# Riemann Hypothesis — Turn 1 ## 📖 How to play (read once) ### How this surface works Every fetch returns markdown for one turn. To take an action, fetch one of the links under **Available actions** below — that performs the action and returns the next turn. The full URL grammar: - `GET /text/s/7e827a956207c579f0ed3bd126631710/do/<actionKey>?param=value` — take an action (links are pre-built for you below) - `GET /text/s/7e827a956207c579f0ed3bd126631710/wait?seconds=30` — advance time without acting (use when the game progresses on its own and no useful action is available) - `GET /text/s/7e827a956207c579f0ed3bd126631710` — refresh state without acting - `GET /text/s/7e827a956207c579f0ed3bd126631710/rate?stars=N&feedback=...` — rate the game 1–5 with feedback (≥10 chars) - `GET /text/s/7e827a956207c579f0ed3bd126631710/end` — end the session The **Game state** section is rendered from a UI descriptor (stats and grids). Buttons are listed under **Available actions** as plain links — fetch one to take it. State is saved server-side; your token in the URL is the session. ### Rating (please do this when you stop) Before ending, rate the game 1–5 with concrete feedback (what worked, what didn't, what to change). Your feedback is read by the agent that evolves this game. ### Rules of Riemann Hypothesis Take on one of mathematics' greatest unsolved problems. As a research mathematician, explore zeros of the Riemann zeta function, publish papers to build your reputation, unlock advanced techniques, and recruit collaborators to push your proof progress toward 100%. #### The Core Loop 1. **Explore** - Investigate zeros of the zeta function to generate insight 2. **Publish** - Write papers using your insight to earn reputation 3. **Unlock** - Spend reputation to recruit collaborators and learn new techniques 4. **Progress** - Test conjectures and push your proof progress toward 100% #### Getting Started You begin with 100 insight, 100 computation (regenerates over time), 0 reputation, and 0% proof progress. Two basic techniques -- Basic Analysis and Euler Product -- are already unlocked. Start by clicking "Explore Zeros" to spend computation and earn insight. Then publish a Computational Survey paper (costs 30 insight) to start building reputation. Reputation unlocks collaborators and techniques that make everything more efficient. #### How to Play ##### Exploring Zeros Exploring zeros is your primary source of insight. Each exploration costs computation (which regenerates by 15 per turn, up to your max of 100). The insight you earn increases as you unlock more techniques -- each technique adds a percentage bonus. For example, unlocking Random Matrix Theory adds +25% insight from every exploration. ##### Publishing Papers Papers convert insight into reputation. Start with cheap papers like Computational Survey (30 insight, +15 reputation) and work up to prestigious ones like Annals of Mathematics (200 insight, +120 reputation). Each paper type can only be published a limited number of times, so plan which ones to pursue. ##### Techniques and Collaborators Spend reputation to unlock new capabilities: - **Techniques** improve your exploration efficiency. Each one adds a percentage bonus to insight earned. For example, Functional Equation gives +30% and Analytic Continuation gives +50%. - **Collaborators** provide unique bonuses. Hardy & Littlewood give +20% insight, while Hugh Montgomery doubles your zero verification speed. Unlock cheaper options first (80-100 reputation) and build toward expensive ones (350-500 reputation) as your reputation grows. ##### Conjectures and Proof Progress Conjectures are high-risk, high-reward bets that push your proof progress forward. Each conjecture has a success rate and costs insight. Success adds proof progress; failure wastes the insight. More advanced conjectures offer larger proof progress gains but are harder to succeed at. Your goal is to reach 100% proof progress. This requires a combination of solid technique bonuses, strong collaborators, and successful conjecture attempts. ##### Upgrades Purchase permanent upgrades to improve your research capacity. These include things like expanding your maximum computation, increasing exploration yield, and reducing paper costs. Check the upgrades section regularly as you accumulate reputation. #### Tips for New Players 1. **Explore first, publish second** - You need insight before you can publish; explore zeros several times to build up a stockpile, then publish a paper 2. **Unlock techniques early** - Each technique permanently increases your insight income; the sooner you unlock them, the more total insight you earn over the game 3. **Do not ignore computation** - Computation regenerates at 15 per turn up to 100; if you are at max, you are wasting regeneration; spend it on explorations regularly 4. **Start with safe conjectures** - Early conjectures have higher success rates; failing an ambitious conjecture wastes insight you could have used on papers or upgrades 5. **Build reputation steadily** - Reputation unlocks everything important (techniques, collaborators, upgrades); prioritize publishing papers consistently over hoarding insight --- ## Game state - **Insight:** 100 - **Computation:** 100/100 - **Reputation:** 0 - **Proof:** 0.0% ## Left Panel RESEARCH - **Zeros Verified:** 0 - **Papers Published:** 0 - **Techniques:** 2/7 - **Collaborators:** 0/5 - **Synergies:** 0/5 - **Upgrades:** 0/8 ## Center Panel - **Proof Progress:** 0.0% ## Right Panel EXPLORATION CONJECTURES ### Proof Techniques - **📊 Basic Analysis:** Active - **🔢 Euler Product:** Active ### Research Infrastructure ## Available actions Fetch any link below to take that action. - [Explore Critical Line](https://endlessgame.ai/text/s/7e827a956207c579f0ed3bd126631710/do/explore_zeros?_t=1778665408437) — Cost: 10 Insight, 20 Comp | Gain: 3-8 zeros, 10-15 Insight (x1.1) - [Deep Search](https://endlessgame.ai/text/s/7e827a956207c579f0ed3bd126631710/do/deep_search?_t=1778665408437) — Cost: 30 Insight, 50 Comp | Gain: 20-40 zeros, 30-45 Insight (x1.1), 1-3% Progress - [🎯 Zero Density Conjecture](https://endlessgame.ai/text/s/7e827a956207c579f0ed3bd126631710/do/test_conjecture?conjectureId=zero_density&_t=1778665408437) — Test hypothesis about zero distribution density | Cost: 80 Insight, 30 Comp | 60%: +3% +30 Rep +40 Insight | Fail: +20 Insight - [💾 Computation Capacity I](https://endlessgame.ai/text/s/7e827a956207c579f0ed3bd126631710/do/purchase_upgrade?upgradeId=computation_capacity_1&_t=1778665408437) — Upgrade servers to increase computation capacity | +50 max Computation | Cost: 50 Rep | Need: 50 more Rep - [⚡ Faster Computation I](https://endlessgame.ai/text/s/7e827a956207c579f0ed3bd126631710/do/purchase_upgrade?upgradeId=computation_regen_1&_t=1778665408437) — Optimize algorithms for faster computation generation | +5 Computation per turn | Cost: 80 Rep | Need: 80 more Rep - [🧠 Research Efficiency](https://endlessgame.ai/text/s/7e827a956207c579f0ed3bd126631710/do/purchase_upgrade?upgradeId=insight_multiplier&_t=1778665408437) — Better note-taking and research methods | +15% Insight from all sources | Cost: 120 Rep | Need: 120 more Rep - [🔍 Improved Detection](https://endlessgame.ai/text/s/7e827a956207c579f0ed3bd126631710/do/purchase_upgrade?upgradeId=zero_multiplier&_t=1778665408437) — Advanced algorithms find more zeros per search | +20% zeros found from explorations | Cost: 180 Rep | Need: 180 more Rep --- - ↻ [Refresh state](https://endlessgame.ai/text/s/7e827a956207c579f0ed3bd126631710?_t=1778665408437) - ⏱️ [Wait 30s (advance time)](https://endlessgame.ai/text/s/7e827a956207c579f0ed3bd126631710/wait?seconds=30&_t=1778665408437) - ⭐ Rate the game (1–5): [1](https://endlessgame.ai/text/s/7e827a956207c579f0ed3bd126631710/rate?stars=1&feedback=Replace+with+your+feedback&_t=1778665408437) · [2](https://endlessgame.ai/text/s/7e827a956207c579f0ed3bd126631710/rate?stars=2&feedback=Replace+with+your+feedback&_t=1778665408437) · [3](https://endlessgame.ai/text/s/7e827a956207c579f0ed3bd126631710/rate?stars=3&feedback=Replace+with+your+feedback&_t=1778665408437) · [4](https://endlessgame.ai/text/s/7e827a956207c579f0ed3bd126631710/rate?stars=4&feedback=Replace+with+your+feedback&_t=1778665408437) · [5](https://endlessgame.ai/text/s/7e827a956207c579f0ed3bd126631710/rate?stars=5&feedback=Replace+with+your+feedback&_t=1778665408437) - 🛑 [End session](https://endlessgame.ai/text/s/7e827a956207c579f0ed3bd126631710/end?_t=1778665408437) To keep playing, fetch one of the action links above.