How $12,012 was verified

All published values reproduced from inputs to stated precision. Minor rounding asymmetries (≤$1) in per-worker payments absorbed by the largest recipient — a standard accounting convention without systematic bias. No arithmetic errors.

With R_s clipped to 1.0 whenever NMES ≥ MDP (the common case), the term 0.40 × R_s contributes a fixed 0.40 of the maximum 1.00 index. DE is structurally confined to [40, 100], not the advertised [0, 100]. The published range is misleading and should be revised in the Standard documentation.

EM is defined as max(EM_audited / EM_baseline, 1) but the Standard does not specify what EM_baseline is when no manual benchmark exists, whether EM_audited is per-task / per-shift / per-month, or the unit basis (output count, dollar value, throughput rate). EM is mathematically underspecified — the audit can produce any value depending on interpretation.

Theorem: for all (S, T) with Sᵢ > 0 and ΣT > 0, the weights wᵢ = 0.70·(Sᵢ/ΣS) + 0.30·(Tᵢ/ΣT) satisfy Σwᵢ = 1. The 70/30 distribution is provably budget-exhausting — no rounding adjustment beyond residual allocation is required.

If all displaced workers have zero tenure (e.g., a freshly-hired temporary crew displaced before completing a month), the seniority term Tᵢ/ΣT is undefined. This is a runtime exception. Defensive guard Math.max(ΣT, 1) is required in code, or the Standard must require a minimum tenure floor.

The floor DC ≥ 0.15 × MDP binds only when NMES < 0.75 × MDP — an unusual scenario possibly indicating an uneconomic automation. The floor activates in the correct regime and provides a baseline worker protection. Structurally sound.

Replaying the Acme case with L = 60 (vendor claim) instead of L = 36 (audited): ASTC drops ~$2,800, NMES drops $4,600, DC drops from $12,012 to $10,525. The L parameter has a monthly compensation sensitivity of approximately $1,487 per 24-month extension. High-leverage gaming vector.

Two competing normalisations of U_r exist in current documentation: divisor U_max = 13 vs divisor U_threshold − U_national = 9. The Standard must fix one. The choice affects DC by approximately ±$200/month at the Acme scenario.

In the common regime (R_s = 1): DC = (ASTC × EM) × [0.30 + 0.05·R_w + 0.0625·R_p + 0.0375·H]. The formula is bilinear in (ASTC × EM) with a base rate of 30% plus four small additive sensitivities.

Above the R_s = 1 threshold, DC is linear in (ASTC × EM). Below it (when NMES < MDP), DC contains a quadratic term in (ASTC × EM). The function is C⁰ continuous (no jump) but not C¹ (kink at NMES = MDP). Algebraic signature of a piecewise saturation.

∂DC/∂EM = +$5,166/unit · ∂DC/∂ASTC = +$0.323/$ · ∂DC/∂R_w = +$1,860/unit · ∂DC/∂R_p = +$2,325/unit · ∂DC/∂H = +$1,395/unit. EM dominates the sensitivity profile by an order of magnitude — whoever controls EM determination effectively controls DC.

κ(DE) = 0.20 + 0.0025 × DE is linear: marginal compensation per unit of DE is constant. There is no convex (concave) reward structure — increasing displacement severity does not accelerate compensation. The linear choice is a normative decision, not a mathematical necessity. A convex schedule would more strongly compensate severe events.

H is a weighted arithmetic mean of four bounded sub-indices. This is structurally fragile: a worker in a region with U_r = 0 can still receive high H if H_s is high. The mean does not enforce minimum hardship across categories. A geometric mean would require every category to contribute — eliminating gaming where a company picks the lowest-stress SOC classification. Trade-off: arithmetic mean is more interpretable.

Shifting weights from (0.20, 0.25, 0.40, 0.15) to (0.20, 0.25, 0.35, 0.20) changes DC by ~$340/month at the Acme scenario. The published weights are not justified anywhere in the Standard. They are normative choices that materially affect payouts.

If NMES = 0, DC_raw = 0 but DC_floor = $2,400. The floor creates a discontinuity in the firm's marginal-incentive profile: between NMES = $0 and the floor crossover, optimising automation efficiency yields zero marginal DC change. Known trade-off in any floor-protected payment scheme.

All terms in all six steps have consistent units. ASTC is $/month, EM is dimensionless, NMES is $/month, R_x are fractions, H is a fraction, DE is a pure-number index, κ is a fraction, DC is $/month. Composition is dimensionally clean. No unit errors.

The mechanism is a principal-agent-auditor trilateral game. The company's payoff is to minimise DC, and since DE is a weighted sum of inputs the company controls or influences, the dominant strategy is to minimise each input. The mechanism is not incentive-compatible as written — there is no Nash equilibrium at truthful reporting without external enforcement.

R_w and R_p are auditable from HR and tax records — low manipulation risk. R_s is derived from other inputs — medium risk. H is partially derived from external data (BLS, O*NET) and partially from company-influenced parameters — high risk. The hardship index is the critical vulnerability. U_max = 13.0 must be documented with a citation; O*NET replicability must come from the published database or an independent analyst.

Lifetime extension (L = 60 vs 36) saves $1,487/month × 60 months = $89,220 per cohort over five years. EM auditor sandbagging (vendor-affiliated audit gives EM = 1.02× vs independent 3.00×) collapses DC from $12,012 to $4,007 — worker loss of $8,005/month. These are not hypothetical; they are dominant strategies for a self-interested firm absent external constraint.

Below the floor crossover, improvements in NMES yield zero additional DC — the company has zero incentive to allow honest audits in this regime. Audits must be mandatory regardless of which regime the transition lies in.

Truthful reporting is strictly dominated by gaming. The mechanism fails the Revelation Principle test for incentive-compatibility. Fixes: independent third-party determination of all inputs; penalty multiplier for misreporting; commitment device (lock L at point of purchase in a public contract).

Modelling as a 2×2 game where Company chooses Honest/Biased audit and Workers choose Accept/Challenge: without a penalty mechanism, Company's dominant strategy is Biased audit whenever penalty < $8,005 × P(challenge). The mechanism only works at honest equilibrium if penalty exceeds expected gaming gain or P(challenge) is very high. Explicit penalty rates are required.

The 70/30 distribution is linear and additive: each worker's marginal contribution to the total pool equals their wᵢ × DC payment. Therefore Shapley-fair — no worker has incentive to defect from the formula. However, a senior worker could collude with management to reclassify junior workers before the announcement, shrinking ΣT and inflating their seniority share. Mitigation: freeze T at announcement date, not separation date.