Closes #016 - Deploy Native KaTeX Rig & Dual-Handbook System
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Antigravity Agent
@@ -26,7 +26,7 @@ export default function TechMathModal({ isOpen, onClose }: TechMathModalProps) {
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if (!isOpen) return null;
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return (
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<div className="fixed inset-0 z-50 flex items-center justify-center bg-slate-955/90 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-900/90 backdrop-blur-md p-4 sm:p-6 md:p-8">
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<div className="bg-slate-900 border border-slate-800/80 rounded-3xl w-full max-w-5xl h-[85vh] flex flex-col overflow-hidden shadow-2xl relative text-slate-350">
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{/* Modal Header */}
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@@ -67,28 +67,28 @@ export default function TechMathModal({ isOpen, onClose }: TechMathModalProps) {
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<p className="text-xs leading-relaxed text-slate-400">
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When technology companies deploy huge amounts of capital for AI clusters and computing nodes, standard revenue metrics may hide margin pressure. The Monetization Gap and ROI-to-CapEx metrics track this by isolating the growth of targeted cloud/AI segments against the velocity of capital investments:
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</p>
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<div className="bg-slate-955/40 p-5 rounded-2xl border border-slate-850 my-2 space-y-4">
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<div className="bg-slate-900/40 p-5 rounded-2xl border border-slate-850 my-2 space-y-4">
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<div>
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<p className="text-xs text-slate-300 mb-2 font-semibold">
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{"Formula for Monetization Gap (\\(G_{\\text{monetization}}\\)):"}
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{"Formula for Monetization Gap ("}<InlineMath math="G_{\text{monetization}}" />{"):"}
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</p>
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<BlockMath math="G_{\\text{monetization}, i, t} = \\Delta \\text{Rev}_{\\text{segment}, i, t} - \\Delta \\text{CapEx}_{i, t}" />
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<BlockMath math="G_{\text{monetization}, i, t} = \Delta \text{Rev}_{\text{segment}, i, t} - \Delta \text{CapEx}_{i, t}" />
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<p className="text-xs text-slate-300 my-2 font-semibold">
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{"Formula for ROI-to-CapEx Ratio (\\(R_{\\text{ROI}}\\)):"}
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{"Formula for ROI-to-CapEx Ratio ("}<InlineMath math="R_{\text{ROI}}" />{"):"}
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</p>
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<BlockMath math="R_{\\text{ROI}, i, t} = \\frac{\\text{Rev}_{\\text{segment}, i, t} - \\text{Rev}_{\\text{segment}, i, t-1}}{\\text{CapEx}_{i, t}} \\times 100" />
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<BlockMath math="R_{\text{ROI}, i, t} = \frac{\text{Rev}_{\text{segment}, i, t} - \text{Rev}_{\text{segment}, i, t-1}}{\text{CapEx}_{i, t}} \times 100" />
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<p className="text-[10px] text-slate-500 mt-3 font-mono leading-relaxed">
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{"Where:"}
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<br />
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{"- "}<InlineMath math="\\Delta \\text{Rev}_{\\text{segment}, i, t}" />{" is the quarter-over-quarter percentage growth rate of isolated Cloud/Segment revenue (e.g., Azure for MSFT, Google Cloud for GOOGL, Data Center for NVDA/AMD, Family of Apps for META)."}
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{"- "}<InlineMath math="\Delta \text{Rev}_{\text{segment}, i, t}" />{" is the quarter-over-quarter percentage growth rate of isolated Cloud/Segment revenue (e.g., Azure for MSFT, Google Cloud for GOOGL, Data Center for NVDA/AMD, Family of Apps for META)."}
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<br />
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{"- "}<InlineMath math="\\Delta \\text{CapEx}_{i, t}" />{" is the quarter-over-quarter percentage growth rate of Capital Expenditures."}
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{"- "}<InlineMath math="\Delta \text{CapEx}_{i, t}" />{" is the quarter-over-quarter percentage growth rate of Capital Expenditures."}
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<br />
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{"- "}<InlineMath math="\\text{CapEx}_{i, t}" />{" is the absolute quarterly capital expenditure of the firm in millions."}
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{"- "}<InlineMath math="\text{CapEx}_{i, t}" />{" is the absolute quarterly capital expenditure of the firm in millions."}
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</p>
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</div>
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<p className="text-xs leading-relaxed text-slate-400">
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<strong className="text-teal-300">Strategic Rationale:</strong>{" A negative Monetization Gap (\\(G_{\\text{monetization}} < 0\\)) indicates that capital spending is growing faster than segment monetization, suggesting diminishing marginal returns. A collapsing ROI-to-CapEx ratio signals that the capital investment is failing to spark immediate segment growth, leading to eventual asset write-downs."}
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<strong className="text-teal-300">Strategic Rationale:</strong>{" A negative Monetization Gap ("}<InlineMath math="G_{\text{monetization}} < 0" />{") indicates that capital spending is growing faster than segment monetization, suggesting diminishing marginal returns. A collapsing "}<InlineMath math="R_{\text{ROI}}" />{" ratio signals that the capital investment is failing to spark immediate segment growth, leading to eventual asset write-downs."}
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</p>
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</div>
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</div>
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@@ -101,22 +101,22 @@ export default function TechMathModal({ isOpen, onClose }: TechMathModalProps) {
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<p className="text-xs leading-relaxed text-slate-400">
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Supply-chain stress is a reliable leading indicator of demand contraction. We monitor the relationship between the key hardware supplier (Nvidia) and the primary cloud buyers (MSFT, GOOGL, META) by comparing buyers' future purchase commitments with the supplier's inventory speeds:
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</p>
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<div className="bg-slate-955/40 p-5 rounded-2xl border border-slate-850 my-2 space-y-4">
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<div className="bg-slate-900/40 p-5 rounded-2xl border border-slate-850 my-2 space-y-4">
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<div>
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<p className="text-xs text-slate-300 mb-2 font-semibold">Nvidia Inventory Turnover (Annualized):</p>
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<BlockMath math="\\text{Turnover}_{\\text{NVDA}, t} = \\frac{\\text{COGS}_{\\text{NVDA}, t}}{\\text{Inventory}_{\\text{NVDA}, t}} \\times 4" />
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<BlockMath math="\text{Turnover}_{\text{NVDA}, t} = \frac{\text{COGS}_{\text{NVDA}, t}}{\text{Inventory}_{\text{NVDA}, t}} \times 4" />
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<p className="text-xs text-slate-300 my-2 font-semibold">
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{"Supply-Chain Velocity Index (\\(V_{\\text{sc}}\\)):"}
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{"Supply-Chain Velocity Index ("}<InlineMath math="V_{\text{sc}}" />{"):"}
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</p>
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<BlockMath math="V_{\\text{sc}, t} = \\frac{\\sum_{j \\in \\text{Buyers}} \\text{Purchase Obligations}_{j, t}}{\\text{Inventory}_{\\text{NVDA}, t}}" />
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<BlockMath math="V_{\text{sc}, t} = \frac{\sum_{j \in \text{Buyers}} \text{Purchase Obligations}_{j, t}}{\text{Inventory}_{\text{NVDA}, t}}" />
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<p className="text-[10px] text-slate-555 mt-3 font-mono leading-relaxed">
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{"Where:"}
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<br />
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{"- "}<InlineMath math="\\text{COGS}_{\\text{NVDA}, t}" />{" is Nvidia's quarterly Cost of Goods Sold."}
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{"- "}<InlineMath math="\text{COGS}_{\text{NVDA}, t}" />{" is Nvidia's quarterly Cost of Goods Sold."}
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<br />
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{"- "}<InlineMath math="\\text{Inventory}_{\\text{NVDA}, t}" />{" is Nvidia's total inventory value on its balance sheet."}
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{"- "}<InlineMath math="\text{Inventory}_{\text{NVDA}, t}" />{" is Nvidia's total inventory value on its balance sheet."}
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<br />
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{"- "}<InlineMath math="\\text{Purchase Obligations}_{j, t}" />{" represents the forward purchase commitments disclosed in the notes of 10-Q filing reports by the buyers (MSFT, GOOGL, META)."}
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{"- "}<InlineMath math="\text{Purchase Obligations}_{j, t}" />{" represents the forward purchase commitments disclosed in the notes of 10-Q filing reports by the buyers (MSFT, GOOGL, META)."}
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</p>
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</div>
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<p className="text-xs leading-relaxed text-slate-400">
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@@ -133,20 +133,20 @@ export default function TechMathModal({ isOpen, onClose }: TechMathModalProps) {
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<p className="text-xs leading-relaxed text-slate-400">
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Aggressive cluster construction requires significant debt or capital consumption. We measure the balance sheet risk of massive computing nodes using the Debt-to-Equity (D/E) and CapEx-to-Depreciation ratios:
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</p>
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<div className="bg-slate-955/40 p-5 rounded-2xl border border-slate-850 my-2 space-y-4">
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<div className="bg-slate-900/40 p-5 rounded-2xl border border-slate-850 my-2 space-y-4">
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<div>
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<p className="text-xs text-slate-300 mb-2 font-semibold">Debt-to-Equity Shift Ratio:</p>
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<BlockMath math="\\text{D/E}_{i, t} = \\frac{\\text{Total Debt}_{i, t}}{\\text{Shareholders' Equity}_{i, t}}" />
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<BlockMath math="\text{D/E}_{i, t} = \frac{\text{Total Debt}_{i, t}}{\text{Shareholders' Equity}_{i, t}}" />
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<p className="text-xs text-slate-300 my-2 font-semibold">
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{"CapEx-to-Depreciation Ratio (\\(R_{\\text{capex-dep}}\\)):"}
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{"CapEx-to-Depreciation Ratio ("}<InlineMath math="R_{\text{capex-dep}}" />{"):"}
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</p>
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<BlockMath math="R_{\\text{capex-dep}, i, t} = \\frac{\\text{CapEx}_{i, t}}{\\text{Depreciation}_{i, t}}" />
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<BlockMath math="R_{\text{capex-dep}, i, t} = \frac{\text{CapEx}_{i, t}}{\text{Depreciation}_{i, t}}" />
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<p className="text-[10px] text-slate-555 mt-3 font-mono leading-relaxed">
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{"Where:"}
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<br />
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{"- "}<InlineMath math="\\text{Total Debt}_{i, t}" />{" represents short-term and long-term interest-bearing debt."}
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{"- "}<InlineMath math="\text{Total Debt}_{i, t}" />{" represents short-term and long-term interest-bearing debt."}
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<br />
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{"- "}<InlineMath math="\\text{Depreciation}_{i, t}" />{" represents the quarterly depreciation expense, reflecting the wear-and-tear of existing physical server arrays."}
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{"- "}<InlineMath math="\text{Depreciation}_{i, t}" />{" represents the quarterly depreciation expense, reflecting the wear-and-tear of existing physical server arrays."}
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</p>
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</div>
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<p className="text-xs leading-relaxed text-slate-400">
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@@ -163,24 +163,24 @@ export default function TechMathModal({ isOpen, onClose }: TechMathModalProps) {
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<p className="text-xs leading-relaxed text-slate-400">
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Investment hyper-leverage creates systematic feedback loops in equity markets. We model the amplification of tech sector risk (asymmetric beta expansion) using a non-linear scaling model:
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</p>
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<div className="bg-slate-955/40 p-5 rounded-2xl border border-slate-850 my-2 space-y-4">
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<div className="bg-slate-900/40 p-5 rounded-2xl border border-slate-850 my-2 space-y-4">
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<div>
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<p className="text-xs text-slate-300 mb-2 font-semibold">Systemic Tech Beta Model:</p>
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<BlockMath math="\\beta_{\\text{tech}, t} = \\beta_{0} \\times \\left(1 + \\gamma \\times \\frac{\\sum_{i} \\text{CapEx}_{i, t}}{\\sum_{i} \\text{Depreciation}_{i, t}}\\right) \\times e^{\\lambda \\times (1 - V_{\\text{sc}, t})}" />
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<BlockMath math="\beta_{\text{tech}, t} = \beta_{0} \times \left(1 + \gamma \times \frac{\sum_{i} \text{CapEx}_{i, t}}{\sum_{i} \text{Depreciation}_{i, t}}\right) \times e^{\lambda \times (1 - V_{\text{sc}, t})}" />
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<p className="text-[10px] text-slate-555 mt-3 font-mono leading-relaxed">
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{"Where:"}
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<br />
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{"- "}<InlineMath math="\\beta_{0}" />{" is the baseline systematic tech beta (historically ~1.10)."}
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{"- "}<InlineMath math="\beta_{0}" />{" is the baseline systematic tech beta (historically ~1.10)."}
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<br />
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{"- "}<InlineMath math="\\gamma" />{" represents the investment intensity multiplier (e.g. 0.05)."}
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{"- "}<InlineMath math="\gamma" />{" represents the investment intensity multiplier (e.g. 0.05)."}
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<br />
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{"- "}<InlineMath math="\\lambda" />{" represents the supply-chain velocity damping constant (e.g. 0.12)."}
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{"- "}<InlineMath math="\lambda" />{" represents the supply-chain velocity damping constant (e.g. 0.12)."}
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<br />
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{"- "}<InlineMath math="V_{\\text{sc}, t}" />{" is the Supply-Chain Velocity Index calculated in Section 2."}
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{"- "}<InlineMath math="V_{\text{sc}, t}" />{" is the Supply-Chain Velocity Index calculated in Section 2."}
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</p>
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</div>
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<p className="text-xs leading-relaxed text-slate-400">
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<strong className="text-teal-300">Economic Rationale:</strong>{" This equation demonstrates that tech equity risk is not static. As CapEx outstrips depreciation (building massive infrastructure) and the Supply-Chain Velocity Index collapses (build-up of unsellable inventory), the systemic beta "}<InlineMath math="\\beta_{\\text{tech}, t}" />{" expands exponentially. Under these parameters, any minor disappointment in earnings results in an asymmetric downward repricing."}
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<strong className="text-teal-300">Economic Rationale:</strong>{" This equation demonstrates that tech equity risk is not static. As CapEx outstrips depreciation (building massive infrastructure) and the Supply-Chain Velocity Index collapses (build-up of unsellable inventory), the systemic beta "}<InlineMath math="\beta_{\text{tech}, t}" />{" expands exponentially. Under these parameters, any minor disappointment in earnings results in an asymmetric downward repricing."}
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</p>
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</div>
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</div>
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@@ -193,26 +193,26 @@ export default function TechMathModal({ isOpen, onClose }: TechMathModalProps) {
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<p className="text-xs leading-relaxed text-slate-400">
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The Sloan Ratio identifies discrepancies between reported net income and actual cash flows. A high proportion of non-cash accruals signals low earnings quality and is a historically proven accounting anomaly predictor:
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</p>
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<div className="bg-slate-955/40 p-5 rounded-2xl border border-slate-850 my-2 space-y-4">
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<div className="bg-slate-900/40 p-5 rounded-2xl border border-slate-850 my-2 space-y-4">
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<div>
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<p className="text-xs text-slate-300 mb-2 font-semibold">
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{"Formula for Accruals (\\(\\text{Accruals}\\)):"}
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{"Formula for Accruals ("}<InlineMath math="\text{Accruals}" />{"):"}
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</p>
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<BlockMath math="\\text{Accruals}_{t} = \\text{Net Income}_{t} - (\\text{CFO}_{t} + \\text{CFI}_{t})" />
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<BlockMath math="\text{Accruals}_{t} = \text{Net Income}_{t} - (\text{CFO}_{t} + \text{CFI}_{t})" />
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<p className="text-xs text-slate-300 my-2 font-semibold">
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{"Formula for Sloan Ratio (\\(\\text{Sloan Ratio}\\)):"}
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{"Formula for Sloan Ratio ("}<InlineMath math="\text{Sloan Ratio}" />{"):"}
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</p>
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<BlockMath math="\\text{Sloan Ratio}_{t} = \\frac{\\text{Accruals}_{t}}{\\text{Total Assets}_{t}} \\times 100" />
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<BlockMath math="\text{Sloan Ratio}_{t} = \frac{\text{Accruals}_{t}}{\text{Total Assets}_{t}} \times 100" />
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<p className="text-[10px] text-slate-555 mt-3 font-mono leading-relaxed">
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{"Where:"}
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<br />
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{"- "}<InlineMath math="\\text{Net Income}_{t}" />{" is the company's net income for the fiscal period."}
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{"- "}<InlineMath math="\text{Net Income}_{t}" />{" is the company's net income for the fiscal period."}
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<br />
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{"- "}<InlineMath math="\\text{CFO}_{t}" />{" is Cash Flow from Operations (operating cash flow)."}
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{"- "}<InlineMath math="\text{CFO}_{t}" />{" is Cash Flow from Operations (operating cash flow)."}
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<br />
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{"- "}<InlineMath math="\\text{CFI}_{t}" />{" is Cash Flow from Investing activities."}
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{"- "}<InlineMath math="\text{CFI}_{t}" />{" is Cash Flow from Investing activities."}
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<br />
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{"- "}<InlineMath math="\\text{Total Assets}_{t}" />{" is the total assets reported on the balance sheet at the end of the period."}
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{"- "}<InlineMath math="\text{Total Assets}_{t}" />{" is the total assets reported on the balance sheet at the end of the period."}
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</p>
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</div>
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<p className="text-xs leading-relaxed text-slate-400">
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