Notation — Canonical Symbol Table

All Wiki derivations and docstrings reference this table. One notation system across the entire library.

Valuation Variables

Symbol	Meaning	Units	Code Variable	Module
$$V$$	Valuation (output)	USD	result.value	all
$$V_{avg}$$	Average regional pre-money valuation	USD	average_valuation	core
$$V_{pre}$$	Pre-money valuation	USD	result.value	core
$$V_{post}$$	Post-money valuation	USD	result.value	core
$$V_{base}$$	Base valuation from comparables	USD	base_valuation	core

Scorecard Method

Symbol	Meaning	Units	Code Variable
$$w_i$$	Factor weight $$i$$ ($$\sum w_i = 1$$)	Dimensionless	weights[i]
$$s_i$$	Factor score $$i$$ (1.0 = average)	Dimensionless	scores[i]
$$n$$	Number of factors (typically 7)	Count	len(weights)

Time Value

Symbol	Meaning	Units	Code Variable
$$r$$	Discount rate (risk-free or WACC)	Annual %	rate
$$t$$	Time (years)	Years	time_to_maturity
$$T$$	Total time horizon	Years	years
$$CF_t$$	Cash flow at time $$t$$	USD	cashflows[t]
$$PV$$	Present value	USD	result.value
$$NPV$$	Net present value	USD	result.value

Option Pricing (Black-Scholes)

Symbol	Meaning	Units	Code Variable
$$S$$	Underlying asset value	USD	underlying
$$K$$	Strike price	USD	strike
$$\sigma$$	Volatility	Annual %	volatility
$$T$$	Time to maturity	Years	time_to_maturity
$$r_f$$	Risk-free rate	Annual %	risk_free_rate
$$N(d)$$	Standard normal CDF	Probability	scipy.stats.norm.cdf(d)
$$d_1$$	Intermediate term 1	Dimensionless	(computed)
$$d_2$$	Intermediate term 2	Dimensionless	(computed)
$$C$$	Call option value	USD	result.value

SaaS Metrics

Symbol	Meaning	Units	Code Variable
$$ARR$$	Annual Recurring Revenue	USD/year	arr_value
$$MRR$$	Monthly Recurring Revenue	USD/month	mrr_value
$$CAC$$	Customer Acquisition Cost	USD	result.value
$$LTV$$	Lifetime Value	USD	result.value
$$NRR$$	Net Revenue Retention	%	result.value
$$\text{Churn}$$	Customer churn rate	%/period	churn_rate

Risk & Probability

Symbol	Meaning	Units	Code Variable
$$P(X)$$	Probability of event $$X$$	[0, 1]	probability
$$\lambda$$	Poisson rate parameter	Events/period	lambda_
$$E[X]$$	Expected value of $$X$$	Same as $$X$$	result.value
$$\beta$$	Portfolio beta	Dimensionless	beta
$$\alpha$$	Jensen's alpha	%	alpha

Biotech

Symbol	Meaning	Units	Code Variable
$$P_{success}$$	Probability of clinical success	[0, 1]	success_probability
$$D_{cost}$$	Development cost	USD	development_cost
$$rNPV$$	Risk-adjusted net present value	USD	result.value

Formatting Rules

1. Display math on its own line: $$V = V_{avg} \times \sum w_i \times s_i$$
2. Inline math within text: $$V_{avg}$$
3. Subscripts for indices: w_i (not wi)
4. Units always stated explicitly
5. Consistent notation across all Wiki pages and docstrings — never switch between $$x_i$$ and x[i] without explanation