Appendix H. Formal Model of Market Realization, Wrapper Flows, and Price Capture

Jason St George. "Appendix H. Formal Model of Market Realization, Wrapper Flows, and Price Capture" in Next Generation Stores of Value: Privacy, Proofs, Compute. Version v1.5. /v/1.5/read/appendix/h-market-realization/

Appendix H: Formal Model of Market Realization, Wrapper Flows, and Price Capture

This appendix develops the flow machinery behind the Market Realization Plane (§6.5) and VerifyFlow (§23.1.1). It is deliberately quarantined here: the main body needs the distinction between value capture and price capture, not the derivations.

Attribution. The flow machinery below — flow elasticity, holder recycling, leveraged-rebalancing mechanics, and the return-coupled versus return-decoupled distinction — is adapted from Michael W. Green’s work on how product mechanics and holder behavior set prices, in particular A Semi-Theory of Almost Everything (Tier1 Alpha, July 2026). The market-impact form follows the inelastic-markets literature, especially Gabaix and Koijen (2021). What is ours is the generalization from equity market structure to monetary telemetry: the claim that these quantities must be published as a distinct verification family (VerifyFlow) precisely so that price movement is not mistaken for monetary adoption. Any errors in that generalization are ours, not theirs.

A caution before the mathematics. These equations describe transmission and magnitude. They do not explain why a narrative ignites a behavioral shift in the first place. Flow elasticity in particular is measured, not explained. Treating any parameter below as a structural constant is a modeling error.

H.1 Flow elasticity

For wrapper $i$, estimate the responsiveness of shares outstanding to changes in value per share:

$\Delta \ln S_{i,t} = \alpha_i + \varepsilon_{i,t}\,\Delta \ln \mathrm{NAV}_{i,t} + u_{i,t}$

where $S_{i,t}$ is shares outstanding, $\mathrm{NAV}_{i,t}$ is value per share, and $\varepsilon_{i,t}$ is flow elasticity. Interpretation: $\varepsilon \approx 0$ means holders largely sit still; $\varepsilon \approx -1$ means holders redeem roughly enough after gains to maintain a constant dollar position.

The regression has three parts and each is allocated to a different place downstream, so the decomposition must be stated rather than assumed. The $\varepsilon$-driven component is return-coupled and belongs in $Q^{RC}$ below. The intercept $\alpha_i$ captures baseline creation or redemption that occurs regardless of the day’s return — distribution growth, model-portfolio adoption, scheduled contributions — and therefore belongs in the return-decoupled term $Q^{RD}$, not in $Q^{RC}$. The residual $u_{i,t}$ stays unexplained and must be published rather than absorbed into either. Assigning $\alpha_i$ to $Q^{RC}$ would overstate momentum amplification; discarding it would understate the structural bid.

Because a daily-reset leveraged wrapper’s NAV return is approximately $L_i r_t$ for underlying return $r_t$:

$\frac{\Delta S_{i,t}}{S_{i,t}} \approx \varepsilon_{i,t} L_i r_t$

H.2 Leveraged rebalancing and flow-induced exposure

A daily-reset fund must trade to restore its target exposure. The gross required rebalance is

$Q^{\text{rebalance}}_{i,t} \approx L_i(L_i - 1) A_{i,t} r_t$

where $A_{i,t}$ is fund assets. Note that $L(L-1) > 0$ both for $L > 1$ and for negative leverage such as $-2$ or $-3$: long and inverse leveraged funds both mechanically chase the underlying move. The inverse product is not a stabilizer.

Separately, creations and redemptions carry exposure equal to leverage times the dollar flow:

$Q^{\text{flow}}_{i,t} \approx \varepsilon_{i,t} L_i^2 A_{i,t} r_t$

Combining the two gives total return-coupled mechanical exposure:

$Q^{RC}_{i,t} \approx \bigl[L_i(L_i-1) + \varepsilon_{i,t} L_i^2\bigr] A_{i,t} r_t$

H.3 Net mechanical gain

Define the net mechanical gain coefficient

$\kappa_{i,t} = L_i(L_i-1) + \varepsilon_{i,t} L_i^2$

so that $Q^{RC}_{i,t} = \kappa_{i,t} A_{i,t} r_t$. The sign and magnitude of $\kappa$ determine whether a wrapper amplifies or absorbs the move it sits on.

H.4 The recycling boundary

A wrapper fully offsets its own gross mechanical trade when $\kappa_i = 0$, which implies a critical elasticity

$\varepsilon_i^{*} = -\frac{L_i - 1}{L_i}$

This is the single most useful conversion in the appendix: it turns “holder behavior matters” into a number that can be measured, plotted, and breached. Empirically, a 3× product whose elasticity sits near −0.68 is close to self-neutralizing; if that elasticity weakens toward −0.40, the same product becomes a material momentum amplifier, and the underlying’s behavior can shift from mean-reverting toward higher volatility with greater trend persistence.

H.5 Wrapper Recycling Ratio

A more legible operator metric normalizes elasticity by its own boundary:

$\mathrm{WRR}_{i,t} = -\varepsilon_{i,t}\,\frac{L_i}{L_i - 1}$

where $\mathrm{WRR} = 1$ means holder flows fully offset gross rebalancing; $\mathrm{WRR} < 1$ means the wrapper amplifies the underlying move; and $\mathrm{WRR} > 1$ means holder flows more than offset it and become countercyclical. This belongs on the public Market Realization & Wrapper Board.

H.6 Return-decoupled allocation flow

Not all flow responds to returns. A thematic or passive wrapper can receive creations largely independent of the current day’s return, arriving on up days and down days alike. For underlying asset $j$:

$Q^{RD}_{j,t} = \sum_k w_{jk,t} F_{k,t}$

where $F_{k,t}$ is net creation flow into wrapper $k$ and $w_{jk,t}$ is that wrapper’s exposure weight to $j$. For leveraged or derivative wrappers, $w_{jk,t}$ must be a delta-equivalent exposure weight rather than a portfolio accounting weight, or the allocation flow will be understated by roughly the leverage factor.

The two flow types do different work. Return-coupled flow governs volatility, momentum, persistence, and reversal severity. Return-decoupled flow governs destination and level: which assets receive the structural bid, how concentrated it becomes, and which prices are accepted without valuation-sensitive selling. For a triad asset, return-decoupled flow could arrive from a spot ETF, a crypto index product, a corporate treasury mandate, an automated wealth-allocation model, a retirement default, an agentic treasury system, or a regulated “digital hard asset” basket — all potentially enormous for price and nearly irrelevant to native triad usage.

H.7 Market impact and liquidity

Flow becomes price only through a liquidity-dependent impact function. The standard empirical form has impact growing roughly with the square root of trade size relative to available liquidity:

$I_{j,t} = Y_j \sigma_{j,t} \operatorname{sgn}(Q_{j,t}) \sqrt{\frac{|Q_{j,t}|}{V_{j,t}}}$

where $Y_j$ is an impact coefficient, $\sigma_{j,t}$ is volatility, $Q_{j,t}$ is exposure demand, and $V_{j,t}$ is executable liquidity over the relevant horizon. Splitting impact into permanent and temporary components with permanence share $\rho_j$:

$\Delta \ln P_{j,t} = \theta_{j,t} + \rho_j I_{j,t} + (1-\rho_j) I^{\text{temporary}}_{j,t} + \eta_{j,t}$

Fitted permanence is case-specific. Import the structure; estimate $Y_j$, $\rho_j$, and $V_{j,t}$ asset by asset.

H.8 Volatility drag on leveraged wrappers

For a daily-reset wrapper with leverage $L$ on an underlying with drift $\mu$ and volatility $\sigma$, the continuous approximation to compound growth is

$g_L \approx L\mu - \frac{L^2 \sigma^2}{2} - (L-1)r_f - f$

where $r_f$ is the financing rate on the levered portion and $f$ is the product’s expense ratio. The first two terms are the standard continuous approximation; the last two are the carry the wrapper actually bears and are frequently omitted, which flatters leveraged products in exactly the high-rate environments where they are most costly to hold. Note also that this section’s results, along with the recycling boundary and WRR of §H.4–H.5, apply to daily-reset products with $L \neq 0, 1$; an unlevered or non-resetting wrapper has no rebalancing obligation and no drag term.

The variance penalty grows with the square of leverage. At sufficiently high volatility a leveraged wrapper destroys capital even when the underlying has a positive average return. This is the formal basis for the object hierarchy in §6.1: a daily-reset leveraged wrapper cannot inherit the underlying asset’s store-of-value status, because its terminal value depends on the path and not merely the endpoints. It is a path-dependent trading instrument that happens to reference a monetary object.

H.9 Dealer hedge decomposition

Product-level exposure demand is not equal to spot orders. Decompose realized hedging by instrument — physical holdings, futures, total-return swaps, options — and track delta- and gamma-adjusted exposure per counterparty, average derivative maturity, collateral and margin requirements, and evidence of counterparty caps. A migration from swaps toward options is a candidate signal that dealer balance-sheet capacity is binding, with the attendant gamma feedback when dealers are short calls. Treat this as a hypothesis to test per asset, not a law.

H.10 Measurement contract

VerifyFlow Measurement Contract

• Use daily or intraday shares outstanding, NAV, price, AUM, holdings, leverage, and derivative disclosures.
• Chain reverse splits and corporate actions before estimating anything.
• Estimate elasticity over multiple rolling windows, never a single fixed window.
• Use structural-break tests rather than assuming fixed holder behavior.
• Report exposure demand separately from realized spot orders.
• Delta-adjust swaps and options.
• Publish top-N counterparty and constituent concentration.
• Separate return-coupled and return-decoupled flows.
• Compare market-exposure growth against native protocol-use growth (WNG).
• Publish confidence intervals and model residuals.
• Report failed hypotheses rather than silently dropping them.

That last clause is not decoration. A flow model that only publishes the specifications that worked is indistinguishable from a narrative, and this thesis has no standing to demand receipts from protocols while exempting its own econometrics.

H.11 Reference stress-harness sketch

For each scenario in §23.5: enumerate wrappers and their $(L_i, A_i, \varepsilon_i)$; compute $\kappa_i$ and $\mathrm{WRR}_i$; simulate a return path; accumulate $Q^{RC}$ and $Q^{RD}$; map aggregate $Q$ through the impact function given $V$; propagate the resulting return back into the next period’s rebalance and creation terms; and record MPR, WNG, and native-use series alongside price. The output of interest is never the simulated price. It is whether the native series moved at all.

H.12 Boundaries and caveats

• This machinery is evidence about market transmission. It is not evidence that Privacy, Proofs, or Compute will earn monetary premium.
• Parameters fitted in one market (equities, semiconductors) do not transfer. Re-estimate everything.
• Unlevered wrappers are not adversaries by construction. The failure mode is the inability to distinguish accessibility, custody concentration, native use, synthetic leverage, and price-insensitive demand.
• Price is never a protocol control target. The purpose of this appendix is to explain price formation, not to defend a price.
• Market realization is orthogonal to the stack. Nothing here becomes a Layer 7.

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