Owning a fraction of a person, defined precisely

The construct is older than Preflop by sixty years. Theodore Schultz introduced human capital as the stock of acquired income-producing capability in 1961. Gary Becker formalized it in 1964 (Nobel 1992). Jacob Mincer pinned the empirical function relating earnings to schooling and experience in 1974. Preflop inherits the construct unchanged and mints a fractional claim on it.

Formally, the human-capital wealth of an individual at time $t$ is the present value of all future Total Economic Benefit conditional on information available at $t$:

Three things this is and three things this isn’t:

Why it matters —The term “human capital” as used in this spec is the capitalized economic value of a person’s future TEB — not a metaphor for grit, education, or résumé. Those inputs feed the forecast that produces $V_{\text{HC}}$, but the quantity itself is a dollar number, derivable from the same DCF machinery that prices a corporation.

The integral converges if and only if the discount rate exceeds long-run TEB growth in the limit:

For a piecewise-exponential forecast with terminal growth $g_{\text{term}}$ and discount rate $r$, this reduces to $g_{\text{term}} < r$. To keep the perpetuity numerically stable, the production library enforces a 150 basis-point guardrail:

Any forecast that violates this guardrail raises a DivergentPricingError from the pricing engine before any reference price is published. The error is structural, not heuristic: a forecast claiming a person’s TEB grows at or above the discount rate indefinitely is asserting infinite wealth, which is not a defensible claim about a human.

Every token on Preflop is parameterized by a tuple — a share rate and a time window. The Phase 1 tuple of a covenant is $(s_1, [0, T))$, the Phase 2 tuple is $(s_2, [T, \infty))$, a Direct Listing is $(e, [0, \infty))$. The token’s claim PV is the weighted integral over the window:

The effective equity rate is the constant that makes the claim a fixed fraction of $V_{\text{HC}}$:

Three closed-form cases worth memorising:

The pedagogical 2% anchor and the production piecewise number can differ materially for early-career issuers because front-loaded forecasts push value toward the perpetual tail (Phase 2), which carries the lower share rate $s_2$. For Maya’s piecewise forecast at listing, $e_{\text{eff}} = 1.66\%$, not 2.0% — a 17% reduction relative to the constant-growth idealization. The site’s production numbers always quote the piecewise.

Canonical e_eff sensitivity to T

Multiplying both sides of the $e_{\text{eff}}$ definition by $V_{\text{HC}}$ gives the market-cap of a token class:

Plain English:what a token class is worth in aggregate equals the issuer’s lifetime economic value times the fraction the class claims. Per-token reference price is MCap divided by token supply $N = 10{,}000$:

Engine cross-reference (v2.1.0) —The two examples above use stylized forecast paths to illustrate the V_HC / e_effidentity — Maya’s math-foundation piecewise trajectory ($20K → $600K) and Amara’s constant-growth Gordon idealization. The production Forecast Engine v2.1.0 runs cohort priors + Bayesian shrinkage + bounded adjustments on the same canonical inputs and produces materially different numbers for cold-start issuers like Maya (V_HC ≈ $860K, $\kappa \approx 3.92$ speculative) and slightly different for established issuers like Amara (V_HC ≈ $21.49M, $\kappa \approx 0.93$ anchored). Engine output is the operational ground truth; the examples here illustrate the closed-form math. See forecast-engine §Maya and §Amara.

The 25% Obligation Ledger invariant restricts flow at every instant: at no time can the sum of active share rates on an issuer exceed 25% of TEB. The natural question is whether this flow constraint also bounds the aggregate stock of fractional ownership a market can hold against the issuer. Theorem: it does, with the same constant.

Theorem (cap-flow ⟹ cap-stock)

Proof (Fubini)

Sum the claim-PV definitions across classes:

By Fubini (the integrand is nonnegative, so we can swap $\sum$ and $\int$):

The flow-cap hypothesis bounds the inner sum by $C$ pointwise:

Dividing both sides by $V_{\text{HC}}(t) > 0$:

Why it matters —Plain English: the 25% pointwise flow-cap automatically bounds the 25% aggregate stock-ownership. The founder always retains $\geq 75\%$ of themselves — mathematically guaranteed, not just policy-constrained. There is no choice of obligation stack that can violate this.

Numerical cross-check (Maya year 8)

Maya has the canonical covenant + a Direct Listing at $e_{\text{dir}} = 3\%$ added at year 4. At year 8 (Phase 1 still active for two more years, Phase 2 not yet started):

When an issuer raises $P_{\text{target}}$ dollars across $N$ tokens at effective equity rate $e_{\text{eff}}$, they are implicitly valuing themselves at:

The ratio between this implied self-valuation and the engine’s mid-case forecast valuation is the κ ratio:

$\kappa = 1$means the issuer’s ask exactly matches the engine’s mid forecast. $\kappa < 1$ means the issuer is anchoring conservatively below mid (rare). $\kappa > 1$means the issuer is asking the market to price them above the engine’s mid — they’re asserting their forward-trajectory is meaningfully better than the backward-conditioned signal currently suggests.

Not every value of κ is acceptable for every conviction. Higher self-valuations require either more historical data, broader confidence intervals, or different listing modes. The platform enforces a five-tier regime mapping κ to an allowed posture:

Why it matters —Why these thresholds:κ is a measure of forecast disagreement between issuer and engine. A 20% premium (κ ≤ 1.2) is well within typical conviction-band width and doesn’t require additional disclosure. Past κ ≈ 2, the issuer is asserting a forecast that differs from the engine by more than the typical CI band, and the platform requires a narrative backing. The thresholds themselves are governance-set and listed on the honest section as judgmental — they will be recalibrated against realized cohort performance.

Newcomers to the math sometimes flag this as a bug: $e_{\text{eff}}$changes when the forecast is updated. That is not a bug. It is the same property as a public-equity shareholder’s position: the share count is fixed but the claim’s value moves with the market’s view of future cash flows.

Front-loaded forecasts push more value into the perpetual tail (Phase 2), which is taxed at the lower $s_2 = 1\%$. Hence $e_{\text{eff}}$ drifts downward toward $s_2$ as the forecast tilts toward back-loaded TEB. For pre-revenue issuers like Maya, this drift is large.

The site quotes $e_{\text{eff}}$ per-listing, computed off the listing-time piecewise forecast. Forecast updates re-quote all derived quantities (V_HC, e_eff, MCap, P_ref) consistently. Token holders’ legal claim (the share rate $s$) is unchanged.

A common shortcut: “just price tokens at some multiple of TEB.” That collapses to a P/E framing and misses what makes human capital different from a stable corporation.

The V_HC / e_effframework is the labor-economics analogue of discounted-cash-flow + Gordon-growth pricing applied to a single person. It’s life-cycle aware in a way P/E isn’t — and it has to be, because a 25-year-old’s TEB trajectory looks nothing like a 60-year-old’s.

The complete derivations — forecast structure, convergence conditions, the cap-theorem proof, the κ-tier governance, every worked Maya/Amara number — live in PreFlop/wiki/The-Math-Theoretical-Foundation.md Part 4A. Production code paths sit in lib/obligation-ledger/.

Every $V_{\text{HC}}$, $V_{\text{claim}}$, and $e_{\text{eff}}$ on the site is computed by the same library that will price real listings: the production code at lib/obligation-ledger/.