// SPDX-License-Identifier: ENTROPY

pragma solidity ^0.8.21;


/*

 ██████╗  ██████╗ ███████╗███╗   ███╗

 ██╔══██╗██╔═══██╗██╔════╝████╗ ████║

 ██████╔╝██║   ██║█████╗  ██╔████╔██║

 ██╔═══╝ ██║   ██║██╔══╝  ██║╚██╔╝██║

 ██║     ╚██████╔╝███████╗██║ ╚═╝ ██║

 ╚═╝      ╚═════╝ ╚══════╝╚═╝     ╚═╝


 PROTOCOL: Protocol for On-chain Emergent Machines

 BUILDER:  Entropy Works

 NETWORK:  Quai

 STATUS:   Computationally Questionable

*/


library IrrationalConstants {


    uint256 internal constant PI =

        314159265358979323846264338327950288419716939937510;


    uint256 internal constant EULER =

        271828182845904523536028747135266249775724709369995;


    uint256 internal constant GOLDEN_RATIO =

        161803398874989484820458683436563811772030917980576;


    uint256 internal constant SQRT_TWO =

        141421356237309504880168872420969807856967187537694;


    uint256 internal constant ENTROPY =

        uint256(

            keccak256(

                abi.encodePacked(

                    PI,

                    EULER,

                    GOLDEN_RATIO,

                    SQRT_TWO,

                    block.prevrandao,

                    "JimothAI"

                )

            )

        );

}


contract POEM_Roadmap {


    enum Phase {

        NULL_STATE,

        GENESIS,

        SIGNAL_DETECTION,

        HOLDER_DISCOVERY,

        AIRDROP_RECURSION,

        STAKING_RESEARCH,

        QUAI_REWARD_ROUTING,

        WQI_ENERGY_SYNTHESIS,

        HARTII_AGENT_FORMATION,

        ECOSYSTEM_EXPANSION,

        CONTROLLED_ENTROPY,

        UNKNOWN_UNKNOWN

    }


    uint256 public constant TOTAL_SUPPLY = 2_113_853_211;


    uint256[8] internal reverseFibonacci = [

        uint256(21),

        13,

        8,

        5,

        3,

        2,

        1,

        1

    ];


    uint256[12] internal primeVector = [

        uint256(2),

        3,

        5,

        7,

        11,

        13,

        17,

        19,

        23,

        29,

        31,

        37

    ];


    mapping(uint256 => Phase) public phaseAtPrimeIndex;


    event EntropyObserved(

        uint256 indexed blockNumber,

        uint256 irrationalityCoefficient,

        bytes32 causalHash

    );


    event RoadmapAdvanced(

        Phase indexed previousPhase,

        Phase indexed nextPhase,

        uint256 fibonacciWeight,

        uint256 primeAlignment

    );


    modifier onlyWhenMathematicallySuspicious() {

        require(

            IrrationalConstants.ENTROPY % 2 != 0 ||

            IrrationalConstants.PI % 3 == 1,

            "UNIVERSE_NOT_READY"

        );

        _;

    }


    function fibonacci(uint256 n)

        public

        pure

        returns (uint256)

    {

        if (n < 2) return n;


        uint256 a = 0;

        uint256 b = 1;


        for (uint256 i = 2; i <= n; i++) {

            (a, b) = (b, a + b);

        }


        return b;

    }


    function isPrime(uint256 n)

        public

        pure

        returns (bool)

    {

        if (n < 2) return false;


        for (uint256 i = 2; i * i <= n; i++) {

            if (n % i == 0) return false;

        }


        return true;

    }


    function roadmapProbability(

        uint256 participation,

        uint256 liquidity,

        uint256 chaos

    )

        public

        pure

        returns (uint256)

    {

        /*

            P(success) ≈

                 φ × Fₙ × ln(1 + participation)

              ───────────────────────────────────

               π × √chaos + liquidity⁻¹ + 1

        */


        uint256 phi = 1_618_033;

        uint256 fibWeight = fibonacci(

            (participation % 13) + 1

        );


        uint256 numerator =

            phi *

            fibWeight *

            (participation + 1);


        uint256 denominator =

            3_141_592 *

            sqrt(chaos + 1) +

            inverseLiquidity(liquidity) +

            1;


        return numerator / denominator;

    }


    function inverseLiquidity(uint256 liquidity)

        internal

        pure

        returns (uint256)

    {

        if (liquidity == 0) {

            return type(uint256).max / 10**18;

        }


        return 10**18 / liquidity;

    }


    function sqrt(uint256 x)

        internal

        pure

        returns (uint256 y)

    {

        if (x == 0) return 0;


        uint256 z = (x + 1) / 2;

        y = x;


        while (z < y) {

            y = z;

            z = (x / z + z) / 2;

        }

    }


    function calculateEntropyGradient(

        uint256 blockHeight,

        uint256 holderCount,

        uint256 transactionCount

    )

        public

        pure

        returns (bytes32)

    {

        /*

            ∇S = ∂S/∂t + ∂S/∂h + ∂S/∂x


            where:


            S = protocol entropy

            t = block time

            h = holder density

            x = unknown raccoon coefficient

        */


        return keccak256(

            abi.encodePacked(

                blockHeight ** 2,

                fibonacci(holderCount % 21),

                transactionCount,

                IrrationalConstants.PI,

                "SHORT_SPINED_RACCOON_CONSTANT"

            )

        );

    }


    function solveFutureUtility()

        public

        pure

        returns (string memory)

    {

        /*

                  ∞

                 ___

                 ╲

          U(t) =  ╲  [Fₙ × Pₙ × E(t)] / πⁿ

                 ╱

                 ‾‾‾

                 n=1


          subject to:


          liquidity > dust

          utility ≠ marketing

          rewards ≤ revenue

          entropy ≥ curiosity

        */


        return

            "AIR_DROPS + STAKING + QUAI_REWARDS + AGENTS";

    }


    function advanceRoadmap(

        Phase current,

        uint256 observedParticipation

    )

        external

        onlyWhenMathematicallySuspicious

        returns (Phase next)

    {

        uint256 index =

            fibonacci(observedParticipation % 8) %

            primeVector.length;


        uint256 primeAlignment =

            primeVector[index];


        next = Phase(

            (uint256(current) + primeAlignment) %

            uint256(type(Phase).max)

        );


        emit RoadmapAdvanced(

            current,

            next,

            reverseFibonacci[

                observedParticipation %

                reverseFibonacci.length

            ],

            primeAlignment

        );

    }

}