Technical Reference

Hecke

Source updated:: 2024-10-28 03:57:05 UTC
Last updated:: 2026-09-19 17:18:07 UTC

Source Revision 0x43eaadc8…4a74de

Property	Value
Source Revision	`0x43eaadc802dbc2559957b17ac5f11129b3490732c0c2e8a44b7e38395f4a74de`
Source URL	https://raw.githubusercontent.com/busytoby/atropa_pulsechain/4524ff259eb1e76fe377a8abb1b2d246a08118bf/solidity/dysnomia/lib/heckemeridians.sol
Source commit	`4524ff259eb1e76fe377a8abb1b2d246a08118bf`
Source Status	Source snapshot; source hashes do not establish deployed bytecode equivalence.
Compiler	solc 0.8.21; optimizer enabled with 200 runs
Compiler Configuration	`{"evmVersion":"compiler-default","optimizer":{"enabled":true,"runs":200},"version":"0.8.21+commit.d9974bed.Linux.g++"}`
Compilation Closure Hash	`0x2c77db20345cff4f5c0d94941dc77b2e8bedc0cfea2e5947488991c90d3861c3`
Compilation Closure Files	20
Hash Generated	2026-04-20T02:38:30Z

Overview

Hecke implements a geographic coordinate system with 90 meridian bands. It maps large numbers (Waat values) to latitude/longitude coordinates, enabling location-based token mechanics.

Kind: Contract
License: Sharia
Solidity: ^0.8.21
Source: lib/heckemeridians.sol

Contract address:

0x29A924D9B0233026B9844f2aFeB202F1791D7593

Inheritance Chain (C3 Linearized)

Immediate Parents

DYSNOMIA

What This Means For Players

Plain English Summary: Hecke is the coordinate system - it turns numbers into map locations. Every QING has a “Waat” (position number) that Hecke converts into latitude and longitude coordinates. This is how the game places venues on the world map.

Real-World Analogy: Think of Hecke like a GPS system that converts numerical addresses into physical locations. Just as your GPS turns an address into “you are here” on a map, Hecke turns a Waat number into a specific latitude/longitude position in the Dysnomia world.

How It Affects Your Gameplay:

Map positions - Every venue has a unique position calculated by Hecke
90 meridian bands - The world is divided into 90 zones from south to north
Territory proximity - When claiming territory, your distance from venues is calculated using Hecke coordinates
Geographic lookup - Find which venue is at any given coordinates

State Variables

Variable	Type	Visibility	Mutability	Initial Value
`Meridians`	`uint256[90]`	public	mutable	`[
476733977057179,
3256639860692891,
…`

Constructor

constructor

constructorconstructor

constructor(address ChoAddress) DYSNOMIA("Dysnomia Hecke", "HECKE", address(DYSNOMIA(ChoAddress).Xiao()))

Modifiers: DYSNOMIA("Dysnomia Hecke", "HECKE", address(DYSNOMIA(ChoAddress).Xiao()))
Parameters: address ChoAddress

Functions

External & Public

Compliment

Complimentfunction

function Compliment(uint256 Waat) public view returns (int256 Longitude, int256 Latitude)

Open this function to load its call form.

Visibility: public
State Mutability: view
Parameters: uint256 Waat
Returns: int256 Longitude, int256 Latitude

GetWaat

GetWaatfunction

function GetWaat(int256 Latitude) public view returns (uint256 Waat)

Open this function to load its call form.

Visibility: public
State Mutability: view
Parameters: int256 Latitude
Returns: uint256 Waat

GetMeridian

GetMeridianfunction

function GetMeridian(uint256 Waat) public view returns (uint256 Meridian)

Open this function to load its call form.

Visibility: public
State Mutability: view
Parameters: uint256 Waat
Returns: uint256 Meridian

Inherited Members

Public and external functions below are callable through this contract’s address. Parent links identify where each member is defined.

From DYSNOMIA

External & Public Functions

Rename

Renamefunction

function Rename(string memory newName, string memory newSymbol) public virtual onlyOwners

Open this function to load its call form.

Visibility: public
Virtual: yes
Modifiers: onlyOwners
Parameters: string memory newName, string memory newSymbol

mintToCap

mintToCapfunction

function mintToCap() public onlyOwners

Open this function to load its call form.

Visibility: public
Modifiers: onlyOwners

GetMarketRate

GetMarketRatefunction

function GetMarketRate(address _a) public view returns (uint256)

Open this function to load its call form.

Visibility: public
State Mutability: view
Parameters: address _a
Returns: uint256

Purchase

Purchasefunction

function Purchase(address _t, uint256 _a) public

Open this function to load its call form.

Visibility: public
Parameters: address _t, uint256 _a

Redeem

Redeemfunction

function Redeem(address _t, uint256 _a) public

Open this function to load its call form.

Visibility: public
Parameters: address _t, uint256 _a

name

namefunction

function name() public view virtual returns (string memory)

Open this function to load its call form.

Visibility: public
State Mutability: view
Virtual: yes
Returns: string memory

symbol

symbolfunction

function symbol() public view virtual returns (string memory)

Open this function to load its call form.

Visibility: public
State Mutability: view
Virtual: yes
Returns: string memory

decimals

decimalsfunction

function decimals() public view virtual returns (uint8)

Open this function to load its call form.

Visibility: public
State Mutability: view
Virtual: yes
Returns: uint8

totalSupply

totalSupplyfunction

function totalSupply() public view virtual returns (uint256)

Open this function to load its call form.

Visibility: public
State Mutability: view
Virtual: yes
Returns: uint256

balanceOf

balanceOffunction

function balanceOf(address account) public view virtual returns (uint256)

Open this function to load its call form.

Visibility: public
State Mutability: view
Virtual: yes
Parameters: address account
Returns: uint256

transfer

transferfunction

function transfer(address to, uint256 value) public virtual returns (bool)

Open this function to load its call form.

Visibility: public
Virtual: yes
Parameters: address to, uint256 value
Returns: bool

allowance

allowancefunction

function allowance(address owner, address spender) public view virtual returns (uint256)

Open this function to load its call form.

Visibility: public
State Mutability: view
Virtual: yes
Parameters: address owner, address spender
Returns: uint256

approve

approvefunction

function approve(address spender, uint256 value) public virtual returns (bool)

Open this function to load its call form.

Visibility: public
Virtual: yes
Parameters: address spender, uint256 value
Returns: bool

transferFrom

transferFromfunction

function transferFrom(address from, address to, uint256 value) public virtual returns (bool)

Open this function to load its call form.

Visibility: public
Virtual: yes
Parameters: address from, address to, uint256 value
Returns: bool

Internal Functions

Function	Signature
`_addLibraryOwner`	`function _addLibraryOwner(VOID Void, string memory what) internal`
`_mintToCap`	`function _mintToCap() internal`
`_addMarketRate`	`function _addMarketRate(address _a, uint256 _r) internal`
`_transfer`	`function _transfer(address from, address to, uint256 value) internal`
`_update`	`function _update(address from, address to, uint256 value) internal virtual`
`_mint`	`function _mint(address account, uint256 value) internal`
`_approve`	`function _approve(address owner, address spender, uint256 value) internal`
`_approve`	`function _approve(address owner, address spender, uint256 value, bool emitEvent) internal virtual`
`_spendAllowance`	`function _spendAllowance(address owner, address spender, uint256 value) internal virtual`

Events

Event	Parameters
`Transfer`	address indexed from, address indexed to, uint256 value
`Approval`	address indexed owner, address indexed spender, uint256 value

Errors

Error	Parameters
`MarketRateNotFound`	address asset
`DysnomiaInsufficientBalance`	address origin, address sender, address from, address to, address what, uint256 balance, uint256 needed
`DysnomiaInsufficientAllowance`	address origin, address sender, address owner, address spender, address what, uint256 allowance, uint256 needed

State Variables (private parent storage is not reachable and is omitted)

Variable	Type	Visibility	Mutability
`__name`	`string`	internal	mutable
`__symbol`	`string`	internal	mutable
`MotzkinPrime`	`uint64`	public	constant
`Xiao`	`atropaMath`	public	mutable
`maxSupply`	`uint256`	public	mutable

From MultiOwnable

External & Public Functions

owner

ownerfunction

function owner() external view virtual returns (address)

Open this function to load its call form.

Visibility: external
State Mutability: view
Virtual: yes
Returns: address

owner

ownerfunction

function owner(address cOwner) public view virtual returns (bool)

Open this function to load its call form.

Visibility: public
State Mutability: view
Virtual: yes
Parameters: address cOwner
Returns: bool

renounceOwnership

renounceOwnershipfunction

function renounceOwnership(address toRemove) public virtual onlyOwners

Open this function to load its call form.

Visibility: public
Virtual: yes
Modifiers: onlyOwners
Parameters: address toRemove

addOwner

addOwnerfunction

function addOwner(address newOwner) public virtual onlyOwners

Open this function to load its call form.

Visibility: public
Virtual: yes
Modifiers: onlyOwners
Parameters: address newOwner

Internal Functions

Function	Signature
`_checkOwner`	`function _checkOwner() internal view virtual`
`_changeOwnership`	`function _changeOwnership(address cOwner, bool cState) internal virtual`

Events

Event	Parameters
`OwnershipUpdate`	address indexed newOwner, bool indexed state

Errors

Error	Parameters
`OwnableUnauthorizedAccount`	address origin, address account, address what
`OwnableInvalidOwner`	address origin, address owner, address what

Modifiers

Modifier	Parameters
`onlyOwners`	(none)

Meridians Array

The Meridians array contains exponentially increasing boundary values:

Meridians[0]  = 476733977057179         // ~4.7e14
Meridians[1]  = 3256639860692891        // ~3.2e15
...
Meridians[88] = 394003890037732925341349197890665503744188106368861304015211794431709973855
Meridians[89] = 788007780075465850682698395781331007488376212737722608030423588863419947711

The array represents:

Meridians 0-88: Southern to Northern hemisphere bands
Meridian 89: Maximum value (wraps to north pole)

Contract Interactions

Depends On

DYSNOMIA V2 - Base functionality
CHO - Receives market rate

Depended On By

MAP - Uses for coordinate mapping
WORLD - Geographic operations

Special Mechanisms

Coordinate System

         North Pole (Meridian 89)
              ↑
    +Lat  ←---|---→  -Lat
              |
         South Pole (Meridian 0)

    West ← Longitude → East
    (-X)              (+X)

Compliment Algorithm

1. Assert Waat <= Meridians[89]
2. Get Meridian index
3. If Meridian == 89:
   - Flip to northern hemisphere
   - Recalculate from inverse
4. Calculate Latitude from Meridians[88] distance
5. Calculate Longitude within meridian band:
   - First half: positive longitude
   - Second half: negative longitude
6. Scale Latitude by 333
7. Apply hemisphere sign

Latitude Scaling

Latitude is divided by 333 to compress the large Waat values into manageable coordinate ranges.

Hemisphere Handling

Values above Meridian 88 represent the northern hemisphere, handled by subtracting from the maximum and recalculating.

Usage Pattern

// Get coordinates for a Waat value
(int256 lon, int256 lat) = hecke.Compliment(someWaat);

// Find meridian for a value
uint256 meridian = hecke.GetMeridian(someWaat);

// Get Waat for latitude
uint256 waat = hecke.GetWaat(lat);

Geographic Token Mechanics

The Hecke system enables:

Location-based tokens: Each QING token has a Waat that maps to coordinates
Proximity checks: Determine if tokens are in the same region
Territory mechanics: Define areas based on meridian bands
Distance calculations: Compare Waat values for relative position

Example Mapping

Waat = 476733977057179 (Meridian 0 boundary)
→ Near equator, specific longitude

Waat = 394003890037732925... (Meridian 88)
→ Near north pole, high latitude

Waat between boundaries
→ Proportional position within band

Integration with MAP

The MAP contract uses Hecke to:

Assign geographic position to new QING tokens
Organize tokens by location
Enable location-based lookup via _map[Latitude][Longitude]

Inherited functions and getters (4)

Hecke.Meridians(uint256)Read

Open this function to load its call form.

Hecke.MotzkinPrime()Read

Open this function to load its call form.

Hecke.Xiao()Read

Open this function to load its call form.

Hecke.maxSupply()Read

Open this function to load its call form.

Compiled ABI

The compiled ABI below is produced by solc 0.8.21 from the exact source bytes recorded in Source details. Consumers can paste it directly into ethers/web3/viem.

Click to expand JSON ABI

[
  {
    "inputs": [
      {
        "internalType": "address",
        "name": "ChoAddress",
        "type": "address"
      }
    ],
    "stateMutability": "nonpayable",
    "type": "constructor"
  },
  {
    "inputs": [
      {
        "internalType": "address",
        "name": "origin",
        "type": "address"
      },
      {
        "internalType": "address",
        "name": "sender",
        "type": "address"
      },
      {
        "internalType": "address",
        "name": "owner",
        "type": "address"
      },
      {
        "internalType": "address",
        "name": "spender",
        "type": "address"
      },
      {
        "internalType": "address",
        "name": "what",
        "type": "address"
      },
      {
        "internalType": "uint256",
        "name": "allowance",
        "type": "uint256"
      },
      {
        "internalType": "uint256",
        "name": "needed",
        "type": "uint256"
      }
    ],
    "name": "DysnomiaInsufficientAllowance",
    "type": "error"
  },
  {
    "inputs": [
      {
        "internalType": "address",
        "name": "origin",
        "type": "address"
      },
      {
        "internalType": "address",
        "name": "sender",
        "type": "address"
      },
      {
        "internalType": "address",
        "name": "from",
        "type": "address"
      },
      {
        "internalType": "address",
        "name": "to",
        "type": "address"
      },
      {
        "internalType": "address",
        "name": "what",
        "type": "address"
      },
      {
        "internalType": "uint256",
        "name": "balance",
        "type": "uint256"
      },
      {
        "internalType": "uint256",
        "name": "needed",
        "type": "uint256"
      }
    ],
    "name": "DysnomiaInsufficientBalance",
    "type": "error"
  },
  {
    "inputs": [
      {
        "internalType": "address",
        "name": "asset",
        "type": "address"
      }
    ],
    "name": "MarketRateNotFound",
    "type": "error"
  },
  {
    "inputs": [
      {
        "internalType": "address",
        "name": "origin",
        "type": "address"
      },
      {
        "internalType": "address",
        "name": "owner",
        "type": "address"
      },
      {
        "internalType": "address",
        "name": "what",
        "type": "address"
      }
    ],
    "name": "OwnableInvalidOwner",
    "type": "error"
  },
  {
    "inputs": [
      {
        "internalType": "address",
        "name": "origin",
        "type": "address"
      },
      {
        "internalType": "address",
        "name": "account",
        "type": "address"
      },
      {
        "internalType": "address",
        "name": "what",
        "type": "address"
      }
    ],
    "name": "OwnableUnauthorizedAccount",
    "type": "error"
  },
  {
    "anonymous": false,
    "inputs": [
      {
        "indexed": true,
        "internalType": "address",
        "name": "owner",
        "type": "address"
      },
      {
        "indexed": true,
        "internalType": "address",
        "name": "spender",
        "type": "address"
      },
      {
        "indexed": false,
        "internalType": "uint256",
        "name": "value",
        "type": "uint256"
      }
    ],
    "name": "Approval",
    "type": "event"
  },
  {
    "anonymous": false,
    "inputs": [
      {
        "indexed": true,
        "internalType": "address",
        "name": "newOwner",
        "type": "address"
      },
      {
        "indexed": true,
        "internalType": "bool",
        "name": "state",
        "type": "bool"
      }
    ],
    "name": "OwnershipUpdate",
    "type": "event"
  },
  {
    "anonymous": false,
    "inputs": [
      {
        "indexed": true,
        "internalType": "address",
        "name": "from",
        "type": "address"
      },
      {
        "indexed": true,
        "internalType": "address",
        "name": "to",
        "type": "address"
      },
      {
        "indexed": false,
        "internalType": "uint256",
        "name": "value",
        "type": "uint256"
      }
    ],
    "name": "Transfer",
    "type": "event"
  },
  {
    "inputs": [
      {
        "internalType": "uint256",
        "name": "Waat",
        "type": "uint256"
      }
    ],
    "name": "Compliment",
    "outputs": [
      {
        "internalType": "int256",
        "name": "Longitude",
        "type": "int256"
      },
      {
        "internalType": "int256",
        "name": "Latitude",
        "type": "int256"
      }
    ],
    "stateMutability": "view",
    "type": "function"
  },
  {
    "inputs": [
      {
        "internalType": "address",
        "name": "_a",
        "type": "address"
      }
    ],
    "name": "GetMarketRate",
    "outputs": [
      {
        "internalType": "uint256",
        "name": "",
        "type": "uint256"
      }
    ],
    "stateMutability": "view",
    "type": "function"
  },
  {
    "inputs": [
      {
        "internalType": "uint256",
        "name": "Waat",
        "type": "uint256"
      }
    ],
    "name": "GetMeridian",
    "outputs": [
      {
        "internalType": "uint256",
        "name": "Meridian",
        "type": "uint256"
      }
    ],
    "stateMutability": "view",
    "type": "function"
  },
  {
    "inputs": [
      {
        "internalType": "int256",
        "name": "Latitude",
        "type": "int256"
      }
    ],
    "name": "GetWaat",
    "outputs": [
      {
        "internalType": "uint256",
        "name": "Waat",
        "type": "uint256"
      }
    ],
    "stateMutability": "view",
    "type": "function"
  },
  {
    "inputs": [
      {
        "internalType": "uint256",
        "name": "",
        "type": "uint256"
      }
    ],
    "name": "Meridians",
    "outputs": [
      {
        "internalType": "uint256",
        "name": "",
        "type": "uint256"
      }
    ],
    "stateMutability": "view",
    "type": "function"
  },
  {
    "inputs": [],
    "name": "MotzkinPrime",
    "outputs": [
      {
        "internalType": "uint64",
        "name": "",
        "type": "uint64"
      }
    ],
    "stateMutability": "view",
    "type": "function"
  },
  {
    "inputs": [
      {
        "internalType": "address",
        "name": "_t",
        "type": "address"
      },
      {
        "internalType": "uint256",
        "name": "_a",
        "type": "uint256"
      }
    ],
    "name": "Purchase",
    "outputs": [],
    "stateMutability": "nonpayable",
    "type": "function"
  },
  {
    "inputs": [
      {
        "internalType": "address",
        "name": "_t",
        "type": "address"
      },
      {
        "internalType": "uint256",
        "name": "_a",
        "type": "uint256"
      }
    ],
    "name": "Redeem",
    "outputs": [],
    "stateMutability": "nonpayable",
    "type": "function"
  },
  {
    "inputs": [
      {
        "internalType": "string",
        "name": "newName",
        "type": "string"
      },
      {
        "internalType": "string",
        "name": "newSymbol",
        "type": "string"
      }
    ],
    "name": "Rename",
    "outputs": [],
    "stateMutability": "nonpayable",
    "type": "function"
  },
  {
    "inputs": [],
    "name": "Xiao",
    "outputs": [
      {
        "internalType": "contract atropaMath",
        "name": "",
        "type": "address"
      }
    ],
    "stateMutability": "view",
    "type": "function"
  },
  {
    "inputs": [
      {
        "internalType": "address",
        "name": "newOwner",
        "type": "address"
      }
    ],
    "name": "addOwner",
    "outputs": [],
    "stateMutability": "nonpayable",
    "type": "function"
  },
  {
    "inputs": [
      {
        "internalType": "address",
        "name": "owner",
        "type": "address"
      },
      {
        "internalType": "address",
        "name": "spender",
        "type": "address"
      }
    ],
    "name": "allowance",
    "outputs": [
      {
        "internalType": "uint256",
        "name": "",
        "type": "uint256"
      }
    ],
    "stateMutability": "view",
    "type": "function"
  },
  {
    "inputs": [
      {
        "internalType": "address",
        "name": "spender",
        "type": "address"
      },
      {
        "internalType": "uint256",
        "name": "value",
        "type": "uint256"
      }
    ],
    "name": "approve",
    "outputs": [
      {
        "internalType": "bool",
        "name": "",
        "type": "bool"
      }
    ],
    "stateMutability": "nonpayable",
    "type": "function"
  },
  {
    "inputs": [
      {
        "internalType": "address",
        "name": "account",
        "type": "address"
      }
    ],
    "name": "balanceOf",
    "outputs": [
      {
        "internalType": "uint256",
        "name": "",
        "type": "uint256"
      }
    ],
    "stateMutability": "view",
    "type": "function"
  },
  {
    "inputs": [],
    "name": "decimals",
    "outputs": [
      {
        "internalType": "uint8",
        "name": "",
        "type": "uint8"
      }
    ],
    "stateMutability": "view",
    "type": "function"
  },
  {
    "inputs": [],
    "name": "maxSupply",
    "outputs": [
      {
        "internalType": "uint256",
        "name": "",
        "type": "uint256"
      }
    ],
    "stateMutability": "view",
    "type": "function"
  },
  {
    "inputs": [],
    "name": "mintToCap",
    "outputs": [],
    "stateMutability": "nonpayable",
    "type": "function"
  },
  {
    "inputs": [],
    "name": "name",
    "outputs": [
      {
        "internalType": "string",
        "name": "",
        "type": "string"
      }
    ],
    "stateMutability": "view",
    "type": "function"
  },
  {
    "inputs": [
      {
        "internalType": "address",
        "name": "cOwner",
        "type": "address"
      }
    ],
    "name": "owner",
    "outputs": [
      {
        "internalType": "bool",
        "name": "",
        "type": "bool"
      }
    ],
    "stateMutability": "view",
    "type": "function"
  },
  {
    "inputs": [],
    "name": "owner",
    "outputs": [
      {
        "internalType": "address",
        "name": "",
        "type": "address"
      }
    ],
    "stateMutability": "view",
    "type": "function"
  },
  {
    "inputs": [
      {
        "internalType": "address",
        "name": "toRemove",
        "type": "address"
      }
    ],
    "name": "renounceOwnership",
    "outputs": [],
    "stateMutability": "nonpayable",
    "type": "function"
  },
  {
    "inputs": [],
    "name": "symbol",
    "outputs": [
      {
        "internalType": "string",
        "name": "",
        "type": "string"
      }
    ],
    "stateMutability": "view",
    "type": "function"
  },
  {
    "inputs": [],
    "name": "totalSupply",
    "outputs": [
      {
        "internalType": "uint256",
        "name": "",
        "type": "uint256"
      }
    ],
    "stateMutability": "view",
    "type": "function"
  },
  {
    "inputs": [
      {
        "internalType": "address",
        "name": "to",
        "type": "address"
      },
      {
        "internalType": "uint256",
        "name": "value",
        "type": "uint256"
      }
    ],
    "name": "transfer",
    "outputs": [
      {
        "internalType": "bool",
        "name": "",
        "type": "bool"
      }
    ],
    "stateMutability": "nonpayable",
    "type": "function"
  },
  {
    "inputs": [
      {
        "internalType": "address",
        "name": "from",
        "type": "address"
      },
      {
        "internalType": "address",
        "name": "to",
        "type": "address"
      },
      {
        "internalType": "uint256",
        "name": "value",
        "type": "uint256"
      }
    ],
    "name": "transferFrom",
    "outputs": [
      {
        "internalType": "bool",
        "name": "",
        "type": "bool"
      }
    ],
    "stateMutability": "nonpayable",
    "type": "function"
  }
]