"""Saturation model v1 (docs/saturation-design.md, after Opus review 2026-09-18). Pure functions.
Idea: N buildings is limited by (a) share of the market's steady traded flow, (b) the queue of existing
sell orders (supply days) and (c) whether buy-side stock covers it. Price is a haircut model, not a book walk."""
import math

S_SHARE = 0.25     # max share of traded flow one producer takes
T_Q = 7            # days of flow the standing sell queue is compared against
T_D = 7            # days of flow standing demand should cover
T_W = 3            # patient-selling window (days)


def tref(traded7: float, traded30: float) -> float:
    """Conservative daily flow: min(7d, 30d); with a Poisson lower bound when 30d volume is small."""
    t = min(traded7, traded30)
    if 0 < traded30 < 20:
        t = min(t, max(0.0, traded30 * (1 - 1.96 / math.sqrt(30 * traded30))))
    return max(0.0, t)


def is_thin(tr: float, demand: float, q_out: float) -> bool:
    return tr < 3 * q_out or demand < 7 * q_out


def n_out(tr: float, supply: float, demand: float, q_out: float) -> float:
    """Buildings the output market absorbs: flow share x queue penalty x demand coverage. 0 if no flow."""
    if tr <= 0 or q_out <= 0:
        return 0.0
    base = S_SHARE * tr / q_out
    queue = min(1.0, T_Q * tr / supply) if supply > 0 else 1.0
    cover = min(1.0, demand / (T_D * tr))
    return base * queue * cover


def p_patient(asks: list[tuple[float, float]], tr: float, produced_per_day: float, bid: float, vwap7: float | None,
              vwap30: float | None, ask: float | None, wide_high: float | None = None) -> float:
    """Price we can hold asks at. asks = [(price, units)] ascending. Find the highest ask level whose units-ahead
    (levels strictly below) <= what buyers will absorb of the queue over T_W days once our output is counted:
    target = T_W * (tr - produced). target <= 0 => sell at the bid. Clamped to [bid, min(vwap7, vwap30, ask, wide_high)]."""
    hi = min(x for x in (vwap7, vwap30, ask, wide_high) if x)
    target = T_W * (tr - produced_per_day)
    if target <= 0:
        return bid
    p, ahead = hi, 0.0
    for price, units in asks:
        if ahead <= target:
            p = price
        ahead += units
    return max(bid, min(p, hi))


def effective_supply(asks: list[tuple[float, float]], ref_price: float | None, band: float = 1.25) -> float:
    """Units of standing sell orders that actually compete: price <= band x reference (vwap7 or ask).
    Stale asks far above market (e.g. 1500 units at 1.5x vwap) are not competition. asks = [(price, units)]."""
    if not ref_price:
        return sum(u for _, u in asks)
    return sum(u for p, u in asks if p <= band * ref_price)