Imagine you have a lemonade stand, and you want to figure out how many people are going to come back tomorrow, next week, or next month. That's exactly what this app does, but for software apps.
This app helps us look into the future to guess things like:
- How much money we need to spend on ads to reach our daily goals.
- What happens if we get a huge shoutout on the news (a massive spike of people showing up).
- How many people will stick around long enough to actually pay us money.
To bridge the gap between today's aggregated marketing environments (SaaS, Mobile Apps) and the decentralized, AI-driven business models of tomorrow, you need to understand the physics of growth.
The underlying math of this engine, compounding cohort decay, is universal. It governs human attention just as well as it governs machine uptime or capital liquidity. This engine calculates the exact thermodynamic energy (marketing budget, token emissions, or compute subsidies) required to achieve system equilibrium.
By using the "Network Paradigm" Toggle globally in the app, you change the business model vocabulary. Here is what a marketer or founder actually experiences in these three paradigms, and how to model them:
- The Vibe: Human attention is flaky but habit-forming. Acquisition is highly competitive.
- What a Marketer Experiences: You pay Meta or Google a CAC (Cost Per Acquisition) to acquire a human DAU (Daily Active User). If the onboarding experience is good, humans form habits and subscribe, yielding an LTV (Lifetime Value).
- How to Model It: Focus heavily on Tab 3 (Cohort Maturity). SaaS businesses only survive if users live long enough to hit the paywall.
- The Vibe: Financialized networks where participants are brutally rational and financially motivated.
- What a Marketer Experiences: You issue Token Bounties / Emissions to acquire DAN (Daily Active Nodes). Users in this space are often "Mercenary Capital." They show up for the quick buck (the airdrop), then instantly dump their tokens and leave, causing massive network volatility.
- How to Model It: Focus heavily on Tab 2 (Volatility vs Stability). To survive, you must model whether slow, algorithmic token drips are safer than massive volatile marketing stunts.
- The Vibe: Machine-to-machine economies where bots execute rapid transactions.
- What a Marketer Experiences: You pay an API Computing Subsidy (CPO) to onboard DAA (Daily Active Agents). These agents need time to train in the network before they generate massive swarms of automated Micro-transaction volume.
- How to Model It: Treat this firmly as an energy-in vs. energy-out equation. Focus on Tab 1 (Liquidity Target) to figure out the exact baseline subsidies needed to keep the system powered.
In Tab 2 (Volatility vs. Stability Modeling), the app allows you to select the mathematical function that plots how rapidly your network decays. Here is what the different mathematical shapes represent behaviorally:
best_fit(The Default): The engine iterates through all mathematical curves and automatically picks the one that mathematically fits your Daily Retention inputs best. Use this if you don't know the exact sociology of your users.log(Logarithmic Decay): Imagine a curve that drops fast early on, but then completely flattens out into a stable line that never quite hits zero. Behavioral Match: SaaS/Consumer Apps. Humans churn initially, but the ones who stick around form a 10-year unbreakable habit.exp(Exponential Decay): A curve that plummets aggressively toward absolute zero and gets there quickly. Behavioral Match: Web3 Airdrop Farmers & Mercenary Capital. They arrive on Day 1, take their money, and instantly churn on Day 2. It represents catastrophic, hyper-rational network flight.power(Power Law): Extremely steep initial drop off that eventually settles into a stable, tiny fraction of power users (the "1% rule"). Behavioral Match: Social Networks and Creator Economies where 99% of people only read, and 1% aggressively post.weibull: A highly flexible curve often used in engineering to model "time-to-failure." Behavioral Match: Hardware failure rates or deterministic bot/API token exhaustion metrics where the decay shifts aggressively at a specific time.
- Tab 1: Network Liquidity Target: How much energy (budget/tokens) is required to hit a specific network size baseline?
- Tab 2: Volatility vs. Stability Modeling: What happens when catastrophic viral moments (PR spikes / mercenary airdrops) inject volatility into the system?
- Tab 3: Cohort Maturity & Value Extraction: When does the network actually generate yield? Calculates exactly how many units survive the decay curve long enough to trigger yield events (hitting a paywall or completing model training).
While this app provides a Streamlit UI, the underlying theseus_growth engine supports deep programmatic use cases perfect for analysts. By using the raw codebase, you can execute:
engine.to_excel(df)orengine.to_json(df): Export raw cohort projections directly to your BI system.project_aged_DAUorproject_exact_aged_DAU: Perform deep Python segmentation to see exactly how many users are mathematically eligible for a specific product milestone based on their age in the network.
Note: The underlying modeling capabilities are provided by Theseus, an open-source MIT-licensed cohort analysis library developed by Eric Benjamin Seufert at Heracles.