Governed portfolio intelligence for unstable regimes

ATLAS

A regime-aware decision system that measures structural state, tactical instability, confidence, disagreement, portfolio risk, and allocation constraints within one auditable framework.

Designed to know when to allocate, when to reduce risk, and when not to act.

Try the Demo Read the Technical Specification

Regime intelligence

Structural regime, transition geometry, velocity, acceleration, and persistence over macro-financial state space.

Tactical instability

Flip risk, confidence decay, disagreement, and fast reversible controls that restrict exposure without redefining regime.

SHELOB allocation

Governed portfolio and sleeve allocation under uncertainty, constraints, and explicit decision authority.

AI briefings

Machine-readable briefing selection and governed narrative generation from authoritative system state.

Audit and governance

Model-change audit, pipeline lineage, provenance, freshness controls, reason codes, and operator authority.

Abstention

Explicit transitional and indeterminate states with explainable triggers, episode lifecycle, and outcome assessment.

Self-Service Demo

Explore ATLAS with sample portfolio data in a sandboxed demo environment. No account required. Demo sessions use delayed market data and include no live portfolio information.

Launch Demo →

What ATLAS Is

ATLAS is decision-support infrastructure for portfolio governance and macro-regime monitoring. It is used to manage exposure to uncertainty in global markets.

Rather than forecasting short-term prices, ATLAS measures whether the current macro-financial environment is stable, transitional, or indeterminate; whether confidence in that assessment is rising or decaying; and whether the resulting posture should be to allocate, reduce, or abstain.

Regime-aware. The structural regime is a slow, persistent classification of macro conditions, estimated on a declared calibration window and held out from live evaluation.
Uncertainty-aware. Confidence, flip risk, score disagreement, and data freshness are explicit inputs to the admissibility map, not afterthoughts.
Governed. Every artifact carries schema, keys, dates, provenance, and freshness state. Overrides require operator identity and reason codes.
Abstention-first. When evidence is insufficient or unstable, the legitimate output is to reduce or abstain. Abstention is tracked, attributed, and evaluated after the fact.

What ATLAS Is Not

ATLAS is not a trading bot or execution engine.
ATLAS is not a short-term market-prediction system.
ATLAS is not a signal-stacking or black-box alpha platform.
ATLAS does not convert every analytical result into a trade.

The system provides a structured, auditable framework for evaluating macroeconomic conditions and portfolio alignment across regimes. Analytical strength does not automatically create operational authority.

SHELOB: Governed Allocation Under Uncertainty

SHELOB is ATLAS's governed allocation and portfolio-construction capability. It combines portfolio mathematics with structural regime state, tactical instability, sleeve constraints, optionality requirements, and explicit decision authority.

More than an optimizer. The live allocation baseline (TILT) is governed and produced by the pipeline. Shadow optimizer families (MVO, Black-Litterman, equal-weight) run as diagnostics and counterfactuals, not as live instructions.
Regime- and confidence-aware. Target changes are gated by abstention state, tactical instability, and portfolio constraints. An unstable or indeterminate state can block or scale a proposed adjustment.
Constraint-bound. Sleeve limits, single-position caps, liquidity-tier scalers, and cash-absorption rules are enforced before any target is emitted.
Descriptive outputs. SHELOB surfaces explain weights, availability, and readiness; the ANDURIL allocation overlay returns an explanatory permission and reason stack, not trade instructions.
Fail-closed. Missing inputs, stale data, unresolved disagreement, or an inactive governance posture routes the output to a restricted or informational state.

Read the SHELOB formalization in the Technical Specification →

AI Briefings: Governed Narrative from Machine-Readable State

ATLAS exposes its governed state through a machine-readable briefing catalog. Structured requests are resolved to approved briefing types, populated from authoritative artifacts, checked against policy and entitlement constraints, and rendered as human-readable analysis.

Catalog-driven. Briefing types, required payload fields, and policy boundaries are registered in a closed vocabulary before any prose is generated.
Parser-based. A structured adapter resolves requests to the correct briefing builder, validates inputs, and enforces guardrails.
Governed context. The AI layer reads pre-computed artifacts—regime state, tactical instability, portfolio health, optionality, governance status—not live market feeds or internal paths.
Policy-checked. Forbidden intents, trade-generation language, and allocation authority are blocked by construction.
Same facts, multiple surfaces. The same governed context can produce operator briefs, sidebar narratives, audit appendices, and research diagnostics.

The AI layer explains governed system state; it does not create the state.

Advanced Capabilities

Measure

Structural and tactical horizon separation
Cross-asset score trajectory and geometry
State velocity, acceleration, and persistence
Confidence decay and transition risk
Cross-model disagreement
Portfolio and sleeve health

Decide

Allocate / Reduce / Abstain posture map
Abstention episode lifecycle
SHELOB governed allocation baseline
Shadow optimizer counterfactuals
Optionality and protection planning
Stress and risk analytics

Govern

Tenant-aware routing and operator scope
Reason-coded overrides with expiry
Promotion committee and candidate evaluation
Model-change reader and changelog
Research-to-production separation
Production / beta / shadow boundary

Explain

Machine-readable AI briefing catalog
Structured parser and context contract
Layered decision explanation
Pipeline manifests and provenance
Freshness and staleness labels
Truthfulness contract per surface

Why Trust ATLAS

Every decision has a lineage

Governed source data and versioned analytical artifacts
Explicit freshness and observability labels
Model, schema, and stage-definition versions
Decomposed decision logic and reason-coded restrictions
Operator-attributed overrides with provenance
Reproducible pipeline runs and run manifests

Research does not equal authority

Lab, shadow, validation, approval, and production are separate states
Inconclusive and falsified results remain visible
No new model receives decision authority by default
Promotion is an explicit, operator-gated event

AI explains; governance decides

Machine-readable briefing parser and catalog
Governed context populated from authoritative artifacts
Policy and entitlement checks before rendering
No independent allocation or trading authority

Development Status

Production · governed Beta · canary Shadow · diagnostics

ATLAS runs in production for governed regime monitoring, portfolio state, and operator-isolated decision tooling. The beta environment hosts canary surfaces and experimental capabilities. Shadow and diagnostic outputs are labeled and do not carry decision authority.

Pricing

For pricing inquiries, institutional licensing, and operator onboarding, please visit the Contact page.

Updates

Release notes and development milestones

May 2026 Production

Production Update — Decision Ledger, Surface Honesty & Calibrated Caution

A production update is live at app.atlas-portal.ca. The release sharpens how ATLAS represents what it knows, what it does not know, and how the platform talks to operators about both.

Unified decision ledger. Decisions, realized economics, regime context, and forward evidence now live behind a single auditable surface, so that the end-to-end story of any decision — from input artifact to outcome — can be reviewed in one place. The unified ledger is a measurement and audit reference; it has no allocation authority of its own.
Surface-level truthfulness. Decision-facing panels now declare their evidence basis explicitly, indicating whether a view is backed by live governance, a shadow replay, a diagnostic model, or insufficient evidence. Missing or stale inputs surface as labeled states rather than silent fallbacks.
Calibrated caution. The platform now maps measurement-uncertainty states to a graduated, minimal-response policy. Where the system cannot yet make a confident statement, it says so, and the appropriate degree of caution is recorded against the abstention ledger for outcome evaluation.
Research discipline for new strategy contexts. Candidate trend and momentum strategy contexts are now tracked through a formal evidence dossier — forward evidence, reconstructed historical evidence, and live-portfolio context — before any promotion into governance. Authorization gates are explicit and time-bound; nothing promotes itself by default.
Adversarial review of decision-facing surfaces. A broad audit was run across the platform’s advisory and shadow surfaces, looking specifically for ways a panel could imply a claim it could not back. Findings were closed before the release shipped.
Operator-visible pipeline state. Pipeline telemetry, run health, and tenant-aware run identifiers are now consistently visible across observability surfaces, so operators can tell at a glance whether what they are reading is current, partial, or stale.

April 2026 Production

Production Update — Multi-Operator Governance, Pipeline Reliability & Structural Forecasting

A major production update is now live at app.atlas-portal.ca. The release brings ATLAS’s multitenant governance posture, pipeline reliability, and structural forecasting capabilities to production grade.

Multi-operator governance. Operator and sleeve identity now flow end-to-end through the platform. Overrides, audit trails, entitlements, and portfolio visibility are isolated by operator context, so each operator sees and acts on only their own scope.
Structural forecasting in production. Regime flip-probability estimation, persistence modeling, and hazard-rate diagnostics are now operational in production across multiple forward horizons. Forecasts are surfaced as diagnostic context, separated from exposure policy.
Forecast calibration. A dedicated calibration artifact now measures how well structural forecasts have matched realized outcomes across horizons, so the platform can be honest about where its forecasts have been reliable and where they have not.
Fail-fast pipeline. The pipeline now validates governance readiness, configuration, and stage prerequisites before expensive computation begins. Problems surface immediately at startup rather than late in a run.
One source of truth for abstention. Abstention state was consolidated behind a single authoritative source feeding both the UI and portfolio gating, eliminating the possibility of disagreement between views.
More robust portfolio ingest. Multi-file upload handling, timestamp safety, and collation were hardened, reducing operator friction during portfolio refreshes.
Forecast observatory. Structural-transition surfaces, horizon-specific transition probabilities, and forecast diagnostics now render consistently across the operator UI.
Abstention economics. Regime-conditioned breakdowns and the abstention economics panel were restored, including episode outcome classification and false-caution tracking by regime.
Sleeve-scoped optionality. The optionality view is now strictly scoped to the selected sleeve, with no silent fallback to an aggregate view when sleeve context is missing.
Production infrastructure. Entitlements infrastructure was modernized with automated migration and operator backfill, provenance guarding was added for containerized runs, and deployment tooling was extended to support the multitenant production surface.

March 26, 2026 Beta

Beta v2 — Regime-Conditioned Model, GitPortfolio & Forecasting

A new beta version is now available at beta.atlas-portal.ca incorporating significant new capabilities:

Regime-Conditioned Model — Portfolio analytics and risk assessments are conditioned on the latest classified macro regime, with its as-of date.
GitPortfolio — Live portfolio replay and counterfactual analysis. Track how portfolio decisions would have played out under alternative regime paths and allocation strategies.
Forecasting — Forward-looking regime-transition probability modeling and macro-forecasting tools for scenario planning and exposure management.

March 16, 2026 Site

Site Launch — Cross-Asset Regime Model

ATLAS Portal is live. The initial release introduces the core cross-asset regime classification model — a system for detecting structural regime shifts, systemic stress, and instability across global financial markets.

Cross-asset regime classification and confidence scoring
Multi-signal macro stress monitoring
Regime flip-risk estimation and transition probability modeling
Portfolio exposure alignment diagnostics
Audit logging and governance tooling built toward an institutional standard

Technical Specification

Formal model objects, governance, and admissible decision rules

1. Decision-Theoretic Objective

ATLAS is specified as a tuple of measurable and governed objects. Every component is defined in the sections that follow with its domain, role, and admissible use.

\mathcal{A}_{\text{ATLAS}} \;=\; \big(\mathcal{X},\, \mathcal{D},\, \mathcal{G},\, \mathcal{S},\, \mathcal{T},\, \mathcal{C},\, \mathcal{F},\, \Pi,\, \mathcal{V}\big)

\(\mathcal{X}\) — observable state space (cross-asset, regime-scoring inputs)
\(\mathcal{D}\) — governed artifact space (schema-validated, provenance-tracked outputs)
\(\mathcal{G}\) — governance / data-quality state space (admissibility of \(\mathcal{D}\))
\(\mathcal{S}\) — structural regime state space (finite, slow, persistent)
\(\mathcal{T}\) — tactical instability state space \(\{\text{Stable},\, \text{Transitional},\, \text{Unstable}\}\)
\(\mathcal{C}\) — confidence / boundary-distance space
\(\mathcal{F}\) — flip-risk / transition-pressure space
\(\Pi\) — admissible policy map (Section 14)
\(\mathcal{V}\) — validation operator family (Section 21)

ATLAS is a measurement and decision-governance system. It is not a return forecaster, an unconstrained optimizer, or an execution engine.

The operative action is a function of structural state, tactical instability, portfolio state, uncertainty/validity, governance state, and authorized operator overlay:

a_t \;=\; D\!\left(S_t,\; T_t,\; P_t,\; U_t,\; G_t,\; O_t\right)

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

The action space is \(\{\text{increase},\, \text{maintain},\, \text{reduce},\, \text{hedge},\, \text{abstain}\}\). In the current implementation the live posture set is \(\{\mathrm{Allocate},\, \mathrm{Reduce},\, \mathrm{Abstain}\}\). Decision authority follows the lane precedence

\text{FRESHNESS} \;\to\; \text{ABSTENTION} \;\to\; \text{TACTICAL_INSTABILITY} \;\to\; \text{BEAR_CONTEXT} \;\to\; \text{EXPOSURE_POLICY} \;\to\; \text{BASELINE}

Protected-parameter convention. The mathematical structure is disclosed. Production coefficients, thresholds, and calibration constants are withheld to preserve model integrity, operational security, and proprietary implementation detail. Where coefficients or thresholds are sensitive, the symbol \(\theta_{\text{protected}}\) is used.

1.1 Standing assumptions

All random variables in this document are defined on a fixed probability space \((\Omega, \mathcal{H}, \mathbb{P})\) equipped with the discrete-time filtration \((\mathcal{F}_t)_{t \in \mathbb{Z}_{\ge 0}}\) introduced in Section 3. Statements of equality involving random variables are understood \(\mathbb{P}\)-almost surely; statements of equality involving deterministic objects are absolute.

A1 (Finite latent state). The structural regime takes values in a finite set, \(|\mathcal{S}| < \infty\), and evolves as a Markov chain with transition matrix \(P\) (Section 9).
A2 (Information adaptation). All decision-time objects — \(S_t,\, T_t,\, C_t,\, F_t,\, D_t^{\,\text{score}},\, \pi_t\) — are \(\mathcal{F}_t\)-measurable.
A3 (Fail-closed tactical layer). Inputs that are NA-driven or whose governing artifacts are inadmissible cannot resolve to \(T_t = \text{Stable}\) (Section 5).
A4 (Deterministic validation). Each validator \(V_j\) is a deterministic function on artifact contracts (Section 21).
A5 (Closed-set authorization). The authorization predicate \(\operatorname{Auth}(o, s, r)\) is two-valued (Section 16).

2. Structural State Model

The slow structural state vector is

S_t \;=\; \big(G_t,\; I_t,\; L_t\big)^{\!T}

PRODUCTION_DEFINITION

where \(G_t\) is growth, \(I_t\) is inflation, and \(L_t\) is liquidity / financial-conditions state. Let \(Z_t = (Z_{1,t}, \ldots, Z_{k,t})\) denote a low-dimensional vector of governed scores. Then the structural regime label is a projection

f_S \,:\, \textstyle\bigcup_{T \ge 1} (\mathbb{R}^k)^T \,\times\, \Theta_S \,\times\, \mathcal{G} \;\longrightarrow\; \mathcal{S}, \qquad R_t \;=\; R(S_t) \;=\; f_S\!\big(Z_{1:t},\, \Theta_S,\, G_t\big), \qquad |\mathcal{S}| < \infty

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

\(\Theta_S\) denotes the governed structural parameters, including normalizations, sign conventions, classification thresholds, and persistence rules. The categorical regime label \(R_t\) is a downstream projection of the continuous state \(S_t\); the full state is not collapsed to the label.

Structural-regime estimation is in the regime-switching tradition (Hamilton, 1989), in which the latent state evolves as a Markov chain with transition matrix

P \;\in\; [0,\, 1]^{|\mathcal{S}| \times |\mathcal{S}|}, \qquad P_{ij} \;=\; \mathbb{P}\!\big(S_{t+1} = j \,\big|\, S_t = i\big), \qquad \sum_{j} P_{ij} \;=\; 1 \;\;\forall\, i

PRODUCTION_DEFINITION

The diagonal \(P_{ii}\) is the one-step self-persistence of regime \(i\); the off-diagonal mass governs reachability between regimes. Structural regime is not tactical instability:

S_t \;\not\equiv\; T_t, \qquad \mathbb{P}(S_{t+h} = S_t) \;\gg\; \mathbb{P}(T_{t+h} = T_t)

3. Alternative Embeddings

The structural state may be represented in several embeddings. Each has a declared status and decision authority.

Embedding	Coordinates	Status	Authority
\(E_{\text{GIL}}\)	\((G_t, I_t, L_t)\)	`PRODUCTION_DEFINITION`	Live input to regime score and classification
\(E_{\text{GILR}}\)	\((G_t, I_t, L_t)\) plus visual time parameter \(\tau\) for helix plotting	`PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS`	Topology diagnostics only
Higher-dimensional research embeddings	Macro + credit + liquidity + volatility axes	`RESEARCH_MEASUREMENT`	Research; not policy-wired

E_{\text{GIL}}(t) \;=\; \big(G_t,\; I_t,\; L_t\big), \qquad E_{\text{GILR}}(t) \;=\; \big(G_t,\; I_t,\; L_t,\; \tau_t\big)

PRODUCTION_DEFINITION RESEARCH_MEASUREMENT

4. State-Space Metric

All geometric quantities are defined with respect to a declared metric. The distance function is

d_M(x, y) \;=\; \sqrt{(x - y)^{T} M (x - y)}

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

\(M\) may define Euclidean, scaled-Euclidean, whitened, covariance-adjusted, or Mahalanobis geometry. The exact \(M\) matrix and axis scales are artifact-specific and protected. The metric must be declared before speed, curvature, path length, or basin distance are interpreted.

5. Kinematics

State velocity and acceleration are defined with respect to the visual time parameter \(\tau\):

V_t \;=\; \frac{dS_t}{d\tau}, \qquad A_t \;=\; \frac{d^{2}S_t}{d\tau^{2}}

PRODUCTION_DEFINITION

Discrete forms used in production are

\Delta S_t \;=\; S_t - S_{t-1}, \qquad \Delta^{2} S_t \;=\; \Delta S_t - \Delta S_{t-1}

and the metric norms are

|V_t|_M \;=\; \sqrt{V_t^{T} M V_t}, \qquad |A_t|_M \;=\; \sqrt{A_t^{T} M A_t}

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

Smoothing windows, finite-difference weights, and minimum-history requirements are governed per artifact.

6. Geometry

Curvature, torsion, directional stability, and path-length quantities are computed on the declared embedding and metric.

\kappa(\tau) \;=\; \frac{|S'(\tau) \times S''(\tau)|}{|S'(\tau)|^{3}}

\mathcal{T}(\tau) \;=\; \frac{\det(S',\, S'',\, S''')}{|S' \times S''|^{2}}

\cos \phi_t \;=\; \frac{V_t^{T} V_{t-1}}{|V_t|\, |V_{t-1}|}

RESEARCH_MEASUREMENT PRODUCTION_DEFINITION

Path geometry over a window \([a, b]\) is

L_{a:b} \;=\; \sum_{t=a+1}^{b} d_M(S_t, S_{t-1}), \qquad D_{a:b} \;=\; d_M(S_b, S_a), \qquad Q_{a:b} \;=\; \frac{L_{a:b}}{D_{a:b}}

RESEARCH_MEASUREMENT

These are geometric descriptors; not all have decision authority. Smoothing method, singular-case handling, and minimum-window length are protected.

7. Regime Centroids and Basin Structure

For each structural regime \(r\), the centroid is

\mu_r \;=\; \mathbb{E}[S_t \mid R_t = r]

The expanding centroid is

\mu_{r,t}^{\text{expanding}} \;=\; \frac{\sum_{u \le t} S_u \, \mathbf{1}(R_u = r)}{\sum_{u \le t} \mathbf{1}(R_u = r)}

and the centroid distance is

d_{r,t} \;=\; d_M(S_t, \mu_r)

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

Centroid calculation mode (retrospective, frozen, expanding, rolling) and basin thresholds are artifact-specific and protected. The public representation discloses the definition and the fit mode per artifact.

8. Boundaries and Transition Surfaces

The quadrant margin is

m_t \;=\; \min\!\left(|G_t - \theta_G|,\; |I_t - \theta_I|\right)

General boundary surfaces are written

B_{ij}(S) \;=\; 0

Boundary distance, normal velocity, and normal acceleration are

d_B(S_t) \;=\; \inf_{z \in B} d_M(S_t, z), \qquad v_t^{\perp} \;=\; V_t^{T} n_B(S_t), \qquad a_t^{\perp} \;=\; A_t^{T} n_B(S_t)

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

Thresholds \(\theta_G, \theta_I\), boundary surface definitions, and normal vectors are protected. Boundary proximity is necessary but not sufficient; direction and acceleration matter.

9. Transition Matrices and Entropy

Transition probabilities are defined by

p_{ij} \;=\; \Pr(R_t = j \mid R_{t-1} = i)

with empirical estimate

\hat{p}_{ij} \;=\; \frac{N_{ij}}{\sum_k N_{ik}}

PRODUCTION_DEFINITION

Four entropy forms are distinguished and are not collapsed into a single “transition entropy”:

H_{\text{state}} \;=\; -\sum_i \pi_i \log \pi_i

H_{\text{pair}} \;=\; -\sum_{i,j} q_{ij} \log q_{ij}

H(R_t \mid R_{t-1} = i) \;=\; -\sum_j p_{ij} \log p_{ij}

H_{\text{rate}} \;=\; -\sum_i \pi_i \sum_j p_{ij} \log p_{ij}

PRODUCTION_DEFINITION

Count minimums, smoothing pseudocounts, and horizon windows are protected.

10. Confidence

Confidence is proximity-to-boundary adjusted for persistence, uncertainty, disagreement, and data quality; it is not certainty. The live confidence object uses the score-margin form

C_t \;=\; \min_{s \neq s'} \big|\, M_s(Z_t) - M_{s'}(Z_t) \,\big| \;\in\; [0, \infty)

PRODUCTION_DEFINITION

A geometric distance formulation

d(Z_t, \Gamma) \;=\; \inf_{g \in \Gamma} \|Z_t - g\|

is a SHADOW research diagnostic; it does not gate policy. In both formulations \(C_t \downarrow 0\) as \(Z_t \to \Gamma\).

Confidence is decomposed as

C_t \;=\; C\!\left(d_B(S_t),\; P_t,\; U_t,\; D_t,\; Q_t\right)

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

Confidence change and the confidence shock are

\Delta C_t \;=\; C_t - C_{t-h}, \qquad Z_{\Delta C, t} \;=\; \frac{\Delta C_t - \mu_{\Delta C}}{\sigma_{\Delta C}}

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

The functional form and the calibration of \(\mu_{\Delta C}\) and \(\sigma_{\Delta C}\) are protected.

11. Flip Risk and Transition Pressure

Flip risk is a transition-risk measure, not a directional market forecast. It is decomposed as

F_t \;=\; F\!\left(d_B(S_t),\; v_t^{\perp},\; a_t^{\perp},\; D_t,\; U_t,\; P_t;\; \theta_{\text{protected}}\right)

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

Flip-risk velocity and acceleration are

\Delta F_t \;=\; F_t - F_{t-1}, \qquad \Delta^{2} F_t \;=\; \Delta F_t - \Delta F_{t-1}

PRODUCTION_DEFINITION

Three properties hold by construction: (i) static-level exceedance alone is not sufficient for elevated transition pressure; (ii) \(\Delta^{2} F_t\) can be informative even when \(F_t\) has not crossed a static threshold; (iii) short or incomplete histories are labeled rather than imputed to Stable.

12. Disagreement

Model disagreement (dispersion) across \(K\) scores or models is

D_t^{\text{model}} \;=\; \sqrt{\frac{1}{K-1} \sum_{k=1}^{K} \big(z_{k,t} - \bar{z}_t\big)^{2}}

Pairwise disagreement is

D_t^{\text{pair}} \;=\; \frac{2}{K(K-1)} \sum_{i<j} |z_{i,t} - z_{j,t}|

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

The set of models/scores \(K\) and the normalization method are protected. Score disagreement as the range across structural-score axes is the live form:

D_t^{\text{score}} \;=\; \max_{1 \le i \le k} Z_{i,t} \;-\; \min_{1 \le i \le k} Z_{i,t}

PRODUCTION_DEFINITION

Surface disagreement, the indicator that two classification surfaces assign different structural labels, is measured but not wired into the live admissibility map. It remains a research track (WS7).

13. Meta-Regimes

The meta-regime space is

M \;\in\; \{\text{STABLE},\; \text{TRANSITIONAL},\; \text{INDETERMINATE}\}

PRODUCTION_DEFINITION

Meta-regime	Definition
`TRANSITIONAL`	Coherent movement (\(\|V_t\| > 0\)) but destination not yet persistent.
`INDETERMINATE`	Caused by \(D_t > \theta_D\), \(Q_t \in \{\text{STALE}, \text{MISSING}, \text{SCHEMA_INVALID}\}\), or excessive estimator sensitivity.

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

Threshold \(\theta_D\) and persistence requirements are protected. Meta-regime labels are explicit states, not error conditions.

14. Abstention

The policy map is

\pi_t \,:\, \Omega_t \;\longrightarrow\; \mathcal{U} \cup \{\varnothing\}

where \(\mathcal{U}\) is the set of admissible non-null exposure actions and \(\varnothing\) denotes abstention. In the current implementation \(\mathcal{U} = \{\mathrm{Allocate},\, \mathrm{Reduce}\}\).

The abstention gate is

A_t^{\text{abstain}} \;=\; \mathbf{1}\!\left[\, g_C(C_t) \;\lor\; g_F(F_t) \;\lor\; g_D(D_t) \;\lor\; g_Q(Q_t) \;\lor\; g_G(G_t) \,\right]

PRODUCTION_DEFINITION

Triggers include confidence shock, confidence decay, flip-risk acceleration, score/model disagreement, stale/invalid data, unresolved transition, governance restriction, and operator hold. Responses include gross reduction, capital preservation, optionality retention, delayed commitment, and operator review.

An abstention episode is a maximal interval over which \(\pi_t = \varnothing\), paired with a post-hoc outcome label at a pre-registered forward horizon:

\mathcal{E}^{\text{abst}} \;=\; \left\{(t_{\text{enter}},\, t_{\text{exit}},\, \omega) \;:\; \pi_t = \varnothing \;\; \forall\, t \in [t_{\text{enter}}, t_{\text{exit}}),\; \omega \in \{\mathrm{JC},\, \mathrm{FC},\, \mathrm{IN}\}\right\}

Justified Caution (JC). Forward drawdown exceeded tolerance; abstaining avoided realized loss.
False Caution (FC). Forward drawdown remained within tolerance; abstaining was unnecessary.
Inconclusive (IN). Insufficient forward data or intermediate outcome.

Abstention follows the reject-option framework of Chow (1970) and its extension to selective classification in El-Yaniv & Wiener (2010).

15. Stress and Risk Mathematics

Portfolio return and variance are

r_{p,t} \;=\; w_t^{T} r_t, \qquad \sigma_p^{2} \;=\; w^{T} \Sigma w

PRODUCTION_DEFINITION

Marginal and component contributions to risk are

\text{MCR}_i \;=\; \frac{(\Sigma w)_i}{\sqrt{w^{T} \Sigma w}}, \qquad \text{CR}_i \;=\; w_i \, \text{MCR}_i

PRODUCTION_DEFINITION

Tracking error, drawdown, VaR, and Expected Shortfall are

\text{TE} \;=\; \sqrt{(w - w_b)^{T} \Sigma (w - w_b)}

\text{DD}_t \;=\; 1 - \frac{V_t}{\max_{u \le t} V_u}

\text{VaR}_{\alpha}(L) \;=\; \inf\{ \ell : \Pr(L \le \ell) \ge \alpha \}

\text{ES}_{\alpha}(L) \;=\; \mathbb{E}[L \mid L \ge \text{VaR}_{\alpha}(L)]

PRODUCTION_DEFINITION CONCEPTUAL_DECOMPOSITION

Variance, MCR, tracking error, and drawdown are live. VaR and ES are conceptual decompositions unless a live artifact proves otherwise.

The live stress-cooked pressure is

\text{pressure}_t \;=\; \max(z_{\text{VIX},t},\; z_{\text{credit HY},t},\; z_{\text{NFCI},t})

with activation \(\text{stress_active}_t = \text{pressure}_t > \text{stress}_z\) where \(\text{stress}_z = 1.0\).

PRODUCTION_DEFINITION

16. Portfolio and Sleeve Health

Constraint headroom is

h_{j,t} \;=\; b_j - A_j w_t

and normalized headroom is

\tilde{h}_{j,t} \;=\; \frac{b_j - A_j w_t}{s_j}

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

Health dimensions include concentration, diversification, risk contribution, exposure drift, sleeve budget utilization, optionality coverage, hedge coverage, liquidity, and stale holdings. Limits \(b_j\), scales \(s_j\), sleeve definitions, and liquidity thresholds are protected. Health is a multi-dimensional constraint and coverage assessment, not a single score.

17. SHELOB

SHELOB is the governed allocation and portfolio-construction layer. The general optimization form is

w_t^{*} \;=\; \arg\min_{w \in \mathcal{W}_t} \left[ \tfrac{1}{2}\, w^{T} \Sigma_t w \;-\; \lambda_t \, \mu_t^{T} w \;+\; P_{\text{turnover}}(w, w_{t-1}) \;+\; P_{\text{concentration}}(w) \;+\; P_{\text{optionality}}(w) \right]

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

subject to

\mathbf{1}^{T} w = 1, \qquad l_i \le w_i \le u_i, \qquad l_g \le \sum_{i \in g} w_i \le u_g, \qquad \|w\|_1 \le G_{\max}, \qquad \|w - w_{t-1}\|_1 \le T_{\max}

\text{CR}_g(w) \le B_g, \qquad (w - w_b)^{T} \Sigma (w - w_b) \le \tau^{2}

and the regime/confidence feasible set

\mathcal{W}_t \;=\; \mathcal{W}(S_t,\; T_t,\; C_t,\; A_t^{\text{abstain}},\; G_t)

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

\(\lambda_t\), penalty weights, \(G_{\max}\), \(T_{\max}\), \(B_g\), \(\tau^{2}\), and sleeve limits are protected. SHELOB governs the feasible allocation space; candidate, governed, and operative weights are separated.

Infeasibility reason codes include INFEASIBLE_CONSTRAINT_SET, MISSING_RISK_MODEL, STALE_INPUT, UNAUTHORIZED_CONTEXT, INSUFFICIENT_HISTORY, and SOLVER_FAILURE.

18. Black-Litterman

Black-Litterman is one candidate within SHELOB, not the sole allocation method. The implied equilibrium return is

\Pi \;=\; \delta \, \Sigma \, w_{\text{mkt}}

and the posterior mean is

\mu_{\text{BL}} \;=\; \left[ (\tau \Sigma)^{-1} + P^{T} \Omega^{-1} P \right]^{-1} \left[ (\tau \Sigma)^{-1} \Pi + P^{T} \Omega^{-1} q \right]

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

\(\delta\), \(\tau\), \(\Omega\), view matrix \(P\), view vector \(q\), and view confidences are protected. Views are governed; BL is a shadow/governance candidate.

19. Optionality and Hedge Mathematics

A protection bundle at decision time \(t\) is a finite set of contracts

\mathcal{P}_t \;=\; \{(k_j,\; n_j,\; c_j) \;:\; j = 1, \ldots, J\}, \qquad k_1 < k_2 < \cdots < k_J, \qquad n_j \in \mathbb{Z}_{\ge 0}

with strike grid \(\{k_j\}\), contract counts \(\{n_j\}\), and per-contract proxy premia \(\{c_j\}\). The coverage ratio is

\text{Coverage} \;=\; \frac{\text{protected_notional}}{\text{eligible_NAV}}

the planning budget is

B_t \;=\; \rho_t \, \text{NAV}_t^{\text{eligible}}

and the put payoff is

\Pi_{\text{put}}(S_T) \;=\; \max(K - S_T,\; 0) - p

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

\(\rho_t\), strike ladders, live positions, budget limits, and tenor targets are protected. Optionality is planned, sized, and reconciled; proxies are labeled.

The protection-cost proxy is

P_t^{\text{proxy}} \;=\; \sum_{j=1}^{J} n_j \, c_j^{(t_0)}

labeled ESTIMATE_PROXY, where \(c_j^{(t_0)}\) is a static proxy premium at snapshot \(t_0\), not the real-time mid-market price. Real option-chain pricing is DEFERRED.

20. Model-Change Auditing

Model changes are governed events. Output difference is

\Delta y_t \;=\; y_t^{(1)} - y_t^{(0)}

Compared deltas include

\Delta S_t,\; \Delta C_t,\; \Delta F_t,\; \Delta D_t,\; \Delta w_t,\; \Delta A_t^{\text{abstain}}

Regime label change is

\mathbf{1}\!\left[ R_t^{(1)} \neq R_t^{(0)} \right]

Allocation distance, risk difference, and constraint change are

\Delta_w \;=\; \|w_t^{(1)} - w_t^{(0)}\|_1, \qquad \Delta_\sigma \;=\; \sqrt{w^{(1)T} \Sigma w^{(1)}} - \sqrt{w^{(0)T} \Sigma w^{(0)}}, \qquad \Delta c_{j,t} \;=\; c_{j,t}^{(1)} - c_{j,t}^{(0)}

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

Attribution is conceptually decomposed as

\Delta y \;=\; \Delta_{\text{data}} \;+\; \Delta_{\text{revision}} \;+\; \Delta_{\text{feature}} \;+\; \Delta_{\text{model}} \;+\; \Delta_{\text{parameter}} \;+\; \Delta_{\text{policy}} \;+\; \Delta_{\text{override}}

CONCEPTUAL_DECOMPOSITION

Change classes include NO_SEMANTIC_CHANGE, DISPLAY_ONLY, SCHEMA_CHANGE, FEATURE_CHANGE, PARAMETER_CHANGE, MODEL_CHANGE, DECISION_POLICY_CHANGE, and GOVERNANCE_CHANGE. Promotion states include PROPOSED, LAB, SHADOW, VALIDATED, INCONCLUSIVE, FALSIFIED, APPROVED, PROMOTED, and RETIRED.

21. Statistical Validation Framework

Validation metrics are defined on pre-registered horizons and held-out windows. False-alarm rate, miss rate, precision, and recall are

\text{FAR} \;=\; \frac{\text{FP}}{\text{FP} + \text{TN}}, \qquad \text{MR} \;=\; \frac{\text{FN}}{\text{FN} + \text{TP}}

\text{Precision} \;=\; \frac{\text{TP}}{\text{TP} + \text{FP}}, \qquad \text{Recall} \;=\; \frac{\text{TP}}{\text{TP} + \text{FN}}

Brier and log scores are

\text{BS} \;=\; \frac{1}{N} \sum (p_t - y_t)^{2}

\text{LS} \;=\; -\frac{1}{N} \sum \left[ y_t \log p_t + (1 - y_t) \log(1 - p_t) \right]

The permutation p-value is

p_{\text{perm}} \;=\; \frac{1 + \sum_{b=1}^{B} \mathbf{1}(T_b^{*} \ge T_{\text{obs}})}{B + 1}

VALIDATION_METHOD

Sensitivity dimensions include embedding, metric, derivative method, calibration window, data vintage, and event definition. \(B\), significance thresholds, and minimum evaluable sample are protected. Negative, inconclusive, unstable, and falsified outcomes remain valid.

22. Data Revisions and Vintage Integrity

Vintage notation distinguishes values by observation date and as-of vintage:

x_{t|v} \;=\; \text{value for period } t \text{ as known at vintage } v

The revision between vintages is

r_{t,v_1,v_2} \;=\; x_{t|v_2} - x_{t|v_1}

CONCEPTUAL_DECOMPOSITION

ATLAS distinguishes latest revised history, real-time vintage history, current incomplete observation, and last complete observation.

23. Freshness and Observability

Data age is

\text{age}_t \;=\; t_{\text{evaluation}} - t_{\text{source}}

Freshness state is

\mathcal{F}_t^{\text{data}} \;=\; F\!\left(\text{age}_t,\; \text{market_status},\; \text{expected_cadence},\; \text{completion_state}\right)

PRODUCTION_DEFINITION

States are \(\{\text{CURRENT},\; \text{CURRENT_DAY_INCOMPLETE},\; \text{STALE},\; \text{MISSING},\; \text{SCHEMA_INVALID},\; \text{UNOBSERVABLE}\}\). Truthfulness status is \(\{\text{AVAILABLE},\; \text{DEGRADED},\; \text{STALE},\; \text{UNAVAILABLE},\; \text{UNKNOWN}\}\) plus closed reason codes. Cadence thresholds and max stale days are protected. Missing data never implies stability; scientific status and data status are separate.

24. Pipeline Mathematics and Contracts

The transformation chain is

\mathcal{D}_0 \;\xrightarrow{f_1}\; \mathcal{D}_1 \;\xrightarrow{f_2}\; \cdots \;\xrightarrow{f_n}\; \mathcal{A}_n

PRODUCTION_DEFINITION

Each stage carries a contract: input schema, output schema, date basis, uniqueness keys, source hash, producer version, validation state, environment, tenant context, and artifact version. The run manifest is

\{\text{run_id},\; \text{code_version},\; \text{source_versions},\; \text{artifact_hashes},\; \text{validation_outcomes},\; \text{execution_environment}\}

PRODUCTION_DEFINITION

Absolute paths, run IDs, git/image digests, and tenant identifiers are protected. Derived analytics do not depend on UI state; the UI consumes governed artifacts.

24.1 Observation and artifact layer

Let \(t\) denote decision time and \(d\) an observation date. Let \(X_t \in \mathcal{X}\) denote the observable state vector and \(\mathcal{D}_t\) the set of artifacts available at \(t\):

\mathcal{D}_t \;=\; \{D_{1,t},\, D_{2,t},\, \ldots,\, D_{m,t}\}

For each artifact define its maximum observation date and lag:

d_i^{\max}(t) \;=\; \max\,\{ d : D_{i,t}(d) \text{ exists}\}, \qquad \ell_i(t) \;=\; t - d_i^{\max}(t)

Artifact state is a closed-set label

q_i(t) \;\in\; \{\mathrm{OK},\, \mathrm{STALE},\, \mathrm{DEGRADED},\, \mathrm{UNAVAILABLE},\, \mathrm{INSUFFICIENT}\}

and eligibility is

E(D_{i,t}) \;=\; \mathbf{1}\!\big\{ \mathrm{schema}(D_i)=1 \,\land\, \mathrm{keys}(D_i)=1 \,\land\, \mathrm{dates}(D_i)=1 \,\land\, q_i(t) \,\in\, \{\mathrm{OK},\, \mathrm{STALE},\, \mathrm{DEGRADED}\} \big\}

PRODUCTION_DEFINITION

The natural artifact filtration is

\mathcal{F}_t \;=\; \sigma\!\Big(\,\big\{\, D_{i,\,t}(d) \,:\, E(D_{i,\,t}) = 1,\;\; d \le t,\;\; i \in I_t\,\big\}\,\Big), \qquad \mathcal{F}_s \;\subseteq\; \mathcal{F}_t \quad (s \le t)

Stale-state truthfulness. A current-day-complete artifact has \(\ell_i(t) = 0\) and \(q_i(t) = \mathrm{OK}\); a latest-available artifact has \(\ell_i(t) \ge 0\) and \(q_i(t) \in \{\mathrm{OK}, \mathrm{STALE}, \mathrm{DEGRADED}\}\). The two are not the same object; the latter must carry its label. Absence of data is not evidence of stability.

25. Governance Mathematics

Authority is a function of entitlement, validity, freshness, research/production status, operator authorization, and execution context:

A_t \;=\; \mathcal{G}\!\left(E_t,\; V_t,\; F_t,\; R_t,\; O_t,\; X_t\right)

CONCEPTUAL_DECOMPOSITION

Authority states are

\{\text{INFORMATIONAL},\; \text{RESEARCH_ONLY},\; \text{SHADOW},\; \text{RESTRICTED},\; \text{ACTIONABLE},\; \text{OPERATOR_REQUIRED},\; \text{BLOCKED}\}

Permission severity is ordered

\text{NORMAL} \;<\; \text{CAUTION_RESTRICTED} \;<\; \text{OPTIONALITY_ONLY} \;<\; \text{DEFENSIVE_ONLY} \;<\; \text{DE_RISK_ONLY} \;<\; \text{NO_ALLOCATION_ADVICE}

PRODUCTION_DEFINITION

Authorization is a closed-set predicate

\operatorname{Auth}(o,\, s,\, r) \;\in\; \{0,\, 1\}

A request is valid only if

o \neq \varnothing \;\;\land\;\; s \in \mathcal{S}_o \;\;\land\;\; \operatorname{Auth}(o,\, s,\, r) = 1

PRODUCTION_DEFINITION

Entitlement mappings, operator IDs, tenant IDs, and approval boundaries are protected. Analytical strength does not automatically create operational authority; the system fails closed with no silent fallbacks.

25.1 Multitenancy and operator scope

The per-operator-sleeve filtration is

\mathcal{F}_t^{(o,\,s)} \;=\; \sigma\!\Big(\,\big\{\, D_{i,\,t}(d) \,:\, E(D_{i,\,t}) = 1,\;\; \mathrm{scope}(D_i) \in \{(o, s),\, (o, \varnothing)\},\;\; d \le t\,\big\}\,\Big)

PRODUCTION_DEFINITION

Cross-sleeve leakage is structurally prohibited. Reports, exports, overrides, governed artifacts, and promotion gates are scoped to \((o, s)\). Overrides carry actor identity, reason code, and expiry; they are never reinterpreted as structural state.

25.2 Policy separation

Four separations are enforced architecturally:

Measurement \(\neq\) policy. \(C_t, F_t, D_t^{\text{score}}\) are inputs to the admissibility map; they are not actions.
Policy \(\neq\) execution. \(\pi_t\) is a posture, not a trade. Execution is a separately scoped function gated by operator authorization.
Reporting \(\neq\) allocation authorization. Reportability does not imply \(\operatorname{Auth}(o,s,r)=1\).
Research \(\neq\) live governance. Shadow artifacts are \(\mathcal{F}_t\)-measurable but do not enter the domain of the admissibility map.
Summary \(\neq\) decision. Natural-language summaries are read-only projections; their range does not intersect \(\mathcal{U}_t\).

26. AI Briefing Parser Mathematics and Contracts

AI prose is downstream of governed facts. Briefing request resolution is

b \;=\; P(q)

where \(q\) is a machine-readable request and \(b\) is the resolved briefing type. Context assembly and narrative generation are

\mathcal{C}_b \;=\; C(A_1, \ldots, A_k;\; E,\; T,\; F)

N_b \;=\; L(\mathcal{C}_b,\; P_b,\; G_b)

PRODUCTION_DEFINITION

AI authority is explanatory only unless the repository proves another bounded role. Parser status labels are BLOCKED_MISSING_SURFACE, PARTIAL_UNAVAILABLE_INPUTS, and AVAILABLE_CONTEXT_ONLY. Forbidden intents include buy, sell, trade now, target weight should be, execute, override gate, guaranteed, prediction, and alpha signal.

The AI layer explains governed state; it does not create, alter, or bypass governance.

27. Outcome Auditing

The abstention avoided-loss counterfactual is

Y_e^{\text{avoided loss}} \;=\; L_e^{\text{counterfactual action}} - L_e^{\text{abstention}}

RESEARCH_MEASUREMENT

Other measures include maximum adverse excursion, maximum favorable excursion, abstention duration, resolution time, false caution, justified caution, avoided drawdown, and opportunity cost. Outcome evaluation is a structured assessment, not causal proof.

28. Measurement Programs

The programs below are measurement and evaluation tracks. None are allocation engines; promotion to live policy requires explicit governance gates.

28.1 HEDGEHOG

STATUS: LIVE. Scope is the tuple of measurement axes

\mathcal{H} \;=\; \big(\mathrm{cov},\, \mathrm{lat},\, \mathrm{per},\, \mathrm{cal},\, \mathrm{lk}\big)

\begin{aligned} \mathrm{cov}_R(W) \;&=\; \frac{1}{|W|}\,\Big|\,\big\{\,t \in W \,:\, R \subseteq \{\,i \,:\, E(D_{i,t}) = 1\,\}\,\big\}\,\Big| \\ \mathrm{lat}_i(W) \;&=\; \mathrm{median}\,\big\{\,\ell_i(t) \,:\, t \in W\,\big\} \\ \mathrm{per}(s) \;&=\; \mathbb{E}\!\big[\,\tau_s\,\big], \qquad \tau_s \;=\; \min\!\big\{\,h \ge 0 \,:\, S_{t+h} \ne s \,\big|\, S_t = s\,\big\} \\ \mathrm{cal}(W) \;&=\; \sum_{k=1}^{K}\,\frac{|B_k|}{|W|}\,\Big|\,\overline{\hat{p}}^{\,(B_k)} - \overline{y}^{\,(B_k)}\,\Big| \\ \mathrm{lk}(W) \;&=\; I\!\big(\,S_t \,;\, T_t \,\big|\, Z_t\,\big) \end{aligned}

PRODUCTION_DEFINITION

28.2 SENTINEL

STATUS: RESEARCH. Transition-forecasting evaluation:

\mathcal{L}^{(M)}(h) \;=\; \frac{1}{|\mathcal{I}_h|} \sum_{t \,\in\, \mathcal{I}_h} \ell\!\big(\hat{p}^{(M)}_{\,\cdot\,j}(t; h),\; \mathbf{1}\{S_{t+h} = j\}\big), \qquad \Delta\mathcal{L}(h) \;=\; \mathcal{L}^{(B)}(h) - \mathcal{L}^{(C)}(h)

RESEARCH_MEASUREMENT

28.3 LANTERN

STATUS: SHADOW. Caution-policy confusion matrix:

\Lambda \;=\; \big(\,M_{\pi,\,\pi^{\star}}\,\big)_{\pi,\,\pi^{\star} \,\in\, \mathcal{U} \cup \{\varnothing\}}, \qquad M_{\pi,\,\pi^{\star}} \;=\; \big|\,\{\,t \,:\, \pi_t = \pi,\;\; \pi_t^{\star} = \pi^{\star}\,\}\,\big|

CONCEPTUAL_DECOMPOSITION

28.4 TICM

STATUS: LIVE labeling. Stress-event window labeling:

\mathcal{E}^{\text{TICM}} \;=\; \{\, W_1,\, W_2,\, \ldots\,\}, \qquad W_e \;=\; [\,t_e^{\text{start}},\, t_e^{\text{end}}\,], \qquad \tau_t^{\text{TICM}} \;=\; \mathbf{1}\!\big\{\, t \,\in\, \textstyle\bigcup_e W_e \,\big\}

PRODUCTION_DEFINITION

28.5 WS7

STATUS: RESEARCH. Surface-disagreement track:

\rho^{\text{WS7}}_{[t_0,\, t_1]} \;=\; \frac{1}{t_1 - t_0 + 1} \sum_{t \,=\, t_0}^{t_1} D_t^{\text{surface}}

RESEARCH_MEASUREMENT

29. Estimation, Calibration, and Uncertainty

Parameters are estimated on a declared calibration window held out from evaluation:

W_{\text{cal}} \,\subset\, \mathbb{Z}, \qquad W_{\text{oos}} \,\subset\, \mathbb{Z}, \qquad W_{\text{cal}} \,\cap\, W_{\text{oos}} = \varnothing

For a generic parameter \(\theta \in \Theta\):

\hat{\theta} \;=\; \arg\min_{\theta \,\in\, \Theta}\; \mathcal{L}\!\big(\,X_{\,t \in W_{\text{cal}}}\,;\, \theta\,\big)

Sample-size guardrail:

|W_{\text{cal}}| \,<\, n_{\min}(\theta) \quad\Longrightarrow\quad \hat{\theta} \;=\; \mathrm{INSUFFICIENT}

PRODUCTION_STRUCTURE_WITH_PROTECTED_PARAMETERS

Parametric confidence intervals, bootstrap-based interval estimation, and spline-based smoothing are not claimed as components of the live estimation stack. Parameter uncertainty is real and is not collapsed into false precision.

30. Limitations and Model Risk

The following limitations are stated explicitly to prevent inferential drift:

Regime classification is uncertain; historical relationships may change.
Model outputs depend on data quality, revisions, and the completeness of cross-asset inputs.
Regime topology describes geometry, not causality.
Confidence is not certainty; a high-confidence day can still precede a regime change.
An optimizer does not eliminate model risk or tail risk.
AI briefings summarize governed state but may still require human review.
Research and shadow results do not automatically become production controls.
No model can remove tail risk or guarantee downside protection.
Abstention can be costly as well as protective.
Counterfactual outcomes are structured assessments, not causal proof.
Nonstationarity, metric dependence, and derivative sensitivity affect geometric quantities.
Stale data and governance latency can restrict authority.
Model and score disagreement are real and are not averaged away.

31. Public Mathematical Notation

Symbols introduced in this specification and their live status. Implementation status is one of LIVE, LIVE labeling, SHADOW, RESEARCH, or DEFERRED.

Symbol	Domain	Interpretation	Status
\(t\)	\(\mathbb{Z}_{\ge 0}\)	decision time index	`LIVE`
\(d\)	calendar dates	observation date	`LIVE`
\(X_t\)	\(\mathcal{X} \subseteq \mathbb{R}^p\)	observable state vector	`LIVE`
\(D_i\)	\(\mathcal{D}\)	governed artifact \(i\)	`LIVE`
\(G_t\)	\(\mathcal{G}\)	artifact-admissibility / governance state	`LIVE`
\(\mathcal{F}_t\)	\(\sigma\)-algebra	natural artifact filtration	`LIVE`
\(S_t\)	\(\mathbb{R}^3\)	structural state \((G, I, L)\)	`LIVE`
\(R_t\)	finite \(\mathcal{S}\)	structural regime label	`LIVE`
\(T_t\)	\(\{\text{Stable}, \text{Transitional}, \text{Unstable}\}\)	tactical instability	`LIVE`
\(Z_t\)	\(\mathbb{R}^k\)	structural-score vector	`LIVE`
\(P\)	row-stochastic matrix	structural transition matrix	`LIVE`
\(M\)	positive-definite matrix	metric tensor	`LIVE`
\(V_t, A_t\)	\(\mathbb{R}^3\)	state velocity / acceleration	`LIVE`
\(\kappa, \mathcal{T}\)	\(\mathbb{R}_{\ge 0}\), \(\mathbb{R}\)	curvature / torsion	`RESEARCH`
\(\mu_r\)	\(\mathbb{R}^3\)	regime centroid	`LIVE`
\(d_B, v^{\perp}, a^{\perp}\)	\(\mathbb{R}\)	boundary distance / normal velocity / normal acceleration	`LIVE`
\(p_{ij}\)	\([0,1]\)	transition probability	`LIVE`
\(H_{\text{state}}, H_{\text{pair}}, H_{\text{rate}}\)	\(\mathbb{R}_{\ge 0}\)	entropy forms	`LIVE`
\(C_t\)	\(\mathbb{R}_{\ge 0}\)	confidence (margin form)	`LIVE`
\(F_t\)	\([0, F^{\max}]\)	flip risk / transition pressure	`LIVE`
\(\Delta^{2} F_t\)	\(\mathbb{R}\)	flip-risk acceleration	`LIVE`
\(D_t^{\text{score}}\)	\(\mathbb{R}_{\ge 0}\)	score-axis disagreement	`LIVE`
\(D_t^{\text{surface}}\)	\(\{0,1\}\)	surface-label disagreement	`RESEARCH`
\(\pi_t\)	\(\mathcal{U} \cup \{\varnothing\}\)	policy posture	`LIVE`
\(w\)	\(\mathbb{R}^n\)	portfolio weights	`LIVE` (TILT); `SHADOW` (MVO/BL/EQW)
\(\Sigma, \mu\)	matrix / vector	covariance and expected return inputs	`LIVE`
\(\text{MCR}_i, \text{CR}_i\)	\(\mathbb{R}\)	marginal / component contribution to risk	`LIVE`
\(\text{TE}, \text{DD}, \text{VaR}, \text{ES}\)	\(\mathbb{R}_{\ge 0}\)	tracking error / drawdown / tail-risk concepts	`LIVE` / `SHADOW`
\(A_t^{\text{abstain}}\)	\(\{0,1\}\)	abstention gate	`LIVE`
\(\mathcal{W}_t\)	constraint set	regime/confidence feasible set	`LIVE`
\(\rho_t\)	\([0,1]\)	optionality budget rate	`LIVE`
\(x_{t\|v}\)	scalar	vintage-aware observation	`CONCEPTUAL`
\(\mathcal{F}_t^{\text{data}}\)	closed set	freshness state	`LIVE`
\(A_t\)	closed set	authority state	`LIVE`
\(b, \mathcal{C}_b, N_b\)	various	AI briefing type, context, narrative	`LIVE`

32. Non-Claims

Three statements, made explicitly to prevent inferential drift.

ATLAS does not assert

\mathbb{E}\!\left[\,r_{t+1} \,\middle|\, \mathcal{F}_t\,\right] \;>\; 0

as a universal trading claim.

ATLAS does not define

a_t \;=\; \arg\max_a\; \mathbb{E}\!\left[\,U(W_{t+1})\,\right]

as an unconstrained return-maximization problem.

ATLAS does define

a_t \,\in\, \mathcal{A}_t\!\left(S_t,\; T_t,\; G_t\right), \qquad \mathcal{A}_t \;\text{governed by}\; \mathcal{V}\;\text{and}\;\operatorname{Auth}(o,\, s,\, r) = 1

The objective is exposure governance under regime instability, subject to validation, operator scope, and layer separation. It is not portfolio-return maximization under regime stability.

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Diebold, F. X. & Rudebusch, G. D. (1996). Measuring business cycles: A modern perspective. Review of Economics and Statistics, 78(1), 67–77.

El-Yaniv, R. & Wiener, Y. (2010). On the foundations of noise-free selective classification. Journal of Machine Learning Research, 11, 1605–1641.

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Harvey, C. R., Liu, Y. & Zhu, H. (2016). … and the cross-section of expected returns. Review of Financial Studies, 29(1), 5–68.

Popper, K. R. (1959). The Logic of Scientific Discovery. Hutchinson.

Taleb, N. N. (2007). The Black Swan: The Impact of the Highly Improbable. Random House.

Tetlock, P. E. & Gardner, D. (2015). Superforecasting: The Art and Science of Prediction. Crown.

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