To solidify the concepts, we apply the EDMNO framework to a real venture scenario. This section illustrates the **scope of the thesis** by mapping the theoretical model to an example case and demonstrating how all the pieces (perception, coordination, bottleneck-breaking) work in concert. Our case of choice is a clean materials startup, **Sublime Systems**, which is developing a novel low-carbon cement. We will walk through Sublime’s early journey and decisions, explaining them through the EDMNO lens. We also present a summary table that maps key mathematical components across the three dimensions (📽️, 🔄, ⚡) to show how each concept manifests in each context. Throughout, we maintain rigorous notation but use intuitive descriptions, and we include references to the appendices for deeper technical details (full derivations, proofs). ## 📋 EDMNO Components Mapped Across Dimensions Before diving into the narrative, **Table 1** provides a “database” view of how each core concept in our model differs when emphasizing perception vs. coordination vs. bottleneck-breaking. This serves as a reference guide: | **Concept** | **📽️ Perception (Stakeholder View)** | **🔄 Coordination (Multi-Stakeholder)** | **⚡ Bottleneck-breaking (Sequential Action)** | | ------------------------------------ | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | **Objective (Primal)** | Minimize uncertainty in a specific stakeholder’s belief or perception. <br>_e.g._ Reduce a customer’s uncertainty about product value (lower $H(p_{\text{customer}})$). | Minimize combined uncertainty across all stakeholders (weighted sum). <br>_e.g._ Reduce misalignment in expectations among customer, investor, regulator (lower $\sum_j W_j U_j$). | Minimize total venture uncertainty through sequence of actions. <br>_e.g._ Reduce aggregate technical/market uncertainty after each experiment (target highest $U_j$ first). | | **Objective (Dual)** | Maximize likelihood of favorable decision by that stakeholder. <br>_e.g._ Increase probability customer will buy or investor will invest, given info provided. | Maximize likelihood of **joint** success (all critical stakeholders onboard). <br>_e.g._ Increase probability that customer buys _and_ investor invests _and_ regulator approves. | Maximize probability of venture success within resource limits. <br>_e.g._ Increase chance that venture hits product-market fit before funds run out (by resolving unknowns). | | **State ($S$)** | Stakeholder’s acceptance state or belief state regarding the venture. <br>_e.g._ Investor’s confidence level, represented as state (Accepted/Not accepted). | Global state of stakeholder alignment. Often a vector $S = [s_{\text{cust}}, s_{\text{inv}}, s_{\text{reg}}, \dots]$ indicating each stakeholder’s status (onboard or not). | Operational state of the venture and knowledge state. <br>_e.g._ Milestone status (prototype built, pilot done) and current knowledge (belief about viability). | | **Action ($A$)** | Information or signaling action targeting one stakeholder’s perception. <br>_e.g._ Provide a demo, share data, tailor pitch to address that stakeholder’s key concern. | Coordinated or parallel action involving multiple stakeholders. <br>_e.g._ Multi-party pilot project, consortium meeting, joint press release to align expectations. | Experiment or development action under resource constraints. <br>_e.g._ Build a prototype, run a market trial, pivot product feature – each consuming budget $R$. | | **Constraints** | Bounded by stakeholder attention and evidence credibility. <br>_e.g._ Can only convey so much info in one meeting; evidence must be relevant to that stakeholder’s model. | Consistency and consensus constraints across stakeholders. <br>_e.g._ All stakeholders’ state transitions must obey the same physics/results (venture reality), resource distribution among stakeholders (time, focus) limited. | Resource budget and temporal constraints dominate. <br>_e.g._ Total cost of experiments ≤ R (runway); each step takes time (deadlines); actions can’t violate logical order (must build prototype before customer pilot). | | **Dual Variables / “Lagrange” View** | Value of information for that stakeholder (how much reducing their uncertainty is “worth” in success probability). <br>_e.g._ If investor uncertainty is high, dual suggests large payoff in converting them (high $\lambda_{\text{inv}}$). | Shadow price of alignment – how much overall success probability is constrained by a particular stakeholder. <br>_e.g._ If regulator is the bottleneck, dual variable for their constraint is highest, indicating aligning regulator yields biggest gain. | Value of a resource unit (runway month, $1) in terms of success odds. <br>_e.g._ Dual $\gamma$ tells how much increasing budget would raise success chance, and guides equalizing info gain per cost across experiments. | **Table 1:** Mapping of EDMNO components across the three dimensions. Each column highlights how the general concepts (objective, state, action, etc.) specialize in the context of **perception**, **coordination**, and **bottleneck-breaking** challenges. With this reference in mind, we now turn to the narrative of Sublime Systems and demonstrate the EDMNO framework in action. ## 🎯 Case Introduction: Sublime Systems and its Triple Challenge **Venture Background:** _Sublime Systems_ is a cleantech startup aiming to produce **carbon-neutral cement** using an electrochemical process. This venture faces a classic trio of uncertainties: **Demand-side** (will customers adopt a new type of cement, and at what price?), **Supply/Technical-side** (can the new cement be produced at scale with consistent quality and cost?), and **Capital-side** (can the company secure sufficient funding to scale, given the long timelines and high capital requirements in the materials industry?). These correspond to our $\textcolor{#3399FF}{U_d}$, $\textcolor{#3399FF}{U_s}$, and $\textcolor{#3399FF}{U_i}$ respectively. Key stakeholders include construction firms (customers), large strategic partners/investors like cement manufacturers (partners/investors fulfilling both supply chain collaboration and capital roles), and regulators or standards bodies (who must approve the use of this new cement in buildings). At the outset, Sublime’s state $S$ can be thought of as **[unproven market, lab-scale tech, seed-funded]**, which we can encode as $S=[0,0,1]$ in shorthand (0 = not yet secured, 1 = secured; here “seed-funded” means they have initial capital so we put 1 for investor side, assuming seed is done, but market and tech proof are 0). Their overall uncertainty $U$ is high on two fronts (market and technical), somewhat lower on capital since at least seed investors are in (though future funding is uncertain). The **weights $W$** might be something like $W_d=0.3$ (market is important, but if the product works someone will likely buy it due to environmental mandates), $W_s=0.5$ (technical success is crucial; if the tech fails, nothing else matters), and $W_i=0.2$ (capital is important but follows if tech and market look good – also strategic investors are interested due to ESG pressure). These weights reflect the venture’s assessment of what’s mission-critical. The resource budget $R$ is limited – perhaps they have $R=$5$ million from seed funding to allocate across development and testing actions until the next round. ## 🚦 Applying 📽️ Perception Modeling in the Case **Stakeholder Perception Challenges:** Early on, Sublime needs to convince at least one major **customer (construction company)** to try their low-carbon cement, and also ensure **investors** remain confident for the next funding round. Customers might doubt that the cement is as strong or cost-effective as traditional cement. Investors might be more concerned about the time to scale and the capital intensity. These are different perceptions of the venture. **EDMNO – Perception Actions:** Sublime’s team identifies the **customer’s uncertainty** about cement performance as a critical perception problem. Using the model, they ask: _What evidence would most reduce the customer’s uncertainty?_ Likely, a **demonstration of concrete strength** using Sublime’s cement would address this. So they plan an action $a_{\text{cust}}$: produce a set of concrete blocks with the new cement and run standard strength tests in an independent lab, sharing the results with the potential customer. This is a targeted 📽️ action: it doesn’t immediately scale the business, but it provides information aligned with the customer’s decision model (which places a high value on meeting building code strength requirements). The cost $C(a_{\text{cust}})$ is moderate (say $50k for lab tests and samples, which is within $R$) and the expected uncertainty reduction $\Delta U_d$ is significant – if results are positive, the customer’s perceived risk drops dramatically (perhaps turning their state from 0 to 1: now they’re willing to pilot the cement in a real project). In parallel, the team might take a targeted perception action aimed at the operational partner (e.g., Holcim). The partner's key uncertainty centers on: **"Can Sublime’s electrochemical cement reliably scale and integrate into our existing facilities?"** The chosen action ($\textcolor{red}{a_{ops-partner}}$) involves detailed integration studies, operational cost analyses, or technical feasibility reviews highlighting compatibility with current infrastructure. Although moderate in cost (engineering hours, consulting fees), this action significantly reduces technical uncertainty ($\textcolor{#3399FF}{U_s}$) by directly addressing operational integration risks. **Outcome:** These perception-focused actions pay off: The lab tests come back showing Sublime’s cement meets the required strength standards. The construction customer’s confidence jumps – qualitatively, they signal willingness to do a pilot pour for a small building. In EDMNO terms, the customer’s state flips to accepted (from 0 to 1) with respect to viability, and $\textcolor{#3399FF}{U_d}$ (demand uncertainty) shrinks because a major concern (technical performance from customer perspective) was resolved. On the investor side, the detailed roadmap answered many of the fund’s timeline questions, slightly reducing $\textcolor{#3399FF}{U_i}$ – although investors still want to see that customer pilot happen (they remain partially uncertain until real deployment data). The **primal effect**: stakeholder-specific uncertainties down. The **dual effect**: increased likelihood of positive decisions – indeed the customer agrees to a pilot (a win), and the investors extend a bridge funding to cover that pilot, seeing progress. _(In **Appendices.md**, see Section A for quantitative analysis of these perception updates, including how the entropy of the customer’s belief distribution over “acceptable vs unacceptable cement” drops after seeing test results.)_ ## 🤝 Applying 🔄 Coordination in the Case **Coordination Challenge:** Now that Sublime has a customer interested and investors on the hook, **alignment with a strategic partner and regulators** comes into play. Cement is heavily regulated (building codes, environmental regulations), and the startup’s process might need regulatory approval or at least acceptance in standards. Also, scaling manufacturing might require partnership with an existing cement company for facilities and distribution. Here we have multiple stakeholders who all need to move forward together: the customer will only do a full project if the product is certified safe and if supply is guaranteed; the strategic partner (a large cement company) will only formally partner if they see market demand and regulatory green lights; the regulator will approve faster if a respected industry player is involved (to ensure compliance and safety). It’s a classic coordination game. **EDMNO – Coordination Actions:** Sublime’s team recognizes a need for **expectation alignment** across these players. They convene a joint meeting (action $a_{\text{coord}}$) with representatives from the customer, the potential strategic partner (let’s say Holcim, a cement giant), and a building materials regulator or standards expert. In this meeting, they share the successful test results (so everyone hears the same evidence) and outline the plan for a pilot plant. This single action is designed to create **information spillover** – the customer hears that Holcim is interested, boosting customer confidence; Holcim hears the customer’s enthusiasm, increasing Holcim’s belief that there’s market demand (reducing Holcim’s uncertainty on market side); the regulator hears that a major industry player is backing this and that initial tests passed standards, which increases the regulator’s trust in the technology’s viability and safety. In EDMNO terms, this is an action that doesn’t map to just one $U_j$, but simultaneously nudges all relevant $U_j$ downward a bit by **propagating consistent information**. It’s chosen because it aligns everyone’s mental models: all parties leave the room with a roughly shared vision that “Sublime’s cement worked in lab tests, X customer wants to try it, Y big partner is likely to come on board, and the path to approval looks feasible.” To formalize, prior to this action, each stakeholder had a different expectation for the timeline to commercialization: customer thought “maybe 1 year if all goes well,” Holcim thought “more like 3-5 years, these things scale slowly,” regulator thought “not sure, need more data, could be 3+ years.” The meeting provided data (lab results, a proposed timeline) that helped update these expectations closer together, perhaps now all converging on “around 2 years to pilot and certify.” Our model would capture that by a reduction in variance of those predictions and the differences between them. The **primal goal** of minimizing misalignment is addressed. After the meeting, Sublime follows up with a **two-step calibration**: they ask Holcim’s engineers to review the pilot plant design (Holcim updates their model using Sublime’s data, like federated learning), and Sublime asks the regulator what metrics they’d like to see monitored during the pilot (Sublime updating its plan based on regulator’s model). This iterative exchange is exactly the expectation calibration loop from the theory. Over a few weeks, Sublime and these stakeholders arrive at a **shared plan**: build a pilot plant of say 100 tons/year capacity, get it certified while the customer uses the material in a small project, then scale up. Everyone’s role is clear, and their expectations are aligned that this plan is viable. **Outcome:** The benefit of this coordination is evident when things move forward smoothly: Holcim formally invests in Sublime (bringing capital and agreeing to host the pilot plant at one of their sites), the regulator grants a provisional permit for the pilot plant and signals that if outcomes are as expected, full approval is likely, and the customer signs a preliminary purchase order for the pilot output. These are **synchronized decisions** that could only happen with alignment – if any party was out of sync (e.g. regulator pessimistic or partner unconvinced), the others would hesitate. Our model’s dual objective (maximize chance of collective success) is effectively achieved in this phase: the probability of “Sublime succeeds in scaling” jumped because now the key players are in harmony. From the primal side, the uncertainties have been greatly reduced: stakeholder uncertainty is now mainly about execution (will the pilot hit targets?) rather than about each other’s commitment. We can denote Sublime’s state now as $S=[1,1,1]$ – core stakeholders (customer, partner, investor/regulator) are all on board for the pilot phase, representing a major milestone in acceptance. _(Additional details and the quantitative consensus update mechanism for this coordination are provided in **Appendices.md**, Section B, including how we model the meeting as a single action that modifies multiple stakeholder belief distributions and how dual variables indicate the balanced trade-offs reached.)_ ## 🔬 Applying ⚡ Bottleneck-breaking Sequencing in the Case **bottleneck-breaking Challenge:** With alignment achieved and a pilot plant in the works, Sublime still faces technical and market risks in execution. They have a finite budget (including Holcim’s investment and perhaps a government grant – let’s say now $R=$20$M for the pilot phase). They must allocate this toward different tasks: scaling the electrochemical reactor, optimizing the chemical process for consistency, conducting field trials with the produced cement, etc. Each of these is an experiment or action that could succeed or fail. The order in which they tackle these tasks can matter – some tests might de-risk others. **EDMNO – bottleneck-breaking Strategy:** Using our bottleneck-driven approach, Sublime’s team identifies the **biggest unknown** at this stage. Suppose the technical scalability of the electrochemical process (can they maintain performance at 100× the lab scale?) is the biggest uncertainty ($U_s$ is high). Market demand risk ($U_d$) at this point is lower because at least one customer is onboard and more are interested if pilot succeeds, and capital ($U_i$) is okay due to recent funding (though future scale-up needs more, it depends on pilot success). So they allocate resources first to address technical scale. They decide the first action in the pilot project is to build a **single full-scale electrolyzer module** and test its output quality and energy consumption (action $a_{\text{tech1}}$). This is an experiment consuming, say, $5M and 6 months. If it fails (output cement doesn’t meet quality or the energy usage is too high), that reveals a critical need to iterate design – but it’s better to know that upfront. If it succeeds, it knocks down a huge portion of $U_s$ (technical uncertainty plummets, as the key scale question is answered). Parallel or next, what about $U_d$ (market)? Perhaps the next bottleneck is whether the cement made in the pilot will be accepted by more conservative customers beyond the pilot partner. So the second action $a_{\text{marketTest}}$ might be to produce a batch of cement from the pilot line and use it in a high-visibility construction project (maybe a small bridge or a building wing) not just with the first customer but also inviting other industry observers. This experiment tests market acceptance and uncovers any hidden requirements (like do contractors need special handling, etc.). Its cost is mostly opportunity cost and some marketing expense, relatively low compared to building infrastructure. The uncertainty drop could be significant if it goes well (others see it works like normal cement, so adoption resistance falls). Using an LP lens: initially, the technical experiment had a very high $\frac{\text{uncertainty reduction}}{$}$ ratio – big drop in $U_s$ for $5M was worth it due to high weight $W_s$. After that, $U_s$ is smaller, maybe now $U_d$ or $U_i$ have higher weighted uncertainty relative to cost. The model would then suggest shifting focus. Indeed, after the technical test, suppose it succeeded: Sublime now knows the process can scale (huge relief to all stakeholders). Now the biggest question might be **can they produce at competitive cost?** This might be a mix of technical and market (if cost is slightly high, will customers still buy for green benefits?). The next experiments could target cost optimization (another technical iteration) or market validation at small scale as mentioned. They might run another LP: if cost uncertainty (a part of $U_s$) has a high weight, invest in R&D to cut cost; if market uptake uncertainty ($U_d$) is higher, do that expanded pilot with more customers. Let’s say they find that their process, while working, is currently 20% more expensive than traditional cement. Now there’s a trade-off: improve the process or bank on green premium? Perhaps $W_d$ (market importance) becomes high because without customers paying that premium, nothing helps. So they attempt an action $a_{\text{costDown}}$: an R&D project to tweak the chemistry to use cheaper feedstock. This is somewhat speculative and might not succeed, so they allocate a smaller budget to it while using remaining funds to keep pilot production going for market learning. Here they are effectively **hedging** – since our framework would show diminishing returns on focusing purely on one uncertainty once it’s low, it encourages balancing. **Decision Sequence Illustration:** Let’s outline a possible sequence and state transitions for clarity: 1. **State $S_0 = [1,1,1]$** (post-alignment, pre-pilot; all stakeholders committed to pilot phase but outcomes unknown). **Uncertainties:** $U_d=0.4$ (will broader market accept?), $U_s=0.7$ (will scale meet cost/quality?), $U_i=0.3$ (next funding round probability). 2. **Action 1: Build & test one full-scale module** ($a_{\text{tech1}}$). _Cost:_ $5M. _Expected effect:_ If success, $U_s \downarrow$ to 0.3 (major technical validation), $S$ transitions to perhaps $[1,1,1]$ but with an internal flag “tech validated” (not a stakeholder state change, but an internal milestone achieved). If failure, $U_s$ might stay high (and stakeholders might waver, but let’s assume success scenario for illustration). 3. **State after $a_{\text{tech1}}$: $S_1 = [1,1,1]$**, but now with tech validated milestone. **Uncertainties:** $U_d=0.4$, $U_s=0.3$, $U_i=0.25$ (investors slightly more confident now seeing tech success). 4. **Action 2: Market pilot with multiple customers** ($a_{\text{marketTest}}$). They produce 100 tons of cement and involve 3 different construction firms in using it. _Cost:_ $1M. _Expected effect:_ If the projects go smoothly, and feedback is positive, $U_d \downarrow$ to 0.2 (broader market validation), and also regulators might gain more confidence (though they were already okay, maybe $U_s$ down a bit more to 0.25 because field performance proven). 5. **State $S_2 = [1,1,1]$** (now pilot usage proven). **Uncertainties:** $U_d=0.2$, $U_s=0.25$, $U_i=0.2$. 6. **Action 3: Cost-reduction R&D** ($a_{\text{costDown}}$). They try a new feedstock mix to reduce electricity use. _Cost:_ $2M. _Effect:_ Suppose it achieves a partial improvement. $U_s$ goes down to 0.2 (still some uncertainty but less, as they found a path to cut cost by say 10%, not full 20% needed but better). 7. **State $S_3 = [1,1,1]$** (pilot phase complete). **Uncertainties:** $U_d=0.2$, $U_s=0.2$, $U_i=0.1$ (because with both market and tech looking better, investors are quite confident of scaling and perhaps an A round is nearly assured). At this point, Sublime has effectively de-risked to a level where they can raise the next large funding round and build a commercial-scale plant. The sequence of actions was chosen by always evaluating “what’s the riskiest assumption now?” and tackling it, which our framework formalized via the objective function and LP heuristic. If we had infinite computing power, maybe a dynamic programming would have chosen a similar sequence – our approach got it without brute force. **Outcome:** Sublime Systems successfully completes the pilot phase: the technology works at pilot scale, customers are satisfied with the product, and costs are close enough to plan to warrant moving forward. They secure a large Series A from both venture capital and strategic investors to build a full-scale plant. The venture transitions into growth mode with significantly lower uncertainty. In terms of EDMNO state, we might say it moved to $S_{\text{validated}} = [1,1,1]$ with $U_d, U_s, U_i$ all below some small threshold – essentially, the model’s conditions for a viable venture have been met (all key stakeholders are convinced and uncertainties are low enough that standard execution and market dynamics take over, outside the scope of extreme uncertainty modeling). The **EDMNO framework** guided Sublime through a logically rigorous yet intuitive path: it **identified critical uncertainties (perception)**, **aligned stakeholders (coordination)**, and **prioritized experiments (bottleneck-breaking)**. At each step, the framework’s suggestions matched what a savvy entrepreneur might do, but importantly, it provided formal justification and a repeatable method, rather than relying purely on gut instinct. This shows the thesis scope: we can maintain academic rigor (the solution was derived from an optimization objective) _and_ practical utility (the actions make sense to a founder) – bridging the theory-practice gap. ## 🔚 Concluding Integration In conclusion, the EDMNO framework – through its triad of 📽️ **perception**, 🔄 **coordination**, and ⚡ **bottleneck-breaking** modules – offers a **tractable approach to entrepreneurial strategy under uncertainty**. The Sublime Systems case exemplifies how an entrepreneur can use the framework to systematically navigate complex decisions: understanding different stakeholder viewpoints, getting everyone on the same page, and running the right experiments at the right time. Each module alone addresses one facet of complexity; together they form a comprehensive decision support system. The outcome is a venture that makes steady, validated progress, essentially **engineering luck** by continuously reducing uncertainty and aligning reality with the venture’s goals. This thesis thereby provides both a **conceptual model and a practical toolkit**. Entrepreneurs can adopt the mindset and qualitative heuristics (as demonstrated in the case), and researchers or quantitatively inclined founders can dive into the mathematical formulations (with guidance from the appendices for implementation details). By balancing realism (multi-stakeholder, dynamic) with tractability (primal-dual decomposition and approximations), EDMNO stands as a blueprint for making entrepreneurial decision models **usable in practice**. Finally, we note that while the scope here focused on early-stage uncertainties, the framework is extensible. Future work (outlined in the Appendices and Conclusion) can adapt EDMNO to later-stage scaling decisions, incorporate more nuanced stakeholder behaviors (using, e.g., theory-of-mind models), and automate parts of the analysis via AI. The core thesis, however, is that **entrepreneurial decision-making under uncertainty can be transformed from an art to a science** without losing the intuitive, creative touch – much as we have seen in the Sublime Systems narrative. The hope is that this integrated approach will empower more entrepreneurs to tackle audacious challenges (like decarbonizing cement) with confidence and rigor, ultimately increasing venture success rates and societal benefit.