2b:null 2c:["$","title",null,{"children":"Discover - A Brave New Curve | Andy Tudhope | Observable"}] 31:Tdad,## Rationale As a user, I simply want to know that the content which appears first is: 1. Relevant to me, and 2. Beneficial to the communities I care about. This means that I also need to be able to see easily: 1. How that "relevance" was calculated 2. How much it will cost me to effect information of which I approve/disapprove. Furthermore, because we know how much [political power is generated for those who control](https://www.aspenreview.com/article/2017/jaron-lanier%3A-beware-of-siren-servers%21/) 'relevance' and 'cost', it's important that no-one owns such systems and that they exist solely to serve the networks of which they are a part. It's not "Don't be evil". It is "We cannot be evil. Here is the proof." ## Economic Design 1. The rankings are determined by who stakes the most SNT. 2. The more SNT you stake, the cheaper it is to vote on your DApp. 3. There are two kinds of votes: upvotes and downvotes. 4. The SNT it costs to upvote is locked directly in the contract and simply adds to the DApp's ranking. 5. The SNT it costs to downvote is sent directly back to the developer of the DApp. The effect it has on the ranking is proportional to how much is already staked on the DApp (i.e. it costs less to move a well-funded DApp further down the rankings than it does to have the same effect on a less well-funded DApp). 6. This is achieved by virtue of a simplified bonding curve, which takes SNT in and works with "virtual votes". It does not mint votes as tokens, for reasons listed below. ### Explanation Yes, it does cost people to cast votes. This may seem counterintuitive, but points to a critical insight. These systems - elsewhere called [hyperstructures](https://jacob.energy/hyperstructures.html) - need to work in the absence of any single point of failure or control, **including the community**. Too many people wave their hands, say "community", and think that that is enough to ensure decentralization. The simple truth is that such systems need to work even in the absence of community input. We outlined our goals above: (i) relevant to me and (ii) beneficial to the communities I care about. Even if no-one votes in this system, the fact that the DApp which ranks highest has locked the most SNT out of circulation - thereby decreasing supply - means that they have, quite literally and measurably, created the most value for the community of SNT holders. While relevance is a bit more subjective, we can see that - even when no-one votes - this simple game meets its economic objectives in a transparent and falsifiable way. The other aspect requiring explanation is the bonding curve. Most constructions like this accept one token in and mint another token based on the way the curve is parameterized. However, our thesis is that people do not wish to handle the overhead required by managing many different kinds of tokens, all with different rights, responsibilities and capabilities. Hence, we never mint "votes": they remain only as mathematical objects in the contract used to determine the cost of downvoting. This means we can leverage what is actually interesting about bonding curves - i.e. that they are powerful ways to program money with incentives that would otherwise not be possible to create - without introducing mental overhead for people using the system: all they see is an upvote and a downvote button and a cost associated with each action, which is then directly reflected in the DApp they're voting on.32:T4b4,viewof discover_curve = vegalite({ $schema: "https://vega.github.io/schema/vega-lite/v3.json", description: "Graph of SNT Staked vs Cost to Downvote", data: {values: data}, vconcat: [{ selection: { "brush": {"type": "interval"} }, mark: "point", encoding: { "x": {"field": "SNT Staked","type": "quantitative"}, "y": {"field": "Cost in SNT","type": "quantitative"} } }, { "transform": [ {"filter": {"selection": "brush"}} ]} ], layer: [ { mark: "line", encoding: { x: { field: "SNT Staked", type: "quantitative", axis: {tickCount: 5} }, y: { field: "Cost to Downvote by 1%", type: "quantitative"} } }, { mark: "line", encoding: { x: { field: "SNT Staked", type: "quantitative"}, y: { field: "Votes Minted", type: "quantitative", orient: "right" }, color: {"value": "firebrick"} } } ], width: 700, height: 400, padding: {"top": 10, "left": 30, "bottom": 30, "right": 90}, resolve: {"scale": {"y": "independent"}} })33:T487,Admittedly, it can be a little difficult to imagine what the Votes Minted curve actually looks like relative to the SNT staked, but this is because the numbers go exponential very quickly in order to achieve the desired parabolic shape for the cost (in SNT) to downvote by 1%. This is another good reason for never actually minting votes, but simply keeping them as mathematical objects in a contract. There are some values of the **ceiling** which result in significantly lower values though - and those are the ones we're looking for (local minima) when playing with the **ceiling** value, as those will be easier to implement in our contract. To the best of our knowledge, this is the only curve like it [in production](https://dap.ps) on Ethereum. Furthermore, the [contract and frontend are entirely open source](https://github.com/dap-ps/discover), and you are welcome to fork them, adapt them, improve them and build your own curation systems in a provably fair, sybil-resistant and transparent way that does not require identity systems premised on the ill-conceived notion of self-sovereignity. It's just programmable money all the way down, folks.34:T548,dollarDemandPerYearChart = { const data = aggregateDollarDemandPerYear .map((value, year) => NPV(discountRate, value, year)) .map((value, year) => ({ value, year, name: `year ${year+1}` })); const color = d3.scaleOrdinal() .domain(data.map(d => d.name)) .range(d3.quantize(t => d3.interpolateSpectral(t * 0.8 + 0.1), data.length).reverse()) const arcs = pie(data); const svg = d3.select(DOM.svg(width, height)) .attr("text-anchor", "middle") .style("font", "12px sans-serif"); const g = svg.append("g") .attr("transform", `translate(${width / 2},${height / 2})`); g.selectAll("path") .data(arcs) .enter().append("path") .attr("fill", d => color(d.data.year)) .attr("d", arc) .append("title") .text(d => `${d.data.name}: ${format(d.data.value)}`); const text = g.selectAll("text") .data(arcs) .enter().append("text") .attr("transform", d => `translate(${arc.centroid(d)})`) .attr("dy", "0.35em"); text.append("tspan") .attr("x", 0) .attr("y", "-0.7em") .style("font-weight", "bold") .text(d => d.data.name); text.filter(d => (d.endAngle - d.startAngle) > 0.25).append("tspan") .attr("x", 0) .attr("y", "0.7em") .attr("fill-opacity", 0.7) .text(d => format(d.data.value)); return svg.node(); }35:T460,final_cost_snt = { let snt_staked = [] let rate = [] let amount_available = [] let votes_minted = [] let effective_balance = [] let votes_required = [] let votes_available = [] let _cost_snt = [] let final_cost_snt = [] for (let i=1;i<1000;i++){ snt_staked[i] = (10000 * i); if (snt_staked[i] < ceiling) { snt_staked[i] = snt_staked[i] } else { snt_staked[i] = NaN } rate[i] = 1 - (snt_staked[i] / ceiling); amount_available[i] = (snt_staked[i] * rate[i]); votes_minted[i] = amount_available[i] ** (1 / rate[i]); if (votes_minted[i] > negative_votes) { effective_balance[i] = snt_staked[i] - ((negative_votes * rate[i])*(amount_available[i]/votes_minted[i])); } else { effective_balance[i] = NaN; } votes_required[i] = percent_effect_of_votes*votes_minted[i]; votes_available[i] = (votes_minted[i] - (votes_required[i] + negative_votes)); if (votes_available[i] > 0) { final_cost_snt[i] = (amount_available[i]/votes_available[i]) * (votes_required[i]); } else { final_cost_snt[i] = NaN; } } return final_cost_snt }36:[] 2f:{"id":"ef4efee162687836","slug":"embedded-discover","title":"Discover - A Brave New Curve","thumbnail":"adb02223e42cbe22179dbdcc9693518d27f4155df60b8857fbcc97d1c2009465","access_level":"public","create_time":"$D2019-05-27T12:31:46.921Z","update_time":"$D2023-05-31T10:53:09.158Z","view_time":null,"first_public_time":"$D2019-05-27T12:44:38.575Z","fork":false,"stars":3,"starred":false,"owner":{"type":"team","id":"1b76ce59e47fe6c2","login":"andytudhope","name":"Andy Tudhope","avatar_url":"https://avatars-next.observableusercontent.com/19bd8c37a73a566bf2f3af0ade4755992ad0386c5c02b4c5c5b3dc508f7ddce2","tier":"starter_2024"},"version":476,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"acf17d2ec20142ab","login":"andytudhope","name":"Andy Tudhope","avatar_url":"https://avatars-next.observableusercontent.com/19bd8c37a73a566bf2f3af0ade4755992ad0386c5c02b4c5c5b3dc508f7ddce2","tier":null}],"members":[{"type":"individual","id":"acf17d2ec20142ab","login":"andytudhope","name":"Andy Tudhope","avatar_url":"https://avatars-next.observableusercontent.com/19bd8c37a73a566bf2f3af0ade4755992ad0386c5c02b4c5c5b3dc508f7ddce2","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":5,"collection":null,"type":"notebook","body":{"title":"Discover - A Brave New Curve","cells":[{"id":0,"value":"md`# Discover - A Brave New Curve`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":426,"value":"> “Manifest plainness, \nEmbrace simplicity, \nReduce selfishness, \nHave few desires.” ― Lao Tzu","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":431,"value":"Below, we present a system designed to curate information in a simple and sybil-resistant way using a single smart contract. The goal is:\n\n> Design an economic system for curating information with no single point of failure and no owner, where information which ranks highly is provably valuable to network stakeholders, while protecting against the rich.\n\nThe game is straightforward. Whoever stakes the most tokens, ranks highest; with one twist. The more you stake, the cheaper it is for other token holders to downvote you. While the first use case is ranking DApps, this system can be applied to arbitrary information, from DApps, products and services; to stickers; extensions; social content and much more.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":436,"value":"$31","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":440,"value":"## Mathematics\n\nThe more SNT you stake, the more virtual \"votes\" can be created on your DApp, so the cheaper each vote becomes. Because there is a set amount of SNT that was minted, we can use this to calculate the (exponential) rate at which we create \"votes\" based on the SNT staked relative to the Total SNT Minted.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":14,"value":"total_snt_minted = 6804870174/100","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":444,"value":"The **ceiling** is the % of Total SNT Minted any one DApp can stake to rank. That is, there is a limit to how much SNT you can stake, defined in relation to the Total SNT that can ever exist. The **ceiling** affects the shape of the curve the most, dictating both how much you can stake and the point at which diminishing returns become too punishing for rational actors (~600k SNT in below). Play with the toggle to see the effect choosing different values has on the axes and curves.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":22,"value":"viewof percent_ceiling = slider({\n min: 0, \n max: 8, \n value: 1.6,\n step: 0.01,\n description: \"% value of Total SNT in Circulation that defines max SNT Staked per DApp\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":19,"value":"ceiling = total_snt_minted * (percent_ceiling/100)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":452,"value":"The curve ends up looking like this:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":85,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":456,"value":"$33","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":175,"value":"## Projections\n\nIn this section, we'll enter into some very rough economic projections of the effect such a system could have on a token economy if it were actively marketed, maintained and developed.\n\n## Calculate DApp Growth/Churn","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":465,"value":"These numbers were based on stateofthedapps.com data as of July 2019.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":94,"value":"numberDApps = 2667","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":100,"value":"mobileAndUseful = 0.03","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":108,"value":"viewof dappGrowthRate = slider({\n min: 0, \n max: 5, \n step: .1, \n value: 0.3, \n title: \"How many DApps stake SNT per annum (growth)\", \n description: \"percentages from 1% through 500%\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":106,"value":"viewof percentageWithdrawn = slider({\n min: 0, \n max: 1, \n step: .01, \n value: .01,\n precision: 3,\n title: \"How many DApps withdraw per annum (churn)\", \n description: \"oercentages from 1 to 100%\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":167,"value":"dapps = {\n let arr = Math.round(numberDApps * mobileAndUseful);\n let dappsArr = [arr];\n for(let i=1; i < 10; i++) {\n let newDApps = dappsArr[i-1] * dappGrowthRate;\n let lostDApps = dappsArr[i-1] * percentageWithdrawn;\n dappsArr[i] = Math.round(dappsArr[i-1] + (newDApps - lostDApps));\n }\n return dappsArr;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":378,"value":"dappsBarData = {\n return dapps.map((users, idx) => ({ name: `year ${idx+1}`, year: idx+1, users, value: users }))\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":382,"value":"dappsBar = vegalite({\n data: { values: dappsBarData },\n mark: \"bar\",\n autosize: \"fit\",\n width: width,\n encoding: {\n x: {\n field: \"year\",\n type: \"quantitative\"\n },\n y: {\n field: \"users\",\n type: \"quantitative\"\n }\n }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":169,"value":"md `## Calculate Value Per DApp and Number of DApps Staking Each Year`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":119,"value":"md `It’s a good practice for lifetime value (LTV) to be 3x customer acquisition cost (CAC). We're assuming most DApp developers will converge on this ratio regardless of size, and have put in a LTV of 0.1 USD (roughly 5 SNT currently) for each user. This seems appropriately conservative for now - most people in Twitter/Discuss seemed to fall between staking 1 000 and 10 000 SNT at first - $30 is around 6000 SNT currently, so that works well.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":327,"value":"md `Currently, other Status workbooks list Total Status Users as around 5000. Perhaps 1000 of these use DApps regularly. You can mess with the User Growth and Churn sliders below under the aggregate dollar demand calculations to see the effect a growing user base has on the avg value staked per DApp (in theory).`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":123,"value":"numberDAppsUsers = 1000","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":118,"value":"avg_value_per_dapp = numberDAppsUsers * 0.3 * 0.1","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":139,"value":"md `## Probability of Failure`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":140,"value":"viewof milestones = createMilestones(3)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":147,"value":"viewof qualifiers = createQualifers(0)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":148,"value":"viewof economicMechanic = createTokenModel(0)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":151,"value":"viewof decentralization = createDecentralization(1)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":134,"value":"viewof probabilityOfFailure = slider({\n min: 0, \n max: 1, \n step: .01, \n value: calculateProbabilityFailure(milestones, economicMechanic, qualifiers, decentralization), \n title: \"Probability of failure\", \n description: \"The probabilty that this project in isolation will fail\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":233,"value":"viewof discountRate = slider({\n min: 0, \n max: 1, \n step: .01, \n value: statusCostOfEquity, \n title: \"Discount Rate\", \n description: \"The rate at which future utility needs to be discounted (higher discounts indicate more uncertainty)\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":161,"value":"md`## Calculate Aggregate Dollar Demand Per Year`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":341,"value":"md `I think our growth will be lower, (as well as our churn) than other authors do.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":266,"value":"viewof userGrowthRate = slider({\n min: .10, \n max: 10, \n step: .10, \n value: 2, \n title: \"User growth rate per annum\", \n description: \"percentages from 10% through 1000%\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":268,"value":"viewof userChurnRate = slider({\n min: .01, \n max: 1, \n step: .01, \n value: .15, \n title: \"User churn rate per annum\", \n description: \"percentages from 1% through 100%\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":200,"value":"aggregateDollarDemandPerYear = {\n let arr = numberDApps * mobileAndUseful;\n let dappsArr = [arr];\n for(let i=1; i < 10; i++) {\n let newDApps = dappsArr[i-1] * dappGrowthRate;\n let lostDApps = dappsArr[i-1] * percentageWithdrawn;\n dappsArr[i] = Math.round(dappsArr[i-1] + (newDApps - lostDApps));\n }\n \n let usersArr = [numberDAppsUsers];\n for(let i=1; i < 10; i++) {\n let newUsers = usersArr[i-1] * userGrowthRate;\n let lostUsers = usersArr[i-1] * userChurnRate;\n usersArr[i] = Math.round(usersArr[i-1] + (newUsers - lostUsers));\n }\n \n let usdArr = [];\n for(let i=0; i < 10; i++) {\n usdArr[i] = Math.round(dappsArr[i] * (usersArr[i] * 0.3 * 0.1));\n }\n return usdArr;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":244,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":277,"value":"md `# Current Utility Value`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":282,"value":"currentUtilityValue = Math.floor(NPVaggregate(discountRate, ...aggregateDollarDemandPerYear) + discountedTerminalValue) * (1-probabilityOfFailure)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":367,"value":"estimate_effect_on_snt_price = currentUtilityValue / snt_in_circ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":307,"value":"slide`Net Present Utility Value \n${currentUtilityValue.toLocaleString(undefined, { style: 'currency', currency: 'USD'})}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":330,"value":"md `## Other Calculations for the Curve Itself`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":54,"value":"snt_staked = {\n let snt_staked = []\n for (let i=1;i<1000;i++){\n snt_staked[i] = 10000*i;\n if (snt_staked[i] < ceiling) {\n snt_staked[i] = snt_staked[i] \n } else {\n snt_staked[i] = NaN\n }\n }\n return snt_staked\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":28,"value":"rate = {\n let snt_staked = []\n let rate = []\n for (let i=0;i<1000;i++){\n snt_staked[i] = (10000 * i); \n rate[i] = 1 - (snt_staked[i] / (percent_ceiling * total_snt_minted / 100));\n }\n return rate\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":70,"value":"votes_minted = {\n let snt_staked = []\n let rate = []\n let amount_available = []\n let votes_minted = []\n for (let i=0;i<1000;i++){\n snt_staked[i] = 10000*i;\n if (snt_staked[i] < ceiling) {\n snt_staked[i] = snt_staked[i] \n } else {\n snt_staked[i] = NaN\n }\n rate[i] = 1 - (snt_staked[i] / ceiling);\n if (rate[i] > 0.02) {\n amount_available[i] = (snt_staked[i] * rate[i]);\n } else {\n amount_available[i] = NaN ;\n }\n votes_minted[i] = amount_available[i] ** (1 / rate[i]);\n }\n return votes_minted\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":68,"value":"viewof negative_votes = slider({\n min: 0, \n max: 100000,\n value: 0,\n step: 100,\n description: \"Amount of Votes Already Cast\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":41,"value":"percent_effect_of_votes = 0.01","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":66,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":82,"value":"data = {\n let data = []\n for (let i=1; i<1000; i++) {\n data[i] = {\"SNT Staked\": snt_staked[i], \"Cost to Downvote by 1%\": final_cost_snt[i], \"Votes Minted\": votes_minted[i]}\n }\n return data\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":331,"value":"md `## Other Calculations for the NPUV`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":290,"value":"viewof terminalGrowthRate = slider({\n min: .01, \n max: 1, \n step: .01, \n value: 0.02, \n title: \"Terminal growth rate per annum (percent)\", \n description: \"percentages from 1% through 100%\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":364,"value":"snt_in_circ = 3470483788","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":288,"value":"terminalValue = {\n let lastYearFees = aggregateDollarDemandPerYear.slice(-1)[0]\n return lastYearFees / (discountRate - terminalGrowthRate)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":303,"value":"discountedTerminalValue = terminalValue / ((1+discountRate)**11)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":226,"value":"NPV = (rate, value, idx) => Math.round(value / Math.pow((1 + rate), idx + 1))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":284,"value":"NPVaggregate = function (rate) {\n var npv = arguments[1];\n for (var i = 2; i < arguments.length; i++) {\n npv +=(arguments[i] / Math.pow((1 + rate), i - 1));\n }\n return Math.round(npv * 100) / 100;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":349,"value":"md `## Imports`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":227,"value":"d3 = require('d3')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":246,"value":"format = d3.format(\",\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":247,"value":"pie = d3.pie().padAngle(0.005).sort(null).value(d => d.value)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":249,"value":" height = Math.min(width, 500)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":388,"value":" width = 700","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":251,"value":"arc = {\n const radius = Math.min(width, height) / 2;\n return d3.arc().innerRadius(radius * 0.67).outerRadius(radius - 1);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":5,"value":"vegalite = require(\"@observablehq/vega-lite@0.1\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":7,"value":"import {slider} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":135,"value":"import {createMilestones, createQualifers, createTokenModel, createDecentralization, calculateProbabilityFailure} from '@bgits/cryptonetwork-probability-of-failure'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":375,"value":"import {statusCostOfEquity, sntCloses} from '@andytudhope/status-network-cost-of-capital'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":309,"value":"import {slide, slide_style} from \"@mbostock/slide\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":321,"value":"slide_style","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W36","stdlib":"1","titling":"auto"}} 30:"$2f:body"