Live audit of every number in the APEX pipeline. The page re-runs every mathematical invariant against current DB state on each request — no cached proofs, no silent drift.
The engine audits itself. When you see score 38 for NVDA, every formula that produced it is checked against its mathematical definition here. If weights stop summing to 1, or a correlation exceeds its legal range, or a regime posterior drifts off the unit simplex — you see a red FAIL label.
Green PASS = mathematical law holds. Each row below is a physical/mathematical invariant the engine must satisfy — not a prediction, an equation. Prediction accuracy on realised returns is tracked separately on the Track Record page as forward-return history accumulates.
Each row below is an automatic law the engine must satisfy. If every check is PASS, the math is self-consistent end to end.
The engine uses one input (one year of S&P 500 daily returns) to drive six coordinated decisions. All six rest on the same probabilistic view of the market state — not six independent models averaged together. This is what we mean by a coherent Bayesian framework.
What this shows. The matrix displays the pair-wise Spearman rank-correlation between our 12 factor scores. Green = factors move the same way, red = opposite ways, white = near-independent.
Why it matters. If two factors duplicate each other (ρ close to 1), counting them as two independent votes is double-counting. The Grinold-Kahn formula collapses the matrix into a single effective-breadth number: N_eff = 6.6 of 12. That\'s the honest factor count — not the naïve 12.
Parameters: avg |ρ| = 0.073 · worst pair |ρ| = 0.494 · sample = 878 observations.
| qualit | value | moment | inside | intera | sector | pead | accrua | spillo | option | nlp | short_ | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| quality | — | -0.11 | -0.04 | 0.00 | -0.07 | -0.19 | 0.02 | -0.03 | -0.09 | -0.03 | 0.02 | 0.24 |
| value | -0.11 | — | 0.06 | 0.00 | 0.15 | 0.14 | 0.04 | -0.07 | 0.05 | -0.04 | 0.18 | -0.10 |
| momentum | -0.04 | 0.06 | — | 0.00 | -0.02 | 0.30 | 0.03 | 0.15 | 0.35 | 0.13 | 0.04 | -0.03 |
| insider | 0.00 | 0.00 | 0.00 | — | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| interact | -0.07 | 0.15 | -0.02 | 0.00 | — | 0.08 | 0.02 | -0.07 | 0.07 | 0.03 | 0.06 | -0.02 |
| sector | -0.19 | 0.14 | 0.30 | 0.00 | 0.08 | — | 0.00 | -0.13 | 0.49 | 0.01 | 0.03 | -0.08 |
| pead | 0.02 | 0.04 | 0.03 | 0.00 | 0.02 | 0.00 | — | -0.04 | 0.03 | -0.02 | 0.12 | 0.13 |
| accruals | -0.03 | -0.07 | 0.15 | 0.00 | -0.07 | -0.13 | -0.04 | — | -0.05 | 0.08 | 0.10 | -0.15 |
| spillove | -0.09 | 0.05 | 0.35 | 0.00 | 0.07 | 0.49 | 0.03 | -0.05 | — | -0.03 | 0.02 | 0.02 |
| options | -0.03 | -0.04 | 0.13 | 0.00 | 0.03 | 0.01 | -0.02 | 0.08 | -0.03 | — | -0.11 | -0.02 |
| nlp | 0.02 | 0.18 | 0.04 | 0.00 | 0.06 | 0.03 | 0.12 | 0.10 | 0.02 | -0.11 | — | -0.09 |
| short_in | 0.24 | -0.10 | -0.03 | 0.00 | -0.02 | -0.08 | 0.13 | -0.15 | 0.02 | -0.02 | -0.09 | — |
Every number in the engine is tagged with a grade:
| GROUP | NAME | VALUE | GRADE | JUSTIFICATION |
|---|---|---|---|---|
| BOCPD | HAZARD_LAMBDA | 60 | LITERATURE | Constant-hazard H(r)=1/λ. 60d ≈ 3 months matches Hamilton's estimated regime duration on post-war US data.— Hamilton 1989, NBER recession avg duration |
| BOCPD | STABILITY_TAU | 20 | OPERATING | stability = 1 − exp(−E[r]/τ). τ=20 ⇒ 95% stability at E[r]≈60d. Matches HMM 10% off-diagonal transition band.— Internal calibration |
| BOCPD | DIRECTION_KAPPA | 2.5 | LITERATURE | Logistic slope on Sharpe-like z. κ=2.5 gives 92%/8% split at z=1 — "strong evidence" per Kass-Raftery BF scale.— Kass & Raftery 1995, Bayes factor strength scale |
| BOCPD | SHRINKAGE_N0 | 50 | OPERATING | Tail-dep shrinkage anchor: w = n/(n+N0). N0=50 so n=50 → raw:prior = 50:50, n=200 → 80:20.— Internal |
| BOCPD | NIG_PRIOR | {"mu":0,"kappa":0.01,"alpha":1,"beta":1} | OPERATING | μ₀=0, κ₀=0.01 (minimal), α=β=1 (inverse-gamma with moderate mass near unit variance — matches % returns).— Weakly informative NIG |
| KALMAN | SIGMA_OMEGA_SQ | 0.01 | HEURISTIC | Baseline β random-walk noise. To be MLE-calibrated once forward returns accumulate (sigma_omega should be the one that maximises likelihood on forward returns).— Internal |
| KALMAN | GAMMA_CP | 10 | OPERATING | Q_t = σ²_ω·(1 + γ·changeProb). γ=10 ⇒ changeProb=0.1 doubles Q; 0.5 inflates Q×6. Verified on CP-shift synthetic.— Internal synthetic calibration |
| KALMAN | SIGMA_EPS_SQ | 625 | HEURISTIC | σ_ε=25 ≈ typical cross-sectional percentile dispersion. Will auto-fit from residual variance pass once OOS data exists.— Internal |
| KALMAN | C0_DIAG | 1 | OPERATING | Moderately uninformative prior on β. σ_0=1 per factor in z-per-point units.— Weakly informative prior |
| KALMAN | BLEND_MATURITY_OBS | 1000 | OPERATING | DLM/Markowitz blend λ_DLM = min(1, obs/1000). 1000 obs ≈ 4 months of full-universe days — at this point the filter has seen enough data to trust over priors.— Internal |
| MARKOWITZ | ALPHA_RISK_OFF | 0.7 | OPERATING | In crashes factors co-move mostly in tails — tail-dep dominates Σ.— Internal |
| MARKOWITZ | ALPHA_RISK_ON | 0.4 | OPERATING | In booms co-movement is less structural; partial tail weight.— Internal |
| MARKOWITZ | ALPHA_TRANSITION | 0.25 | OPERATING | Midway blend of both tails.— Internal |
| MARKOWITZ | ALPHA_ALL | 0 | OPERATING | Neutral baseline = pure Spearman ρ Σ.— Internal |
| MARKOWITZ | RIDGE_INITIAL | 0.05 | LITERATURE | Standard starting ridge for near-singular correlation matrices.— Tikhonov regularization, Hoerl-Kennard 1970 |
| MARKOWITZ | RIDGE_CAP | 1 | OPERATING | Auto-tune doubles ridge until matrix inverts, capped at 1 (full-identity regulariser).— Internal |
| CONFLUENCE | TAU_REFERENCE | 0.25 | LITERATURE | Anchor tail-alignment for γ = 1 (neutral). λ=0.25 is roughly the t-copula ν=3, ρ=0.5 baseline — "moderate" empirical tail dep.— Kraskov-Stögbauer-Grassberger 2004 moderate-dependence threshold |
| CONFLUENCE | GAMMA_FLOOR | 0.5 | OPERATING | Cap confidence-scale below so pattern never completely nullified.— Internal |
| CONFLUENCE | GAMMA_CEIL | 1.75 | OPERATING | Cap above so extreme tail-alignment (λ>0.5) doesn't dominate the other confidence inputs.— Internal |
| MONDRIAN | MIN_BIN_SAMPLES | 20 | LITERATURE | Per-bin conformal needs ≥ ⌈(n+1)(1−α)⌉ ≥ 20 for α=0.05 to guarantee coverage ≥ 1 − α − 1/(n+1).— Vovk et al 2003 + Angelopoulos-Bates 2021 |
| MONDRIAN | TAIL_BUCKET_TIGHT | 0.25 | LITERATURE | Partition boundary co-calibrated with Confluence τ_ref so patterns and conformal see the same tail semantics.— Matches τ_ref |
| MONDRIAN | TAIL_BUCKET_MODERATE | 0.1 | OPERATING | Between tight and loose — "detectable but not structural" tail-dep.— Internal |
| CONFORMAL | PRIOR_HALFWIDTH | 15 | HEURISTIC | Fallback when no calibration exists. To be replaced by bootstrap on first 30 residuals (2026-05-16+).— Internal |
| CONFORMAL | CONFIDENCE_FACTOR_MIN | 0.6 | OPERATING | At confidence 100, interval is 60% of marginal halfwidth.— Internal |
| CONFORMAL | CONFIDENCE_FACTOR_MAX | 1.4 | OPERATING | At confidence 0, interval is 140% of marginal halfwidth.— Internal |
| CONFORMAL | MIN_CALIBRATION_N | 30 | LITERATURE | Below n=30 the conformal coverage bound 1-α-1/(n+1) is too loose to trust.— Vovk et al 2005 |
| CONFORMAL | TAIL_INFLATION_SENSITIVITY | 0.5 | OPERATING | halfwidth ×= 1 + 0.5·λ. At λ=0.3 interval widens 15%, matching published stress-vs-normal spread across factor model drawdowns.— Internal |
| COMPOSITE | Z_PER_POINT | 15 | OPERATING | 2σ ticker ≈ composite 80, 1σ ≈ 65. Preserves 0-100 clipped spread for UI consistency.— Internal v8 calibration |
| COMPOSITE | Z_CLIP | 4 | OPERATING | Cap per-factor z at ±4σ — beyond this it's outlier or data error.— Internal |
| COMPOSITE | CLIP_LOWER | 5 | OPERATING | Floor to avoid "0/100" extremes that confuse UX.— Internal |
| COMPOSITE | CLIP_UPPER | 95 | OPERATING | Ceiling for the same reason.— Internal |
| BAYES | SHRINKAGE_ANCHOR | 200 | OPERATING | Bayesian shrinkage ρ = n/(n+200). n=200 → 50/50 prior+data. n=1000 → 83/17 data.— Internal |
| BAYES | MIN_PER_FACTOR | 30 | LITERATURE | Below 30 per-factor observations, Spearman IC std is too high to trust.— Standard IC statistical sig threshold |