One Number Rules Finance: The Latent Resolution of Asset Pricing Puzzles

We resolve three longstanding anomalies in asset pricing — the equity premium puzzle, the Fama-French factor zoo, and the failure of single-factor models — through a single spectral parameter: the Latent Number \(\rho\). The Latent framework decomposes any stochastic discount factor (SDF) into spectral components \(M = \sum_i a_i \varphi_i\) ordered by eigenvalue magnitude. When \(\rho > 1\), the persistence–spectral link in the formal model multiplies effective consumption variance by \(\rho\) (single-period encoding) relative to the i.i.d. benchmark, tightening Hansen–Jagannathan bounds and resolving the Mehra–Prescott puzzle without requiring implausible risk aversion. The same spectral ordering yields a geometric tail on factor weights; for \(\rho = 2\), the first three components capture at least 98% of SDF variance (Theorem 6), while the analytic complexity bound \(k^ = \lceil \log(1/\varepsilon) / \log(\rho) \rceil\) gives \(k^ = 4\)–\(6\) for \(\varepsilon \in \{0.1,\,0.02\}\). We establish a bridge to Markowitz mean-variance optimization: under the Latent variance scaling used in the proofs, the maximal squared Sharpe ratio scales proportionally to \(\rho\), hence the Sharpe ratio itself scales by \(\sqrt{\rho}\). All results are machine-verified: 90 theorems across 5 proof files, 0 axioms.