INTEGRITY LAYER v7

Zenodo v7 — Energy-Field Appendix Energy-Field Model (Appendix A) We define the market as a discrete dynamical system evolving under an integrity-constrained energy field. Let price process PtP_tPt generate returns rtr_trt. Core quantities: Dispersion Dt=σtmax⁡(σt−k:t)D_t = \frac{\sigma_t}{\max(\sigma_{t-k:t})}Dt=max(σt−k:t)σt Persistence Πt=1−Dt\Pi_t = 1 - D_tΠt=1−Dt Stress St=E[σt]S_t = \mathbb{E}[\sigma_t]St=E[σt] Entropy Ht=E[∣rt∣]H_t = \mathbb{E}[|r_t|]Ht=E[∣rt∣] Energy Balance Et=Πt−StE_t = \Pi_t - S_tEt=Πt−St This quantity measures whether structural coherence dominates volatility pressure. Regime Confidence Rt=Πt⋅(1−St)R_t = \Pi_t \cdot (1 - S_t)Rt=Πt⋅(1−St) Decision Rule SAFEt ⟺ {Πt≥0.45St≤0.40Et≥0\text{SAFE}_t \iff \begin{cases} \Pi_t \ge 0.45 \\ S_t \le 0.40 \\ E_t \ge 0 \end{cases}SAFEt⟺⎩⎨⎧Πt≥0.45St≤0.40Et≥0 BLOCK dominance is expected:markets spend most time in entropic or transitional regimes. SAFE Streaks SAFE streak length LLL is a proxy for regime stability and predictive survivability. Regime Transitions A transition occurs when: decisiont≠decisiont−1\text{decision}_t \ne \text{decision}_{t-1}decisiont=decisiont−1 Transitions precede drawdowns with high probability. Methods 1. Data Ingestion and Normalization Input data consist of time-indexed observations for one or more assets, including price and optional volume fields. The pipeline automatically detects a valid price column (avg_price, close, Close/Last, or price) and resolves timestamps from either an explicit timestamp field, a Date field, or a synthesized monotonic time index when unavailable. All assets are processed under identical transformations to preserve comparability. 2. Rolling Dynamical Feature Construction Let PtP_tPt denote the asset price at time ttt. Log-returns are computed as: rt=Pt−Pt−1Pt−1r_t = \frac{P_t - P_{t-1}}{P_{t-1}}rt=Pt−1Pt−Pt−1 All subsequent metrics are computed over a rolling window of fixed length WWW (default W=30W = 30W=30). Volatility is defined as the rolling standard deviation: σt=Std(rt−W:t)\sigma_t = \mathrm{Std}(r_{t-W:t})σt=Std(rt−W:t) Dispersion is a normalized volatility measure: Dt=σtmax⁡(σt−W:t)withDt∈[0,1]D_t = \frac{\sigma_t}{\max(\sigma_{t-W:t})} \quad \text{with} \quad D_t \in [0,1]Dt=max(σt−W:t)σtwithDt∈[0,1] Persistence is defined as the complement of dispersion: Πt=1−Dt\Pi_t = 1 - D_tΠt=1−Dt Entropy is approximated as the rolling mean absolute return magnitude: Ht=E[∣rt−W:t∣]H_t = \mathbb{E}[|r_{t-W:t}|]Ht=E[∣rt−W:t∣] Stress is defined as the rolling mean volatility: St=E[σt−W:t]S_t = \mathbb{E}[\sigma_{t-W:t}]St=E[σt−W:t] 3. Energy-Field Construction The system defines an energy balance scalar: Et=Πt−StE_t = \Pi_t - S_tEt=Πt−St and a regime confidence scalar: Ct=Πt⋅(1−St)withCt∈[0,1]C_t = \Pi_t \cdot (1 - S_t) \quad \text{with} \quad C_t \in [0,1]Ct=Πt⋅(1−St)withCt∈[0,1] These quantities define a low-dimensional “energy field” describing the local structural integrity of the system. 4. SAFE / BLOCK Regime Classification Each time step is classified deterministically: SAFEt={1if Πt≥0.45∧St≤0.40∧Et≥00otherwise\text{SAFE}_t = \begin{cases} 1 & \text{if } \Pi_t \ge 0.45 \land S_t \le 0.40 \land E_t \ge 0 \\ 0 & \text{otherwise} \end{cases}SAFEt={10if Πt≥0.45∧St≤0.40∧Et≥0otherwise Observations not satisfying these constraints are labeled BLOCK. Importantly, BLOCK states are not errors; they represent periods of structural instability or regime transition where exposure is intentionally suppressed. 5. Elite SAFE Identification An Elite SAFE subset is defined for enterprise-grade filtering: Πt≥Q90(Π),St≤Q10(S),Ct≥median(C)\Pi_t \ge Q_{90}(\Pi), \quad S_t \le Q_{10}(S), \quad C_t \ge \mathrm{median}(C)Πt≥Q90(Π),St≤Q10(S),Ct≥median(C) Elite SAFE states represent rare, high-confidence structural alignment. 6. Regime Transitions and SAFE Streaks Regime transitions are detected via first-order state changes: Tt=I(decisiont≠decisiont−1)T_t = \mathbb{I}(\text{decision}_t \ne \text{decision}_{t-1})Tt=I(decisiont=decisiont−1) SAFE streaks are computed as the cumulative count of consecutive SAFE states. These quantities characterize regime durability and instability frequency. 7. Cross-Asset Integrity Correlation For multi-asset inputs, an integrity correlation matrix is constructed using the Pearson correlation of energy balance time series across assets. This reveals synchronized integrity failures or resilience clusters without relying on price correlation. 8. Benchmark Metrics Each asset is summarized by SAFE rate, Elite SAFE rate, mean persistence, mean stress, mean energy balance, and a composite Integrity Rank Score: IRS=E[SAFE]⋅E[Π]⋅(1−E[S])\text{IRS} = \mathbb{E}[\text{SAFE}] \cdot \mathbb{E}[\Pi] \cdot (1 - \mathbb{E}[S])IRS=E[SAFE]⋅E[Π]⋅(1−E[S]) II. SAFE-Universe Daily Report (Design Spec) This is the client-facing artifact. Page 1 — Executive Summary Asset name SAFE rate (last 30 / 90 / full sample) Current regime: SAFE or BLOCK Current SAFE streak length Integrity Rank Score percentile Page 2 — Regime Timeline Price chart (greyed) SAFE periods highlighted (green bands) Regime transition markers (vertical red lines) Page 3 — Energy Field Diagnostics Persistence vs Stress scatter Energy balance over time Regime confidence curve Page 4 — Risk Suppression Evidence Cumulative return (SAFE-only vs full exposure) Drawdown comparison Time spent BLOCK (explicitly framed as protection) Page 5 — Cross-Asset Context (Enterprise) Integrity correlation heatmap Cluster annotations Synchronized failure alerts