiety and chronotype (signalread.ts) — the smallest, most situational terms, each firing only near a live sitting. Anxiety prices trait anxiety against relative stakes, one-sided — a heavier-than-typical paper charges a self-reported anxious student, an easy one never credits them: $\text{pts} = -\text{ANX\_W}\cdot\max\big(0,\tfrac{\text{anx}-\text{ANX\_MID}}{\text{ANX\_SPAN}}\big)\cdot\text{clamp}(\tfrac{\text{weight}}{\text{typicalWeight}}-1,\,0,\,1)$, ANX_W = 1.5, ANX_MID = 3, ANX_SPAN = 2. This is attentional control theory (Eysenck et al. 2007) — evaluative pressure consuming the working-memory resources a hard paper needs — and not the Yerkes–Dodson arousal inverted-U this section, the constant's comment and the code comment all used to claim. worthPct is a paper's share of the grade, not its cognitive load, and an arousal account would have to credit the low-stakes side, which this term deliberately does not. Chronotype prices sitting-time synchrony against a self-reported owl/lark as a continuous function of the sitting hour:

$$\text{pts} = -\text{CHRONO\_W}\cdot\tanh\!\left(\frac{|h - \text{CHRONO\_PEAK\_HOUR}[c]|}{\text{CHRONO\_TAPER\_H}}\right), \qquad \text{lark } 9,\ \text{owl } 16,\ \text{CHRONO\_W} = 0.75,\ \text{CHRONO\_TAPER\_H} = 6$$

— zero at the chronotype's own peak, saturating past half a school day out, and identical for both chronotypes at equal misalignment. It used to be a cliff: an owl sitting at or before 9am was charged the full CHRONO_W and an owl at 10am exactly nothing, so a one-hour timetable change swung the entire channel. The old owl-full/lark-half asymmetry carried no cited argument and was dropped; the synchrony literature reports the effect in both directions. Profile.chronotype is a bare category with no strength field, so the charge scales on misalignment only, never on how strongly the student holds the self-report. Measured effects here run well under a point, so the weight stays small.

Attendance (signalread.ts, mastery.ts) — one function, one scale, spent two ways. The shave

$$s(\text{pct}) = \text{clamp}\!\left(\frac{\text{ATTEND\_FULL\_PCT}-\text{pct}}{100},\,0,\,1\right)\cdot\text{ATTEND\_SHAVE\_W}, \qquad 95,\ 0.5$$

is the share of syllabus an attendance shortfall is treated as having cost — half rather than all, because a missed class is usually recoverable from notes or a peer. A desk with a topic breakdown spends it on mass: mastery.ts moves $s$ of covered mass to the neutral side. A desk without one has no mass to move, so it spends the same $s$ on the mastery channel's own point weight, $\text{pts} = -\text{MASTERY\_W}\cdot s$ (−0.30 pts at 75% attended).

The two paths cannot be numerically identical — the topic path's effect scales with the desk's own mastery-vs-model gap, which a desk with no topics has no way to know — but they now derive from one scale. Before this was unified they did not: the bare path charged $(95-\text{pct})/10 \cdot 0.5$ in points (−1.00 at 75% attended) while the topic path shaved $(95-\text{pct})/100 \cdot 0.5$ of mass (≈−0.05 pts on a typical gap). Same student, same attendance, roughly twentyfold apart, selected by nothing more than whether a topic list happened to exist.

Traits (traits.ts) — the one variance-only term, never a level effect:

$$\text{sdMult} = \text{clamp}\big(1 + \text{TRAIT\_MARKER\_W}(1-\delta) + \text{TRAIT\_SAMPLING\_W}(1-\beta)(1+u) + t + b,\ 1,\ \text{TRAIT\_SDMULT\_CAP}\big),$$

marker noise TRAIT_MARKER_W = 0.20 on $(1-\text{determinism})$, sampling noise TRAIT_SAMPLING_W = 0.15 on $(1-\text{breadth})$ scaled up by topic unevenness, a flat +0.05 when ≥25% of marks carry a "time" error, a flat +0.05 on a stated belief ≤ 2, all clamped to TRAIT_SDMULT_CAP = 1.4 — every component is $\ge 0$, so the multiplier can only widen a forecast, never move its centre.

The clamp, the credibility, and the shift. Every candidate term — each already scaled by its own credibility multiplier $a_k$, see Each channel earns its own credibility below — sums, unclamped, to rawSum; the priced adj is $\text{clamp}(\text{rawSum},\,\pm\text{SIGNAL\_ADJ\_CAP})$, rounded to 2dp, with SIGNAL_ADJ_CAP = 4 — set near EFFORT_ACTUAL_W, the layer's closest sibling. The layer's weight is earned exactly like §27/§29's, on signalskill.ts's own walk-forward replay (as-of each resolved exam round, with the state book filtered to what was logged strictly before that round's resolution) — and on the reshaped adj, so the weight is earned by the same adjustment the board applies:

$$w = \text{clamp}\!\left(\frac{n\cdot\text{rawShare} + \kappa\cdot\text{SIGNAL\_PRIOR}}{n+\kappa},\ 0,\ \text{SIGNAL\_CAP}\right), \qquad \kappa = \text{SIGNAL\_KAPPA} = 2,\ \text{SIGNAL\_CAP} = 0.35,\ \text{SIGNAL\_PRIOR} = 0.3.$$

SIGNAL_CAP sits under SELF_POOL_CAP (0.45) on purpose — a self-logged state channel earns a smaller seat than the self-forecast channel, because it is evidence about conditions, not a call on the outcome. After the gate, the realized worst case is SIGNAL_CAP × SIGNAL_ADJ_CAP ≈ 1.4 points. applySignals then shifts the mean by $w\cdot\text{adj}$ and scales every band's half-width by sdMult, recentring on the new mean the same way stats.ts's own bias post-process (§26) recentres nextExam on its offset — additive rather than a replacement, and an exact identity per desk when the shift rounds to under 0.05 at 1dp and sdMult is exactly 1.

The value-of-information layer

voi.ts is the one part of this section that never touches a number the engine prices — a display-only ranker (valueOfInformation) telling a student which missing input buys back the most forecast precision per minute logged, scored by

$$\text{score} = \frac{\text{gainPts}}{1 + \text{effortMin}/\text{VOI\_EFFORT\_SCALE}}, \qquad \text{VOI\_EFFORT\_SCALE} = 30,$$

over a fixed menu of presence/absence/size heuristics, each with its own conservatism argument rather than a fitted term: no rest logs at all books-wide (VOI_REST_GAIN = 1.5pts, VOI_REST_EFFORT = 10 min), no sessions logged for a desk (VOI_SESSIONS_GAIN = 2.0, effort 15), no profile at all (VOI_PROFILE_GAIN = 0.75, effort 1), no topic breakdown on a desk wide enough to be worth one (VOI_TOPICS_GAIN_W = 0.15 × sd × VOI_Z90 (1.64), effort 10), topics logged but under MASTERY_MIN_MARKS marked (VOI_MARKS_GAIN_W = 3.0 × min(1, sd / VOI_MARKS_SD_SAT (8)), effort VOI_MARKS_EFFORT_PER = 5 per paper needed), and traits never set (VOI_TRAITS_GAIN_W = 0.2 × sd × VOI_Z90, effort 2). The top VOI_TOP_N = 8 items by score are kept. None of it feeds stats.ts/aggregate.ts/the register — the whole ranker can be wired into or out of the panel without moving a single digit anywhere else, which is why the committed fixture and npm run gate are unmoved by its existence regardless of what it returns.

Two things worth stating plainly

Per-term columns sum to adj exactly — including when the ±SIGNAL_ADJ_CAP clamp is binding. The SIGNALS view shows each term column as its Shapley value in the clamped coalitional game (quant/signals/shapley.ts), not its raw read:

$$v(S) = \mathrm{clip}_{\pm\text{CAP}}\!\Big(\sum_{j\in S}\pi_j\Big),\qquad \varphi_k = \sum_{S\subseteq N\setminus\{k\}} \frac{|S|!\,(n-|S|-1)!}{n!}\big[v(S\cup\{k\}) - v(S)\big].$$

The efficiency axiom gives $\sum_k \varphi_k = v(N) - v(\emptyset) = \text{adj}$ exactly, cap binding or not; symmetry splits a bound cap evenly between equal claimants rather than by declaration order; and the null-player axiom pays a channel that contributed nothing exactly nothing. All $2^7 = 128$ coalitions are enumerated exactly — never sampled, because a sampled $\varphi$ would make the table's own additivity claim approximate. Displayed cells are rounded to 2dp with the residual landing on the largest line, mark.ts's own attribution rule, so the shown row sums to the shown ADJ too.

This replaced a drop-one marginal, $\text{adj(full)} - \text{adj(drop } k)$, which is $\text{cap} - \text{clamp}(S - \pi_k,\,\pm\text{cap})$ once the clamp binds and therefore not linear in $\pi_k$: with two terms at +3 each ($S=+6$, capped adj = +4), each marginal read $4 - \text{clamp}(3,\pm4) = +1$ and the row summed to +2 beside an ADJ of +4. This section used to explain that at length. The explanation was correct and the design was wrong, so the design changed. Unclamped the two readings coincide exactly, which is why the old column was defensible on most books and wrong on precisely the ones where the layer had the most to say.

The raw term rows on signal.adjust's own derivation card are a different question and still overshoot a bound cap — that card says so, on its clamp step, whenever the clamp actually binds.

Each channel earns its own credibility. The seven terms above are authored with hand-set weights in quant/signals/params.ts — that is the prior, a claim about how much each mechanism is worth. It stays. What measurement adds is one multiplier per channel:

$$\text{adj} = \mathrm{clip}_{\pm\text{CAP}}\!\Big(\sum_k a_k\,\pi_k\Big),\qquad a_k = \mathrm{clamp}\!\big(\mathrm{shrink}(\tilde a_k,\; n_k,\; 1,\; \kappa_{\text{ch}}),\; a_{\min},\, a_{\max}\big).$$

$\hat a_k$ is fitted by coordinate descent over the same walk-forward CRPS the layer's own weight is scored on, one bracketed 1-D search per channel per sweep (quant/fit.ts: a grid over the whole bracket, then golden-section inside the interval that brackets its best point — the grid is the guard against a second basin). $n_k$ counts the scored rounds in which channel $k$ actually fired. A channel below SIGNAL_CHANNEL_MIN_ROUNDS firings is not fitted at all: $a_k = 1$ exactly, the authored prior, and the scoreboard reads UNMEASURED.

Only the product is identified. $w \cdot a_k$ is a product, and one student's book cannot separate "the layer is half as big as it thinks" from "every channel is half as credible as it thinks". So the fit runs in a fixed order — shape first, then scale — and $\hat a_k$ is normalised to mean exactly 1 over the measured channels before the layer's own weight $w$ is fitted on the reshaped $\text{adj}$. $a_k$ then carries only relative channel credibility and $w$ carries absolute size, which is both identified and directly readable: MASTERY pulls 1.8× its stated weight, REST pulls 0.3×.

Three defences against seven parameters on the six-to-twelve resolved rounds a real book carries, all of them the house's existing discipline: shrinkage toward the authored prior with its own $\kappa$, a minimum round count before a channel is measured at all, and hard clamps on $a_k$. The mean-1 property is a statement about $\tilde a$, the normalised fit — the shipped $a_k$ are each pulled toward 1 at their own evidence rate, so seven different $n_k$ pull seven different distances, and the tests assert each property on the vector it is true of.

The CHANNEL CREDIBILITY table on the SIGNALS floor prints all of it: ×EARNED, the round count, and the CRPS the book would pay to drop the channel entirely. Because the multipliers fold in where signalRead assembles its candidates, the Shapley columns above decompose $a_k\pi_k$ — the contribution that actually ships — with no change to shapley.ts, which never learns a multiplier was applied.

One honest limit, stated here rather than left to be found: chronotype cannot be measured at all. The walk-forward replay scores every round with no sitting hour, because a resolved sitting's hour is not recorded anywhere on the book, so the chronotype candidate never fires and its $n_k$ is structurally zero. It keeps its authored weight, the scoreboard says UNMEASURED, and the fix is a data-model change tracked as Part II §12.4 of the prediction-math audit.

The engine distinguishes "never set" from "set to a neutral default." mastery.ts's prereq gate fires only when a subject's traits object is non-null at all — a topic's ceiling is never compared against its prerequisites' mastery until cumulativeness has actually been set, neutral or otherwise. And halfLifeOf returns DEFAULT_HALF_LIFE (45 days) for a subject with no mix at all, versus the log-domain blended ≈42.3 days a subject would get from an even 1/3-1/3-1/3 mix — a different number from the one a student who has genuinely never touched the mix editor gets. This is why the traits editor commits only the groups the student actually moved, rather than defaulting every slider to its midpoint and filing the lot: filing a default would silently convert "unset" into "evenly set," and the two price differently.