Here's a comprehensive summary table of our paper's structure with key contributions and tables: ## ๐Ÿ“Š Paper Structure: Optimal Ignorance Level Framework |Section|Content|Core Message|Tables/Tools| |---|---|---|---| |**1. Introduction**|||| |1.1|Tesla earned precision, Better Place assumed it|๐Ÿš— Tesla survived through ambiguity; Better Place died defending specificity|| |1.2|Problem: Exogenous P and informativeness|โš ๏ธ Existing theory treats success probability as given, not designed|| |1.3|Solution: ฯ„ as endogenous variable|๐ŸŽฏ Founders design learning capacity through precision choice|| |1.4|OIL Formula|๐Ÿ“ ฯ„* = max{0, โˆš(V/4i) - 1}|| |1.5|Why matters for founders|๐Ÿชค Precision trap + ๐Ÿ”ง Nail-to-scale toolkit|| |1.6|Why matters for scholars|๐Ÿ”ฌ Endogenizing P via ฯ„ bridges micro-macro|| |1.7|Three contributions|๐Ÿš™ Endogeneity + ๐Ÿฃ Formula/toolkit + ๐Ÿ‘จโ€๐Ÿ‘ฉโ€๐Ÿ‘ง Sectoral heterogeneity|| |**2. Theory**|||| |2.1|Part I: Endogeneity [Theorists]|๐Ÿš™ ฯ„ โ†’ ฮ”(ฮผ;ฯ„) = ฮผ/(1+ฯ„) โ†’ P mechanism|๐Ÿ—„๏ธMT: Terrain vs Map| |2.2|Part II: Formula [Practitioners]|๐Ÿฃ When V<4i: ฯ„=0; When Vโ‰ฅ4i: earn precision|๐Ÿ—„๏ธOT: Operational Tools| |2.3|Part III: Heterogeneity [Investors]|๐Ÿ‘จโ€๐Ÿ‘ฉโ€๐Ÿ‘ง R&D (epistemic) vs Consumer (aleatoric)|๐Ÿ—„๏ธUT: Uncertainty Types| |**3. Model**|||| |3.1|M1: Complexity discipline|๐Ÿ“‰ ฯ†* = 1/(c+1) - complexity constrains promises|| |3.2|M2: Empirical Bayes|๐Ÿ“Š ฮผ* = 1/(log c + ฮณ) - calibrate aspiration|| |3.3|M2': OIL as decision variable|๐ŸŽฎ Full model with ฯ„ as choice variable|| |**4. Application**|||| |4.1|Tesla case|โœ… Low ฯ„ โ†’ gradual increase โ†’ high ฯ„|| |4.2|Better Place case|โŒ High ฯ„ from start โ†’ learning trap|| |4.3|Comparative analysis|๐Ÿ“ˆ 3D evolution paths (ฯ„, V, i)|| |**5. Discussion**|||| |5.1|Theoretical synthesis|๐Ÿ”— Effectuation (ฯ„=0) โ†” Causation (ฯ„โ†’โˆž)|| |5.2|Practical implications|๐Ÿ’ผ Stage-gate for R&D, portfolio for consumer|| |5.3|Future research|๐Ÿ”ฎ Dynamic ฯ„ trajectories, industry studies|| ### ๐ŸŽฏ Key Formulas & Concepts |Concept|Formula/Definition|Meaning| |---|---|---| |**Precision (ฯ„)**|Prior concentration|Rigidity of promises| |**Update Capacity**|ฮ”(ฮผ;ฯ„) = ฮผ/(1+ฯ„)|Learning ability| |**OIL Formula**|ฯ„* = max{0, โˆš(V/4i) - 1}|Optimal precision rule| |**Phase Transition**|V = 4i boundary|Nail โ†’ Scale threshold| |**Success Probability**|P = ฯ†(1-ฯ†)^c|Sell ร— Deliver tension| ### ๐Ÿ“‘ Three Tables (MOUT) |Table|File Name|Purpose|Target Audience| |---|---|---|---| |๐Ÿ—„๏ธMT|`table_mountain_terrain.tex`|Literature comparison: endogenous vs exogenous|Theorists| |๐Ÿ—„๏ธOT|`table_operational_tool.tex`|V/i management tools by stage|Practitioners| |๐Ÿ—„๏ธUT|`table_uncertainty_types.tex`|Epistemic/aleatoric ร— R&D/consumer|Investors| This structure shows how precision (ฯ„) threads through the entire paper as the central mechanism connecting founder decisions to venture outcomes.