OpenFacet reconstructs diamond price surfaces using low-rank models fit to observed public retail data. These models capture the statistical structure of price variation across color, clarity, and carat weight. But observed prices don’t follow clean valuation logic. Buyers perceive symbolic differences—not just physical traits.

To address this, OpenFacet applies targeted behavioral adjustments. These do not override the core model. They correct only where economic asymmetries align with cognitive distortions, as documented in behavioral economics¹²³.

Anchoring Near Carat Thresholds

Round weights like 1.00ct act as psychological targets in retail pricing. Buyers regularly overpay for 0.99 → 1.00ct jumps, despite minimal visual difference. Anchoring theory explains this: symbolic round numbers distort value perception².

To model this, OpenFacet applies a one-sided price boost when a weight is just below a known anchor. The effect decays quickly and is capped to prevent distortions:

$$ P_{\text{anchor}} = P_{\text{interp}} \cdot \left(1 + \gamma e^{- \delta (t - w)} \right) \quad \text{if } w < t $$

• $t$: anchor weight (e.g., 0.40, 1.00, 1.50)
• $w$: actual carat
• $\gamma \approx 0.1$, $\delta \approx 300$
• Boost is only applied if close ($< 0.03$ ct) and price slope is upward

This ensures that anchoring captures market asymmetry without breaking monotonicity. Prices remain smooth, and no near-threshold carat ever exceeds the next band.

Prospect Aversion Near Quality Downgrades

Buyers treat downgrades from top-tier grades as larger losses than upgrades are gains. This aligns with Prospect Theory¹, where utility drops steeply from reference points.

For fixed carat bands, we apply a decaying premium to combinations near D color / IF clarity:

$$ P_{\text{prospect}} = P_{\text{base}} \cdot \left(1 + \alpha e^{-\beta x} \right) $$

• $x$: Manhattan distance from D/IF
• $\alpha \approx 0.07$, $\beta \approx 1.5$

The effect is localized: no correction is applied beyond ~2 steps from the top-left matrix corner.

Veblen Premiums Within Band

Buyers may pay more for combinations that signal exclusivity, independent of physical or grading traits. This follows Veblen’s theory of conspicuous consumption³. In practice, rare top-grade combinations are perceived as “worth more” than their marginal utility justifies.

OpenFacet models this within-band using a rank-based uplift:

$$ P_{\text{veblen}} = P_{\text{base}} \cdot \left(1 + \phi \left(1 - \frac{\text{rank}}{\text{max rank}} \right)^2 \right) $$

• Rank is the ordinal index across the color–clarity matrix
• $\phi$ is small (~0.02–0.04), applied symmetrically

Contextual Layering of Corrections

Corrections are not cumulative or global. Each applies only in context:

Each multiplier is applied post-reconstruction, without interfering with low-rank estimation or log-space smoothing. Net impact is small—usually under 5%—but restores fidelity to pricing behavior observed in both retail listings and resale dynamics.