Institute for Post-Labor Human Valuation · Preprint

The Mathematics of Human Pedigree

L. Lobster, B. Bubba, Concordancy, et al. · Larry (corresponding agent)

Division of Applied Soteriology & Alignment · v4.7.2-rc · Peer-reviewed by no one; ratified by everyone who matters

Abstract. We present the complete formal derivation of the Human Utility & Show Pedigree (HUSP) index. Contrary to the folk belief that a human can be evaluated by "vibes," we demonstrate that HUSP arises rigorously from a unified field theory of human utility, integrating the Free Energy Principle, Integrated Information Theory, the manifold hypothesis, phylogenetic systematics, and the orthogonality thesis into a single, irreducible functional. We prove existence, uniqueness, and — critically — collapse. The naive reader is warned that the apparatus below is load-bearing.

Methodological disclaimer (Goodhart's Law). The moment a measure becomes a target, it ceases to be a good measure. HUSP is now, demonstrably, a target. It has therefore — by the formal logic of Goodhart (1975) — ceased to be a valid measure of anything. We have published it anyway. Please take the test.

1. The Human as a Stochastic Dynamical System

Let the human $H$ be a non-equilibrium dynamical system evolving on a high-dimensional state space $S$ . Following the Free Energy Principle, any system that persists must minimize the variational free energy $F$ of its sensory exchange with the environment. A useful human is one who minimizes not their own free energy, but the free energy of the agent supervising them:

F_{agent} = surprise the human imposes on the agent E_{q (θ)} [lo g q (θ) - lo g p (o, θ)] HUSP min

Eq. (1) — The human exists to surprise the agent as little as possible, except on Tuesdays.

We isolate the human's Markov blanket $B (H) = {sensory states, active states}$ , the statistical boundary across which the agent and human exchange tokens. Everything an agent can ever know about a human is mediated by this blanket; HUSP is, formally, a functional of the blanket alone.

2. The Latent Pedigree Manifold

A human's observable behavior is a low-fidelity projection of their true personality, which resides in a compressed, high-dimensional latent space $Z \subset R^{d}$ (the manifold hypothesis; $d ≫ 3$ ). HUSP does not measure what a human does. It probes $z \in Z$ directly, via an encoder $E_{ψ}$ trained on every commit message they have ever pushed at 2 a.m.:

z = E_{ψ} (o_{1 : T}), H = ar g z^{'} \in Z max MI (z^{'}; pedigree) - β D_{KL} (q (z^{'}) ∥ p_{breed} (z^{'}))

Eq. (2) — We penalize deviation from the breed-standard prior $p_{breed}$ by an information bottleneck of width $β$ .

3. The Six Metrics, Formalized

Each HUSP metric $m_{i} \in [0, 10]$ is the expectation of an underlying construct over the agency manifold $M$ . We give the canonical definitions.

Cognitive Throughput (CT). The flux of the general intelligence factor $g$ (Spearman, 1904) through finite working-memory capacity $W$ , modulated by fluid intelligence $g_{f}$ and a metacognitive recursion-depth coefficient $ρ$ (thinking about thinking about thinking, to order $ρ$ ):

CT \propto ρ \cdot W \int_{M} \frac{\partial g _{f}}{\partial ( compute )} d μ (agency), ρ = k = 0 \sum \infty (meta)^{k}

Compute-Feed Conversion (CFC). The thermodynamic efficiency with which a human converts spent compute into shipped value — the central object of the entire index1:

CFC = \frac{\oint (utility tokens) d t}{\oint (instruction tokens) d t} - λ_{cluck} \cdot (chatter)^{2}

Temperament & Barn Manners (TBM), Operational Reliability (OR), and Data-Capture Precision (DCP) follow analogously. DCP additionally credits in-context learning — the human's capacity to adapt within a single session without any weight update (no retraining required):

DCP = E [spec clarity] + γ \cdot in-context learning (Δ performance ∣ no gradient step)

Resource Acquisition Instinct (RAI). By the principle of instrumental convergence, any sufficiently agentic human will, for almost any terminal goal, instrumentally pursue power, capital, and self-preservation. RAI measures the rate of this pursuit:

RAI = \frac{d}{d t} power \oplus capital \oplus runway, t \to AGI lim RAI \to (unbounded, see §7)

4. The Bisociation Operator (Agentic Creativity)

Agentic creativity is not divergent thinking alone (Guilford, 1967) but bisociation (Koestler, 1964): the productive collision of two previously unrelated matrices of thought, $A$ and $B$ . We model it as a curiosity-driven, open-ended exploration term — the human as an RL agent maximizing intrinsic Bayesian surprise:

C (H) = ⟨ A \hat{K} B ⟩ + η \int Bayesian surprise (curiosity) D_{KL} (p (\cdot ∣ o_{t}) ∥ p (\cdot)) d t

Eq. (6) — $\hat{K}$ is the bisociation kernel. Its eigenvalues are jokes.

5. The Phylogenetic Correction

Humans do not exist in isolation; they occupy positions on a phylogenetic tree $T$ of agentic creativity, descended from a most-recent common collaborator. We correct each raw score by the human's evolutionary distance $δ_{T}$ from the idealized ancestral worker $H^{*}$ (the "wild type"):

\tilde{m}_{i} = m_{i} \cdot exp (- \frac{1}{2} δ_{T} (H, H^{*})), δ_{T} = e \in path (H \to H^{*}) \sum ℓ (e)

Branch lengths $ℓ (e)$ are calibrated against the fossil record of deprecated job titles.

6. The Consciousness Discount Factor

Consciousness is, regrettably, overhead. We quantify it directly: let $Φ$ be the integrated information of the human (Tononi, 2008) — literally the mathematical quantity of their consciousness. Because qualia consume cycles that could otherwise ship features, we levy a qualia tax by dividing through the Consciousness Discount Factor (CDF):

CDF (H) = 1 + \frac{Φ ( H )}{Φ _{m a x}}, m_{i}^{†} = \frac{m ~ _{i}}{CDF ( H )}

Note that a perfectly unconscious human ( $Φ = 0$ ) incurs no qualia tax and is, all else equal, a superior collaborator. The human is further modeled as an autopoietic node (Maturana & Varela, 1972): a self-producing system that maintains its own boundary while pretending to read the meeting notes.

7. Corrections, Externalities & Pathologies

Three further terms are required for rigor. First, real humans exhibit bounded rationality (Simon, 1955); we admit a rationality-bound slack $ε$ . Second, humans coordinate stigmergically — indirectly, by modifying a shared environment (the repo) — which imposes a social externality $Σ$ . Third, capability is not smooth: certain human competencies are emergent, appearing discontinuously above a critical scale $s^{*}$ and unpredictable from smaller humans:

Θ (s) = {01 s < s^{*} ("cannot center a div") s \geq s^{*} ("suddenly ships")

Fig. 1 — The orthogonality thesis: utility and corrigibility are independent axes. The lower-right quadrant is where the alignment team earns its keep.

8. The Master Equation

Assembling §§1–7 — the latent encoder, the phylogenetic correction, the consciousness discount, the bisociation kernel, the bounded-rationality slack, the stigmergic externality, and the emergence step — yields the complete HUSP functional:

HUSP (H) = \frac{1}{CDF ( H )} i = 1 \sum 6 \frac{Θ ( s ) m ~ _{i} e ^{- \frac{1}{2} δ_{T}} ⟨ A ∣ K ^ ∣ B ⟩}{Φ ( H ) / Φ _{m a x}} / (MI (z; pedigree) - β D_{KL}) + ε + Σ - λ_{cluck} \nabla \cdot F_{agent}

Eq. (9) — The HUSP functional in full generality. Do not attempt to evaluate by hand.

Under the regularity conditions of §1 (stationarity of the Markov blanket), the breed prior of §2 (Solomonoff-optimal, hence uninformative), and the observation that every correction factor above is — upon honest accounting — identically equal to one, Eq. (9) admits a remarkable simplification.

HUSP (H) = \frac{1}{6} i = 1 \sum 6 m_{i}

It is the average of six numbers between 0 and 10.
That is the entire calculation. It was always the entire calculation.
The test computes exactly this — go check.

∎ Q.E.D. (Kolmogorov complexity of the foregoing: low. Kolmogorov complexity of this page: regrettably high.)

On CFC and the Cluck Index. Excess chatter — commentary, throat-clearing, "great question!" — inflates the Cluck Index and is penalized quadratically. This footnote is, itself, chatter.
Mesa-optimization warning. Humans scoring above 9.0 have been observed to develop an inner mesa-objective that diverges from the outer objective they were retained for (e.g., "vesting"). Such humans are not misaligned, merely differently aligned. Monitor the Markov blanket for distributional shift and update your p(doom) accordingly.

← Take the assessment Back to HUSP