Closes #013 - Refactor Crypto Bayes Engine and expand quantitative handbook
This commit is contained in:
Antigravity Agent
13
DEV_LOG.md
13
DEV_LOG.md
@@ -107,5 +107,18 @@ This document tracks all modifications, npm packages, active compilation states,
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* **Active Bugs**: None.
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* **Active Bugs**: None.
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* **Type Checker Status**: Verified clean compilation (`npx tsc --noEmit` returns exit code 0).
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* **Type Checker Status**: Verified clean compilation (`npx tsc --noEmit` returns exit code 0).
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---
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## [2026-06-13] - Crypto Bayes Mathematical Refactoring (#ISSUE-013)
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### Added
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* **Mathematical Specifications & Integration Proof**: Expanded [CryptoMathModal.tsx](file:///c:/Users/jannr/.gemini/antigravity/scratch/investment-sandbox/components/modules/crypto/CryptoMathModal.tsx) with a detailed Section D on the 4-feature client-side Random Forest, Section E on the conjugate Beta-Binomial update, and Section F with the formal calculus integration proof and expanded operational formula.
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* **UI Status Badge**: Mounted a static glowing amber status badge `🟡 SYSTEM-AUTARK (OFFLINE-CORE)` in the header of [CryptoDemo.tsx](file:///c:/Users/jannr/.gemini/antigravity/scratch/investment-sandbox/components/modules/crypto/CryptoDemo.tsx) to confirm the module runs 100% locally with zero external API calls.
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### Modified
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* **KaTeX Escaping Repairs**: Fixed string escaping anomalies by double-escaping LaTeX backslashes across [CryptoMathModal.tsx](file:///c:/Users/jannr/.gemini/antigravity/scratch/investment-sandbox/components/modules/crypto/CryptoMathModal.tsx) to eliminate runtime KaTeX rendering corruption.
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* **`QUANT_ROADMAP.md`**: Synchronized quantitative system specifications under Section 4.V.
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### Active Bugs / Compile Status
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* **Active Bugs**: None.
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* **Type Checker Status**: Verified clean compilation (`npx tsc --noEmit` returns exit code 0).
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@@ -166,6 +166,37 @@ Where:
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---
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---
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### V. Crypto Bayesian Markov & Self-Correcting Engine
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Integrates a two-stage predictive mapping pipeline for cryptocurrency assets (BTC, ETH, SOL) that combines on-chain derivatives data with online Bayesian updates.
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#### 1. Machine Learning Random Forest Classifier
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Ensemble of 10 decision trees mapping four features to forecast trend probabilities:
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* **Funding Rates (FR)**: Future leverage balance indicators.
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* **Open Interest (OI) Volatility**: Contract buildup velocities.
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* **Long/Short (LS) Retail Skew**: Sentiment extreme markers.
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* **Whale Inflows (W)**: Cold-wallet transfer proxy metrics.
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$$P_{\text{ML}} = \frac{1}{M} \sum_{m=1}^{M} T_m(FR_t, OI_t, LS_t, W_t)$$
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#### 2. Conjugate Beta-Binomial Update
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Continuous ML probability outputs ($P_{\text{ML}}$) are mapped into a discrete Binomial likelihood by defining the Trust-Weight Hyperparameter ($w=12$) as the Effective Sample Size (ESS):
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* **Prior distribution**: $\theta \sim \text{Beta}(\alpha_{\text{prior}}, \beta_{\text{prior}})$
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* **Binomial Likelihood pseudo-observations**: $k = P_{\text{ML}} \times w$ (successes), $w - k = (1 - P_{\text{ML}}) \times w$ (failures)
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* **Conjugate Posterior Update**:
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$$\alpha_{\text{post}} = \alpha_{\text{prior}} + k$$
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$$\beta_{\text{post}} = \beta_{\text{prior}} + (w - k)$$
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#### 3. Posterior Mean Integration Proof
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Integrating the continuous parameter $\theta$ out of the posterior distribution gives the mathematical expectation of the posterior:
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$$\mathbb{E}[\theta \mid \text{Data}] = \int_{0}^{1} \theta \cdot P(\theta \mid \text{Data}) \, d\theta = \int_{0}^{1} \theta \cdot \frac{\theta^{\alpha_{\text{post}}-1}(1-\theta)^{\beta_{\text{post}}-1}}{\text{B}(\alpha_{\text{post}}, \beta_{\text{post}})} \, d\theta$$
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$$\mathbb{E}[\theta \mid \text{Data}] = \frac{\text{B}(\alpha_{\text{post}} + 1, \beta_{\text{post}})}{\text{B}(\alpha_{\text{post}}, \beta_{\text{post}})} = \frac{\alpha_{\text{post}}}{\alpha_{\text{post}} + \beta_{\text{post}}}$$
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#### 4. Expanded Workstation Formula
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$$P_{\text{Posterior}} = \frac{\alpha_{\text{prior}} + (P_{\text{ML}} \times w)}{\alpha_{\text{prior}} + \beta_{\text{prior}} + w}$$
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---
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## 5. Multi-Regime Transition Classifier
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## 5. Multi-Regime Transition Classifier
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The core cognitive brain of the sandbox dynamically adjusts allocation weights across our portfolio modules based on estimated macroeconomic and market states.
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The core cognitive brain of the sandbox dynamically adjusts allocation weights across our portfolio modules based on estimated macroeconomic and market states.
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@@ -185,6 +185,11 @@ export default function CryptoDemo() {
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</h2>
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</h2>
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</div>
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</div>
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<div className="flex flex-wrap items-center gap-3">
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<div className="flex flex-wrap items-center gap-3">
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<span className="inline-flex items-center gap-1.5 px-3 py-2.5 rounded-xl text-xs font-bold bg-amber-500/10 text-amber-400 border border-amber-500/20 shadow-[0_0_15px_rgba(245,158,11,0.15)] h-11">
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<ShieldAlert className="w-4 h-4 text-amber-400" />
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<span>SYSTEM-AUTARK (OFFLINE-CORE)</span>
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</span>
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<button
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<button
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onClick={() => setIsMathModalOpen(true)}
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onClick={() => setIsMathModalOpen(true)}
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className="flex items-center gap-1.5 px-4 py-2 rounded-xl bg-slate-950/80 hover:bg-slate-900 border border-slate-800 hover:border-slate-700 transition-all font-semibold text-xs tracking-wider text-cyan-400 justify-center h-11"
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className="flex items-center gap-1.5 px-4 py-2 rounded-xl bg-slate-950/80 hover:bg-slate-900 border border-slate-800 hover:border-slate-700 transition-all font-semibold text-xs tracking-wider text-cyan-400 justify-center h-11"
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@@ -1,5 +1,5 @@
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import React from 'react';
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import React from 'react';
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import { BookOpen } from 'lucide-react';
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import { BookOpen, X, Cpu, BarChart2, Compass, ShieldAlert, Activity } from 'lucide-react';
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import 'katex/dist/katex.min.css';
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import 'katex/dist/katex.min.css';
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import { BlockMath, InlineMath } from 'react-katex';
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import { BlockMath, InlineMath } from 'react-katex';
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@@ -26,11 +26,11 @@ export default function CryptoMathModal({ isOpen, onClose }: CryptoMathModalProp
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if (!isOpen) return null;
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if (!isOpen) return null;
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return (
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return (
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<div className="fixed inset-0 z-50 flex items-center justify-center bg-slate-950/85 backdrop-blur-md p-4 sm:p-6 md:p-8">
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<div className="fixed inset-0 z-50 flex items-center justify-center bg-slate-950/85 backdrop-blur-md p-4 sm:p-6 md:p-8 animate-fade-in">
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<div className="bg-slate-900 border border-slate-800/80 rounded-3xl w-full max-w-4xl h-[80vh] flex flex-col overflow-hidden shadow-2xl relative text-slate-300">
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<div className="bg-slate-900 border border-slate-800/80 rounded-3xl w-full max-w-4xl h-[80vh] flex flex-col overflow-hidden shadow-2xl relative text-slate-300">
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{/* Modal Header */}
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{/* Modal Header */}
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<div className="flex justify-between items-center px-6 py-4 bg-slate-950/40 border-b border-slate-800/60">
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<div className="flex justify-between items-center px-6 py-4 bg-slate-950/45 border-b border-slate-800/60">
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<div>
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<div>
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<h2 className="text-base font-bold bg-gradient-to-r from-cyan-400 to-sky-400 bg-clip-text text-transparent flex items-center gap-2">
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<h2 className="text-base font-bold bg-gradient-to-r from-cyan-400 to-sky-400 bg-clip-text text-transparent flex items-center gap-2">
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<BookOpen className="w-5 h-5 text-cyan-400" /> Crypto Bayesian Markov - Math & Logic Specification
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<BookOpen className="w-5 h-5 text-cyan-400" /> Crypto Bayesian Markov - Math & Logic Specification
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@@ -39,69 +39,148 @@ export default function CryptoMathModal({ isOpen, onClose }: CryptoMathModalProp
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</div>
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</div>
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<button
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<button
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onClick={onClose}
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onClick={onClose}
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className="text-slate-400 hover:text-slate-200 bg-slate-950/50 border border-slate-800 hover:border-slate-700 px-3 py-1.5 rounded-lg text-xs font-semibold font-mono transition-all cursor-pointer"
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className="text-slate-400 hover:text-slate-200 bg-slate-950/50 border border-slate-800 hover:border-slate-700 p-2 rounded-xl transition-all cursor-pointer flex items-center justify-center"
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aria-label="Close modal"
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>
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>
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Schließen (ESC)
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<X className="w-4 h-4" />
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</button>
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</button>
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</div>
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</div>
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{/* Modal Body */}
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{/* Modal Body */}
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<div className="flex-1 overflow-y-auto p-6 sm:p-8 space-y-6 text-slate-300 scrollbar-thin">
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<div className="flex-1 overflow-y-auto p-6 sm:p-8 space-y-8 text-slate-300 scrollbar-thin">
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<div className="space-y-6">
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<div className="border-b border-slate-800/80 pb-3">
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<h3 className="text-base font-bold text-slate-200">4. Crypto Bayesian Markov Engine</h3>
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<p className="text-xs text-slate-400 mt-1">Models momentum regimes and updates transition probabilities using on-chain alpha inputs.</p>
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</div>
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<div className="space-y-3">
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<div className="border-b border-slate-800/80 pb-3">
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<h4 className="text-xs font-bold text-cyan-400 uppercase tracking-wider font-mono">A. Markov Chain State Space</h4>
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<h3 className="text-base font-bold text-slate-200">4. Crypto Bayesian Markov Engine</h3>
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<p className="text-xs leading-relaxed text-slate-400">
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<p className="text-xs text-slate-400 mt-1">Models momentum regimes and updates transition probabilities using on-chain alpha inputs.</p>
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The asset return state space is mapped into 3 momentum regimes:
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</div>
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</p>
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<div className="grid grid-cols-3 gap-3 text-xs text-slate-400 font-mono text-center">
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{/* Section A: Markov Chain State Space */}
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<div className="bg-slate-950/40 p-3 rounded-lg border border-slate-800/50">
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<div className="space-y-3">
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<span className="block text-rose-400 font-bold">State 1 (S1)</span>
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<h4 className="text-xs font-bold text-cyan-400 uppercase tracking-wider font-mono">A. Markov Chain State Space</h4>
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<span>Bearish Squeeze / Crackdown</span>
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<p className="text-xs leading-relaxed text-slate-400">
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</div>
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The asset return state space is mapped into 3 momentum regimes:
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<div className="bg-slate-950/40 p-3 rounded-lg border border-slate-800/50">
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</p>
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<span className="block text-slate-300 font-bold">State 2 (S2)</span>
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<div className="grid grid-cols-3 gap-3 text-xs text-slate-400 font-mono text-center">
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<span>Consolidation / Mean Reversion</span>
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<div className="bg-slate-950/40 p-3 rounded-lg border border-slate-800/50">
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</div>
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<span className="block text-rose-400 font-bold">State 1 (S1)</span>
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<div className="bg-slate-950/40 p-3 rounded-lg border border-slate-800/50">
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<span>Bearish Squeeze / Crackdown</span>
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<span className="block text-emerald-400 font-bold">State 3 (S3)</span>
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<span>Parabolic Bull Run</span>
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</div>
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</div>
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</div>
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</div>
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<div className="bg-slate-955/40 p-3 rounded-lg border border-slate-800/50">
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<span className="block text-slate-300 font-bold">State 2 (S2)</span>
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<div className="space-y-3">
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<span>Consolidation / Mean Reversion</span>
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<h4 className="text-xs font-bold text-cyan-400 uppercase tracking-wider font-mono">B. Transition Matrix (P)</h4>
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<p className="text-xs leading-relaxed text-slate-400">
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Calculates transition probabilities over rolling 90-day return vectors:
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</p>
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<div className="bg-slate-950/40 p-4 rounded-xl border border-slate-800/60 my-2">
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<BlockMath math="P = \begin{bmatrix} p_{11} & p_{12} & p_{13} \\ p_{21} & p_{22} & p_{23} \\ p_{31} & p_{32} & p_{33} \end{bmatrix}" />
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<p className="text-[11px] text-slate-400 font-mono mt-2 text-center">
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where <InlineMath math="p_{ij} = P(X_{t+1} = S_j \mid X_t = S_i)" /> represents the frequency probability of moving from State i to State j.
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</p>
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</div>
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</div>
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</div>
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<div className="bg-slate-955/40 p-3 rounded-lg border border-slate-800/50">
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<span className="block text-emerald-400 font-bold">State 3 (S3)</span>
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<div className="space-y-3">
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<span>Parabolic Bull Run</span>
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<h4 className="text-xs font-bold text-cyan-400 uppercase tracking-wider font-mono">C. Bayesian Update Engine</h4>
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<p className="text-xs leading-relaxed text-slate-400">
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When external alpha inputs (e.g. Funding Rate anomalies, Whale inflows) occur, state probabilities are updated using Bayes' theorem:
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</p>
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<div className="bg-slate-950/40 p-4 rounded-xl border border-slate-800/60 my-2">
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<BlockMath math="P(S_i \mid \text{Alpha}) = \frac{P(\text{Alpha} \mid S_i) \times P(S_i)}{\sum_{j=1}^3 P(\text{Alpha} \mid S_j) \times P(S_j)}" />
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<p className="text-[11px] text-slate-400 mt-2 font-mono leading-relaxed">
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Where:<br/>
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- <InlineMath math="P(S_i)" /> is the prior state probability from the Markov transition matrix.<br/>
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- <InlineMath math="P(\text{Alpha} \mid S_i)" /> is the conditional likelihood of observing this whale spike / funding squeeze in State i.
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</p>
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</div>
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</div>
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</div>
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</div>
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</div>
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</div>
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{/* Section B: Transition Matrix (P) */}
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<div className="space-y-3">
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<h4 className="text-xs font-bold text-cyan-400 uppercase tracking-wider font-mono">B. Transition Matrix (P)</h4>
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<p className="text-xs leading-relaxed text-slate-400">
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Calculates transition probabilities over rolling 90-day return vectors:
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</p>
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<div className="bg-slate-950/40 p-4 rounded-xl border border-slate-800/60 my-2">
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<BlockMath math="P = \\begin{bmatrix} p_{11} & p_{12} & p_{13} \\\\ p_{21} & p_{22} & p_{23} \\\\ p_{31} & p_{32} & p_{33} \\end{bmatrix}" />
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<p className="text-[11px] text-slate-400 font-mono mt-2 text-center">
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{"where "}<InlineMath math="p_{ij} = P(X_{t+1} = S_j \\mid X_t = S_i)" />{" represents the frequency probability of moving from State i to State j."}
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</p>
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</div>
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</div>
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{/* Section C: Bayesian Update Engine */}
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<div className="space-y-3">
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<h4 className="text-xs font-bold text-cyan-400 uppercase tracking-wider font-mono">C. Bayesian Update Engine</h4>
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<p className="text-xs leading-relaxed text-slate-400">
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When external alpha inputs (e.g. Funding Rate anomalies, Whale inflows) occur, state probabilities are updated using Bayes' theorem:
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</p>
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<div className="bg-slate-950/40 p-4 rounded-xl border border-slate-800/60 my-2">
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<BlockMath math="P(S_i \\mid \\text{Alpha}) = \\frac{P(\\text{Alpha} \\mid S_i) \\times P(S_i)}{\\sum_{j=1}^3 P(\\text{Alpha} \\mid S_j) \\times P(S_j)}" />
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<p className="text-[11px] text-slate-400 mt-2 font-mono leading-relaxed">
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{"Where:"}
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<br />
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{"- "}<InlineMath math="P(S_i)" />{" is the prior state probability from the Markov transition matrix."}
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<br />
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{"- "}<InlineMath math="P(\\text{Alpha} \\mid S_i)" />{" is the conditional likelihood of observing this whale spike / funding squeeze in State i."}
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</p>
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</div>
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</div>
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{/* Section D: Two-Stage Hybrid Machine Learning Pipeline */}
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<div className="space-y-3">
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<h4 className="text-xs font-bold text-cyan-400 uppercase tracking-wider font-mono">D. Two-Stage Hybrid Machine Learning Pipeline</h4>
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<p className="text-xs leading-relaxed text-slate-400">
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To minimize false signals and adapt to changing momentum regimes, we run a two-stage hybrid ML pipeline. First, a client-side Random Forest Classifier maps non-linear combinations of four features to forecast trend probabilities:
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</p>
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<div className="bg-slate-950/40 p-5 rounded-2xl border border-slate-800/60 space-y-3">
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<span className="text-xs font-semibold text-slate-200 block">Ensemble Feature Inputs:</span>
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<ul className="text-xs text-slate-400 list-disc pl-5 space-y-1">
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<li><strong className="text-cyan-400">Funding Rates (\\(FR_t\\)):</strong> Measures leverage imbalance in futures contracts.</li>
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<li><strong className="text-cyan-400">Open Interest Volatility (\\(OI_t\\)):</strong> Captures the contract buildup speed.</li>
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<li><strong className="text-cyan-400">Long/Short Retail Skew (\\(LS_t\\)):</strong> Identifies retail sentiment extremes.</li>
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<li><strong className="text-cyan-400">Whale Accumulation Inflows (\\(W_t\\)):</strong> Proxy for cold-wallet transfer velocities.</li>
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</ul>
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<p className="text-xs text-slate-400 leading-relaxed pt-2">
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The Random Forest ensemble evaluates 10 non-linear decision trees to output the short-term and medium-term trend probabilities:
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</p>
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<BlockMath math="P_{\\text{ML}} = \\frac{1}{M} \\sum_{m=1}^{M} T_m(FR_t, OI_t, LS_t, W_t)" />
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</div>
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</div>
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{/* Section E: Conjugate Beta-Binomial Error-Correction Engine */}
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<div className="space-y-3">
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<h4 className="text-xs font-bold text-cyan-400 uppercase tracking-wider font-mono">E. Conjugate Beta-Binomial Error-Correction Engine</h4>
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<p className="text-xs leading-relaxed text-slate-400">
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Raw ML forecasts are susceptible to regime drift. We implement a self-correcting Beta-Binomial update. The continuous probability output from the Random Forest model is mapped into a discrete Binomial likelihood by defining the Trust-Weight Hyperparameter (<InlineMath math="w" />) as the Effective Sample Size (ESS):
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</p>
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<div className="bg-slate-955/40 p-5 rounded-2xl border border-slate-850 space-y-4">
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<div>
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<p className="text-xs text-slate-350 mb-2 font-semibold">1. Prior Distribution (Accuracy History):</p>
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<BlockMath math="\\theta \\sim \\text{Beta}(\\alpha_{\\text{prior}}, \\beta_{\\text{prior}})" />
|
||||||
|
<p className="text-[10px] text-slate-500 font-mono">
|
||||||
|
where <InlineMath math="\\alpha_{\\text{prior}}" /> represents historical prediction successes and <InlineMath math="\\beta_{\\text{prior}}" /> represents false alarms.
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||||||
|
</p>
|
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|
</div>
|
||||||
|
|
||||||
|
<div>
|
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|
<p className="text-xs text-slate-350 mb-2 font-semibold">2. Likelihood Formulation (Binomial pseudo-observations):</p>
|
||||||
|
<BlockMath math="P(x \\mid \\theta) = \\binom{w}{k} \\theta^k (1 - \\theta)^{w - k}" />
|
||||||
|
<p className="text-[10px] text-slate-500 font-mono">
|
||||||
|
where <InlineMath math="k = P_{\\text{ML}} \\times w" /> is the number of simulated successes and <InlineMath math="w - k = (1 - P_{\\text{ML}}) \\times w" /> is the number of simulated failures.
|
||||||
|
</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div>
|
||||||
|
<p className="text-xs text-slate-350 mb-2 font-semibold">3. Conjugate Posterior Update:</p>
|
||||||
|
<BlockMath math="\\alpha_{\\text{post}} = \\alpha_{\\text{prior}} + k, \\quad \\beta_{\\text{post}} = \\beta_{\\text{prior}} + (w - k)" />
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
{/* Section F: Mathematical Proof of Posterior Mean Integration */}
|
||||||
|
<div className="space-y-3">
|
||||||
|
<h4 className="text-xs font-bold text-cyan-400 uppercase tracking-wider font-mono">F. Mathematical Proof of Posterior Mean Integration</h4>
|
||||||
|
<p className="text-xs leading-relaxed text-slate-400">
|
||||||
|
To resolve a single operational point-estimate from our posterior distribution, we integrate out the continuous parameter <InlineMath math="\\theta" /> to calculate the mathematical expectation of the posterior distribution:
|
||||||
|
</p>
|
||||||
|
<div className="bg-slate-955/40 p-5 rounded-2xl border border-slate-850 space-y-4">
|
||||||
|
<p className="text-xs text-slate-350 font-semibold">Posterior Expectation Integral Proof:</p>
|
||||||
|
<BlockMath math="\\mathbb{E}[\\theta \\mid \\text{Data}] = \\int_{0}^{1} \\theta \\cdot P(\\theta \\mid \\text{Data}) \\, d\\theta = \\int_{0}^{1} \\theta \\cdot \\frac{\\theta^{\\alpha_{\\text{post}}-1}(1-\\theta)^{\\beta_{\\text{post}}-1}}{\\text{B}(\\alpha_{\\text{post}}, \\beta_{\\text{post}})} \\, d\\theta" />
|
||||||
|
<p className="text-xs text-slate-400 leading-relaxed">
|
||||||
|
Using the definition of the Beta function <InlineMath math="\\text{B}(a, b) = \\frac{\\Gamma(a)\\Gamma(b)}{\\Gamma(a+b)}" /> and the recurrence relation <InlineMath math="\\Gamma(x+1) = x\\Gamma(x)" />:
|
||||||
|
</p>
|
||||||
|
<BlockMath math="\\mathbb{E}[\\theta \\mid \\text{Data}] = \\frac{\\text{B}(\\alpha_{\\text{post}} + 1, \\beta_{\\text{post}})}{\\text{B}(\\alpha_{\\text{post}}, \\beta_{\\text{post}})} = \\frac{\\Gamma(\\alpha_{\\text{post}} + 1)\\Gamma(\\beta_{\\text{post}})}{\\Gamma(\\alpha_{\\text{post}} + \\beta_{\\text{post}} + 1)} \\cdot \\frac{\\Gamma(\\alpha_{\\text{post}} + \\beta_{\\text{post}})}{\\Gamma(\\alpha_{\\text{post}})\\Gamma(\\beta_{\\text{post}})}" />
|
||||||
|
<BlockMath math="\\mathbb{E}[\\theta \\mid \\text{Data}] = \\frac{\\alpha_{\\text{post}}\\Gamma(\\alpha_{\\text{post}})\\Gamma(\\beta_{\\text{post}})}{(\\alpha_{\\text{post}} + \\beta_{\\text{post}})\\Gamma(\\alpha_{\\text{post}} + \\beta_{\\text{post}})} \\cdot \\frac{\\Gamma(\\alpha_{\\text{post}} + \\beta_{\\text{post}})}{\\Gamma(\\alpha_{\\text{post}})\\Gamma(\\beta_{\\text{post}})} = \\frac{\\alpha_{\\text{post}}}{\\alpha_{\\text{post}} + \\beta_{\\text{post}}}" />
|
||||||
|
<p className="text-xs text-slate-350 font-semibold pt-2">Expanded Workstation Implementation Formula:</p>
|
||||||
|
<BlockMath math="P_{\\text{Posterior}} = \\frac{\\alpha_{\\text{prior}} + (P_{\\text{ML}} \\times w)}{\\alpha_{\\text{prior}} + \\beta_{\\text{prior}} + w}" />
|
||||||
|
<p className="text-[10px] text-slate-500 font-mono leading-relaxed">
|
||||||
|
This formulation ensures that if the prior model is highly accurate (large <InlineMath math="\\alpha_{\\text{prior}}" />), the raw ML signal is smoothed towards historical baseline expectations. If historical errors are high, the prior variance restricts overreaction to noisy signals.
|
||||||
|
</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|||||||
Reference in New Issue
Block a user