# Requirements Document — Signal Math Upgrade

## Introduction

The Stonks Oracle platform uses a three-layer signal aggregation engine (company-specific, macro, competitive) to produce market intelligence and drive paper-trading decisions. The current mathematical models are structurally too deterministic and too linear for a market system that is fundamentally probabilistic, regime-dependent, and nonlinear. The pipeline behaves as weighted sentiment aggregation with heuristics rather than a probabilistic forecasting engine.

This feature upgrades the signal processing mathematics across all pipeline stages — from signal scoring through trend assembly, macro impact, competitive signals, trend projection, and recommendation generation — to replace heuristic formulas with probabilistic, regime-aware, and adaptive alternatives. The goal is to transform prediction quality while preserving the existing `WeightedSignal` abstraction, three-layer architecture, and database schema compatibility.

## Glossary

- **Aggregation_Engine**: The core pipeline in `services/aggregation/worker.py` that merges signals from all three layers and computes `TrendSummary` objects across five time windows.
- **Signal_Scorer**: The scoring module in `services/aggregation/scoring.py` that transforms raw intelligence records into `WeightedSignal` objects with composite aggregation weights.
- **Trend_Assembler**: The component in `services/aggregation/worker.py` that derives trend direction, strength, confidence, and contradiction from merged weighted signals.
- **Macro_Scorer**: The macro impact scoring module in `services/aggregation/interpolation.py` that computes per-company impact from global events using overlap-based exposure profiles.
- **Competitive_Scorer**: The competitive signal modules in `services/aggregation/pattern_matcher.py` and `services/aggregation/signal_propagation.py` that mine historical patterns and propagate cross-company signals.
- **Projection_Engine**: The trend projection module in `services/aggregation/projection.py` that computes forward-looking trend estimates from momentum and macro decay.
- **Recommendation_Engine**: The recommendation pipeline in `services/recommendation/` that translates trend assessments into actionable buy/sell/hold/watch decisions with position sizing.
- **WeightedSignal**: The core data abstraction pairing a document reference with a composite aggregation weight, sentiment value, and impact score.
- **Beta_Distribution**: A probability distribution on [0, 1] parameterized by α and β, used to model the posterior probability of bullish vs bearish sentiment.
- **Regime_Detector**: A new component that classifies the current market regime (trend-following, panic, mean-reversion, uncertainty) from price and volume statistics.
- **Sigmoid_Function**: The logistic function σ(x) = 1/(1+e^(-x)) used to convert log-likelihood accumulations into probabilities.
- **Adaptive_Decay**: A recency decay mechanism where the half-life varies per signal based on event impact, surprise, and market reaction rather than using a fixed constant per window.
- **Information_Gain**: A measure of how surprising an event is relative to its base rate, computed as -log P(event_type), used to weight novel signals more heavily.
- **Entropy**: Shannon entropy H = -p·log(p) - (1-p)·log(1-p), used to detect mixed sentiment states where the probability distribution is spread rather than concentrated.
- **EMA**: Exponential Moving Average, a weighted moving average giving more weight to recent observations, used for trend and volatility regime detection.

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## Requirements

### Requirement 1: Probabilistic Sentiment Accumulation via Bayesian Evidence

**User Story:** As a quantitative analyst, I want the signal scoring layer to accumulate sentiment evidence probabilistically using Bayesian methods, so that the system captures uncertainty structure instead of collapsing sentiment into binary ±1 labels.

#### Acceptance Criteria

1. WHEN a set of weighted signals is provided for a ticker and window, THE Signal_Scorer SHALL compute a log-likelihood accumulation L_t = Σ(w_i · s_i) where w_i is the combined signal weight and s_i is the sentiment value.
2. WHEN the log-likelihood L_t has been computed, THE Signal_Scorer SHALL convert the accumulation to a bullish probability using the Sigmoid_Function: P_bull = σ(L_t) = 1/(1+e^(-L_t)).
3. WHEN weighted signals are provided, THE Signal_Scorer SHALL maintain a Beta_Distribution posterior with parameters α_t = α_0 + W_bull and β_t = β_0 + W_bear, where W_bull is the sum of combined weights for positive signals and W_bear is the sum for negative signals, and α_0 = β_0 = 1.0 as uninformative priors.
4. THE Signal_Scorer SHALL compute Bayesian confidence from the Beta_Distribution posterior variance as C = 1 - 4αβ/(α+β)², where C ranges from 0.0 (maximum uncertainty at α=β) to approaching 1.0 (strong evidence concentration).
5. WHEN no signals exist for a ticker and window, THE Signal_Scorer SHALL return P_bull = 0.5, α = 1.0, β = 1.0, and C = 0.0, representing the uninformative prior state.
6. THE Signal_Scorer SHALL preserve the existing `WeightedSignal` dataclass interface, adding the Bayesian posterior fields (P_bull, α, β, Bayesian confidence) as additional output alongside the existing weighted sentiment average.
7. FOR ALL valid sets of weighted signals, computing the Beta posterior then extracting P_bull SHALL produce a value within 0.05 of σ(L_t) when signal weights are uniform (round-trip consistency between the two probabilistic representations).

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### Requirement 2: Sigmoid Confidence Gate Replacing Binary Gate

**User Story:** As a quantitative analyst, I want the binary confidence gate replaced with a smooth sigmoid transition, so that marginally confident signals contribute proportionally rather than being completely discarded or fully included.

#### Acceptance Criteria

1. WHEN a document signal has extraction confidence x, THE Signal_Scorer SHALL compute a soft gate value p = σ(5·(x - 0.5)) = 1/(1+e^(-5·(x-0.5))) instead of the current binary 0/1 gate.
2. WHEN extraction confidence is 0.5, THE Signal_Scorer SHALL produce a gate value of 0.5 (the sigmoid midpoint).
3. WHEN extraction confidence is below 0.2, THE Signal_Scorer SHALL produce a gate value below 0.05, preserving near-zero weight for very low confidence signals.
4. WHEN extraction confidence is above 0.8, THE Signal_Scorer SHALL produce a gate value above 0.95, preserving near-full weight for high confidence signals.
5. THE Signal_Scorer SHALL use the sigmoid gate value as a multiplicative factor in the combined weight formula in place of the current binary G_conf.
6. FOR ALL extraction confidence values in [0.0, 1.0], THE Signal_Scorer SHALL produce gate values that are monotonically increasing (higher confidence always produces equal or higher gate values).

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### Requirement 3: Information Gain Surprise Weighting

**User Story:** As a quantitative analyst, I want signals weighted by their information gain (surprise factor), so that rare and unexpected events receive proportionally higher influence than routine signals.

#### Acceptance Criteria

1. WHEN a signal has a known event type (e.g., earnings, product_launch, regulatory, legal, m_and_a), THE Signal_Scorer SHALL compute an information gain factor r = 1 + λ·(-log₂ P(event_type)), where P(event_type) is the empirical base rate of that event type and λ is a configurable scaling parameter with default 0.3.
2. WHEN the event type base rate is not available, THE Signal_Scorer SHALL use a default base rate of 0.1 (treating the event as moderately rare).
3. THE Signal_Scorer SHALL multiply the information gain factor r into the combined weight formula as an additional multiplicative component.
4. THE Signal_Scorer SHALL clamp the information gain factor to a maximum of 3.0 to prevent extremely rare events from dominating the aggregation.
5. FOR ALL event types with base rate in (0, 1], THE Signal_Scorer SHALL produce information gain factors that are monotonically decreasing with increasing base rate (rarer events always receive higher surprise weight).

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### Requirement 4: Historical Source Accuracy Tracking

**User Story:** As a quantitative analyst, I want source credibility to incorporate historical prediction accuracy, so that sources with a track record of correct directional calls receive higher weight.

#### Acceptance Criteria

1. THE Signal_Scorer SHALL maintain a per-source accuracy metric computed as the fraction of past signals from that source where the predicted direction matched the subsequent 7-day price movement direction.
2. WHEN a source has at least 10 historical signals with known outcomes, THE Signal_Scorer SHALL incorporate the source accuracy as a multiplicative factor on the credibility weight, scaled linearly from 0.5 (0% accuracy) to 1.5 (100% accuracy).
3. WHEN a source has fewer than 10 historical signals, THE Signal_Scorer SHALL use a neutral accuracy factor of 1.0 (no adjustment).
4. THE Signal_Scorer SHALL update source accuracy metrics asynchronously after each aggregation cycle, using realized price data from the market data tables.
5. THE Signal_Scorer SHALL store source accuracy metrics in a database table with columns for source identifier, accuracy ratio, sample count, and last updated timestamp.

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### Requirement 5: Adaptive Recency Decay with Event-Specific Half-Lives

**User Story:** As a quantitative analyst, I want recency decay half-lives to adapt based on event characteristics, so that high-impact events persist longer in the aggregation while routine signals decay faster.

#### Acceptance Criteria

1. WHEN computing recency decay for a signal, THE Signal_Scorer SHALL use an adaptive half-life τ_i = τ_base · (1 + β_impact) · (1 + β_surprise) · (1 + β_market_reaction), where τ_base is the current fixed half-life for the window.
2. THE Signal_Scorer SHALL compute β_impact from the signal's impact score, scaled linearly from 0.0 (impact_score = 0) to 1.0 (impact_score = 1.0).
3. THE Signal_Scorer SHALL compute β_surprise from the information gain factor (Requirement 3), scaled linearly from 0.0 (r = 1.0, no surprise) to 1.0 (r = 3.0, maximum surprise).
4. THE Signal_Scorer SHALL compute β_market_reaction from the market context multiplier, scaled linearly from 0.0 (multiplier = 1.0, no market reaction) to 0.5 (multiplier = 1.45, maximum market reaction).
5. WHEN all three β factors are at their maximum, THE Signal_Scorer SHALL produce an adaptive half-life of at most 6× the base half-life (τ_base · 2.0 · 2.0 · 1.5 = 6.0 · τ_base).
6. WHEN all three β factors are zero (routine, unsurprising signal in calm market), THE Signal_Scorer SHALL produce the same half-life as the current fixed system (τ_base).
7. FOR ALL combinations of impact, surprise, and market reaction values, THE Signal_Scorer SHALL produce adaptive half-lives that are greater than or equal to τ_base (adaptive decay is always slower or equal to the base decay, never faster).

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### Requirement 6: Volatility-Adjusted Normalization (Regime-Aware Scoring)

**User Story:** As a quantitative analyst, I want signal weights normalized by current market volatility and volume conditions, so that the same signal magnitude is interpreted differently in calm vs volatile markets.

#### Acceptance Criteria

1. WHEN market data is available for a ticker, THE Signal_Scorer SHALL compute a return z-score z_r = (r_t - μ_20) / σ_20, where r_t is the current return, μ_20 is the 20-day mean return, and σ_20 is the 20-day return standard deviation.
2. WHEN market data is available for a ticker, THE Signal_Scorer SHALL compute a volume z-score z_v = (log(V_t) - μ_V) / σ_V, where V_t is the current volume, μ_V is the 20-day mean of log-volume, and σ_V is the 20-day standard deviation of log-volume.
3. THE Signal_Scorer SHALL compute a regime multiplier M_regime = 1 + 0.15·|z_r| + 0.10·|z_v|, which amplifies signal weights during abnormal market conditions.
4. THE Signal_Scorer SHALL clamp M_regime to the range [1.0, 2.5] to prevent extreme z-scores from producing runaway weight amplification.
5. WHEN market data is not available for a ticker, THE Signal_Scorer SHALL use M_regime = 1.0 (no regime adjustment).
6. THE Signal_Scorer SHALL replace the current market context multiplier (M_context) with M_regime in the combined weight formula.

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### Requirement 7: Regime Detection and Classification

**User Story:** As a quantitative analyst, I want the system to detect and classify the current market regime for each ticker, so that scoring thresholds and behavior adapt to whether the market is trending, panicking, mean-reverting, or uncertain.

#### Acceptance Criteria

1. WHEN market data is available, THE Regime_Detector SHALL compute a trend indicator R = sign(EMA_20 - EMA_100), where EMA_20 and EMA_100 are exponential moving averages of closing prices over 20 and 100 days respectively.
2. WHEN market data is available, THE Regime_Detector SHALL compute a volatility ratio V_r = σ_20 / σ_100, where σ_20 and σ_100 are the 20-day and 100-day return standard deviations.
3. THE Regime_Detector SHALL classify the market regime into one of four categories based on R and V_r: trend-following (R ≠ 0 AND V_r < 1.2), panic (V_r > 1.5), mean-reversion (R = 0 AND V_r < 1.0), uncertainty (all other cases).
4. WHEN the regime is classified as panic, THE Aggregation_Engine SHALL reduce the bullish/bearish threshold from ±0.15 to ±0.10 (making the system more sensitive to directional signals during high-volatility periods).
5. WHEN the regime is classified as mean-reversion, THE Aggregation_Engine SHALL increase the bullish/bearish threshold from ±0.15 to ±0.20 (requiring stronger evidence for directional calls in range-bound markets).
6. WHEN the regime is classified as trend-following, THE Aggregation_Engine SHALL use the default thresholds of ±0.15.
7. WHEN the regime is classified as uncertainty, THE Aggregation_Engine SHALL use the default thresholds of ±0.15 and increase the contradiction penalty multiplier from 0.4 to 0.6.
8. THE Regime_Detector SHALL persist the current regime classification per ticker to the database for auditability and dashboard display.
9. WHEN market data is insufficient to compute EMA_100 (fewer than 100 days of price history), THE Regime_Detector SHALL default to the uncertainty regime.

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### Requirement 8: Bayesian Posterior Confidence Replacing Heuristic Confidence

**User Story:** As a quantitative analyst, I want trend confidence derived from the Bayesian posterior distribution rather than the current heuristic weighted formula, so that confidence reflects actual evidence concentration rather than an ad-hoc combination of factors.

#### Acceptance Criteria

1. WHEN computing trend confidence, THE Trend_Assembler SHALL use the Bayesian confidence C = 1 - 4αβ/(α+β)² from the Beta_Distribution posterior (Requirement 1) as the primary confidence component with weight 0.5.
2. THE Trend_Assembler SHALL retain the source count factor (min(N_unique/15, 0.8)) as a secondary confidence component with weight 0.25, rewarding evidence breadth.
3. THE Trend_Assembler SHALL retain the contradiction penalty (contradiction_score × 0.4) as a confidence reduction.
4. THE Trend_Assembler SHALL compute the combined confidence as: confidence = 0.5 × C_bayesian + 0.25 × F_count + 0.25 × C_avg_credibility - P_contradiction, clamped to [0.0, 1.0].
5. THE Trend_Assembler SHALL preserve the existing confidence thresholds for recommendation eligibility (0.35 minimum, 0.50 paper, 0.70 live) without modification.
6. FOR ALL signal sets where all signals agree on direction, THE Trend_Assembler SHALL produce Bayesian confidence that increases monotonically with the number of agreeing signals.

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### Requirement 9: Entropy-Based Mixed Signal Detection

**User Story:** As a quantitative analyst, I want mixed trend detection based on Shannon entropy rather than simple contradiction thresholds, so that the system can distinguish between genuine uncertainty (high entropy) and weak signal (low total weight).

#### Acceptance Criteria

1. WHEN the bullish probability P_bull has been computed from the Bayesian posterior, THE Trend_Assembler SHALL compute Shannon entropy H = -P_bull·log₂(P_bull) - (1-P_bull)·log₂(1-P_bull).
2. WHEN H > 0.9 (entropy close to maximum of 1.0, indicating near-equal probability of bullish and bearish), THE Trend_Assembler SHALL classify the trend direction as mixed, regardless of the weighted sentiment average.
3. WHEN H ≤ 0.9 AND P_bull > 0.65, THE Trend_Assembler SHALL classify the trend direction as bullish.
4. WHEN H ≤ 0.9 AND P_bull < 0.35, THE Trend_Assembler SHALL classify the trend direction as bearish.
5. WHEN H ≤ 0.9 AND 0.35 ≤ P_bull ≤ 0.65, THE Trend_Assembler SHALL classify the trend direction as neutral.
6. THE Trend_Assembler SHALL persist the entropy value H alongside the trend summary for auditability.
7. FOR ALL P_bull values in (0, 1), THE Trend_Assembler SHALL compute entropy values in (0, 1], with maximum entropy of 1.0 occurring at P_bull = 0.5.

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### Requirement 10: Multiplicative Macro Exposure Scoring

**User Story:** As a quantitative analyst, I want macro impact computed using multiplicative exposure rather than linear weighted sums, so that a company exposed across multiple dimensions receives compounding impact rather than simple addition.

#### Acceptance Criteria

1. WHEN computing macro impact for a company, THE Macro_Scorer SHALL use the multiplicative exposure formula S_macro = severity · (1 - Π_k(1 - w_k · O_k)), where O_k are the overlap components (geographic, supply chain, commodity, sector) and w_k are their respective weights.
2. THE Macro_Scorer SHALL use the following overlap weights: w_geo = 0.35, w_supply = 0.25, w_commodity = 0.25, w_sector = 0.15 (matching the current linear weight distribution).
3. WHEN a company has zero overlap across all dimensions, THE Macro_Scorer SHALL produce S_macro = 0.0 (no impact).
4. WHEN a company has maximum overlap across all dimensions (all O_k = 1.0), THE Macro_Scorer SHALL produce S_macro = severity · (1 - (1-0.35)·(1-0.25)·(1-0.25)·(1-0.15)), which is approximately severity · 0.724.
5. THE Macro_Scorer SHALL preserve the existing severity weight mapping (critical=1.0, high=0.75, moderate=0.5, low=0.25).
6. THE Macro_Scorer SHALL preserve the existing resilience modifier (R_tier) applied after the multiplicative exposure computation.
7. FOR ALL overlap configurations, THE Macro_Scorer SHALL produce impact scores where adding a non-zero overlap in any dimension increases the total impact (monotonicity property).

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### Requirement 11: Conditional Macro Signal Integration

**User Story:** As a quantitative analyst, I want macro signals treated as conditional modifiers on company signals rather than additive contributions, so that macro context amplifies or dampens existing company-level evidence rather than independently shifting the trend.

#### Acceptance Criteria

1. WHEN both company signals and macro signals exist for a ticker, THE Aggregation_Engine SHALL apply macro impact as a multiplicative modifier on the company signal strength: S_adjusted = S_company · (1 + M_macro · sign_alignment), where M_macro is the normalized macro impact and sign_alignment is +1 when macro and company signals agree in direction, -1 when they disagree.
2. THE Aggregation_Engine SHALL clamp the macro modifier (1 + M_macro · sign_alignment) to the range [0.5, 1.5] to prevent macro signals from inverting or excessively amplifying company signals.
3. WHEN only macro signals exist (no company signals), THE Aggregation_Engine SHALL fall back to the current additive behavior with the existing macro weight of 0.3, preserving the macro-only suppression safety mechanism.
4. WHEN only company signals exist (macro layer disabled or no macro events), THE Aggregation_Engine SHALL use company signals without modification (modifier = 1.0).
5. THE Aggregation_Engine SHALL log the macro modifier value applied to each ticker for auditability.

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### Requirement 12: Graph-Distance Competitive Signal Attenuation

**User Story:** As a quantitative analyst, I want competitive signal transfer attenuated by network graph distance and historical correlation, so that signals propagate more strongly to closely related competitors and decay for distant relationships.

#### Acceptance Criteria

1. WHEN propagating a signal from a source company to a target company, THE Competitive_Scorer SHALL compute transfer strength as S_transfer = S_source · ρ_historical · e^(-d_network), where S_source is the source signal strength, ρ_historical is the historical price correlation between the two companies, and d_network is the graph distance in the competitor relationship network.
2. THE Competitive_Scorer SHALL compute graph distance d_network as the shortest path length in the competitor relationship graph, where direct competitors have distance 1, competitors-of-competitors have distance 2, and so on.
3. WHEN the graph distance exceeds 3, THE Competitive_Scorer SHALL not propagate the signal (e^(-3) ≈ 0.05, below meaningful contribution).
4. THE Competitive_Scorer SHALL compute ρ_historical as the 90-day rolling Pearson correlation of daily returns between the source and target companies.
5. WHEN historical correlation data is insufficient (fewer than 30 trading days of overlapping data), THE Competitive_Scorer SHALL use a default correlation of 0.3 for same-sector companies and 0.1 for cross-sector companies.
6. THE Competitive_Scorer SHALL preserve the existing relationship strength threshold (R_relationship ≥ 0.2) as a pre-filter before applying the graph-distance attenuation.
7. FOR ALL source-target pairs, THE Competitive_Scorer SHALL produce transfer strengths that decrease monotonically with increasing graph distance (closer competitors always receive stronger signal transfer).

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### Requirement 13: Exponentially Weighted Momentum

**User Story:** As a quantitative analyst, I want trend momentum computed using exponentially weighted historical changes rather than a simple current-minus-previous difference, so that the momentum estimate is smoother and less sensitive to single-cycle noise.

#### Acceptance Criteria

1. WHEN computing trend momentum, THE Projection_Engine SHALL use an exponentially weighted sum M_t = Σ_{k=0}^{K-1} λ^k · ΔS_{t-k}, where ΔS_{t-k} is the signed strength change at lag k, λ = 0.7 is the decay factor, and K is the number of available historical cycles (up to 10).
2. THE Projection_Engine SHALL normalize the momentum by dividing by the geometric series sum Σ λ^k to produce a value in [-1, 1].
3. WHEN fewer than 2 historical cycles are available, THE Projection_Engine SHALL fall back to the current heuristic (momentum = direction_sign × strength × 0.5).
4. THE Projection_Engine SHALL compute volatility-scaled momentum M_adj = M_t / max(σ_20, 0.01), where σ_20 is the 20-day return standard deviation, to normalize momentum relative to the ticker's typical price movement.
5. THE Projection_Engine SHALL clamp M_adj to [-2.0, 2.0] to prevent division by very small σ_20 from producing extreme values.
6. FOR ALL sequences of monotonically increasing signed strengths, THE Projection_Engine SHALL produce positive momentum values (correctly detecting strengthening bullish trends).

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### Requirement 14: Expected Value Recommendation Gate

**User Story:** As a quantitative analyst, I want recommendation eligibility based on expected value rather than simple confidence and strength thresholds, so that the system only recommends trades with positive risk-adjusted expected outcomes.

#### Acceptance Criteria

1. WHEN evaluating recommendation eligibility, THE Recommendation_Engine SHALL compute expected value EV = P_bull · R_up - P_bear · R_down, where P_bull is the Bayesian bullish probability, P_bear = 1 - P_bull, R_up is the estimated upside return, and R_down is the estimated downside return.
2. THE Recommendation_Engine SHALL estimate R_up and R_down from the trend strength and the ticker's 20-day historical volatility: R_up = strength · σ_20 · √(horizon_days) and R_down = (1 - strength) · σ_20 · √(horizon_days), where horizon_days corresponds to the trend window duration.
3. WHEN EV is positive and exceeds a configurable threshold (default 0.005, representing 0.5% expected return), THE Recommendation_Engine SHALL allow the recommendation to proceed through the existing eligibility gates.
4. WHEN EV is negative or below the threshold, THE Recommendation_Engine SHALL force the recommendation to informational mode regardless of confidence and strength.
5. THE Recommendation_Engine SHALL persist the computed EV alongside the recommendation for auditability.
6. THE Recommendation_Engine SHALL preserve all existing eligibility gates (confidence ≥ 0.35, strength ≥ 0.10, contradiction ≤ 0.60, evidence ≥ 2, direction ≠ neutral) as additional requirements beyond the EV gate.

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### Requirement 15: Contradiction Handling via Weighted Disagreement Entropy

**User Story:** As a quantitative analyst, I want contradiction detection to use weighted disagreement entropy rather than a simple minority/majority ratio, so that the system better distinguishes between a few strong dissenting signals and many weak ones.

#### Acceptance Criteria

1. WHEN computing contradiction, THE Trend_Assembler SHALL compute weighted disagreement entropy using the effective weight distribution across positive and negative signal groups.
2. THE Trend_Assembler SHALL compute the positive weight fraction f_pos = W_positive / (W_positive + W_negative) and negative weight fraction f_neg = W_negative / (W_positive + W_negative), where W_positive and W_negative are the sums of effective weights (combined_weight × impact_score) for each sentiment group.
3. THE Trend_Assembler SHALL compute contradiction entropy as H_contradiction = -f_pos·log₂(f_pos) - f_neg·log₂(f_neg), normalized to [0, 1] (maximum at f_pos = f_neg = 0.5).
4. THE Trend_Assembler SHALL weight the contradiction entropy by the total evidence mass: contradiction_score = H_contradiction · min(1.0, (W_positive + W_negative) / W_threshold), where W_threshold is a configurable parameter (default 5.0) representing the evidence mass at which contradiction becomes fully significant.
5. WHEN only positive or only negative signals exist (no disagreement), THE Trend_Assembler SHALL produce a contradiction score of 0.0.
6. THE Trend_Assembler SHALL preserve the existing `ContradictionResult` interface, populating the overall score with the entropy-based value and retaining the `DisagreementDetail` objects for catalyst-level analysis.
7. FOR ALL signal sets with both positive and negative signals, THE Trend_Assembler SHALL produce contradiction scores that increase monotonically as the weight distribution approaches equal split (f_pos → 0.5).

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### Requirement 16: Backward Compatibility and Migration

**User Story:** As a platform operator, I want the mathematical upgrades to be backward-compatible with the existing database schema and deployable incrementally, so that the upgrade does not require downtime or data migration.

#### Acceptance Criteria

1. THE Aggregation_Engine SHALL preserve the existing `WeightedSignal`, `SignalWeight`, `TrendSummary`, and `Recommendation` dataclass interfaces, adding new fields as optional attributes with default values.
2. THE Aggregation_Engine SHALL store new mathematical outputs (P_bull, α, β, entropy, regime, EV) in the existing JSONB metadata fields of `trend_windows` and `recommendations` tables rather than requiring new columns.
3. THE Aggregation_Engine SHALL support a feature flag `probabilistic_scoring_enabled` in `risk_configs` that toggles between the current heuristic pipeline and the new probabilistic pipeline, defaultable to `false` for safe rollout.
4. WHEN `probabilistic_scoring_enabled` is false, THE Aggregation_Engine SHALL produce identical outputs to the current system (no behavioral change).
5. WHEN `probabilistic_scoring_enabled` is true, THE Aggregation_Engine SHALL use the new Bayesian, regime-aware, and adaptive formulas for all pipeline stages.
6. IF the feature flag toggle fails to read from the database, THEN THE Aggregation_Engine SHALL default to the current heuristic pipeline (fail-safe behavior).
7. THE Aggregation_Engine SHALL log which pipeline mode (heuristic or probabilistic) is active at the start of each aggregation cycle.

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### Requirement 17: Property-Based Testing for Mathematical Correctness

**User Story:** As a developer, I want comprehensive property-based tests validating the mathematical correctness of all new formulas, so that edge cases and numerical stability issues are caught before deployment.

#### Acceptance Criteria

1. THE test suite SHALL include property-based tests using Hypothesis for the sigmoid confidence gate verifying monotonicity (higher confidence input always produces higher or equal gate output) across all float inputs in [0.0, 1.0].
2. THE test suite SHALL include property-based tests for the Beta_Distribution posterior verifying that α + β increases monotonically with the number of signals processed (evidence always accumulates).
3. THE test suite SHALL include property-based tests for the Bayesian confidence formula verifying that confidence is 0.0 when α = β (maximum uncertainty) and approaches 1.0 as the ratio α/β or β/α increases.
4. THE test suite SHALL include property-based tests for the adaptive decay verifying that the adaptive half-life is always greater than or equal to the base half-life for all valid input combinations.
5. THE test suite SHALL include property-based tests for the multiplicative macro exposure verifying monotonicity (adding non-zero overlap in any dimension increases total impact).
6. THE test suite SHALL include property-based tests for the exponentially weighted momentum verifying that monotonically increasing strength sequences produce positive momentum.
7. THE test suite SHALL include a round-trip property test verifying that computing the Beta posterior from signals, extracting P_bull, then reconstructing approximate signal weights produces values consistent with the original inputs.
8. THE test suite SHALL include property-based tests for the expected value computation verifying that EV is positive when P_bull > 0.5 and R_up > R_down (basic directional consistency).
9. THE test suite SHALL include property-based tests for numerical stability verifying that no formula produces NaN, infinity, or values outside documented ranges for any valid input combination.
10. THE test suite SHALL use `@settings(max_examples=100)` and follow the project convention of `test_pbt_*` file naming.
