In the conference call yesterday (2022-01-10) we agreed to have Will take a shot at integrating the substance of Jacob's draft document (https://xalgorithms.redminepro.net/documents/10 (and also here's a copy with Joseph's comments and some discussion between Jacob and Joseph https://docs.google.com/document/d/1wHrk-8-G9PhaoUqbcKVC3DFeM6ymfmzmZACqpwzJC9c/edit ) with the substance of what is proposed in my spreadsheet, taking account of the general relation that arose from a conversation between Jacob and Joseph a couple of days ago (2022-01-09) https://docs.google.com/drawings/d/1r_GR5G7h6A2VVZAnahNvtdMXMvYQwrcF1nq-1poRWsQ/edit?pli=1

Permit me to highlight an important distinction between the ERA Framework with Deposit Receipts, and this ER Index work in the economic model: the ERA Framework for real implementation does not require the detailed data appearing in the spreadsheet for 'labour' and 'firms'. However in the economic model, we need to endogenously generate some coherent data to have an ER Index function. In the real world these functions happen, and we get to measure relevant results (e.g. via remote sensing) to build ER Indices.

That being said, here is my spreadsheet that provides a way to generate ERiP (Earth Reserve Index of a Patch) with data intrinsic to the Economic Petri Dish model, in a manner that is also consistent with the 'real' ER Index method.
https://xalgorithms.redminepro.net/attachments/106
I also put it into GoogleDocs, which seems to have done a good job keeping it intact
https://docs.google.com/spreadsheets/d/1WAq2Y9ASuIPIDSEHzXNnqZGoTK08FHEfnmtj4NgDSak/edit?usp=sharing
And here is the Desmos graph that I worked from https://www.desmos.com/calculator/pokghdqjwm
I have also created a short graphic+text summary for how I'm thinking about this:
https://xalgorithms.redminepro.net/attachments/download/107/ERiP_OverallLogic_2022-01-11PDF.pdf

BTW, my cranium finds the Bezier spline formulas, as conventionally expressed, hard to think about when they are expressed with the semantically-neutral variables, so in my spreadsheet I expressed the formulas for X and Y of the graph using named cells, as follows. The one remaining variable that I've not yet found or come up with a good name for is 't' (any suggestions?):

X-Axis=
((1-(t))^3)*(WorstX)
+3*(t)*(1-(A62))^2*DeterX
+3*(t)^2*(1-(A62))*IncentX
+((t)^3)*OptimalX

Y-Axis=
((1-(t))^3)*(WorstY)
+3*(t)*(1-(t))^2*DeterY
+3*(t)^2*(1-(t))*IncentY
+((t)^3)*OptimalY