machine

// the coil, the flux machine
interface IFlux {
    // immutable parameters
    function quantum() external view returns (uint256);   // wei, minimum jar for a press
    function cap() external view returns (uint256);       // wei, ceiling of one press before gain
    function h0() external view returns (uint256);        // wei, jar at which saturation is one half
    function d0() external view returns (uint256);        // 1e18 scaled fraction, drop at which lean reaches one
    function nmax() external view returns (uint256);      // distinct pressers at which gain reaches two
    function rewardBps() external view returns (uint256); // presser share of spend, basis points
    function window() external view returns (uint256);   // blocks in the flux window
    function ringBase() external view returns (uint256);  // 1e18 scaled, ring width base
    function token() external view returns (address);
    function pool() external view returns (address);
    function adapter() external view returns (address);
    function deployBlock() external view returns (uint256);

    // live state
    function jar() external view returns (uint256);          // wei held, equals address(this).balance
    function totalIn() external view returns (uint256);      // wei ever received
    function totalSpent() external view returns (uint256);   // wei ever sent to the adapter
    function totalRewards() external view returns (uint256); // wei ever paid to pressers
    function inductions() external view returns (uint256);   // press count
    function pressers() external view returns (uint256);     // distinct presser count
    function hasPressed(address) external view returns (bool);
    function anchor() external view returns (uint256);       // tokens per eth, 1e18, at end of last press
    function lastBlock() external view returns (uint256);    // block of last press
    function reserve() external view returns (uint256);      // tokens held by the adapter for pairing
    function sample(uint256 i) external view returns (uint256 blockNumber, uint256 cumulative);
    function rate() external view returns (uint256);         // wei per block over the window

    // preview of the next press, all computed the same way induce computes them
    function preview() external view returns (
        bool armed,
        uint256 spend,
        uint256 reward,
        uint256 b,        // 1e18 scaled lean
        uint256 g,        // 1e18 scaled gain
        uint256 ringIndex,
        uint256 lower,    // tokens per eth, 1e18
        uint256 upper
    );

    // the button
    function induce() external;

    receive() external payable;

    event Received(uint256 amount, uint256 blockNumber, uint256 cumulative);
    event Induced(
        uint256 indexed press,
        address indexed presser,
        uint256 spend,
        uint256 reward,
        uint256 b,
        uint256 tokensBought,
        uint256 ethPaired,
        uint256 tokensPaired,
        uint256 spotBefore,
        uint256 anchorBefore,
        uint256 blockNumber
    );
    event RingMinted(
        uint256 indexed press,
        uint256 ring,
        uint256 lower,
        uint256 upper,
        uint256 positionId,
        uint256 ethPaired,
        uint256 tokensPaired
    );
}

// the pool adapter, written against the pons pool at deployment, set once, never changed
interface IFluxAdapter {
    function spot() external view returns (uint256);        // tokens per eth, 1e18
    function burnedCount() external view returns (uint256); // positions held by the burn address
    function reserve() external view returns (uint256);
    function execute(uint256 b, uint256 ringIndex) external payable
        returns (uint256 tokensBought, uint256 ethPaired, uint256 tokensPaired, uint256 positionId, uint256 lower, uint256 upper);
}

Φ(n)      = cumulative wei received up to block n
rate      = (Φ(now) − Φ(now − window)) / window
armed     = jar ≥ quantum  and  block.number > lastBlock
g         = 1 + min(pressers, nmax) / nmax
S         = min(jar, cap × g × jar / (jar + h0))
reward    = S × rewardBps / 10000
deploy    = S − reward
d         = max(0, (anchor − spot) / anchor)          (d = 0 on the first press)
b         = ½ + ½ × min(1, d / d0)
buy       = b × deploy
pairEth   = (1 − b) × deploy
ringIndex = floor(log2(inductions + 1))
lower     = spot / (1 + ringBase)^(ringIndex + 1)
upper     = spot × (1 + ringBase)^(ringIndex + 1)
after     : anchor = spot(after execute), lastBlock = block.number, inductions += 1
invariant : totalIn = jar + totalSpent + totalRewards